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Addis Ababa University School of Graduate Studies Department of Statistics ADDIS ABABA UNIVERSITY SCHOOL OF GRADUATE STUDIES COLLEGE OF NATURA SCIENCES DEPARTMENT OF STATISTICS STATISTICAL ANALYSIS OF SPATIAL DISTRIBUTION OF MALARIA IN WEST SHOA ZONE, ETHIOPIA BY MITIKU MOSISSA AYANA A THESIS SUBMITTED TO THE SCHOOL OF GRADUATE STUDIES OF ADDISA ABABA UNIVERSITY IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE IN STATISTICS MAY, 2011 ADDISA ABABA, ETHIOPIA Addis Ababa University School of Graduate Studies Department of Statistics Title of Thesis: Statistical Analysis of Spatial Distribution of Malaria in West Shoa Zone, Ethiopia By Mitiku Mosissa Ayana Approved by the Board of Examiners: _____________________________ ……………… Department Head Signature _____________________________ ………………. Examiner Signature _____________________________ ……………… Examiner Signature CONTENTS Page Acronyms--------------------------------------------------------------------------------------------iv Acknowledgments----------------------------------------------------------------------------------v Abstract----------------------------------------------------------------------------------------------vi CHAPTER 1: Introduction -----------------------------------------------------------1 1.1. Background of the study----------------------------------------------------------------------1 1.2. Use of Spatial autocorrelation-----------------------------------------------------------------4 1.3. Statement of the problem----------------------------------------------------------------------6 1.4. Objectives of the study-------------------------------------------------------------------------7 1.5. Significance of the study-----------------------------------------------------------------------7 1.6. Limitations of the study------------------------------------------------------------------------7 CHAPTER 2: REVIEW OF LITERATURE----------------------------------8 CHAPTER 3: DATA AND METHODOLOGY------------------------------13 3.1. Source of data ---------------------------------------------------------------------------------13 3.2 Study area ---------------------------------------------------------------------------------------13 3.3. Methodology of the study--------------------------------------------------------------------14 3.3.1. The Concept of Spatial Dependence------------------------------------------------14 3.3.2. Global and local measures of spatial autocorrelation------------------------------15 3.3.2.1. Global measures of spatial autocorrelation---------------------------------15 3.3.2.2. Local measures of spatial autocorrelation-----------------------------------22 3.3.3. Diagnostics for spatial dependence---------------------------------------------------26 3.3.4. Modeling spatial dependence---------------------------------------------------------30 CHAPTER 4: RESULTS AND DISCUSSION--------------------------------38 4.1. Spatial distribution of malaria incidence by woreda--------------------------------------38 4.2. Testing for spatial autocorrelation ----------------------------------------------------------39 4.2.1. Moran’s I and Geary’s C test statistic for global spatial autocorrelation--------40 4.2.2. Local Moran’s I test statistic for local spatial autocorrelation-------------------42 i * 4.2.3. Local Gi test for spatial autocorrelation--------------------------------------------45 4.3. Diagnostics for spatial dependence ---------------------------------------------------------48 4.4. Fitting Spatial Autoregressive Model-------------------------------------------------------49 4.5. Normality test for residuals------------------------------------------------------------------53 4.6. Summary ---------------------------------------------------------------------------------------54 CHAPTER 5: CONCLUSIONS AND RECOMMENDATIONS---------55 5.1. Conclusions ------------------------------------------------------------------------------------55 5.2. Recommendations-----------------------------------------------------------------------------55 LIST OF TABLES Table 4.1: Results of Global Moran’s I and Geary’s C Statistics ----------------------------41 Table 4.2: Results of Local Moran’s I Test-----------------------------------------------------43 * Table 4.3: Results of Local Gi Test--------------------------------------------------------------46 Table 4.4: Diagnostics for Spatial Dependence ------------------------------------------------48 Table 4.5: Results of Spatial Lag Model Estimation-------------------------------------------51 Table 4.6: Summary Output of Regression Diagnostics for Spatial Lag Model-----------52 Table 4.7: Normality Test of Residuals----------------------------------------------------------53 LIST OF FIGURES Figure 3.1: Contiguity case of representation of spatial weights matrix --------------------18 Figure 3.2: Moran’s Scatter Plot------------------------------------------------------------------22 Figure 4.1: Spatial Distribution of the Malaria Incidence rate in West Shoa Zone--------39 Figure 4.2: Global Moran’s I Scatter Plot for Malaria Incidence----------------------------42 Figure 4.3: Local Moran’s I Scatter Plot for Malaria Incidence------------------------------44 * Figure 4.4: Local Gi Clustering Map of Malaria Incidence in West Shoa Zone, Ethiopia------------------------------------------------------------------------47 REFERENCES------------------------------------------------------------------------------------56 ii APPENDIX-----------------------------------------------------------------------------------------60 LIST OF TABLES AND FIGURES Figure A: Moran’s Scatter Plot Based on Neighborhood-------------------------------------60 Figure B: Moran’s Scatter Plot Based on Threshold Distance--------------------------------61 Figure C: Moran’s Scatter Plot Based on K-nearest Neighbors------------------------------61 Figure D: Normal Plot-----------------------------------------------------------------------------62 Table 1: Diagnostic for Multicollinearity--------------------------------------------------------62 Table 2: Malaria Incidence per 1000 people in each Woreda in West Shoa Zone, Ethiopia----------------------------------------------------------------------------------63 Table 3: Spatial Weighted Matrix W for Neighboring Relation among Woreda in West Shoa Zone, Ethiopia------------------------------------------------------------64 Table 4: Results of Maximum Likelihood Estimation (spatial lag model)------------------65 iii ACRONYMS CSA Central Statistical Agency FHOM Federal Ministry of Health ITN Insecticide treated nets IRS Indoor residual insecticide spraying LLINs Long-lasting insecticide treated nets OLS Ordinary Least Squares LM Lagrange Multiplier RLM Robust Langrage Multiplier VIF Variance inflation factor WHO World Health Organization iv ACKNOWLEDGMENTS First, and foremost, I express deepest gratitude to Dr. Butte Gotu, my advisor for his unlimited constructive advice, suggestions, ideas and comments. My thanks also to Central Statistical Agency and West Shoa Zone Health Bureau for providing me with the data for this thesis. Grateful acknowledgement is also expressed to the Department of Statistics, Addis Ababa University for kind assistance in many ways. Furthermore, I want to thank all my friends, my family members and others who have provided me a great help and moral support directly and indirectly contributed to wards the completion of this study. v ABSTRACT Malaria is a major cause of illness and death in large parts of the developing world, especially in Africa. Accurate estimates of malaria distribution are required for planning, implementation and evaluation of malaria control programs. The main objective of this study is to examine spatial patterns of malaria distribution in West Shoa zone, Oromia Region, Ethiopia. Malaria incidence data for 2009 from all health centers of the zone, population size and meteorological data were used. The statistical methods used include global and local measures of spatial autocorrelation as well as spatial autoregressive model. The results of this study indicate that malaria incidence varies according to geographical location, with eco-climatic condition and showing significant positive spatial autocorrelation. Significant local clustering of malaria incidence occurs between pairs of neighboring districts (known as Woredas). Malaria incidence was higher in the western part of the zone and lower in the eastern part of the zone. The results of spatial lag model indicate a significant relationship between malaria incidence and meteorological variables (mid-land zone, hot zone, rainfall, minimum temperature and maximum temperature). vi Chapter One Introduction 1.1 Background of the Study Malaria is the most common tropical disease, remaining widespread throughout the tropical and subtropical regions, including parts of Africa, Asia and America. It is a major cause of illness and death in large area of the developing world, especially Africa. According to the World Health Organization report (WHO, 2008), at the end of 2007 there were 109 malaria endemic countries and 3.3 billion people were at the risk of malaria. Malaria causes at least 300 million and possibly as many as 500 million cases of acute illness each year, which result in 1to 3 million deaths each year. Ninety percent of deaths occur in sub-Sahara Africa. The majority of these deaths are among children less than five years of age and pregnant women. These estimates are not reliable because of inadequate malaria case reporting in most endemic
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