Kwame Nkrumah University of Science and Technology, Kumasi

KWAME NKRUMAH UNIVERSITY OF SCIENCE AND TECHNOLOGY, KUMASI

STATISTICAL MODELS OF INFANT MORTALITY DUE TO MALARIA (A CASE OF KUMASI DISTRICT AND KATH)

BY Lincoln Tetteh-Ahinakwa

A THESIS SUBMITTED TO THE DEPARTMENT OF MATHEMATICS, KWAME NKRUMAH UNIVERSITY OF SCIENCE AND TECHNOLOGY IN PARTIAL FUFILLMENT OF THE REQUIREMENT FOR THE DEGREE OF M.PHIL MATHEMATICAL STATISTICS

April 2016 DECLARATION

I hereby declare that this submission is my own work towards the award of the M. Phil degree and that, to the best of my knowledge, it contains no material previously published by another person nor material which had been accepted for the award of any other degree of the university, except where due acknowledgement had been made in the text.

Lincoln Tetteh-Ahinakwa ......

Student Signature Date

Certiﬁed by:

Dr. F.T. Oduro ......

Supervisor Signature Date

Certiﬁed by:

Prof S.K. Amponsah ......

Head of Department Signature Date

i DEDICATION

This thesis is dedicated to my parents, my siblings and all those who helped me in diverse ways.

ii ABSTRACT

The research examines the factors that contribute to infant deaths at the Komfo Anokye Teaching Hospital (KATH) from 2010 to 2015(March) with malaria being the main focus, assesses the occurrence and incidence of infant deaths in Kumasi district from 2008 to 2014 and determines the survival rate of infants in the Komfo Anokye Teaching Hospital (KATH). Poisson and logistic regression models, the Kaplan-Meier estimate and the Cox Regression model are employed. Poisson regression model is used to examine the occurrence and incidence of infant deaths while logistic regression is used to assess the factors that contribute to infant deaths at KATH. The Kaplan –Meier estimate and Cox Regression model are used to determine the survival rate of infants in the Komfo Anokye Teaching Hospital (KATH). SPSS statistical software is used to analyze the data. Results show that the mean number of occurrence of infant mortality is higher in 2008, 2009 and 2012 as compared to 2014 (reference year) and also establishes that the mean number of occurrence of infant mortality significantly reduced over the study period 2008-2014. The incidence of infant mortality is higher in 2008, 2009 and 2012 as compared to 2014 (reference year). It is also found that, the mean incidence of infant death cases reduced significantly during the study period. Finally, it is revealed that duration of stay in the hospital contributed significantly to infant death at the KATH. Malaria, did not contribute significantly to the outcome. Infants diagnosed of a disease apart from malaria generally have a higher probability of dying than those diagnosed of malaria. However, an infant with malaria has zero (0) probability of surviving if the duration of stay in the hospital extends to 297 days (approximately 10 months) whereas an infant without malaria has zero (0) probability of surviving at 310 days (a little above 10 months).

iii ACKNOWLEDGMENT

My sincere gratitude ﬁrst and foremost to the Almighty God for seeing me through the completion of this programme particularly this thesis. My gratitude goes to my parents in the Lord,Pastor and Pastor Mrs Obeng-Addae, for their prayer support and giving me diverse reasons to continue this research work. I would like to express my gratitude also to my supervisor Dr F. T. Oduro for supervising this thesis and oﬀering timely directions and suggestions during the entire duration of the research work. I am in debted to Mrs Mary Dampson, Mrs Elizabeth Agyrako and Mrs Sarah Fordah of Ghana Health Service Kumasi for their immense aid during the data collection. I am also grateful to Dr Akoto Osei of the Child Health Department of KATH for approval for relevant data usage not forgetting to make mention of Dr Blaye of the Research and Development Department for provision of data. I duly acknowledge here, the contribution of my course mates, friends and family.

iv CONTENTS

Declaration ...... i

Dedication ...... ii

Acknowledgment ...... iv abbreviation ...... vii

List of Tables ...... ix

List of Figures ...... x

1 INTRODUCTION ...... 1 1.1 Background of the study ...... 1 1.2 Statement of Research Problem ...... 5 1.3 Research Objectives ...... 5 1.4 Methodology ...... 6 1.5 Justiﬁcation of study ...... 7 1.6 Scope of Study ...... 8 1.7 Organisation of the Thesis ...... 8

2 LITERATURE REVIEW ...... 10 2.1 Introduction ...... 10 2.2 State of Infant Mortality ...... 10 2.2.1 Medical Factors ...... 11 2.2.2 Environmental Factors ...... 17 2.2.3 Socio-Cultural Factors ...... 19

v 2.2.4 Socio – Political Factors ...... 21 2.2.5 Statistical Methods ...... 21 2.2.6 Educational Factors ...... 28 2.2.7 Geographical Factors ...... 29 2.3 Some Applications of Logistic Regression ...... 30

3 METHODOLOGY ...... 34 3.1 INTRODUCTION ...... 34 3.2 GENERALIZED LINEAR MODELS ...... 34 3.2.1 The Link Function ...... 35 3.3 The Poisson Distribution ...... 36 3.3.1 Poisson Regression Model ...... 37 3.3.2 Poisson Model for Rate Data ...... 39 3.4 Estimation ...... 39 3.4.1 Maximum Likelihood Estimate (GLMs) ...... 40 3.4.2 Maximum Likelihood Estimate (Poisson) ...... 41 3.4.3 Fisher Scoring in Log-Linear Model ...... 42 3.4.4 The Poisson Deviance ...... 43 3.5 Logistic Regression ...... 44 3.5.1 Parameters in Logistic Regression ...... 46 3.5.2 Multiple Logistic Regression ...... 47 3.5.3 Fisher Scoring in Logistic Regression ...... 47 3.6 Survival Analysis ...... 48 3.6.1 3.6.1 The Survival Function ...... 51 3.6.2 The Hazard Function ...... 52 3.6.3 Expectation of Life ...... 54 3.6.4 The Likelihood Function for Censored Data ...... 55 3.7 Survival Methods ...... 57 3.7.1 The Kaplan-Meier Method ...... 58 3.7.2 The Cox Regression Method ...... 62

vi 4 ANALYSIS AND RESULTS ...... 63 4.1 Introduction ...... 63 4.2 Preliminary Analysis ...... 64 4.3 Further Analysis ...... 67 4.3.1 Modelling The Occurrence of Infant Mortality Cases . . . 67 4.3.2 Modelling The Incidence of Infant Mortality Cases . . . . 70 4.3.3 Model containing Factors that Aﬀect Infant Outcome at KATH ...... 72 4.3.4 Survival of Infants in the Hospital ...... 74 4.4 Discussion ...... 92

5 CONCLUSION AND RECOMMENDATIONS ...... 96 5.1 Introduction ...... 96 5.2 Conclusion ...... 96 5.2.1 Signiﬁcance of Occurrence and Incidence of Malaria on Infant Mortality ...... 96 5.2.2 Factors that Contribute to Infant Mortality due to Malaria in the Komfo Anokye Teaching Hospital (KATH) . . . . . 97 5.2.3 Survival Rate of Infants in the Komfo Anokye Teaching Hospital (KATH) ...... 98 5.3 Recommendations ...... 99

References ...... 101

vii LIST OF TABLES

4.1 Age group distribution (in months), number of deliveries and infant deaths at KATH from 2010-2015 (March) ...... 64 4.2 Diseases diagnosed and the number of infants aﬀected from 2010 to 2015 (March ...... 65 4.3 Analysis of parameter estimates for occurrence of infant mortality 69 4.4 Analysis of parameter estimates for incidence of infant mortality . 71 4.5 Analysis of parameter estimates for factors that aﬀect infant mortality...... 73 4.6 Mean survival time between malaria diagnoses (time-to-death) . . 74 4.7 Survival Estimate of infants diagnosed of disease other than malaria (time-to-death) ...... 76 4.8 Survival Estimate of infants diagnosed of malaria (time-to-death) 77 4.9 Hazard ratio between malaria diagnosis (time-to-death) ...... 79 4.10 Mean survival time between malaria diagnoses (time-to-discharge) 80 4.11 Survival Estimate of infants diagnosed of disease other than malaria (time-to-discharge ...... 81 4.12 Survival Estimate of infants diagnosed of malaria (time-to-discharge) 82 4.13 Hazard ratio between malaria diagnosis (time-to-discharge) . . . . 83 4.14 Mean survival time between pneumonia diagnosis (time-to-death) 84 4.15 Survival Estimate of infants diagnosed of disease other than pneumonia (time-to-death) ...... 85 4.16 Survival Estimate of infants diagnosed of pneumonia (time-to-death) 87 4.17 Hazard ratio between pneumonia diagnosis (time-to-death) . . . . 88

viii 4.18 Mean survival time between pneumonia diagnoses (time-to- discharge) ...... 89 4.19 Survival Estimate of infants diagnosed of disease other than pneumonia(time-to-discharge) ...... 90 4.20 Survival Estimate (time-to-discharge) of infants diagnosed of pneumonia ...... 91 4.21 Hazard ratio pneumonia between diagnosis (time-to-discharge) . . 92

ix LIST OF FIGURES

1.1 Infant mortality rate by location and sex ...... 3 1.2 Infant mortality rate by region ...... 4

4.1 Pie chart showing yearly distribution of infant mortality at KATH. 66 4.2 Bar chart showing the distribution of infant mortality ratios in Kumasi district for 2008 - 2014...... 66 4.3 Chart showing trend of supervised infants on admission in Kumasi district from 2008- 2014...... 67 4.4 Survival of infants (between malaria diagnosis) against duration of stay in hospital (time-to-death) ...... 79 4.5 Survival of infants (between malaria diagnosis) against duration of stay in hospital (time-to-discharge) ...... 83 4.6 Survival of infants (between pneumonia diagnosis) against duration of stay in hospital (time-to-death) ...... 88 4.7 Survival of infants (between pneumonia diagnosis ) against duration of stay in hospital (time-to-discharge) ...... 92

x CHAPTER 1

INTRODUCTION

1.1 Background of the study

Childbirth is the main source of increase in the size of a family and in effect leads to an increase in the size of a community, society and country at large. This is really held in high esteem particularly in the developing countries where the size of a family or community reflects its social status. In certain areas, women are valued by the number of children they have borne. However, this is usually breached by the occurrence of deaths in infants. A lot of babies lose their lives every year. The Global Health Observatory (GHO) data indicates that regardless of significant reduction in countries between 1990-1999 and 2000-2011, infant mortality rate is disproportionately higher among the urban poorest populations. Comparatively, developing countries are presently experiencing infant death rates that developed countries had over eighty (80) years ago. It was estimated in the 2010 Mortality Survey of Afghanistan, a developing country that 73 infants die for every 1000 births whereas in England, a developed country, infant mortality rate of that sort (76 per 1000 births) was during 1921-1925 (Meyer, 2014: Barker and Osmond, 1986). This situation is no different in Africa and Ghana especially. Infant mortality is the death of a child before reaching one year of age The World Health Report (2005) indicates that eleven million children under five years of age will die from causes that are largely preventable. Among them are four million babies who will not survive the first month of life. In 2013, Global Health Observatory (GHO) reported that 4.6 million deaths (74 percent of all under- five deaths) occurred within the first year of life The risk of a child dying before completing the first year of age was highest in the World Health Organisation

1 (WHO) African region (60 per 1000 live births), about five times higher than that in the WHO European region (11 per 1000 live births). A global forum at Johannesburg, 1 July 2014, shows newborns were the top of the child survival agenda. The commitments made by governments and public and private sector organizations have the potential to transform the outlook for newborn babies, millions of whom die each year (UNICEF, 2014). The Bill and Melinda Gates Foundation, in its contribution to curb Infant Mortality in Ghana gave a 5 million dollar grant to a Massachusetts non-profit group with the aim of encouraging women to give birth at the hospital.(McNeil Jr, 2012). Research has shown that U.S were able to reduce their infant mortality rates through reduction in cigarette smoking by pregnant women and a decline in birth rate among teenagers in all ethnic groups. Further efforts were made to improve upon this statistics by promoting access to prenatal and infant care, promoting healthy choices to reduce mortality risks and promoting research to reduce infant mortality ( United States Department of Health and Human Services, 2006).

Chang (2009) in a review of an article written by Bill Hendrick tittled, “Preemies Raise U.S Infant Mortality” explained that a high infant mortality rate in the U.S was mainly caused by high percentage of preterm babies. In 2013, malaria caused an estimated 584 000 deaths (with an uncertainty range of 367 000 to 755 000), mostly among African children. In Africa, a child dies every minute from malaria. Children with severe malaria frequently develop one or more of the following symptoms: severe anaemia, respiratory distress in relation to metabolic acidosis, or cerebral malaria. An indoor spraying with residual insecticides strategy involving the administration of monthly courses of amodiaquine plus sulfadoxine-pyrimethamine to all children under 5 years of age during the high transmission season was suggested as one of the preventive methods doses of intermittent preventive treatment with sulfadoxine- pyrimethamine is recommended delivered alongside routine vaccinations was

2 recommended for infants living in high transmission areas of Africa (WHO-Fact sheet N04, 2015). Gaisie (1975) attempted to measure infant mortality levels in Ghana and also determine their structure. He conducted and used the results of the 1968-1969 National Demographic Sample Survey. The estimated infant mortality rates ranged from 56 per 1,000 live births in the Accra Capital District to 192 in the Upper Region during the late 1960’s. The urban rate is lower than the rural rate, 98 as against 161 per 1,000 live births. One major challenge he faced was the adjustment of current raw mortality data and the estimation of infant mortality from independent source material. Infant mortality rate as at the 2010 Population and Housing Census (PHC) results stood at 59 deaths per 1000 live births. This result shows a decline in the last ten years from 90 deaths per 1000 live births in 2000 (Ghana Statistical Service, 2011). The last Ghana Demographic Health Survey (2014) report, however, indicates a 41 per 1000 live births over the survey period. Infant mortality rate in the urban areas and rural areas are 55 and 60 deaths per 1000 live births respectively. A male child is more likely to die before year one than their female counterparts. The infant mortality rates of male and female in urban areas are 60 and 49 deaths per 1000 live births, respectively. In rural areas, infant mortality rates for male and female are 65 and 53 deaths per 1000 live births, respectively. This is shown in the ﬁgure below.

Figure 1.1: Infant mortality rate by location and sex

3 Source Ghana Statistical Service, 2010 Population and Housing Census.

At the regional level, substantial variation exists in infant mortality. Greater Accra has the lowest infant mortality at 48 deaths per 1000 live births, whereas Upper West has the highest infant mortality at 81 deaths per 1000 live births (Ghana Statistical Service, 2013) as shown in Figure 2.

Figure 1.2: Infant mortality rate by region

Source Ghana Statistical Service, 2010 Population and Housing Census.

A Community Health Planning and Service (CHPS) strategy aimed to improve geographic access to comprehensive health care used Community-Based Surveillance (CBS) as an entry point in Ashanti Region in 2001. Its focus was to obtain baseline data and define the magnitude and extent of specific health outcome. 967 infant deaths were recorded (IMR 36.4/1000Lbs). It was concluded that with a health institutional data and CBS, health outcomes can be well defined in the CHPS concept and thus contribute immensely to community action with stakeholders (Kyei-Faired et al, 2006).

In Ghana, the current infant mortality rate is 38.52 deaths/1,000 live births - 42.58 deaths/1,000 live births in males and 34.34 deaths/1,000 live births in

4 females (CIA World Factbook, 2014).

Ghana has a target of reducing infant mortality rate to 26 per 1000 live births by 2015 (Millennium Development Goal-4) Although results in the last ten years show that the country has made a substantial progress, challenges such as funding to support programmes and policies, low coverage of comprehensive health and nutrition services, inadequate human resources and skills within the health system to improve the poor quality of care among others still persist (Ghana Statistical Service, 2013).

1.2 Statement of Research Problem

Statistical methods have rarely been employed to identify the main causes of infant mortality in Ghana so as to curb this phenomenon. Although a binary logistic regression model has been used in analysing malaria mortality among children, there are few studies on mortality among infants in Ghana. This aﬀects the quality of decision made by stakeholders.

It is based on this premise that a retrospective study is necessary determinning the impact and causes of infant mortality over the years.

1.3 Research Objectives

To determine the signiﬁcance of occurrence and incidence of malaria on infant mortality in Kumasi district using the poisson regression model.

To assess the factors that contribute to infant mortality due to malaria in the Komfo Anokye Teaching Hospital (KATH) using the binary logistic regression model.

5 To determine the survival rate of infants in the Komfo Anokye Teaching Hospital (KATH) using the Kaplan-Meier estimate and Cox Regression (Malaria and Pneumonia Comorbidities).

1.4 Methodology

Sources of data would include the Komfo Anokye Teaching Hospital (KATH) record database from the year 2010 – 2015 (March) and the regional annual reports of Ghana health service, Kumasi from the year 2008–2014. The KATH, located in Bantama, a surburb of Kumasi in the Ashanti region, is one of the major teaching hospitals in Ghana. The hospital has a Child Health Department (CHD). This department has a malaria disease clinic of over 1,000 patients in shared facilities in the hospital. With experienced and committed specialists, the clinic of the hospital is most suitable for this study.

The variables of interest for the study include outcome (dead or alive), diagnosis, age of infant (in months), infant weight level, length of stay at the hospital (duration in days). Poisson regression model is employed to examine the occurrence and incidence of infant mortality in Kumasi district. The model determines the improvement of the dependent variable during the times understudy with reference to a particular time.

Binary logistic regression model is used to determine which factors aﬀect the outcome of infant mortality due to malaria at the Komfo Anokye Teaching Hospital. This model determines the impact of multiple independent variables presented simultaneously to predict membership of a dependent variable. It also provides knowledge of the relationships and strengths among the variables.

Kaplan –Meier estimate and Cox regression is used to determine the survival

6 rate of infants in the Komfo Anokye Teaching Hospital (KATH). The Kaplan – Meier estimate is a descriptive procedure that examines the distribution of time-to-event variables and also compares the distribution by levels of a factor variable. Cox regression, similar to the logistic regression, assesses the relationship between survival time and covariate(s).

Statistical package SPSS (version 17) would be used to analyze the data. This software is uses the Maximum Likelihood Estimation (MLE) method which maximizes the probability of classifying the observed data into appropriate categories given the regression co-eﬃcients.

1.5 Justiﬁcation of study

According to World Health Statistics (2009), Ghana is ranked 25th in Africa for malaria mortality rate per 100,000 population with a value of 109 higher than the average value of 104 for Africa. Pregnant women are more likely than others to be inoculated with and infected by malaria parasites (Hartman et al, 2010) Infant mortality has been shown to be one of the results of malaria in pregnancy. Various attempts, including the test of eﬀectiveness of drugs, have been made to control its occurrence (Osei Tutu et al., 2010). Laudable policies, programmes have been carried out but little improvement has been realised. The Ashanti Region recorded an infant mortality rate of 54 deaths per live births in 2008 (Ghana Health Demographic Survey) and 53 in 2010 (Ghana Statistical Services).

The Komfo Anokye Teaching Hospital (KATH) is the referral hospital for the Ashanti Region and Northern part of Ghana. The ﬁndings of this study will be of relevance to all stakeholders concerned on the need to reduce infant mortality by adapting proper infant health care in the study area and the country at large. It would also provide essential statistical

7 evidence required to justify the success or failure of programs implemented so far. The model generated would be useful in predicting the likelihood of infant deaths in the Komfo Anokye Teaching Hospital. The study also seeks to furnish decision makers and other stakeholders with vital information in the facility for possible policy intervention. Finally, this study would stimulate further research in the application of Poisson regression model in the area of infant health and mortality.

1.6 Scope of Study

This research was limited or restricted to the Kumasi district in the Ashanti Region because of limited resources and time. Data on infants admitted and infant deaths in Kumasi district from 2008 to 2014 were obtained from the Ghana Health Service District Oﬃce in Kumasi. A little over ﬁve years -2010 to 2015 (March) information was also extracted from the registers at the Research and Department (R&D) Unit of the Komfo Anokye Teaching Hospital. This information includes; duration of stay in hospital, age (in months), diagnosis, infant weight level and outcome for further analysis.

1.7 Organisation of the Thesis

The study is organized in five chapters. Chapter one is the introduction which comprises background issues, statement of research problem, research objective, methodology, justification of the study, the scope of the study and finally the organization of the thesis.

Chapter two contains the review of related literature and research in other ﬁelds in the mathematical theories and models under consideration have been applied.

8 Chapter three, deals with the mathematical concept of Poisson regression model and logistic regression analysis.

Chapter four covers analysis, results and discussions. It deals with preliminary statistical analysis of the data, further analysis using the statistical models mention above and discussion of the results from the analysis.

The final part is chapter five. It presents conclusions and recommendations based on the findings.

9 CHAPTER 2

LITERATURE REVIEW

2.1 Introduction

In this chapter, we discuss the various methods (including statistical methods) used in available literature on Infant Mortality, places these researches were undertaken and factors considered.

2.2 State of Infant Mortality

Infant mortality is deﬁned as the number of infants dying before reaching one year of age, per 1,000 live births in a given year (The World Bank). The Infant Mortality Rate (IMR) for a given region given as follows:

Numberofchildrendyingunderoneyearofage IMR = × 1000 (2.1) Numberoflivebirthsduringtheyear

There are various forms of infant mortality:

• Perinatal mortality is late fetal death (22 weeks gestation to birth), or death of a new born up to one week after delivery.

• Neonatal mortality is new born death occurring within 28 days after delivery.This accounts for 40–60% of infant mortality in developing countries

• Postneonatal mortality is the death of children aged 29 days to one year.

The Millennium Development Goal Four aims at reducing infant mortality by two-thirds between 1990 and 2015. The national target for Ghana is to

10 hit 26 deaths per 1,000 live births by 2015. In this thesis, we look at infant mortality as a result of malaria infection and survival of infants delivered and those who go to the Komfo Anokye Teaching Hospital. Infant mortality caused by several factors. Common causes are preventable with low-cost measures.

2.2.1 Medical Factors

Infant mortality related to medical factors include low birth weight, malnutrition and infectious disease.

Low Birth Weight

Infant mortality is a major indicator of the health of a nation as it is associated with a variety of factors such as maternal health, quality and access to medical care, socioeconomic conditions, and public health practices. It is a complex and multi-factorial problem that has proved resistant to intervention eﬀorts. Despite the rapid decline in infant mortality during the 20th century, the U.S. infant mortality rate did not decline from 2000 to 2005, and declined only marginally in 2006. After decades of improvement, the infant mortality rate for very low birth weight infants remained unchanged from 2000 to 2005. Infant mortality rates from congenital malformations and sudden infant death syndrome declined; however, rates for preterm-related CODs increased. The U.S. international ranking in infant mortality fell from 12th place in 1960 to 30th place in 2005. Continual increase in preterm and low birth weight delivery present major challenges to further improvement in the infant mortality rate (MacDorman and Mathews., 2009).

In a population based study of causes of death in Southern Brazil, low birth weight infants were found to be more likely to die if not carefully attended to

11 at primary level, especially during the first six months. Perinatal problems were responsible for 43% of these deaths and infectious diseases for 32%. In the group who died of infectious diseases, respiratory infections and diarrhoea were equally important, each accounting for 12% of all deaths. A total of 87% of the deaths occurred in the first six months of life, and this proportion remained high (77%) even after perinatal causes had been excluded. On the other hand, 53% of the infants who died were of low birth weight, as opposed to 7-9% of the survivors. It was estimated that if the incidence of low birth weight was reduced from the present 8-8% to 5% the likely reduction in infant mortality would be 20%. This reduction would be 33% for deaths due to perinatal causes, 14% for respiratory infections, and only 5% for diarrhoea. Efforts for the prevention of infant deaths in southern Brazil are more likely to be effective if they concentrate on improving perinatal health care and environmental conditions. (Barros et al., 1987)

In a research to identify the factors that which are associated with infant deaths in a typical rural community in South-western Nigeria with mid- year population of 3,308, infant mortality was found to be 68.2 per 1,000 live births. This is lower than the national rate but higher than the regional rate. First birth order and old mothers (34 years) at time of death were associated with significantly higher risk for mortality in the village (p=0.004). Females were twice as likely as males to die in infancy which is contrary to what is generally found. Information on births and deaths were collected for five consecutive years (1993-1997) by trained Village Health Workers (VHW) and Traditional Birth Attendants (TBA). Significantly, more neonatal deaths occurred during the rainy season than in the dry season suggesting that environmental factors play a role in neonatal deaths. The commonest cause of death was due to complications of low birth weight due to infant mortality. (Lawoyin, 2001).

12 In a study on the contribution of singletons, twins and triplets to low birth weight, infant mortality and handicap in the United States, the risks for infant mortality and for post-neonatal morbidity and handicap were calculated from race-, plurality- and birth weight-specific mortality rates from the National Infant Mortality Surveillance (NIMS). Project and birth weight-specific post-neonatal handicap rates from the Office of Technology Assessment report Healthy Children in proportion to the 1988 U.S. birth cohort. U.S. health objectives for the year 2000 for race-specific birth weight and infant mortality rates were used for comparison. Compared with that of singletons, twins’ and triplets’ relative risks for LBW were 10.3 and 18.8, respectively. Their relative risks for VLBW were 9.6 and 32.7. Compared with singletons, twins and triplets had relative risks for infant mortality of 6.6 and 19.4, respectively. For twins and triplets, post-neonatal survivors’ relative risks for severe handicap are 1.7 and 2.9 while those for overall handicap were 1.4 and 2.0, respectively. Recommendations for optimizing pregnancy outcomes in multiple gestations included liberalized weight gains, reduced physical effort and early, comprehensive prenatal care (Luke and Geith, 1992).

A journal article showing the survival chances of low birth weight infants in a rural hospital in Ghana as at 1994 indicates that out of 567 recorded low- birth weight infants born/admitted during a seven (7) year period in Agogo hospital, situated in a rainforest area in Ghana, one hundred and ﬁfty-two (26.8%) of these children died in hospital, 87 (57%) of them in the ﬁrst 48 hours. The average length of stay in hospital of the surviving children was 11.6 days. The death rate varied from 8.4% in the 1,751 to 2,000 g group to 83.3% in infants with a birth weight ≤ 1000 g. The proportion LBW children to the total newborn population was 5.5%; the proportion of extreme LBW (≤ 1000 g) to the total number LBW infants was 7.3% (Van der Mei, 1994).

13 Malnutrition

Although breastfeeding is universal in Ghana, some infants are deprived of essential nourishments (GSS and MI, 1999). Nutrition is another contributor to infant mortality. Bahl et al (2005), in their objective to determine the association of different feeding patterns for infants (exclusive breastfeeding, predominant breastfeeding, partial breastfeeding and no breastfeeding) with mortality and hospital admissions during the first half of infancy, found out that non-breastfed infants had a higher risk of dying when compared with those who had been predominantly breastfed (Hazard Ratio (HR) = 10.5; 95% Confidence Interval (CI) = 5.0–22.0; P <0.001) as did partially breastfed infants (HR = 2.46; 95% CI = 1.44–4.18; P = 0.001). This has two implications. First, the extremely high risks of infant mortality associated with not being breastfed need to be taken into account when informing HIV-infected mothers about options for feeding their infants. Second, in areas where rates of predominant breastfeeding are already high, promotion efforts should focus on sustaining these high rates rather than on attempting to achieve a shift from predominant breastfeeding to exclusive breastfeeding. Their research was based on a secondary analysis of data from a multicentre randomized controlled trial on immunization-linked vitamin A supplementation. Altogether, 9424 infants and their mothers (2919 in Ghana, 4000 in India and 2505 in Peru) were enrolled when infants were 18–42 days old in two urban slums in New Delhi, India, a periurban shanty town in Lima, Peru, and 37 villages in the Kintampo district of Ghana.

A study to assess the eﬀect of early infant feeding practices (delayed initiation, prelacteal feeding, established neonatal breastfeeding) on infection-speciﬁc neonatal mortality in breastfed neonates aged 2–28 days

14 employed a prospective observational cohort study was based on 10 942 breastfed singleton neonates born between 1 July 2003 and 30 June 2004, who survived to day 2, and whose mothers were visited in the neonatal period. Verbal autopsies were used to ascertain the cause of death. One hundred forty neonates died from day 2 to day 28; 93 died of infection and 47 of non-infectious causes. The risk of death as a result of infection increased whenever initiation of breastfeeding delayed. The study provided the ﬁrst epidemiologic evidence of a causal association between early breastfeeding and reduced infection-speciﬁc neonatal mortality in young human infants (Edmond et al. 2007).

Infectious Disease

Intermittent preventive treatment in pregnancy (IPTp) with sulfadoxine–pyrimethamine has recently been adopted by many African countries to reduce neonatal morbidity and mortality associated with malaria in pregnancy. The impact of a newly established national IPTp program on neonatal health in Gabon was assessed. Data on prevalence of Plasmodium falciparum infection, anemia, premature birth, and birth weight were collected in cross-sectional surveys in urban and rural regions of Gabon before and after the implementation of IPTp in a total of 1403 women and their offspring. After introduction of IPTp, the prevalence of Plasmodium falciparum infection decreased dramatically (risk ratio 0.16, P< 0.001). There was a marked benefit on the prevalence of low birth weight and premature birth for women adhering to national recommendations. These effects were most pronounced in primi- and secundigravid women (Ramharter et al, 2007).

A research conducted in Malawi showed that Maternal vitamin A deﬁciency during HIV infection may contribute to increased infant mortality. 474 HIV- infected mothers and their infants were followed from pregnancy through

15 the infants’ 12th month of life. Of the 474 HIV-infected pregnant women, 300 (63.3%) were deﬁcient in vitamin A (serum level of vitamin A, <1.05 µmol/L). Mean serum vitamin A levels among mothers whose infants died were 0.78 ± 0.03 µmol/L compared with 1.02 ± 0.02 µmol/L among mothers whose infants had survived for the ﬁrst 12 months of life (P <.0001). The overall infant mortality rate was 28.7%. HIV-positive mothers were divide into six groups according to serum vitamin A levels (µmol/L) as follows: group 1, <0.35; group 2, between 0.35 and 0.70; group 3, between 0.70 and 1.05; group 4, between 1.05 and 1.40 group 5, between 1.40 and 1.75; and group 6, between 1.05 and 1.40 group 5, between 1.40 and 1.75; and group 6, >1.75. Infant mortality rates for each group were 93.3%, 41.6%, 23.4%, 18.5%, 17.7%, and 14.2%, respectively (P <.0001). (Semba et al., 1995)

In South Africa, a research conducted indicated that an increase in the number of post-neonatal infant deaths over time likely to be associated with HIV/AIDS at all age under 1 year is high. There was a peak in HIV- related deaths, centred at 2-3 months of age rising monotonically over time. This was an indicator of paediatric AIDS in South African population. The aim was to identify any trends over recent time and to examine these trends for HIV-associated and non-HIV associated causes of mortality. By 2002, recorded infant deaths before age 1 has in absolute terms increased from 11,469 representing 43.8 percent in deaths within the ﬁrst year of life in 1997 to 12,152 representing 33 percent. Deaths at 2-3 months of age increased from 30.5 percent to 35.5 percent of the post-neonatal mortality within the ﬁrst year of life (Bourme et al, 2009).

Various studies across Africa have demonstrated that 7%–10% of newborns may have malaria parasites in their cord blood. Malaria in infants may be diﬃcult to diagnose because the clinical presentation may mimic other diseases In Mozambique, clinical malaria incidence in infants aged 1–6 months was substantial (320/1,000 child-years at risk in 2003–2004

16 and 146/1,000 child-years at risk in 2004–2005). Although malaria in infants aged under six months represented less than 20% of the total outpatient visits, infants with malaria were admitted in a signiﬁcantly higher proportion than children aged 1–4 years Reports of congenital malaria have predominantly come from Nigeria and varied widely between 0.7% and 46.7% Also, malaria infections were common in Ghanaian infants less than 6 months of age, although clinical malaria symptoms were rare or uncommon (fever, vomiting, diarrhoea and coughing occurred in 1.8%, 1.8%, 3.0% and 4.8% of infants aged 0–3 months, respectively, and in 4.5%, 3.0%, 8.0% and 10.6% of infants aged 3–6 months) (D’Alessandro et al, 2012)

Luxemburger et al. (2001) estimated the impact of malaria during pregnancy on infant mortality in a Karen population living in Thailand. Between 1993 and 1996, a cohort of 1,495 mothers and their infants was followed weekly from admission of the mother to antenatal clinics until the ﬁrst birthday of the infant. They realised that malaria during pregnancy increased neonatal mortality by lowering birth weight, whereas fever in the week before birth had a further independent eﬀect in addition to inducing premature birth. The prevention of malaria in pregnancy and, thus, of malaria-attributable low birth weight should increase the survival of young babies.

2.2.2 Environmental Factors

Currie and Neidell (2005) investigated the impact of three key pollutants: carbon monoxide (CO), particulate matter less than 10 microns in diameter (PM10), and ozone (O3) on infant mortality rates using data from California for the 1990s. Their ﬁndings show that exposure to high level of ambient carbon monoxide does increase the infant mortality rate. According to their estimates, the reduction in CO emissions in California to about 40

17 percent saved the lives of about 1,000 infants over the decade. Potential harm of CO to infants is very great because of their immature respiratory systems. This achievement requires the investment of considerable resources in pollution control. This adds significantly to our stock of knowledge, showing that some of the costs of pollution can come in the form of elevated infant mortality. In studying its effects on infants, the authors are able to control for an extraordinary array of other factors that might play a role in infant health outcomes. Most importantly, they control for the age and birth weight of infants, two factors known to play critical roles in influencing their mortality. But the authors also control for racial, ethnic, and educational factors, as well as the age of the mother, pollution exposure before birth, and even the key weather features of the relevant geographic area. Moreover, they measure pollutants with far greater accuracy than is typically the case, which adds to the precision with which they are able to estimate its effects on infant mortality. One particularly striking feature of the study is the finding of lethal effects of carbon monoxide at the relatively low levels to which infants were exposed. The data come from a period in which CO levels in California were on average about two-thirds below the national ambient air quality standards established by the Environmental Protection Agency. The hazards of CO in higher concentrations are well known, but this is the first time significant adverse effects of the pollutant have been observed at such low concentrations. Over the period covered by the research, there were 4.6 million infants born in California, about 18,000 of whom died in their first year of life. The vast majority of these deaths were caused by such factors as inadequate pre or post-natal health care, premature birth, and low birth weight. Overall, the estimated impact of the reduction in CO during this period,about 1,000 fewer infant fatalities was a cut in the infant mortality rate of about 5 percent.

18 2.2.3 Socio-Cultural Factors

Large differences in climate within the African continent influence not only nutrition but also the type of culture and the presence or absence of certain infections. Data on infant and child mortality in Africa are fragmentary; they come mostly from vital statistics registration which is very poor in rural areas. Main causes of infant mortality in Africa as found out by Cantrelle and Viviane (1980) are infections and parasitic diseases followed by diseases in respiratory tracts, diarrhoea and rubella. These account for the greatest number of deaths. Seasonal variations in mortality rates are very great and differ widely in the different zones, that is, November-January in the equatorial zones, January through April in the north, and the Spring in tropical zones. They also realised that infant mortality seem higher in rural areas in most countries though not all. Though it is still high in Africa, it has however decreased steadily. For example, while in West, East, and North Africa it was 215/1000 in 1931, it was only 160/1000 in 1971. Data on infant mortality in Africa is mostly gotten from vital statistics registration. These are always in fragments and are very poor in rural areas. Many studies are currently being conducted to explore African infant and child mortality in more exact terms. However, data on causes of infant mortality were available only for some African countries, notable Algeria, Senegal, Nigeria, and Mauritius.

A cross-sectional survey design employed to examine socio-cultural factors inﬂuencing infant feeding practices of mothers in Cape Coast Metropolis indicate that infant feeding practices in the Metropolis are far from the ideal. Respondents who reported having primary education were signiﬁcantly more likely to exclusively breastfeed than were respondents who reported having higher levels of schooling. Mother’s marital status, employment status, friends’ way of feeding their babies, social support and baby’s age

19 were also inﬂuential in infant feeding practices. Among the respondents, the majority were Akan, married, aged 30-34 and held at least junior high school certiﬁcate (Sika-Bright, 2009).

Gyimah (2002) premised on the hypothesis that ethnic specific socio- cultural practices such as dietary taboos and food avoidances on mothers and infants, as well as perceptions of disease aetiology and treatment patterns may be salient to infant mortality differentials in Ghana. The bivariate results using data on 3298 recent births from the 1998 Ghana Demographic and Health Survey indicated significant ethnic differences in the risk of infant data. Thus, the observed ethnic differences in infant mortality mainly reflect socio-economic disparities among groups rather than intrinsic cultural norms. To improve child survival, efforts should be geared towards enhancing the socio-economic status of women from the disadvantaged ethnic groups

In a research to examine ethnic differences in post-neonatal mortality and the incidence of sudden infant death in England and Wales, five years records were analysed, the mother’s country of birth being used to determine ethnic group. Crude rates were lower in infants of mothers born in West Africa (3.0/1000) than infants of mothers born in the United Kingdom despite less favourable birth weights. Ratio for infants of Indian and East African mothers did not show significant differences after standardization. Several immigrant groups including those from West Africa recorded an increase in post-neonatal mortality. It was recommended that surveillance of post-neonatal mortality among ethnic communities should be continued. Research is also needed to identify the causes underlying the differences (Balarajan et al., 1989).

20 2.2.4 Socio – Political Factors

Infant mortality has continually been of much concern in the public health sector of developing countries. In his ﬁndings, Kudamatsu (2012) realised that good democratization reduced infant mortality to about 1.8 percent in Sub-Saharan Africa. He conducted a retrospective fertility surveys in 28 African countries making a comparison between the survival of infants born to the same mother before and after democratization to identify the eﬀect of democracy. However, this is not conclusive (Lipset 1959). Only 33% of the population enjoyed improved sanitation facilities in 1990 (World Development Indicators, 2005) and 40% of births in that region was attended by skilled health person.

2.2.5 Statistical Methods

Kramer et al, (2000) assessed the quantitative contribution of mild (birth at 34–36 gestational weeks) and moderate (birth at 32-33 gestational weeks) preterm birth to infant mortality. They measured the Relative risks (RRs) and etiologic fractions (EFs) for overall and cause speciﬁc early neonatal (age 0–6 days), late neonatal (age 7–27 days), post-neonatal (age 28–364 days) and total infant death among mild and moderate preterm births vs term births (at ≥37 gestational weeks). They realised that mild– and moderate–preterm birth infants are at high RR for death during infancy and are responsible for an important fraction of infant deaths.

A reviewed article aimed at developing mathematical models of malaria shows that nearly a million child mortality was recorded in about 109 countries declared to be endemic to malaria and its prevalence is highest in infants and children. With the disease still thriving and threatening to be a major source of death and disability due to changed environmental and socio-economic conditions, it is necessary to make a critical assessment of

21 the existing models, and study their evolution and eﬃcacy in describing the host parasite biology. The research emphasised more on the evolution of the deterministic diﬀerential equation based epidemiological compartment models with a brief discussion on data based statistical models .under the age of 5-years. The Ross model was used as a basis to develop this model (Mandel et al., 2011).

Ross and Smith (2006) proposed a mathematical model for the association between Plasmodium falciparum transmission and neonatal death. Their model related neonatal mortality resulting from malaria infection during pregnancy to the age-specific prevalence of Plasmodium falciparum infection in the general population. This allowed it to be integrated into a comprehensive simulation and uses a parasitologic model as a foundation. Data summaries were used to provide information on the relationship between malaria infection among the population and the risk of neonatal mortality. Various sources of information on malaria infection during pregnancy were collected. This included literature search for sub-Saharan Africa sites and observational data and data from controlled clinical trials of anti-malarial drugs in pregnancy. Results showed that there is no evidence of an association between neonatal mortality and malaria transmission intensity, yet such an association is evident for both post- neonatal and overall infant mortality. They concluded that the relationship of transmission intensity with the risk of neonatal mortality is much weaker than that with post-neonatal mortality. A research by Nakul et al. (2006) also revealed that malaria kills about 1 to 3 million people a year of whom 75% are African children. It presents an ordinary differential equation mathematical model for the spread of malaria in human and mosquito populations. He defined a reproductive number,

R0, for the number of secondary cases that one infected individual will cause through the duration of the infectious period.

22 A spatial analysis was carried out to identify factors related to geographic differences in infant mortality risk in Mali by linking data from two spatially structured databases: the Demographic and Health Surveys of 1995–1996 and the Mapping Malaria Risk in Africa database for Mali. Socioeconomic factors measured directly at the individual level and site-specific malaria prevalence predicted for the Demographic and Health Surveys’ locations by a spatial model fitted to the Mapping Malaria Risk in Africa database were examined as possible risk factors. The analysis was carried out by fitting a Bayesian hierarchical geostatistical logistic model to infant mortality risk, by Markov Chain Monte Carlo simulation. It confirmed that mother’s education, birth order and interval, infant’s sex, residence, and mother’s age at infant’s birth had a strong impact on infant mortality risk in Mali. The residual spatial pattern of infant mortality showed a clear relation to well- known foci of malaria transmission, especially the inland delta of the Niger River. Spatial statistical models of malaria prevalence were recommended as they are useful for indicating approximate levels of endemicity over wide areas and, hence, for guiding intervention strategies. However, at points very remote from those sampled, it is important to consider prediction error (Gemperli et al, 2002).

Victoria (2000) conducted a pooled analysis of studies that assessed the effect of not breastfeeding on the risk of death due to infectious diseases. Studies were identified through consultations with experts in international health, and from a MEDLINE search for 1980–98. The protective effect of breastfeeding was assessed according to the age and sex of the infant, the cause of death, and the educational status of the mother using meta- analytical techniques. Eight studies were identified, data from 6 of which were available (from Brazil, the Gambia, Ghana, Pakistan, the Philippines and Senegal). In the African studies, virtually all babies were breastfed well into the second year of life, making it impossible to include them

23 in the analyses of infant mortality. On the basis of the other 3 studies, protection provided by breastmilk declined steadily with age during infancy (pooled odds ratios: 5.8 (95% CI 3.4–9.8) for infants aged <2 months, 4.1 (2.7–6.4) for 2–3 months old, 2.6 (1.6–3.9) for 4–5 months old, 1.8 (1.2–2.8) for 6–8 months old, and 1.4 (0.8–2.6) for 9–11 months old). In the ﬁrst 6 months of life, protection against diarrhoea was substantially greater (odds ratio 6.1 (4.1–9.0)) than against deaths due to acute respiratory infections (2.4 (1.6–3.5)). However, for infants aged 6–11 months, similar levels of protection were observed (1.9 (1.2–3.1) and 2.5 (1.4–4.6), respectively). For second-year deaths, the pooled odds ratios from 5 studies ranged between 1.6 and 2.1. Protection was highest when maternal education was low. She suggested that suggested that these results may help shape policy decisions about feeding choices in the face of the HIV epidemic.

Apponte et al. (2009) based on their research found out that IPTi with sulfadoxine-pyrimethamine was safe and efficacious across a range of malaria transmission settings, suggesting that this intervention is a useful contribution to malaria control. They undertook a pooled analysis of the safety and efficacy of IPT in infants (IPTi) with sulfadoxine- pyrimethamine in Africa. Pooled data from six double-blind, randomised, placebo-controlled trials (undertaken one each in Tanzania, Mozambique, and Gabon, and three in Ghana) that assessed the efficacy of IPTi with sulfadoxine-pyrimethamine was used in the analysis. Data from the trials for incidence of clinical malaria, risk of anaemia (packed-cell volume <25% or haemoglobin <80 g/L), and incidence of hospital admissions and adverse events in infants up to 12 months of age were reanalysed by use of standard outcome definitions and time periods. The six trials provided data for 7930 infants (IPTi, n=3958; placebo, n=3972). IPTi had a protective efficacy of 30.3% (95% CI 19.8–39.4, p<0.0001) against clinical malaria, 21.3% (8.2–32.5, p=0.002) against the risk of anaemia, 38.1% (12.5–56.2, p=0.007)

24 against hospital admissions associated with malaria parasitaemia, and 22.9% (10.0–34.0, p=0.001) against all-cause hospital admissions. There were 56 deaths in the IPTi group compared with 53 in the placebo group (rate ratio 1.05, 95% CI 0.72–1.54, p=0.79).

In a study on the effect of weather fluctuations and infant mortality in Africa over the last half century, a combination of individual level data obtained from retrospective fertility surveys (DHS) for nearly a million births in 28 African countries and data for weather outcomes, obtained from re-analysis with climate models (ERA-40) were used. Robust statistical evidence of quantitatively significant effects via malaria and malnutrition was found. Infants in areas with epidemic malaria that experience worse malarious conditions during the time in utero than the site-specific seasonal means face a higher risk of death, especially when malaria shocks hit low-exposure areas. Infants in arid areas who experience droughts when in utero face a higher risk of death, especially if born in the so-called hungry season. Based on the estimates, the study estimates the number of infant deaths due to extreme weather events and the total number of infant deaths due to maternal malaria in epidemic areas (Kudamatsu et al. 2012).

The timing of initiation of breastfeeding has a lot of inﬂuence on infant mortality. A prospective observational cohort study based on 10 942 breastfed singleton neonates born between 1 July 2003 and 30 June 2004, who survived to day 2, and whose mothers were visited in the neonatal period shows that One hundred forty neonates died from day 2 to day 28; 93 died of infection and 47 of non-infectious causes. The risk of death as a result of infection increased with increasing delay in initiation of breastfeeding from 1 h to day 7; overall late initiation (after day 1) was associated with a 2.6-fold risk [adjusted odds ratio (adj OR): 2.61; 95% Conﬁdence Interval (CI): 1.68, 4.04]. Partial breastfeeding was associated with a 5.7 fold adjusted risk of death as a result of infectious disease (adj

25 OR: 5.73; 95% CI: 2.75, 11.91). No obvious associations were observed between these feeding practices and non-infection-speciﬁc mortality. Pre- lacteal feeding was not associated with infection (adj OR: 1.11; 95% CI: 0.66, 1.86) or non-infection speciﬁc (adj OR: 1.33; 95% CI: 0.55, 3.22) mortality. (Edmond et al, 2006).

A variety of data sources and methods were used to assess levels of infant mortality and their trend over time in one Central Asian republic, Kyrgyzstan, between 1980 and 2010. An abrupt halt to an already established decline in infant mortality was observed to occur during the decade following the break-up of the Soviet Union, contradicting the oﬃcial statistics based on vital registration. Infants of Central Asian ethnicity and those born in rural areas were also considerably more at risk of mortality than suggested by the oﬃcial sources. This posed a great deal of uncertainty over the levels of, and trends in, infant mortality in the former Soviet republics of Central Asia. As a result, the impact of the break-up of the Soviet Union on infant mortality in the region is not known, and proper monitoring of mortality levels is impaired (Guillot et al. 2013).

Guyant and Snow (2001) modelled the possible impact of placental malaria infection on infant mortality through reduced birth weight. It was shown that a baby is twice as likely to be born of low birth weight if the mother has an infected placenta at the time of delivery (allpaArities: 23% vs 11%, primigravidae only: 32% vs 16%), and that the probability of premature mortality of African newborns in the ﬁrst year of life is 3 times higher in babies of low birth weight than in those of normal birth weight (16% vs 4•6%). That is, 5.7 percent of infant deaths in malaria prone areas could be an indirect cause of malaria in pregnancy assuming 25% of pregnant women in malaria-endemic areas of Africa harbour placental malarial infection. This would imply that, in 1997, malaria in pregnancy could have been responsible for around 3700 infant deaths under the diverse epidemiological

26 conditions in Kenya. A report on infant and early childhood mortality from 29 national fertility surveys carried out within the World Fertility Survey program discusses the sources and quality of data, the methodology for calculating the mortality statistics, and presents tables of infant and child mortality rates by selected demographic variables for the 4 African, 12 Latin American, and 13 Asian countries. The variation in levels of infant, neonatal, postneonatal, toddler, and child mortality was very great. On average male mortality is 14% in excess of female mortality below 1 year, but is about the same or slightly lower than female mortality at older ages under 5. Maternal age at birth had the expected U-shaped relationship for mortality, especially for infants. Order of birth had a U-shaped relationship with infant mortality only, while at other ages mortality increased with order. Children born less than 2 years after the next older sibling and children from multiple births were much more likely to die. A reduction of births to women aged under 20 or over 40, as well as to women at high parities, and a reduction of births after short intervals might substantially reduce mortality in many countries ( Rutstein, 1983).

The Petra Study Team in a Lancet (2002) assessed the eﬃcacy of short- course regimens with zidovudine and lamivudine in preventing early and late transmission of HIV-1 from mother to child in a predominantly breastfeeding population with regards to infant mortality. A randomised, double-blind, placebo-controlled trial was carried out in South Africa, Uganda, and Tanzania. Between June, 1996, and January, 2000, HIV-1-infected mothers were randomised to one of four regimens: A, zidovudine plus lamivudine starting at 36 weeks’ gestation, followed by oral intrapartum dosing and by 7 days’ postpartum dosing of mothers and infants; B, as regimen A, but without the prepartum component; C, intrapartum zidovudine and lamivudine only; or placebo. From Feb

27 18, 1998, onward, women were only randomised to one of the active treatment groups. HIV-1 infection and infant mortality at week 6 rates were 7.0%, 11.6%, 17.5%, and 18.1%, respectively, with relative risks of 0.39 (0.24–0.64), 0.64 (0.42–0.97), and 0.97 (0.68–1.38). 1081 (74%) of the women analysed initiated breastfeeding. It was realised that at week 6 after birth, regimens A and B were eﬀective in reducing HIV-1 transmission, Kalipeni (1993) examined the spatial variation of infant mortality in Malawi between 1977 and 1987. Data from the 1977 and 1987 censuses are used in simple correlation and forward stepwise regression analysis to explain and/or predict the variation and change of infant mortality at district (county) level. The results indicate that, at the macro-level, the variation of infant mortality is strongly associated with a number of demographic and socio-economic variables. Region in which a district ﬁnds itself also matters as far as levels of infant mortality are concerned. The study concludes that the reduction of infant mortality throughout the country should be vigorously pursued by the government of Malawi. Fertility will continue to be high if infant mortality persist at current level.

2.2.6 Educational Factors

Studies have shown an inverse relationship between educational level and employment status on infant mortality. This study examined the eﬀects of education level and employment status on full-term and preterm infant mortality in Korea Low paternal and maternal education levels were associated with high infant mortality in both full-term and preterm infants. In total, 1,316,184 singleton births registered in Korea’ Registration Database between January 2004 and December 2006 were included in the study. Multivariate logistic regression analysis was performed. Low parental employment status was found to be associated with infant mortality in preterm infants but not in full-term infants. In order to reduce

28 inequalities in infant mortality, public health interventions should focus on providing equal access to education. (Ko et al, 2014).

2.2.7 Geographical Factors

Pathania (2014) used large pre-existing differences in the regional risk of malaria coupled with the sharp timing of the renewed campaign to study the impact of malaria control on infant mortality in Kenya. Kenya adopted a new national malaria strategy in 2001. The strategy emphasized the distribution of insecticide-treated bed nets (ITNs). He found that before the intervention, infant mortality in the malarious regions was substantially higher than that in the non-malarious regions. Much of that difference was due to higher post-neonatal mortality in the malarious regions, consistent with a key stylized fact from malaria epidemiology. Post-intervention, he found a significant fall in post-neonatal mortality in the malarious regions in comparison to the non-malarious regions. Also in Sichuan Province (Wu et al., 2011), decrease in infant mortality in the rural and urban areas from 2001 to 2009 was due to decrease in avoidable deaths such as pneumonia and diarrhoea in infants. Data presented in this report was obtained from the child mortality surveillance network with target population as children under 5 years of age. Rates on infant mortality, neonatal mortality and indirect estimation of infant mortality were calculated. The neonatal mortality rate and infant mortality rate in Sichuan dropped from 18.6, 25.5 in 2001 to 7.6, 12.1 per 10to 2009. In urban areas of Sichuan, the neonatal and infant mortality rates dropped from 4.7, 7.5 in 2001 to 3.7 and 6.5 per 1000 live birth in 2009, with the rates of decline as 22.3% and 13.1%. In the rural areas of Sichuan, the neonatal and infant mortality rates dropped from 25.2 and 34.0 in 2001 to 9.6, 14.3 per 1000 live birth in 2009, with rates of decline as 62.0%, 57.9% from 2001 to 2009. In both urban and rural areas, the neonatal and infant mortality rates had decreased drastically from 2001

29 to 2009, due to the decrease of avoidable deaths as pneumonia and diarrhoea in infants.

Titmuss (1943) indicates that the lesson of his study is that infants of the poor are dying in relatively greater numbers than they were before the 1914 war. This is attributed to worse living conditions. Also, wide regional disparities in the environmental causes of death showed that where a district is economically depressed the social class diﬀerences within that region are greatly accentuated.

Kramer et al, (2000) assessed the quantitative contribution of mild (birth at 34–36 gestational weeks) and moderate (birth at 32–33 gestational weeks) preterm birth to infant mortality. They measured the Relative risks (RRs) and etiologic fractions (EFs) for overall and cause speciﬁc early neonatal (age 0–6 days), late neonatal (age 7–27 days), post-neonatal (age 28-364 days) and total infant death among mild and moderate preterm births vs term births (at ≥ 37 gestational weeks). They realised that mild– and moderate–preterm birth infants are at high RR for death during infancy and are responsible for an important fraction of infant deaths.

2.3 Some Applications of Logistic Regression

A study was conducted in the United States to examine the relationship between post-neonatal infant mortality and particulate matter. This involved analysis of cohorts consisting of approximately 4 million infants between 1989 and 1991. Infants were categorised as having high, medium or low exposures based on teriles of PM10. Total and cause-speciﬁc post-neonatal mortality rates were examined using logistic regression to control for demographic and environmental factors. Overall post-neonatal mortality rates were 3.1 among infants with low PM10 exposures, 3.5 among infants with medium PM10 exposure and 3.7 among highly exposed infants.

30 The odds ratio (OR) and 95% confidence interval (CI) for total post- neonatal mortality for the high exposure versus the low exposure group was 1.10(1.04, 1.16). In normal birth weight infants, high PM10 exposure was associated with respiratory causes [OR=1.40, (1.05, 1.85)] and sudden infant death syndrome [(OR)=1.26, (1.14, 1.39)]. For low birth weight babies, high PM10 exposure was associated but not significantly, with mortality from respiratory causes [(OR)=1.18, (0.86, 1.61)]. The study agreed that particulate matter is associated with risk of post-neonatal mortality and recommended continued attention to air quality to ensure optimal health of infants in the United States (Woodruff et al. 1997).

Abdul-Aziz et al (2012) analyzed the risk factors of malaria mortality among children using a logistic regression model and also assessed the interaction effect between age and treatment of malaria patient. Secondary data from January 1, 2008 to December 31, 2010 from the inpatient morbidity and mortality returns register at Tamale Teaching Hospital was used. The results showed that risk factors such as referral status, age, distance, treatment and length of stay on admission were important predictors of malaria mortality. However, it was found that the risk factors; sex and season were not good predictors of malaria mortality. The interaction effect between age and treatment was found to be significant. We also consider how logistic regression has been applied in other field of life. Zhao et al. (2013) used elastic net logistic regression to investigate relapsing-remitting multiple sclerosis classification on gene expression data. It was sought to identify a robust diagnostic signature for relapsing-remitting multiple sclerosis from gene expression data. In this regard, they built a classier that discriminates samples into two phenotype groups, either RRMS or controls, using the transcriptome of peripheral blood mononuclear cells. For their classier, they used logistic regression with elastic net regression as implemented in the glmnet package in R. They selected the values of the

31 regularization hyper-parameters using cross-validation performance on the provided training data, number of non-zero parameters in their model, and based on the distribution of output values when the input vector for the test data were used with their classier. They analyzed their classier performance with two different strategies for feature extraction, using either only genes or including additional constructed features from gene pathways data. The two different strategies produced little differences in performance when comparing the 10-fold cross-validation of the training data and prediction on the test data. Their final submission for the sub-challenge used only genes as features, and identified a diagnostic signature consisting of 58 genes, that was ranked second out of a total of 39 submissions.

Das and Rahman (2011), in their study, attempted to develop an ordinal logistic regression (OLR) model to identify the determinants of child malnutrition instead of developing traditional binary logistic regression (BLR) model using the data of Bangladesh Demographic and Health Survey 2004. Based on weight-for-age anthropometric index (Z-score) child nutrition status was categorized into three groups-severely undernourished (< 3:0), moderately undernourished (-3.0 to -2.01) and nourished (2:0). Since nutrition status is ordinal, an OLR model proportional odds model (POM) can be developed instead of two separate BLR models to find predictors of both malnutrition and severe malnutrition if the proportional odds assumption satisfies. The assumption was satisfied with low p- value (0.144) due to violation of the assumption for one co-variate. So partial proportional odds model (PPOM) and two BLR models were also developed to check the applicability of the OLR model. Graphical test was also adopted for checking the proportional odds assumption. All the models determine that age of child, birth interval, mothers’ education, maternal nutrition, household wealth status, child feeding index, and incidence of fever, ARI and diarrhoea were the significant predictors of

32 child malnutrition; however, results of PPOM were more precise than those of other models. The study concluded that, the findings clearly justified that OLR models (POM and PPOM) were appropriate to find predictors of malnutrition instead of BLR models.

Generally, little work on infant mortality using poisson, logistic or survival models has been done.

33 CHAPTER 3

METHODOLOGY

3.1 INTRODUCTION

Discussions in this chapter includes the method of data collection and some statistical tools used in analyzing infant mortality in the Kumasi District and the Komfo Anokye Teaching Hospital including their survival rates. The statistical tools for this research work include Poisson and Logistic Regression Models, Kaplan – Meier Estimate and Cox Regression.

Binary logistic regression model is used to assess the factors that contribute to infant death in Komfo Anokye Teaching Hospital while Poisson Regression model is used to examine the signiﬁcance of the occurrence and incidence of infant mortality in Kumasi District. Kaplan – Meier estimate and Cox Regression is used to determine the survival rate of infants admitted at the Komfo Anokye Teaching Hospital.

3.2 GENERALIZED LINEAR MODELS

Generalized linear model (GLMs) was ﬁrst formulated by Nelder and Wedderburn in 1972. Generalized linear models extend ordinary regression models to encompass non-normal response distributions and modelling functions of the mean. It includes linear regression models, analysis of variance models, logistic regression models, Poisson regression models, loglinear models, as well as many other models. Generalized linear models consist of three components;

34 1. A random component, specifying the conditional distribution of

the response variable, Yi (for the ith of n independently sampled observations), given the values of the explanatory variables in the model.

2. A linear predictor-that is a linear function of regressors

ηi = α + β1 ∗ xi1 + β2 ∗ xi2 + ... + βkxik (3.1)

3. A smooth and invertible linearising link function g(.), which transforms

the expectation of the response variable µi = E(Yi) to the linear predictor:

g(µi) = ηi = α + β1 ∗ xi1 + β2 ∗ xi2 + ... + βkxik (3.2)

3.2.1 The Link Function

The link function g(ui) is a one-to-one continuous diﬀerentiable function.

It links ui to the linear predictor ηi

T hus ηi = g(ui)

T W here ηi = Xi β

T Hence g(ui) = Xi β (3.3)

Since the link is one-to-function, we can’t invert it to obtain:

−1 T (ui) = g (Xi β) (3.4)

Examples of link functions include the identity, log, reciprocal, logit and probit

35 3.3 The Poisson Distribution

The Poisson distribution was named after a French mathematician, Simeon Denis Poisson (1781 –1840) who developed it. This distribution is a discrete probability distribution that expresses the probability of a number of events occurring in a ﬁxed period of time if these events occur with a known average rate and independent of the time since the last event. For instance, if the expected number of occurrences in an interval is λ, then the probability that there are exactly k occurrences (k is non-negative integer, k = 0, 1, 2, . . .) is equal to λke−λ P (k, λ) = (3.5) k

Where e is the base of the natural logarithm (e = 2.71828...), k is the number of occurrences of an event - the probability of which is given by the function, k! is the factorial of k, λ is a positive real number, equal to the expected number of occurrences that occur during the given interval. Lambda λ is not only the mean but also the variance of the distribution. The Poisson distribution has several assumptions:

– Observations are independent.

– Probability of another occurrence in such a short interval is zero.

– Probability of occurrence in a short interval is proportional to the length of the interval

An example involving Poisson distribution is shown below:

Example

Vehicles pass through a junction on a busy road at an average rate of 300 per hour. a. Find the probability that none passes in a given minute.

36 b. What is the expected number passing in two minutes? c. Find the probability that this expected number actually pass through in a given two-minute period.

Answer

300 The average number of cars per minute is µ = 60 = 5

e−550 −3 (a) P (0, 5) = 0! = 0.73379 × 10

(b) Expected number each 2 minutes = E(X) = 5 × 2 = 10

e−101010 (c) Now, with µ = 10, we have P (10,10) = 10! = 0.12511

3.3.1 Poisson Regression Model

The basic GLM for count data is the Poisson regression model with log link. It is a technique used to describe count data as a function of a set of predictor variables. Although a GLM can model a positive mean using the identity link, it is more common to model the log of the mean. Like the linear predictor (α + βx), the log mean can take any real value. The log mean is the natural parameter for the Poisson distribution, and the log link is the canonical link for a Poisson GLM. A Poisson loglinear GLM assumes a Poisson distribution for Y and uses the log link. The Poisson loglinear model with explanatory variable X is

log µ = α + βx (3.6) for this model, the mean satisﬁes the exponential relationship

µ = exp(α + βx) = eαeβx (3.7)

37 The result indicate that a unit increase in x has a multiplicative impact of eβ on µ When there are a set of predictor variables, then the model becomes

T µ = exp(Xi β) (3.8)

Where; µ = E(Y ) = V ar(Y ). This is the major assumption of the Poisson regression model. An example is shown below: Whyte, et al 1987 (Dobson, 1990) reported the number of deaths due to AIDS in Australia per 3 month period from January 1983 – June 1986.

Xi= time point (quarter), Yi= number of deaths

xi 1 2 3 4 5 6 7 8 9 10 11 12 13 14

yi 0 1 2 3 1 4 9 18 23 31 20 25 37 45

The estimated GLM with model Random: Y follows Poisson distribution

∗ Systematic: α + β log(xi) = α + βxi Link:log −→ log µ As a loglinear model

∗ log(ˆµi) = −1.9442 + 2.1748xi

Or equivalently, as a multiplicative model

−1.9442 2.1748x∗ µˆi = e e i

Interpretation: For a 1 unit increase in log(month), the estimated count increases by a factor e2.1748 = 8.80

38 3.3.2 Poisson Model for Rate Data

When events of a certain type occur over time, space, or some other index of size, it is usually more relevant to model the rate at which they occur than the number of them. For instance, our study of infant deaths in a given year for a number of admissions might model the infant mortality rate, deﬁned for a year as its number of infant deaths divided by its total admissions. For the rate occurrence of an event let Y = count and t = index of time or space, then the rate of occurrence is Y/t and the expected value of the rate is 1 E(Y/t) = E(Y ) = µ/t (3.9) t

Thus, the Poisson loglinear regression model for the rate of occurrence is

log(µ/t) = α + βx

log(µ) − log(t) = α + βx

µ = t exp(α + βx) = teαeβx (3.10)

Where -log t is an adjustment term and is referred to as oﬀset. With multiple explanatory variables, the rate model becomes

T µ = t exp(Xi β) (3.11)

3.4 Estimation

Estimation involves estimating the regression parameters. Here we will consider the maximum likelihood for GLMs and zero in to Poisson regression model.

39 3.4.1 Maximum Likelihood Estimate (GLMs)

An important practical feature of generalized linear models is that they can all be fit to data using the same algorithm, a form of iteratively re-weighted least squares. We first of all begin with a trial estimate of the parameters ˆ T ˆ β, we compute the estimated linear predictor ηî = Xi β and use that to

−1 obtain the ﬁtted values – µˆi = g (ˆηi). Using these quantities, we compute the working dependent variable

dηi Zi =η ˆi + (yi − µˆi) dµi

l Zi =η î + (yi − µî)g (µ î) (3.12) where the rightmost term is the derivative of the link function evaluated at the trial estimate. Then

E(zi) = ηi = α + β1X1 + β2X2 + ... + βkXk (3.13) and

2 V (zi) = [´g(ˆµi)] aiv(ˆµi) (3.14)

Next we compute the iterative weight ωi which is inversely proportional to the variance of the working dependent variable zi given the current estimate of the parameters. That is

1 ωi = 2 (3.15) [´g(ˆµi)] aiv(ˆµi)

Finally, we obtain an improved estimate of regressing the working dependent variable zi on the predictors xi using the weights ωi , i.e. we compute the weighted least-squares estimate

βˆ = (XI WX)−1XI WZ (3.16)

40 Where βˆ is a (k + 1 × 1) vector of regression coeﬃcients at the current iteration, X is an (n × k+1) model matrix, W is an (n × n) diagonal weighted matrix and Z is an (n × 1) working response vector.

The procedure is repeated until successive estimates change by less than a speciﬁed small amount. At this point βˆ converges to the maximum likelihood estimates of the βs.

3.4.2 Maximum Likelihood Estimate (Poisson)

Let Y1...Yn be an i.i.d. collection of Poisson (µ)random variables, where µ > 0. Thus, the likelihood function is

n Y e−µµyi L(µ; y) = y ! i=1 i

n −nµ X 1 = e µ yi (3.17) Qn y ! i=1 i=1 i n n X Y log L(µ; y) = −nµ + yi log µ − log yi! (3.18) i=1 i=1

We note that L(µ; y) is a diﬀerentiable function over the domain (0, ∞) and so we determine the critical point by equating the diﬀerential to zero. Thus

d log L(µ; y) = 0 dµ

Pn y −n + i=1 i = 0 µ

µ =y ¯(mean) (3.19)

41 Checking whether µ =y ¯ is maximum, we take the second derivative, ie

2 n d −2 X log L(µ; y) = −µ yi < 0 (3.20) dµ2 i=1

Thus, there is a local maximum at µ =y ¯. That is the maximum likelihood estimate of µ is µˆ =y ¯

3.4.3 Fisher Scoring in Log-Linear Model

ηi = log L(µ) (3.21)

The derivative of the link is dni 1 = (3.22) dµi µi

Thus, the working dependent variable has the form

(yi − mµi) zi = ni + (3.23) µi

And the iterative weight is

¨ dηi 2 ωi = 1/[b(θi)( ) ] dµi

1 = 1/[µ 2 ] µi

And simpliﬁed to

ωi = µi (3.24)

Note that the iterative weight ωi is inversely proportional to the variance of the working dependent variable zi

42 3.4.4 The Poisson Deviance

Let µˆ denote the maximum likelihood estimate of µi under the model of interest and let µ¯ = yi denote the maximum likelihood estimate of µi under the saturated model. From ﬁrst principles, the deviance is

X D = 2 [yi log(yi) − yi − log(yi!) − yi log(µ ˆi) +µ ˆi + log(yi!)] (3.25)

The term on yi! cancel out. Grouping like terms, we have

X yi D = 2 [yi log − (yi − µˆi)] (3.26) µi

The ﬁrst term in the poisson deviance has the form

X oi D = 2 oi log( ) (3.27) ei

This is identical to the Binomial deviance. For a canonical link the score is

d log L = XI (y − µ) (3.28) dβ

Setting this to zero leads to the estimation equation

XI y = XI µˆ (3.29)

Maximum likelihood estimation for Poisson log-linear models - and more generally for any generalized linear model with canonical link - requires equating certain functions of the MLE’s (namely X´µˆ) to the same functions of the data (namely Xy´ ). If the model has a constant, one column of X will consist of ones and therefore one of the estimating equations will be

X X yi = µˆi or

43 X (yi − µî) (3.30) so the last term in the Poisson deviance is zero. The Poisson deviance has an asymptotic chi-squared distribution as n −→ ∞ with the number of parameters p remaining fixed, and can be used as a goodness of fit test.

3.5 Logistic Regression

Logistic regression is statistical tool that allows one to test models to predict categorical outcomes with two or more categories, Pallant (2007). It was introduced in the 1940s as an alternative to Fisher’s 1936 classiﬁcation method, linear discriminant analysis. The model can be seen as a special case of a generalized linear model and thus ambiguous to linear regression. In particular, the key diﬀerences between the model of logistic regression model and that of linear regression can be seen in the following two features of logistic regression:

– The conditional mean P (Y/X) follows a Bernoulli distribution rather than a Gaussian distribution, because logistic regression is a classiﬁer.

– The linear combination of inputs ωT X ∈ R is restricted to [0, 1] through the logistic distribution function because logistic regression predicts the probability of the instance being positive.

The predictor (independent) variables can be either categorical or continuous, or a mix of both in one model. Where the outcome of the response (dependent) variable is dichotomous, the approach is called binary logistic regression. On the other hand, multinomial logistic regression is applied when the outcome of the response variable is more than two categories. In this research, the dependent variable is the outcome (result) of an infant (died or discharged) hence the use of binary logistic regression as the appropriate statistical tool.

44 Logistic regression is used increasingly in a wide variety of applications. Early uses were in biomedical studies but the past 20 years have also seen much use in social science research and marketing. It has also become a popular tool in business application Agresti (2007). There are basically four reasons for its wide use:

– It is a traditional tool used for applied statistics and discrete data analysis.

– The quantity log[p/(1 − p)] plays an important role in the analysis of contingency tables (the “log odds”). Classification is a bit like having a contingency table with two columns (classes) and infinitely many rows (values of x). With a finite contingency table, we can estimate the log-odds for each row empirically, by just taking counts in the table. With infinitely many rows, we need some sort of interpolation scheme; logistic regression is linear interpolation for the log-odds.

– It’s closely related to “exponential family” distributions, where the Pm probability of some vector v is proportional t0 exp β0 + j=1 fj(v)βj. If

one of the components vis binary, and the functionfj are all the identity function, then we get a logistic regression. Exponential families arise in many contexts in statistical theory (and in physics!), so there are lots of problems which can be turned into logistic regression.

– It often works surprisingly well as a classiﬁer. But, many simple techniques often work surprisingly well as classiﬁers, and this doesn’t really testify to logistic regression getting the probabilities right.

45 3.5.1 Parameters in Logistic Regression

For a binary response variable Y and an explanatory variable X, let π(x) = p(Y = 1/X = x) = 1 − p(Y = 0/X = x). The logistic regression model is

exp(α + βx) π(x) = (3.31) 1 + exp(α + β)

Equivalently, the log odds, called the logit, has a linear relationship

π log it[π(x)] = log( ) = α + βx (3.32) 1 − π

This equates the logit link function to the linear predictor. The sign of β in the equation determines whether π(x) is increasing or decreasing as x increases. The rate of climb or descent increases as |β| increases, as β → 0 the curve ﬂattens to a horizontal straight line. When β = 0, Y is independent of X. For a quantitative x with β > 0, the curve for π(x) has the shape of cumulative density function (cdf) of the logistic distribution. Since the logistic density is symmetric, π(x) approaches 1 at the same rate that it approaches 0. An example is shown below: Example

A group of students were asked if they have ever driven after drinking. They also were asked, “How many days per month do you drink at least two beers?” In the following discussion, π =the probability a student says “yes” they have driven after drinking. x = days per month of drinking two beers. (Given α = −1.5514andβ = 0.1903x, the probability of ever having driven after drinking is )

exp(−1.5514 + 0.19031x) πˆ(x) = 1 + exp(−1.5514 + 0.19031x)

46 If x = 4 days per month of drinking beer, then the estimated probability is calculated as:

exp(−1.5514 + 0.19031x) exp(−0.79016) πˆ(x) = = = 0.312 1 + exp(−1.5514 + 0.19031x) 1 + exp(−0.79016)

3.5.2 Multiple Logistic Regression

Like ordinary regression, logistic regression extends to models with multiple explanatory variables. For instance, the model for π(x) = P (Y = 1) at values x = (xi...xp) of p predictors is

log it[π(x)] = α = β1x1 + β2x2 + ... + βnxn (3.33)

The alternative formula directly specifying π(x) is

exp(α = β1x1 + β2x2 + ... + βpxp) π(x) = (3.34) 1 + exp(α = β1x1 + β2x2 + ... + βpxp)

The parameter βi refers to the effect of xi on the log odds that Y = 1, controlling the other xj. For instance, exp(β) is the multiplicative effect on the odds of a 1 - unit increase in x, at a fixed level of other xj. The explanatory variable can be qualitative, using dummy variables for categories.

3.5.3 Fisher Scoring in Logistic Regression

In ﬁnding the working dependent variable and the iterative weight used in the Fisher scoring algorithm for estimating the parameters in logistic regression, we model

ηi = log it(πi) (3.35)

47 It is usually convenient to write the link function in terms of the mean µi as π µi ηi = log( ) = log( ) (3.36) 1 − π ηi − µi

The equation can also be written as

ηi = log(µi) − log(ηi − µi) (3.37)

Diﬀerentiating with respect to µi, we have

dηi 1 1 ηi 1 = + = = (3.38) dµi µi ηi − µi µi(ηi − µi) ηiπ(1 − πi)

The working dependent variable is given as

dηi Zi = ηi + (vi − µi) (3.39) dµi

This turns out to be yi − ηiπi Zi = ηi + (3.40) ηiπi(1 − πi)

The iterative weight which is inversely proportional to the variance of the working dependent variable is given

¨ dηi 2 ωi = 1/[b(θi)( ) ] dµi

1 2 = [ηiπi(1 − πi)] ηiπi(1 − πi)

ωi = ηiπi(1 − πi) (3.41)

3.6 Survival Analysis

Survival analysis is a statistical method for analyzing longitudinal data on the occurrence of events. It was primarily developed in the medical and

48 biological sciences, but they are also widely used in the social and economic sciences, as well as in engineering (reliability and failure time analysis). It is concerned with looking at how long it takes to an event to happen of some sort. Events may include death, injury, length of stay in a hospital, duration of a strike, occurrence of a disease, marriage, divorce etc. Survival studies include:

– Clinical trials

– Prospective cohort studies

– Retrospective cohort studies

– Retrospective correlative studies

Survival Analysis has three main characteristics:

– the dependent variable or response is the waiting time (survival time) until the occurrence of a well-deﬁned event

– observations are censored, in the sense that for some units the event of interest has not occurred at the time the data are analyzed

– there are predictors or explanatory variables whose eﬀect on the waiting time (survival time) we wish to assess or control

There are also several features which are typically encountered in analysis of survival data:

– individuals do not enter study at the same time

– when study ends, some individuals have not had the event yet

– other individuals drop out or get lost in the middle of the study, and all was known about them was the last time they were still ‘free’ of the event.

The ﬁrst feature is referred to as staggered entry and the last two features relate to censoring of the failure times.

49 Failure times random variables are always non-negative . If failure time is denoted by T , then T ≥ 0. T can either be discrete or continuous. A random variable X is called a censored failure time random variable if X = min(T,U), where U is a non-negative censoring variable. There are three types of censoring:

– Right censoring

Only the random variable Xi = min(Ti,Ui) is observed due to loss to follow-up, drop-out or study termination. It is right-censoring because the true unobserved event is to the right of our censoring time; that is, all is known is that the event has not happened at the end of follow-up. The failure indicator is given as:

δ = {1 ifTi≤Ui i 0 ifTi>Ui (3.42)

The censoring indicator on the other hand is also given as:

c = {0 ifTi≤Ui i 1 ifTi>Ui (3.43)

Right-censoring is the most common type of censoring assumption we will deal with in survival analysis.

– Left-censoring

Here, observation is made on only the random variable Yi =

max(Ti,Ui) and the failure indicators:

δ = {1 ifUi≤Ti i 0 ifUi>Ti (3.44)

An example is the study of age at which African children learn a task. Some already knew (left-censored), some learned during study (exact), some had not yet learned by end of study (right-censored).

– Interval-censoring

50 Observation is made on (Li,Ri) where Ti ∈ (Li,Ri) Examples include: time to prostate cancer (observe longitudinal PSA measurements), time to undetectable viral load in AIDS studies (based on measurements of viral load taken at each clinic visit and detect recurrence of colon cancer after surgery (follow patients every 3 months after resection of primary tumor.

3.6.1 3.6.1 The Survival Function

Let T be a non-negative random variable representing the waiting time until the occurrence of an event, say death. We assume for now that T is a continuous random variable with probability density function (p.d.f.)f(t) and cumulative distribution function (c.d.f.)F (t) = P r{T < t}, giving the probability that the event has occurred by duration t. The survival function, complement of the c.d.f, is given as:

Z ∞ S(t) = P r{T ≥ t} = 1 − F t = f(x)dx (3.45) t which gives the probability of being alive just before duration t, or more generally, the probability that the event of interest has not occurred by duration t. For a discrete random variable:

X S(t) = f(x) x≥t

X = f(au)

aj ≥t X = fj (3.46)

aj ≥t

51 3.6.2 The Hazard Function

An alternative characterization of the distribution of T is given by the hazard function, or instantaneous rate of occurrence of the event, deﬁned as P r(t < T < t + dt|T > t) h(t) = lim (3.47) dt−→0 dt

The numerator of this expression is the conditional probability that the event will occur in the interval [t; t + dt] given that it has not occurred before, and the denominator is the width of the interval. Dividing one by the other we obtain a rate of event occurrence per unit of time. Taking the limit as the width of the interval goes down to zero, we obtain an instantaneous rate of occurrence. The conditional probability in the numerator may be written as the ratio of the joint probability that T is in the interval [t; t + dt) and T ≥ t (which is, of course, the same as the probability that t is in the interval), to the probability of the condition T ≥ t. The former may be written as f(t)dt for small dt, while the latter is S(t) by deﬁnition. Dividing by dt and passing to the limit gives the useful result

f(t) h(t) = (3.48) s(t) which is given as the deﬁnition of the hazard function. In words, the rate of occurrence of the event at duration t equals the density of events at t, divided by the probability of surviving to that duration without experiencing the event. Equation 3.45 that f(t) is the derivative of S(t). This suggests rewriting Equation 3.48 as

d h(t) = − log S(t) dt

52 For discrete random variables:

h(aj) = hj = P (T = aj | T ≥ aj)

P (T = a ) = j P (T ≥ aj) f(a ) = j S(aj) f(t) = P (3.49) k1ak ≥ ajf(ak)

If we now integrate from 0 to t and introduce the boundary condition S(0) = 1 (since the event is sure not to have occurred by duration (0), we can solve the above expression to obtain a formula for the probability of surviving to duration t as a function of the hazard at all durations up to t:

Z 1 S(t) = exp{− h(x)dx} (3.50) 0

The integral in curly brackets in this equation is called the cumulative hazard (or cumulative risk) and is denoted

Z 1 δ(t) = h(x)dx (3.51) 0 where δ(t) is the sum of the risks you face during 0 to t. For the discrete random variables:

X δ(t) = h(t) (3.52)

k:ak

These results show that the survival and hazard functions provide alternative but equivalent characterizations of the distribution of T . Given the survival function, we can always diﬀerentiate to obtain the density and then calculate the hazard using Equation 3.48. Given the hazard, we can always integrate to obtain the cumulative hazard and then exponentiate to

53 obtain the survival function using Equation 3.50. Example: The simplest possible survival distribution is obtained by assuming a constant risk over time, so the hazard is

h(t) = h for all t. The corresponding survival function is

S(t) = exp{−ht}

This distribution is called the exponential distribution with parameter h. The density may be obtained multiplying the survivor function by the hazard to obtain f(t) = hexp{−ht},

The mean turns out to be 1/h. This distribution plays a central role in survival analysis, although it is probably too simple to be useful in applications in its own right.

3.6.3 Expectation of Life

Let µ denote the mean or expected value of T . by deﬁnition, one would calculate µ multiplying t by the density f(t)and integration, so

Z ∞ µ = tf(t)dt 0

Integrating by parts, and making use of the fact that −f(t) is the derivative of S(t), which has limits or boundary conditions S(0) = 1 and S(∞) = 0, one can show that Z ∞ µ = S(t)dt (3.53) 0

In words, the mean is simply the integral of the survival function.

54 3.6.4 The Likelihood Function for Censored Data

Suppose then that we have n units with lifetimes governed by a survivor function S(t) with associated density f(t) and hazard h(t). Suppose unit i is observed for a time ti. If the unit died at ti, its contribution to the likelihood function is the density at that duration, which can be written as the product of the survivor and hazard functions

Li = F (ti) = S(ti)h(ti)

If the unit is still alive at ti, all we know under non-informative censoring is that the lifetime exceeds ti. The probability of this event is

Li = S(ti) which becomes the contribution of a censored observation to the likelihood.

Both types of contribution share the survivor function S(ti), because in both cases the unit lived up to time ti. A death multiplies this contribution by the hazard h(ti), but a censored observation does not. The two contributions can be written in a single expression. To this end, let dibe a death indicator, taking the value one if unit i died and the value zero otherwise. Then the likelihood function may be written as follows

n Y Y di L = Li = h(ti) S(ti) i=1 i=1

Taking logs, and recalling the expression linking the survival function S(t) to the cumulative hazard function h(t), we obtain the log-likelihood function for censored survival data

n X log L = {di log h(ti) − ∆(ti)} (3.54) i=1

55 Example: Suppose we have a sample of n censored observations from an exponential distribution. Let ti be the observation time and di the death indicator for unit i. In the exponential distribution h(t) = h for all t. The cumulative risk turns out to be the integral of a constant and is therefore ∆(t) = ht. Using these two results on Equation 3.54 gives the log-likelihood function X log L = {di log h − ht}.

P P Let D = di denote the total number of deaths, and let T = ti denote the total observation (or exposure) time. Then we can rewrite the log- likelihood as a function of these totals to obtain

log L = D log h − ht (3.55)

Diﬀerentiating this expression with respect to h we obtain the score function

D v(h) = − T h

D hˆ = (3.56) T the total number of deaths divided by the total exposure time. The estimator is optimal (in a maximum likelihood sense) only if the risk is constant and does not depend on age. We can also calculate the observed information by taking minus the second derivative of the score, which is

D I(h) = h2

To obtain the expected information we calculate the expected number of deaths, but this depends on the censoring scheme. For example under Type I censoring with ﬁxed duration τ, one would expect n(1 − S(τ)) deaths.

56 Under Type II censoring the number of deaths would have been fixed in advance. Under some schemes calculation of the expectation may be fairly complicated if not impossible. A simpler alternative is to use the observed information, estimated using the MLE. of h given in Equation 3.56. Using this approach, the large sample variance of the MLE of the hazard rate may be estimated as D varˆ (hˆ) = T 2 a result that leads to large-sample tests of hypotheses and confidence intervals for h. If there are no censored cases, so that di = 1for all i and D = n, then the results obtained here reduce to standard maximum likelihood estimation for the exponential distribution, and the MLE of h turns out to be the reciprocal of the sample mean. It may be interesting to note in passing that the log-likelihood for censored exponential data given in Equation 3.55 coincides exactly (except for constants) with the log-likelihood that would be obtained by treating D as a Poisson random variable with mean hT . To see this point, the Poisson log-likelihood is written when D ∼ P (hT ).This differs from Equation 3.55 only in the presence of a term D log(T ), which is a constant depending on the data but not on the parameter h Thus, treating the deaths as Poisson conditional on exposure time leads to exactly the same estimates (and standard errors) as treating the exposure times as censored observations from an exponential distribution.

3.7 Survival Methods

A number of models are available to analyze the relationship of a set of predictor variables with the survival time. Methods include parametric, non-parametric and semi-parametric approaches. Parametric methods assume that the underlying distribution of the survival times follows certain

57 known probability distributions. A nonparametric estimator of the survival function is widely used to estimate and graph survival probabilities as a function of time. A semi-parametric model makes fewer assumptions than typical parametric methods but more assumptions than non-parametric methods. In particular, and in contrast with parametric models, it makes no assumptions about the shape of the baseline hazard function.

3.7.1 The Kaplan-Meier Method

The Kaplan-Meier method (Kaplan and Meier, 1958), also known as the "product-limit method", is a nonparametric method used to estimate the probability of survival past given time points with the presence of censored cases. Thus, it calculates a survival distribution. The basic idea is to first compute the conditional probabilities at each time point when an event occurs and then, compute the product limit of those probabilities to estimate the survival rate at each point in time. Furthermore, the survival distributions of two or more groups of a between-subjects factor can be compared for equality. This method can be used to obtain descriptive statistics for survival data, including the median survival time, and compare the survival experience for two or more groups of subjects. It is used also to test for overall differences between estimated survival curves of two or more groups of subjects, such as males versus females, or treated versus untreated (control) groups, several tests are available, including the log-rank test. This can be motivated as a type of chi-square test, a widely used test in practice, and in reality is a method for comparing the Kaplan-Meier estimates for each group of subjects. For instance, the Kaplan-Meier method could be used to determine whether the (distribution of) time to failure of a knee replacement differs based on exercise impact amongst young patients (the survival time would be "time to knee replacement failure" and the between-

58 subjects factor would be "exercise impact", which has two groups:"low impact" and "high impact"). Comparison could also be made on the survival distributions (experiences) between the two levels of exercise impact to determine if they are equal, and if not, where any diﬀerences lie, that is, whether time to knee replacement failure was lower in the "low impact" exercise group compared to the "high impact" exercise group.

There are several assumptions to this method:

– The event status should consist of two mutually exclusive and collectively exhaustive states: "censored" or "event"

– The time to an event or censorship (known as the "survival time") should be clearly deﬁned and precisely measured.

– Where possible, left-censoring should be minimized or avoided. Left- censoring occurs when the starting point of an experiment is not easily identiﬁable.

– There should be independence of censoring and the event.

– There should be no secular trends (also known as secular changes).

– There should be a similar amount and pattern of censorship per group.

Given k distinct observed event times t1 < tj < ...tk. At each event time tj, there are nj individuals at – risk dj is the number who have the event at time tj. The estimated survival probability at time t : P (T > t) is given as

Y dj Sd(t) = [1 − ] (3.57) nj j:tj ≤t

This gives the product-limit estimate of survival at each time an event happens. The risk set nj at time tj consists of the original sample minus all those who have been censored or had the event before tj.

Typically, dj = 1person, unless data are grouped in time intervals (for

59 instance, everyone who had the event in the 3rd month). dj/nj is the proportion that failed at the event time tj, 1 − dj/nj is the proportion surviving the event time The probability of surviving event time t is multiplied with the probabilities of surviving all the previous event times.

An example is shown below: Example

Calculate the product-limit estimate of survival for the following data (n = 7)

Time-to-event (months) Survival (1=died/0=censored)

10 0

2 1

4 0

8 1

12 0

14 0

10 1

Solution

60 Time-to-events (months) dj nj

2 1 7

4 0 6

8 1 5

10 1 4

12 0 2

14 0 1

Y dj Sd(t) = [1 − ] nj j:tj ≤t

1 6 Sd(2) = 1 − = = 0.857 7 7 1 0 6 6 Sd(4) = [1 − ][1 − ] = × 1 = = 0.857 7 6 7 7

1 0 1 6 4 24 2 Sd(8) = [1 − ][1 − ][1 − ] = × 1 × = = = 0.686 7 6 5 7 5 35 3

1 0 1 1 6 4 3 72 18 S(\t = 10) = [1− ][1− ][1− ][1− ] = ×1× × = = = 0.514 7 6 5 4 7 5 4 140 35

1 0 1 1 0 6 4 3 18 S(\t = 12) = [1− ][1− ][1− ][1− ][1− ] = ×1× × ×1 = = 0.514 7 6 5 4 2 7 5 4 35

1 0 1 1 0 0 6 4 3 18 S(\t = 14) = [1− ][1− ][1− ][1− ][1− ][1− ] = ×1× × ×1×1 = = 0.514 7 6 5 4 2 2 7 5 4 35

61 3.7.2 The Cox Regression Method

The Cox regression model is a semi-parametric model, making fewer assumptions than typical parametric methods but more assumptions than those non-parametric methods described above. In particular, and in contrast with parametric models, it makes no assumptions about the shape of the so-called baseline hazard function. It assess the relationship between survival time and covariates. The Cox regression model provides useful and easy to interpret information regarding the relationship of the hazard function to predictors. The central statistical output is the hazard ratio. The hazard ratio comparing any two observations is assumed to be constant over time. This assumption is called the proportional hazards assumption. The Cos regression model has two components:

– A baseline hazard function that is left unspeciﬁed but must be positive (equals the hazard when all covariates are 0).

– A linear function of a set of k ﬁxed covariates that is exponentiated. (equals the relative risk)

Thus

log hi(t) = log h0(t) + β1xi1 + ... + βkxik

β1xi1+...+βkxik hi(t) = h0(t)e (3.58) where i, ..., kis the number of covariates Comparing the hazard rate of individuals with diﬀerent covariates, we have

h (t) h (t)eβx1 1 0 β(x1−x2) HR = = βx = e (3.59) h0(t) h0(t)e 2

Hazard functions should be strictly parallel.

62 CHAPTER 4

ANALYSIS AND RESULTS

4.1 Introduction

This chapter deals with the analysis of data and discussion of ﬁndings. Secondary data was used for the thesis. Infants admitted and infant deaths in the Kumasi district from 2008-2014 were recorded from the regional annual report and other documents of GHS Kumasi. Data from 2010 to 2015(March) information was recorded from the registers at the Research and Development Unit of the Komfo Anokye Teaching Hospital (KATH). The variables of interest recorded were;

– Duration of stay at the hospital (duration in days)

– Infant weight level

– Age of infant (in months)

– Diagnosis ( Malaria or Not Malaria)

– Outcome of admission (died or discharged).

We shall first look at preliminary analysis and then further analysis using SPSS. The chapter uses Poisson regression model to examine the significance of the occurrence and incidence of infant mortality in Kumasi district while logistic regression was used to assess factors that affect infant mortality at the Komfo Anokye Teaching Hospital (KATH).

63 4.2 Preliminary Analysis

Infants admitted during the study period were a total of 587. There were 378 infant deaths.

Table 4.1: Age group distribution (in months), number of deliveries and infant deaths at KATH from 2010-2015 (March) Age group (in months) No. of infants Infant Death P% of deaths within Age group 0 - 3 98 64 65.31 4 - 6 167 120 71.86 7 - 9 171 104 60.82 10 - 12 151 90 59.60 total 587 378 64.40

From the table, the age group of 4 – 6 recorded the highest percentage of infant deaths within age group (71.86%), followed by age group 0 – 3 (65.31%). The least percentage of death (59.60%) was recorded among the age group of 10 – 12. A total of twenty-six (26) different diseases were diagnosed. An infant was diagnosed averagely of two (2) diseases. Malaria recorded the highest number of infants affected. It affected 149 infants (20.11%) followed by Pneumonia affecting 120 infants (16.19%). Respiratory distress, Jaundice and Tuberculosis recorded the lowest number of infants affected. They affected only 1 infant (0.13%) each. This is shown in the table below:

64 Table 4.2: Diseases diagnosed and the number of infants aﬀected from 2010 to 2015 (March Disease Infants Aﬀected Percentage Acute Asthmatic Attack 2 0.27 Acute Respiratory Distress 1 0.13 Anaemia 33 4.45 Bacterial Infection 3 0.40 Bleeding 3 0.40 Bronchiottis 21 2.83 Clinically Dead 22 2.97 Dehydration 12 1.62 Diarrhoea 71 9.58 Down Syndrome 6 0.81 Dysentry 3 0.40 Fertile Convolution 14 1.89 Fertile Seizure 2 0.27 Heart Disease 10 1.35 Heart Failure 9 1.21 Jaundice 1 0.13 Liver Failure 2 0.27 Malaria 146 20.11 Malnutrition 69 9.31 Meningitis 64 8.64 Pneumonia 120 16.19 Sepsis 44 5.94 Shock 57 7.69 Tuberculosis 1 0.13 UTI 14 1.89 Vomiting 8 1.88 Total 178 100

See Appendix for detailed statistics of diseases diagnosed and the number of infants aﬀected for each year.

The highest infant mortality of 91 deaths (24.07%) was recorded in 2013

65 Figure 4.1: Pie chart showing yearly distribution of infant mortality at KATH.

and the lowest of 25 (6.61%) was recorded in 2012.

Figure 4.2: Bar chart showing the distribution of infant mortality ratios in Kumasi district for 2008 - 2014.

From the chart the highest infant mortality ratio of 45.6 /1,000 live births was recorded in 2008 and the least of 20.1 /1,000 live births was recorded in 2013. Infant mortality ratio declined from 2008 at 45.6/1,000 live births to 2011 at 26.6/1,000 live births. It then experienced consecutive years of upward and downward trend from 27.9/1,000 live births in 2012 to 20.1/1,000 live births in 2013 and ﬁnally 20.3/1,000 live births in 2014.

66 Figure 4.3: Chart showing trend of supervised infants on admission in Kumasi district from 2008- 2014.

The chart indicates that, infants admitted dropped steadily from 2008 to 2010. It rose at an increasing rate the following year and then at a decreasing rate from 2011 to 2013. It ﬁnally dropped in 2014.

4.3 Further Analysis

In this session, further analysis will be made on the data set with the help of Poisson and logistic regression models. We shall first examine the significance of the occurrence and incidence of infant mortality in Kumasi district. Finally, logistic regression would be employed to assess the contribution of some identified variables on infant mortality at the KATH.

4.3.1 Modelling The Occurrence of Infant Mortality

Cases

SPSS is used in modelling the occurrence of infant mortality cases in Kumasi district. Poisson distribution with log link function was used in modelling. Four hundred and ﬁfty-eight (458) observations were used in 7 years period. In the model, infant deaths is used as the response variable while time (years) is used as the only predictor variable.

67 The major assumption of Poisson regression model is that the mean and the variance should be the same. This assumption determines the appropriateness of a Poisson model. To assess, an objective test for over dispersion which follows the Pearson chi-square was performed. For the appropriateness of Poisson model, the dispersion parameter should not be signiﬁcantly diﬀerent from one. The model is given as follows;

log(meandeath) = α + β ∗ yeari

Where i= 1 – 7

α β∗yeari meandeath = exp(α + β ∗ yeari) = e e

The ﬁtted model has a deviance value of 122.602 which follows a chi-square distribution with 77 degrees of freedom. The ratio of the deviance and the degrees of freedom is 1.592. This indicates the data is over dispersed. The scaled deviance and the scaled Pearson chi-square had 122.602 and 104. 046 values respectively with the same degrees of freedom of 77. See Table 5.1 in appendix for the detailed Analysis of the Criteria for Assessing Goodness of Fit.

68 Table 4.3: Analysis of parameter estimates for occurrence of infant mortality Parameter DF Estimate Std Error Wald 95% Conf. Int Chi-sq P-Value Intercept 1 1.365 0.1459 (1.079, 1.651) 87.602 0.000 Year 2008 1 0.638 0.1803 (0.285, 0.992) 12.539 0.000 Year 2009 1 0.481 0.1856 (0.117, 0.844) 6.707 0.010 Year 2010 1 0.021 0.2052 (-0.381, 0.423) 0.011 0.918 Year 2011 1 0.369 0.1897 (-0.002, 0.741) 3.791 0.052 Year 2012 1 0.454 0.1865 (0.088, 0.819) 5.922 0.015 Year 2013 1 0.175 0.1978 (-0.213, 0.563) 0.784 0.376 Year 2014 1 0.000 0.0000 (0.000, 0.000) Scale 1 1.000 1.0000 (1.000, 1.000)

Table 4.3 presents detailed analysis of the of infant mortality cases in Kumasi district from 2008 to 2014. Time in years, the only predictor variable, is treated as a discrete variable. The intercept has a chi-square and p-value of 87.602 and 0.000 respectively. This implies that the intercept is significant (α < 0.05). It can be seen that the parameter estimates for the years 2008, 2009, 2010, 2011, 2012, and 2013 were all positive showing that the mean number of occurrence of infant deaths is higher in those years than the reference year (2014). The years 2008, 2009 and 2012 experienced significant increase in the mean occurrence of infant mortality cases in the Kumasi district compared to 2014. That is, the mean number of infant deaths for all the months in 2008(e0e0.638) = 1.894, that of 2009(e0e0.481) = 1.617 and 2012(e0e0.454) = 1.574 higher than the mean number of infant deaths for all months in 2014. Appendix 8 (see Apendix) which contains detailed analysis of parameter estimates for the occurrence of infant deaths for continuous time revealed that the mean number of occurrence of infant deaths throughout the period under study (2008 – 2014) is significant. This implies that the mean number of occurrence of infant death cases in Kumasi district has significantly reduced over the period under study.

69 4.3.2 Modelling The Incidence of Infant Mortality

Cases

We also use SPSS in modelling the incidence of infant mortality cases in Kumasi district. Poisson distribution with log link function was used in modelling. Four hundred and ﬁfty-eight (458) observations were used in 7 years period. In the model, infant deaths was used as the response variable while time (years) was used as the only predictor variable. The model is given as follows

log(meandeath/admitted) = α + β ∗ yaeri

Where i=1–7

log(meandeath) − log(admitted) = α + β ∗ yaeri

α β∗yeari meandeath = admitted{exp(α + β ∗ yeari)} = adm.e e

Appendix 9 (see appendix) presents a detailed analysis of the Criteria for Assessing Goodness of Fit. From the table, the dispersion parameter was 1.646 indicating presence of over dispersion in the data. The dispersion parameter is the ratio of the deviance value 126.735 which follows the Pearson chi-square to the degrees of freedom 77.

70 Table 4.4: Analysis of parameter estimates for incidence of infant mortality Parameter DF Estimate Std Error Wald 95% Conf. Int Chi-sq P-Value Intercept 1 -0.919 0.1459 (-1.205, -0.633) 39.670 0.000 Year 2008 1 0.721 0.1803 (0.368, 1.075) 16.003 0.000 Year 2009 1 0.615 0.1856 (0.251, 0.979) 10.982 0.001 Year 2010 1 0.175 0.2052 (-0.228, 0.577) 0.724 0.395 Year 2011 1 0.331 0.1897 (-0.041, 0.702) 3.039 0.081 Year 2012 1 0.400 0.1865 (0.035, 0.766) 4.607 0.032 Year 2013 1 0.099 0.1978 (-0.288, 0.487) 0.253 0.615 Year 2014 1 0.000 0.0000 (0.000, 0.000) Scale 1 1.000 1.0000 (1.000, 1.000)

Table 4.4 presents detailed analysis of infant mortality cases in Kumasi district from 2008 to 2014. The value of the intercept -0.919 is significant with chi-square value 39.670 and p-value of 0.000. Positive values of parameter estimates for the years 2008, 2009, 2010, 2011, 2012 and 2013 indicates that the mean number of occurrence of infant deaths was higher in those years than the reference year (2014). From the results, there was a statistically significant difference between 2014 and years 2008, 2009 and 2012. They had chi-square values of 16.003, 10.982 and 4.607 with p-values of 0.000, 0.001 and 0.032 respectively. In 2008, infant mortality rate increased by (e−0.919e0.721) = 0.820, (e−0.919e0.615) = 0.738in2009and(e−0.919e0.400) = 0.595 in 2012 respectively compared to the reference year 2014. Appendix 10 (See Appendix) presents detailed analysis of parameter estimates for incidence of infant mortality for continuous time. It is obvious from the table that the mean incidence of infant mortality in Kumasi district has reduced over the period under study. With a p-value of 0.000, we can conclude statistically that the mean rate of infant death cases is significant over the period considered.

71 4.3.3 Model containing Factors that Aﬀect Infant

Outcome at KATH

SPSS statistical package version 17 is used in modelling the factors that contribute to infant mortality at the Komfo Anokye Teaching Hospital. It must be well noted that out of the 587 cases, only 466 (79.4A direct binary logistic regression is performed to assess the impact of age, duration of stay in hospital, diagnosis and weight on the likelihood of infant on admission at Komfo Anokye Teaching Hospital dying. The response variable is the outcome of admission. The outcome and diagnosis are categorical variables. Their categories are as follows;

1, if Malaria Outcome = {0, ifNon−Malaria

1, if Malaria Diagnosis = {0, ifNon−Malaria

The model containing all the predictor variables (PVs) is statistically signiﬁcant with chi-square value of 15.463 with p-value of 0.004 for Omnibus Test of Model Coeﬃcients and chi-square value of 7.537 with p-value of 0.480 for Hosmer and Lemeshow Test. The Cox and Small R2 of 0.033 and the Nagelkerke R2 of 0.045 indicate that between 3.3% and 4.5% of the variation in the response variable is explained by the predictor variables (PVs). The binary logistic regression model is given as:

1 prob(outcome = ) P V s

exp(α + β × diagnosis + β × weight + β × duration + β × age) = 1 2 3 4 1 + exp(α + β1 × duration + β2 × diagnosis + β3 × weight + β4 × age

72 Where PVs are predictors

The model predicts the likelihood of an infant on admission at the KATH dying of malaria.

Table 4.5: Analysis of parameter estimates for factors that aﬀect infant mortality. Variable Odds Ratio Estimate Std Error 95% Conf Interval P-Value Intercept 1.642 0.496 0.314 0.114 Diagnosis 1.244 0.218 0.239 (0.788, 1.988) 0.362 Weight 1.007 0.007 0.004 (0.989, 1.014) 0.099 Duration 1.005 0.005 0.002 (1.002, 1.008) 0.002 Age 0.959 -0.041 0.020 (0.904, 1.018) 0.171

Table 4.5 presents details of the analysis of parameter estimates for duration, diagnosis, weight and age. The table also presents the individual parameter estimates with their p-values, standard error (S.E), odds ratio and conﬁdence interval.

From the table, the only signiﬁcant predictor variable is duration of stay. Thus, the binary logistic regression model for signiﬁcant predictors then becomes:

1 exp(β × duration) prob(outcome = ) = 3 PV 1 + exp(β3 × duration)

Hence 1 exp(0.005β ) prob(outcome = ) = 3 PV 1 + exp(0.005β3)

The odds ratio of 1.005 indicates that the duration of stay is 1.005 more likely to contribute to infants on admission dying than surviving. The positive coeﬃcient of 0.005 indicates that the higher the duration of stay the higher the likelihood of infants on admission dying.

73 4.3.4 Survival of Infants in the Hospital

We again use SPSS version 17 in analysing infant survival over time stay in the hospital. Out of 466 cases included, 301 infants (64.6%) died while 165 infants (35.4%) were discharged. A Kaplan- Meier Estimate and Cox Regression were used to asses of infants on admission at the Komfo Anokye Teaching Hospital (KATH). The Kaplan-Meier procedure is used to estimate the mean survival time between diagnosis of infants admitted and their survival estimates. The Cox Regression is used to assess the relationship between survival time and diagnosis. Time variable is duration of stay in the hospital and factor variable was diagnosis. Comparison is made between two events (died and discharged). Taking a close look at the event death (time-to-death), inference can be made that there is much diﬀerence in the mean survival time between diagnosis (malaria or non-malaria) since the conﬁdence intervals do not overlap as seen in the table below.

Table 4.6: Mean survival time between malaria diagnoses (time-to-death) Mean 95% Conﬁdence Interval Diagnosis Estimate Std Error Lower Boud Upper Bound Non-Malaria 53.474 6.949 39.854 67.095 Malaria 123.162 13.853 96.010 160.313 Overall 72.142 6.546 59.312 84.972

From table 4.6, the mean survival time of infants diagnosed of a disease other than malaria is 53.474 and 123.162 for infants diagnosed of malaria. This implies that infants diagnosed of malaria averagely have a higher chance of surviving than infants diagnosed otherwise. The median survival time for infants diagnosed of disease other than

74 malaria is approximately 3 days and 74 days for infants diagnosed of malaria (See Appendices). The overall tests of the equality of survival times across diagnosis shows that there is a statistical signiﬁcant diﬀerence between diagnosis in survival time with chi-square value of 14.483 and p-value of 0.000 for Log Rank test, chi-square value of 10.252 and p-value of 0.001 for Breslow test and a chi-square value of 13.572 and p-value of 0.000 for Tarons-Ware test.

75 Table 4.7: Survival Estimate of infants diagnosed of disease other than malaria (time-to-death) Survival Time (Days) Estimate Standard Error 0 1 0.022 1 0.614 0.026 2 0.523 0.029 3 0.448 0.030 4 0.422 0.031 5 0.365 0.031 6 0.342 0.031 7 0.318 0.031 8 0.306 0.031 9 0.294 0.031 11 0.281 0.031 13 0.269 0.031 14 0.262 0.031 29 0.256 0.031 30 0.250 0.031 44 0.243 0.031 57 0.236 0.030 67 0.229 0.030 70 0.233 0.030 76 0.216 0.030 131 0.209 0.030 132 0.201 0.030 135 0.194 0.29 150 0.187 0.029 175 0.179 0.029 177 0.172 0.029 178 0.164 0.029 199 0.146 0.028 205 0.137 0.028 208 0.119 0.027 222 0.110 0.026 224 0.101 0.026

76 Survival Time (Days) Estimate Standard Error 246 0.092 0.025 258 0.069 0.023 265 0.057 0.022 281 0.046 0.020 286 0.023 0.015 292 0.011 0.011 310 0.000 0.000

Table 4.8: Survival Estimate of infants diagnosed of malaria (time-to-death) Survival Time (Days) Estimate Standard Error 0 1 0.030 1 0.708 0.045 2 0.640 0.048 3 0.617 0.049 5 0.602 0.050 37 0.584 0.052 42 0.566 0.053 47 0.548 0.055 48 0.530 0.056 55 0.511 0.057 74 0.492 0.058 89 0.473 0.059 129 0.455 0.059 152 0.436 0.060 159 0.417 0.060 178 0.398 0.060 186 0.378 0.060 240 0.358 0.061 242 0.316 0.060 243 0.295 0.060 249 0.253 0.058 252 0.231 0.057 262 0.185 0.054

77 Survival Time (Days) Estimate Standard Error 267 0.162 0.054 272 0.139 0.050 274 0.116 0.046 278 0.069 0.038 282 0.046 0.031 296 0.023 0.023 297 0.000 0.000 262 0.185 0.054 267 0.162 0.054 272 0.139 0.050 274 0.116 0.046 278 0.069 0.038 282 0.046 0.031 296 0.023 0.023 297 0.000 0.000

Tables 4.7 and 4.8 shows the survival estimates of infants not diagnosed of malaria and infants diagnosed of malaria respectively. The tables indicate that infants diagnosed of a disease apart from malaria generally have a higher probability of dying than those diagnosed of malaria. For instance, an infant with malaria has 0.698 probability of still being admitted after 178 days whereas an infant without malaria has 0.164 probability. However, an infant with malaria has zero (0) probability of surviving if the duration of stay in the hospital extends to 297 days (approximately 10 months) whereas an infant without malaria has zero (0) probability of surviving at 310 days (a little above 10 months). The probability of survival at day one (1) drops from 1 to 0.708 for infants diagnosed of malaria and from 1 to about 0.614 for infants diagnosed of disease apart from malaria. Survival for infants diagnosed of malaria fall in the range of 0.4 to 0.6 for about 155 days (about 5 months) but reduces sharply at an increasing rate afterwards. Also, survival time of infants diagnosed of disease other than malaria reduces fairly (at a decreasing rate) from day one (1) till 310 days.

78 This is graphically shown below:

Figure 4.4: Survival of infants (between malaria diagnosis) against duration of stay in hospital (time-to-death)

The table below examines the hazard ratio of the hazard rate in infants diagnosed of disease apart from malaria to the hazard rate in infants diagnosed of malaria. The value of Exp (B) for diagnosis means that the mortality hazard for a non-malaria infant admitted at the hospital is 1.646 times that of an infant diagnosed of malaria. Thus, the probability of an infant diagnosed of a disease apart from malaria dying the next day after surviving before that day is 64.6% higher than an infant diagnosed of malaria.

Table 4.9: Hazard ratio between malaria diagnosis (time-to-death) B SE Wald DF Sig Exp(B) DIAGNOSIS 0.499 0.141 12.435 1 0.000 1.646

On the other hand, a close look at the event discharge (time-to-discharge), there is not much diﬀerence (only about 20) in the mean survival time between diagnosis (malaria or non-malaria) as compared to the event death (time-to-death) since the conﬁdence intervals overlap as seen in the table

79 below.

Table 4.10: Mean survival time between malaria diagnoses (time-to-discharge) 95% Conﬁdence Interval Diagnosis Estimate Std Error Lower Boud Upper Bound Non-Malaria 128.436 12.012 104.893 151.978 Malaria 148.423 17.019 115.065 181.790 Overall 136.976 9.797 117.775 156.78

From table 4.10, the mean survival time of infants diagnosed of a disease other than malaria is 128.436 and 148.423 for infants diagnosed of malaria. This implies that infants diagnosed of malaria averagely have a higher chance of staying in the hospital than infants diagnosed otherwise. The median survival time for infants diagnosed of disease other than malaria is approximately 32 days and 221 days for infants diagnosed of malaria (See Appendix). The overall tests of the equality of survival times across diagnosis shows that there is no statistical signiﬁcant diﬀerence between diagnosis in survival time (they are the same) with chi-square value of 2.747 and p-value of 0.097 for Log Rank test, chi-square value of 2.188 and p-value of 0.139 for Breslow test and a chi-square value of 2.562 and p-value of 0.109 for Tarons-Ware test.

80 Table 4.11: Survival Estimate of infants diagnosed of disease other than malaria (time-to-discharge Survival Time (Days) Estimate Standard Error 0 1 0.013 1 0.746 0.026 2 0.670 0.030 3 0.611 0.032 4 0.561 0.035 5 0.553 0.035 6 0.545 0.036 7 0.526 0.037 8 0.516 0.037 16 0.503 0.039 32 0.478 0.041 116 0.463 0.042 124 0.448 0.043 167 0.431 0.045 171 0.413 0.046 181 0.394 0.048 197 0.374 0.050 203 0.352 0.051 250 0.317 0.057 256 0.282 0.061

81 Table 4.12: Survival Estimate of infants diagnosed of malaria (time-to-discharge) Survival Time (Days) Estimate Standard Error 0 1 0.026 1 0.844 0.036 2 0.818 0.039 3 0.728 0.049 4 0.635 0.056 5 0.573 0.058 7 0.558 0.059 28 0.542 0.059 41 0.525 0.059 64 0.506 0.060 221 0.481 0.062 226 0.456 0.064 255 0.414 0.070

Tables 4.11 and 4.12 show the survival estimates of infants not diagnosed of malaria and infants diagnosed of malaria respectively. The tables indicate that infants diagnosed of malaria generally have a higher probability of staying longer in the hospital than those diagnosed of malaria. For instance, an infant with malaria has 0.558 probability of still being admitted after 7 days whereas an infant without malaria has 0.526 probability. The probability of an infant being admitted after day one (1) drops from 1 to 0.844 for infants diagnosed of malaria and from 1 to about 0.746 for infants diagnosed of disease apart from malaria. Survival for infants diagnosed of malaria fall in the range of 0.4 to 0.6 for about 250 days (about 8 months). This is graphically shown below:

Figure 4.5 Survival of infants (between malaria diagnosis) against duration of stay in hospital (time-to-discharge) The table below examines the hazard ratio of the hazard rate in infants diagnosed of disease apart from malaria to the hazard rate in infants diagnosed of malaria. The p-value of 0.116 shows that there is no

82 Figure 4.5: Survival of infants (between malaria diagnosis) against duration of stay in hospital (time-to-discharge)

statistically signiﬁcant diﬀerence in the hazard ratio. The probability of an infant diagnosed of a disease apart from malaria being discharged the next day after still being admitted before that day is 33.3% higher than an infant diagnosed of malaria.

Table 4.13: Hazard ratio between malaria diagnosis (time-to-discharge) B SE Wald Df Sig Exp(B) DIAGNOSIS 0.288 0.183 2.471 1 0.116 1.33

Further, analysis is done on Pneumonia since it is the second highest ranked disease aﬀecting 120 infants (16.19%) in the hospital. Taking a look at the event death (time-to-death), inference can be made that there is exist a diﬀerence in the mean survival time (about 33) between diagnosis (pneumonia or non-pneumonia).

83 Table 4.14: Mean survival time between pneumonia diagnosis (time-to-death) 95% Conﬁdence Interval Diagnosis Estimate Std Error Lower Boud Upper Bound Non-Pneumonia 82.033 7.900 66.550 97.517 Pneumonia 49.016 10.853 27.744 70.289 Overall 72.142 6.546 59.312 84.972

From table 4.14, the mean survival time of infants diagnosed of a disease other than pneumonia is 82.033 and 49.016 for infants diagnosed of pneumonia. This implies that infants diagnosed of pneumonia averagely have a lower chance of surviving than infants diagnosed otherwise. The median survival time for infants diagnosed of disease other than pneumonia is approximately 4 days and 3 days for infants diagnosed of pneumonia (See Appendix) . The overall tests of the equality of survival times across diagnosis shows that there is no statistical signiﬁcant diﬀerence between diagnosis in survival time with chi-square value of 1.878 and p-value of 0.171 for Log Rank test, chi-square value of 0.10 and p-value of 0.740 for Breslow test and a chi-square value of 0.701 and p-value of 0.402 for Tarons-Ware test.

84 Table 4.15: Survival Estimate of infants diagnosed of disease other than pneumonia (time-to-death) Survial Time (Days) Esimate Standard Error 0 1 0.021 1 0.633 0.026 2 0.560 0.028 3 0.510 0.029 4 0.490 0.030 5 0.454 0.031 6 0.442 0.031 7 0.429 0.032 9 0.416 0.032 11 0.402 0.032 29 0.395 0.033 30 0.388 0.033 37 0.381 0.033 44 0.374 0.033 48 0.367 0.033 56 0.360 0.033 67 0.352 0.034 70 0.345 0.034 74 0.338 0.034 76 0.330 0.034 89 0.323 0.034 129 0.315 0.034 135 0.308 0.034 150 0.300 0.034 152 0.293 0.034 159 0.285 0.034 175 0.278 0.034 178 0.270 0.034 186 0.262 0.034 199 0.246 0.033 205 0.237 0.033 208 0.220 0.033

85 Survial Time (Days) Esimate Standard Error 222 0.211 0.033 224 0.203 0.033 240 0.193 0.032 242 0.184 0.032 243 0.175 0.032 246 0.166 0.031 249 0.147 0.031 252 0.138 0.030 258 0.128 0.029 262 0.109 0.028 265 0.099 0.027 267 0.099 0.026 272 0.079 0.025 278 0.059 0.022 281 0.049 0.021 282 0.039 0.019 286 0.030 0.016 296 0.020 0.014 297 0.010 0.010 310 0.000 0.000

86 Table 4.16: Survival Estimate of infants diagnosed of pneumonia (time-to-death) Survival Time(Days) Estimate Standard Error 0 1 0.037 1 0.647 0.048 2 0.529 0.052 3 0.443 0.053 4 0.430 0.053 5 0.363 0.052 6 0.335 0.052 7 0.307 0.051 8 0.279 0.050 13 0.251 0.049 14 0.237 0.048 42 0.223 0.047 47 0.208 0.046 57 0.193 0.045 131 0.177 0.044 132 0.161 0.043 177 0.143 0.042 178 0.125 0.040 242 0.107 0.038 258 0.080 0.037 274 0.054 0.033 286 0.027 0.025 292 0.000 0.000

Tables 4.15 and 4.16 shows the survival estimates of infants not diagnosed of pneumonia and infants diagnosed of pneumonia respectively. From the tables above, infants diagnosed of pneumonia generally have a higher probability of dying than those diagnosed a disease apart from pneumonia. An infant with pneumonia has zero (0) probability of surviving after 292 days (approximately 10 months) whereas an infant without pneumonia has zero (0) probability of surviving after 310 days (a little above 10 months). The probability of survival on day one (1) drops from 1 to 0.647 for infants

87 diagnosed of pneumonia and from 1 to about 0.633 for infants diagnosed of disease apart from pneumonia. Survival for infants reduces steadily for both diagnoses. This is graphically shown below:

Figure 4.6: Survival of infants (between pneumonia diagnosis) against duration of stay in hospital (time-to-death)

The table below examines the hazard ratio of the hazard rate in infants diagnosed of disease apart from pneumonia to the hazard rate in infants diagnosed of pneumonia. The p-value of 0.203 shows that there is no statistically signiﬁcant diﬀerence in the hazard ratio Thus, the probability of an infant diagnosed of a disease apart from pneumonia dying the next day after surviving before that day is 15.4%(100% ˘ (100% × 0.846) = 15.4%) lower than an infant diagnosed of pneumonia.

Table 4.17: Hazard ratio between pneumonia diagnosis (time-to-death) B SE Wald Df Sig. Exp(B) DIAGNOSIS -0.167 0.131 0.619 1 0.203 0.846

On the other hand, a close look at the event discharge (time-to-discharge),

88 inference can be made that there is much diﬀerence in the mean survival time between diagnosis(pneumonia or non-pneumonia) since the conﬁdence intervals do not overlap as seen in the table below.

Table 4.18: Mean survival time between pneumonia diagnoses (time-to-discharge) 95% Conﬁdence Interval Diagnosis Estimate Std Error Lower Boud Upper Bound Non-Pneumonia 122.425 10.769 101.318 143.532 Pneumonia 184.261 19.832 145.391 223.131 Overall 136.976 9.797 117.775 156.178

From table 4.18, the mean survival time of infants diagnosed of a disease other than pneumonia is 122.425 and 184.261 for infants diagnosed of pneumonia. This implies that infants diagnosed of pneumonia averagely have a higher chance of staying in the hospital than infants diagnosed otherwise. The median survival time for infants diagnosed of disease other than pneumonia is approximately 5 days and 250 days for infants diagnosed of pneumonia (See Appendix). The overall tests of the equality of survival times across diagnosis shows that there is a statistically signiﬁcance diﬀerence between diagnosis in survival time (they are the same) with chi-square value of 11.287 and p-value of 0.001 for Log Rank test, chi-square value of 11.253 and p-value of 0.001 for Breslow test and a chi-square value of 12.419 and p-value of 0.000 for Tarons-Ware test.

89 Table 4.19: Survival Estimate of infants diagnosed of disease other than pneumonia(time-to-discharge) Survival Time (Days) Estimate Standard Error 0 1 0.014 1 0.742 0.025 2 0.671 0.029 3 0.590 0.032 4 0.524 0.034 5 0.498 0.035 6 0.492 0.035 7 0.471 0.035 8 0.463 0.036 16 0.456 0.036 26 0.448 0.036 32 0.432 0.036 64 0.423 0.037 116 0.414 0.037 167 0.403 0.038 181 0.391 0.038 197 0.379 0.040 203 0.367 0.040 221 0.353 0.041 226 0.337 0.042 255 0.315 0.045

90 Table 4.20: Survival Estimate (time-to-discharge) of infants diagnosed of pneumonia Survival Time (Days) Estimate Standard Error 0 1 0.017 1 0.874 0.036 2 0.843 0.041 3 0.823 0.044 4 0.776 0.053 5 0.752 0.056 41 0.708 0.068 124 0.653 0.082 171 0.588 0.086 250 0.490 0.120 256 0.392 0.130

Tables 4.19 and 4.20 show the survival estimates of infants not diagnosed of pneumonia and infants diagnosed of pneumonia respectively. The tables indicate that infants diagnosed of pneumonia generally have a higher probability of staying longer in the hospital than those diagnosed otherwise. For instance, an infant with pneumonia has 0.752 probability of still being admitted after 5 days whereas an infant without pneumonia has 0.498 probability. The probability of an infant being admitted after day one (1) drops from 1 to 0.874 for infants diagnosed of pneumonia and from 1 to about 0.742 for infants diagnosed of disease apart from pneumonia. Survival for infants diagnosed of pneumonia fall in the range of 0.4 to 0.6 for about 125 days (about 4 months) This is graphically shown below:

91 Figure 4.7: Survival of infants (between pneumonia diagnosis ) against duration of stay in hospital (time-to-discharge)

The table below examines the hazard ratio of the hazard rate in infants diagnosed of disease apart from pneumonia to the hazard rate in infants diagnosed of pneumonia. The p-value of 0.02 shows that there is statistically signiﬁcant diﬀerence in the hazard rate. Thus, the probability of an infant diagnosed of a disease apart from pneumonia being discharged the next day after still being admitted before that day is 104.5% higher than an infant diagnosed of pneumonia.

Table 4.21: Hazard ratio pneumonia between diagnosis (time-to-discharge) B SE Wald Df Sig Exp(B) DIAGNOSIS 0.716 0.229 9.749 1 0.02 2.045

4.4 Discussion

Infants admitted in Kumasi district assumed a downward trend from 2008 to 2010. It later increased at an increasing rate from 2010 to 2011, then at a decreasing rate from 2011 to 2013. After 2013, it assumed a downward trend to 2014.

92 Infant mortality ratio was highest in 2008(45.62/1,000). It then reduced in 2009(43.53/1,000) and further reduced significantly to 29.34/1,000 the following year (2010). It was lowest in 2013(20.06/1,000). However, analysis on the data from the KATH from 2008 to 2015(March) indicate that infants in the age group 4-6 months recorded the highest number of infant deaths followed by those in the age group of 7-9 months. The lowest number of infant deaths was recorded in the age group of 0-3 months. This implies that infants in the age group of 4-6 months are most vulnerable to death. The study reveals that 2008, 2009 and 2012 experienced significantly higher number of occurrence of infant mortality in the Kumasi district than 2014. It further shows that the mean number of occurrence of infant mortality throughout the period under study (2008-2014) is significant.

With regards to the incidence of infant mortality in the Kumasi district, there was a statistically significant difference between the reference year 2014 and years 2008, 2009 and 2012. Their chi-square values were 16.003, 10.982 and 4.607 with p-values of 0.000, 0.001 and 0.032 respectively. Infant death rate was significantly high in these years compared to 2014. For instance, in 2008 infant mortality rate increased by(e−0.919e0.721) = 0.820, (e−0.919e0.615) = 0.738 in 2009 and (e0e0.400) = 0.595 in 2012 respectively compared to the reference year 2014. The research also revealed that the mean incidence of infant mortality in Kumasi district has reduced over the period under study. With a p-value of 0.000, we can conclude statistically that the mean rate of infant death cases is significant over the period considered. The results of the logistic regression analysis reveal that malaria does not have any significant effect on the outcome of an infant on admission. However, duration of stay at the

93 hospital aﬀects the outcome of infant on admission. Duration of stay results in a 0.5% greater likelihood of infants on admission dying than living. The variable accounted between 3.3% and 4.5% of the variations in the outcome.

Further, estimates for mean survival time (time-to-death) for infants diagnosed of a disease apart from malaria and those diagnosed of malaria are 53.474 and 123.162 respectively whereas estimates for mean survival time (time-to-discharge) for infants diagnosed of a disease apart from malaria and those diagnosed of malaria are 128.436 and 148.423 respectively. This implies that infants diagnosed of malaria are more likely to survive and at the same time stay in the hospital longer than those diagnosed otherwise. Also, the median survival time (time-to-death) for infants diagnosed of disease other than malaria is 3 days and 74 days for infants diagnosed of malaria whereas the median survival time (time-to-discharge) for infants diagnosed of disease other than malaria is 32 days and 221 days for infants diagnosed of malaria. The probability of an infant diagnosed of a disease apart from malaria dying the next day after surviving just before that day is 64.6% higher than an infant diagnosed of malaria whiles the probability of an infant diagnosed of a disease apart from malaria being discharged the next day after still being admitted before that day is 33.3% higher than an infant diagnosed of malaria (however, it is not statistically signiﬁcant). Comparatively, estimates for mean survival time (time-to-death) for infants diagnosed of a disease apart from pneumonia and those diagnosed of pneumonia are 82.033 and 149.016 respectively whereas estimates for mean survival time (time-to-discharge) for infants diagnosed of a disease apart from pneumonia and those diagnosed of pneumonia are 122.425 and 184.261 respectively. This implies that infants diagnosed of pneumonia are more likely to survive and at the same time stay in the hospital longer than

94 those diagnosed otherwise. Also, the median survival time (time-to-death) for infants diagnosed of disease other than pneumonia is 4 days and 3 days for infants diagnosed of pneumonia whereas the median survival time (time-to-discharge) for infants diagnosed of disease other than pneumonia is 5 days and 250 days for infants diagnosed of pneumonia. The probability of an infant diagnosed of a disease apart from pneumonia dying the next day after surviving before that day is 15.4% lower than an infant diagnosed of pneumonia (however, it is not statistically signiﬁcant) whiles the probability of an infant diagnosed of a disease apart from pneumonia being discharged the next day after still being admitted before that day is 104.5% higher than an infant diagnosed of pneumonia.

95 CHAPTER 5

CONCLUSION AND RECOMMENDATIONS

5.1 Introduction

This chapter focuses on the outcome of the analysis in the last chapter and considers the extent to which the objectives of the research have been achieved. Further, it also includes recommendations the researcher wishes to put across for consideration and beneﬁcial to all stakeholders.

5.2 Conclusion

The aim of this research was ﬁrstly, to examine the signiﬁcance of the occurrence and incidence of infant mortality in Kumasi district and secondly, to assess the factors that contribute to infant mortality at the Komfo Anokye Teaching Hospital (KATH).

5.2.1 Signiﬁcance of Occurrence and Incidence of

Malaria on Infant Mortality

The Poisson regression model for the occurrence of infant mortality in Kumasi district was considered. Only parameter estimates 2008, 2009 and 2012 were signiﬁcant with chi-square values of 87.602, 12.539 and 3.791 with p-values of 0.000, 0.010 and 0.015 respectively That is, the mean number of infant deaths for all the months in 2008(e0e0.638) = 1.894, that

96 of 2009(e0e0.481) = 1.617 and 2012(e0e0.454) = 1.574 higher than the mean number of infant deaths for all months in 2014. With a chi-square value of 10.646 and p-value of 0.001, we can conclude that the occurrence of infant mortality has signiﬁcantly reduced over the period under study.

Parameter estimates for incidence of infant mortality for the years 2008, 2009 and 2012 were signiﬁcant with chi-square values of 16.003, 10.982 and 4.607 with p-values of 0.000, 0.001 and 0.032 respectively. Their parameter estimates were positive. This means that in 2008, infant mortality rate increased by (e−0.919e0.721) = 0.820, (e−0.919e0.615) = 0.738 in 2009 and (e0e0.400) = 0.595 in 2012 respectively compared to the reference year 2014. The research reveals that the mean incidence of infant mortality in Kumasi district has reduced over the period under study. With a p-value of 0.000, we can conclude statistically that the mean rate of infant death cases is signiﬁcant over the period considered.

5.2.2 Factors that Contribute to Infant Mortality

due to Malaria in the Komfo Anokye Teaching

Hospital (KATH)

It is realised that malaria does not have any signiﬁcant eﬀect on the outcome of infant on admission at the Komfo Anokye Teaching Hospital.

97 5.2.3 Survival Rate of Infants in the Komfo Anokye

Teaching Hospital (KATH)

The mean survival time (time-to-death) for infants diagnosed of a disease apart from malaria and those diagnosed of malaria are 53.474 and 123.162 whiles mean survival time (time-to-death) for infants diagnosed of a disease apart from pneumonia and those diagnosed of pneumonia are 82.033 and 149.016 respectively. Also, the mean survival time (time-to-discharge) for infants diagnosed of a disease apart from malaria and those diagnosed of malaria are 128.436 and 148.423 respectively whiles the mean survival time (time-to-discharge) for infants diagnosed of a disease apart from pneumonia and those diagnosed of pneumonia are 122.425 and 184.261 respectively. Inference can be made generally that infants diagnosed of pneumonia are more likely to survive and stay longer in the hospital than those diagnosed of malaria.

The probability of an infant diagnosed of a disease apart from malaria dying the next day after surviving just before that day is 64.7% higher than an infant diagnosed of malaria. The probability of an infant diagnosed of a disease apart from pneumonia being discharged the next day after still being admitted before that day is 104.5% higher than an infant diagnosed of pneumonia.

However, probability of survival (time-to-death) is less than 50% from 74 days onwards and 3 days onwards for infants diagnosed of malaria and those diagnosed otherwise respectively whereas the probability of survival (time-to-death) is less than 50% from 3 days onwards and 4 days onwards for infants diagnosed of pneumonia and those diagnosed otherwise respectively. Also the probability of survival (time-to-discharge) is less

98 than 50% from 221 days onwards and 32 days onwards for infants with malaria and those diagnosed otherwise respectively whereas the probability of survival (time-to-discharge) is less than 50% from 250 days onwards and 5 days onwards for infants with pneumonia and those diagnosed otherwise respectively. The probability of an infant diagnosed of a disease apart from pneumonia being discharged the next day after still being admitted before that day is 104.5% higher than an infant diagnosed of pneumonia.

Also, the literature reveals that educational level of mother, nutritional level and mother’s health status are some major causes of infant mortality in Sub-Saharan Africa. However, data on these variables were not readily available at the Research and Development Unit of the hospital.

5.3 Recommendations

1. The mean number of occurrence and incidence of infant mortality in Kumasi district has reduced over the thirteen year period under study (1998 – 2010). We therefore recommend that government, stakeholders and policy makers should continue all the existing intervention programs of infant health since they seem to have yielded the expected results over the past seven years (2008 – 2014).

2. The study shows that malaria is not a signiﬁcant cause of infant deaths at KATH. On this fact, we recommend that management continue with whatever existing program that is helping solves this problem.

3. The study also reveals that duration of stay in the hospital contributes signiﬁcantly to infant deaths at the KATH. We recommend that management of the hospital should give special attention to infants with malaria who have spent about 74 days (approximately 3 months) at the hospital and infants without malaria who have spent about

99 3 days. More eﬀort at implementing and strictly following existing programs aimed at reducing this problem and also introduce new ones if necessary should be ensured.

4. Although malaria is not a signiﬁcant cause of infant mortality at KATH, comparison between survival times on malaria and pneumonia reveals that more eﬀort should be geared towards reducing malaria infection among infants to the barest minimum.

5. Finally, we recommend that proper and detailed data information should be taken consistently to help check progress and increase the quality of decision making.

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108 Appendices

Appendix 1 : Diseases diagnosed and the number of infants aﬀected for 2010

Disease Infants Aﬀected Percentage Acute respiratory disease 1 0.49 Anaemia 10 4.88 Bleeding 2 0.98 Bronchitis 1 0.49 Clinically dead 8 3.90 Dehydration 9 4.39 Diarrhoea 5 2.44 Dysentry 1 0.49 Fertile convulsion 4 1.95 Fertile Seizure 1 0.49 Heart disease 3 1.46 Heart failure 1 0.49 Jaundice 1 0.49 Liver failure 2 0.98 Malaria 47 22.93 Malnutrition 21 10.24 Meningitis 27 13.17 Pneumonia 23 11.22 Sepsis 15 7.32 Shock 19 9.27 UTI 4 1.95 Total 205 100.00

109 Appendix 2: Disease diagnosed and the number of infants aﬀected for 2011 Disease Infants Aﬀected Percentage Acute Asthmatic attack 1 0.71 Anaemia 9 6.98 Bronchitis 3 2.12 Clinically dead 2 1.42 Dehydration 3 2.13 Diarrhoea 10 7.09 Down syndrome 2 1.42 Dysentry 2 1.42 Fertile Convulsion 4 2.84 Heart disease 1 0.71 Heart failure 2 1.42 Malaria 49 34.75 Malnutrition 12 8.51 Meningitis 8 5.67 Pneumonia 18 12.77 Sepsis 3 2.13 Shock 8 5.67 UTI 2 1.42 Vomiting 2 1.42 Total 141 100.00

110 Appendix 3: Disease diagnosed and the number of infants aﬀected for 2012 Disease Infants Aﬀected Percentage Anaemia 4 12.50 Bronchitis 1 3.13 Diarrhoea 3 9.39 Malaria 13 40.63 Malnutrition 4 12.50 Meningitis 1 3.13 Pneumonia 2 6.25 Sepsis 1 3.13 Shock 1 3.13 UTI 2 6.25 Total 32 100.00

111 Appendix 4: Disease diagnosed and the number of infants aﬀected for 2013 Disease Infants Aﬀected Percentage Anaemia 6 3.33 Asthmatic Attack 1 0.56 Bacterial Infection 1 0.56 Bleeding 1 0.56 Bronchitis 6 3.33 Diarrhoea 21 11.67 Down Syndrome 2 1.11 Fertile Convulsion 4 2.22 Fertile Seizure 1 0.56 Heart disease 4 2.22 Heart failure 1 0.56 Malaria 18 10.00 Malnutrition 19 10.56 Meningitis 21 11.76 Pneumonia 49 27.22 Respiratory distress 1 0.56 Sepsis 9 5.00 Shock 11 6.11 UTI 3 1.67 Vomiting 1 0.56 Total 180 100.00

112 Appendix 5: Disease diagnosed and the number of infants aﬀected for 2014 Disease Infants Aﬀected Percentage Anaemia 4 3.05 Bacterial Infection 2 1.53 Bronchitis 8 6.11 Clinically Dead 3 2.29 Diarrhoea 25 19.08 Down Syndrome 2 1.53 Fertile Convulsion 1 0.76 Heart disease 2 1.53 Heart failure 3 2.29 Malaria 20 15.27 Malnutrition 11 8.40 Meningitis 4 3.05 Pneumonia 22 16.79 Sepsis 9 6.87 Shock 12 9.16 tuberculosis 1 0.76 Vomiting 2 1.53 Total 131 100.00

113 Appendix 6: Disease diagnosed and the number of infants aﬀected for 2015(March) Disease Infants Aﬀected Percentage Anaemia 1 1.89 Bronchitis 2 3.77 Clinically Dead 9 16.98 Diarrhoea 7 12.21 Heart failure 1 1.89 Malaria 2 3.77 Malnutrition 2 3.77 Meningitis 3 5.66 Pneumonia 6 11.32 Sepsis 7 13.21 Shock 6 11.32 UTI 4 7.55 Vomiting 3 5.66 Total 53 100.00

Appendix 7: Criteria for assessing goodness of ﬁt for the occurrence of Infant Mortality Criterion DF Value Value/DF Deviance 77 122.602 1.592 Scaled Deviance 77 122.602 1.592 Pearson Chi-square 77 104.046 1.351 Scaled Pearson X2 77 104.046 1.351 Log Likelihood -201.154

114 Appendix 8: Analysis of parameter estimate for occurrence of infant mortality for continuous time Parameter DF Estimate Std Err. Wald 95% Conf. Int. Chi-sq p-value Intercept 1 1.991 0.0987 (1.798,2.185) 407.037 0.000 Time 1 -0.077 0.0235 (-0.123,-0.031) 10.646 0.001 Scale 0 1.000 0.000 (1.000,1.000)

Appendix 9: Criteria for assessing goodness of ﬁt for the incidence of infant mortality Criterio DF Value Value/DF Deviance 77 126.735 1.545 Scaled Deviance 77 126.735 1.646 Pearson Chi-square 77 111.656 1.450 Scaled Pearson X2 77 111.656 1.450 Log Likelihood -203.221

Appendix 10: Analysis of parameter estimate for incidence of infant mortality for continuous time Parameter DF Estimate Std Err. Wald 95% Conf. Int. Chi-sq. p-value Intercept 1 -239.342 0.0034 (-239.349,239.336) 4.969E9 0.000 Time 1 -12.320 0.0008 (-12.321,-12.318) 2.107E8 0.000 Scale 0 1.000 0.000 (1.000,1.000)

115 Appendix 11 : Criteria for assessing goodness of ﬁt for logistic regression model Criterion Value Chi-square 15.453 Prob; Chi-square 0.004 Cox and Snell R2 0.033 Nagelkerke R2 0.045 Log Likelihood 580.275 Number of Observations 587

Appendix 12: A matrix determining the correlation between variables Variable Constant Diagnosis Weight Duration Age Constant 1.000 -0.633 -0.059 -0.229 -0.720 Diagnosis -0.633 1.000 -0.127 0.184 0.076 Weight -0.069 -0.0127 1.000 0.081 -0.066 Duration -0.229 0.184 0.081 1.000 -0.008 Age -0.720 0.076 -0.066 -0.008 1.000

Appendix 13: Median survival time between malaria diagnosis. (time-to-death)

116 Appendix 14: Cummulative Hazard function of infants (between malaria diagnosis) against duration of stay in hospital (time-to-death)

Appendix 15: Log Survival Function of infants (between malaria diagnosis) against Duration of stay in hospital (time-to-death)

Appendix 16: Median survival time between malaria diagnosis.(time-to- discharge)

117 Appendix 17: Cummulative Hazard function of infants (between malaria diagnosis) against duration of stay in hospital (time-to-discharge)

Appendix 18: Log Survival Function of infants (between malaria diagnosis) against Duration of stay in hospital (time-to-discharge)

Appendix 19: Median survival time between pneumonia diagnosis.(time-to-death)

118 Appendix 20: Cummulative Hazard function of infants (between pneumonia diagnosis) against duration of stay in hospital (time-to-death)

Appendix 21: Log Hazard function of infants (between pneumonia diagnosis) against duration of stay in hospital (time-to-death)

Appendix 22: Median survival time between malaria diagnosis.(time-to- discharge)

119 Appendix 23: Cummulative Hazard function of infants (between pneumonia diagnosis) against duration of stay in hospital (time-to-dischar

Appendix 24: Log Hazard function of infants (between pneumonia diagnosis) against duration of stay in hospital (time-to-discharge)

120