Bayesian Spatial Modeling of Malnutrition and Mortality among Under-five Children in sub-Saharan Africa Rasheed Alani Adeyemi June, 2019 Bayesian Spatial Modeling of Malnutrition and Mortality among Under-five Children in sub-Saharan Africa Rasheed Alani Adeyemi Master of Statistics, University of Ilorin, Kwara State, Nigeria Master of Mathematical Statistics, University of Cape Town, South Africa Bachelor of Technology (Ind. Mathematics), Federal University of Technology, Akure A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy Thesis Supervisors: Professor Temesgen Zewotir Professor Shaun Ramroop School of Mathematics, Statistics and Computer Science College of Agriculture, Engineering and Science University of KwaZulu-Natal, South Africa Copyright in relation to this Thesis ©Copyright 2019. All rights reserved, University of KwaZulu-Natal, South Africa Dedication ‘Acquire knowledge, it enables its possessor to distinguish right from wrong; it lights the way to Heaven; it is our friend in the desert; our society in solitude, our companion when friendless; it guides us to happiness; it sustains us in misery” ::::::::::::::::::::: The Prophet Mohammad(pbuh). To: Nike my Lovely wife and friend & Halimat Adebusola(F) and Abdulbasit Adedeji(M) my blessed children. i Declaration of Authorship I, RASHEED ALANI ADEYEMI, declare that this thesis titled ’Bayesian spatial Model- ing of Malnutrition and Mortality among under-five children in sub-Saharan Africa’ and the work presented in it are my own. I confirm that: • This work was done wholly or mainly while in candidature for a research de- gree at this University. • No part of this thesis has previously been submitted for a degree or any other qualification at this University or any other institution. • Where I have consulted the published work of others, this is always clearly attributed. • Where I have quoted from the work of others, the source is always given. With the exception of such quotations, this thesis is entirely my own work. Author: Rasheed A. Adeyemi Date Approved by Supervisors: Supervisor: Prof. Temesgen Zewotir Date Co-Supervisor: Prof. Shaun Ramroop Date ii List of Publications 1. Rasheed A. Adeyemi, Temesgen Zewotir & Shaun Ramroop. ”Semi-parametric Mutinomial Ordinal Models to analyze the spatial patterns of child birthweight in Nigeria.” published Int. J. Environ. Res. Public Health 2016, 13, 1145; doi:10.3390/ijerph13111145. 2. Rasheed A. Adeyemi, Temesgen Zewotir & Shaun Ramroop. “A Bayesian Hierarchical analysis of geographical patterns for child mortality in Nigeria.” published The Open Public Health Journal, 2019. vol.13: 247-262; doi: 10.2174/1874944501912010247. 3. Rasheed A. Adeyemi, Temesgen Zewotir & Shaun Ramroop. Multivariate Spatial Joint Mapping of the risk of Childhood anaemia and Malnutrition in sub-Saharan Africa: A cross-sectional study of small-scale geographical dis- parities. African Health Sciences. 2019. vol.19(3): 2692-2712. https://dx.doi.org/10.4314/ ahs.v19i3.45. Conference Papers/ Proceeding / Symposium 1. Rasheed A. Adeyemi, Temesgen Zewotir & Shaun Ramroop. “Bayesian Multi- nomial Ordinal Models to analyze the risk factors and spatial patterns of child- hood anaemia in Tanzania” published Annual Proceedings of the South African Statistical Association (SASA), Congress 1, Nov 2016, p. 9 - 16 Available at: http://hdl.handle.net/10520/EJC198858. 2. Rasheed A. Adeyemi, Temesgen Zewotir & Shaun Ramroop. Spatial-Temporal Modeling of Under-five mortality rates in the context of a developing country Paper Presented at UKZN College Research Day inQubate, Westville Durban South African. 2018. 3. Rasheed A. Adeyemi, Temesgen Zewotir & Shaun Ramroop. Spatial Patterns Of Childhood Mortality And Morbidity In Sub-Saharan Africa: A Bayesian iii Geo-Additive Multinomial Models Approach Paper Presented at UKZN College Research Day Oct. 2017. 4. Rasheed A. Adeyemi, Temesgen Zewotir & Shaun Ramroop. “Bayesian Multi- nomial Ordinal Models to analyze the spatial patterns of Childhood anaemia in Tanzania” presented 58th Annual Conference of the South African Statistical Association (SASA) held at University of Cape Town November 2016. 5. Rasheed A. Adeyemi, , Temesgen Zewotir & Shaun Ramroop. Bayesian Joint modeling of Disease Co-morbidity among under-five children in Nigeria and Tanzania; Accepted for Presentation 2016.: UKZN College Research Day: Postgrad- uate iv Abstract The aim of this thesis is to develop and extend Bayesian statistical models in the area of spatial modeling and apply them to child health outcomes, with particular focus on childhood malnutrition and mortality among under-five children. The easy availability of a geo-referenced database has stimulated a paradigm shift in method- ological approaches to spatial analysis. This study reviewed the spatial methods and disease mapping models developed for areal (lattice) data analysis. Observa- tional data collected from complex design surveys and geographical locations often violates the independent assumption of classical regression models. By relaxing the restrictive linearity and normality assumptions of classical regression models, this study first developed a flexible semi-parametric spatial model that accommodates the usual fixed effect, nonlinear and geographical component in a unified model. The approach was explored in the analysis of spatial patterns of child birth out- comes in Nigeria. The study also addressed the issue of disease clustering, which is of interest to epidemiologists and public health officials. The study then pro- posed a Bayesian hierarchical analysis approach for Poisson count data and formu- lated a Poisson version of generalized linear mixed models (GLMMs) for analyz- ing childhood mortality. The model simultaneously addressed the problem of over- dispersion and spatial dependence by the inclusion of the risk factors and random effects in a single model. The proposed approach identified regions with elevated relative risk or clustering of high mortality and evaluated the small scale geograph- ical disparities in sub-populations across the regions. The study identified another challenge in spatial data analysis, which are spatial autocorrelation and model mis- specification. The study then fitted geoadditive mixed (GAM) models to analyze childhood anaemia data belonging to a family of exponential distributions (Gaus- sian, binary and multinomial). The GAM models are extension of generalized linear mixed models by allowing the inclusion of splines for continuous covariate (or time) trends with the parametric function. Lastly, the shared component model originally developed for multiple disease mapping was reviewed and modified to suit the bi- nary data at hand. A multivariate conditional autoregressive (MCAR) model was v developed and applied to jointly analyze three child malnutrition indicators. The approach facilitated the estimation of conditional correlation between the diseases; assess the spatial association with the regions and geographical variation of indi- vidual disease prevalence. The spatial analysis presented in this thesis is useful to inform health-care policy and resource allocation. This thesis contributes to method- ological applications in life sciences, environmental sciences, public health and agri- culture. The present study expands the existing methods and tools for health impact assessment in public health studies. KEYWORDS: Conditional Autoregressive (CAR) model, Disease Mapping Models, Multiple Disease mapping, Health Geography, Ecology Models, Spatial Epidemiol- ogy, Childhood Health outcomes. vi Acknowledgements All Praises due to God Almighty, The Creator of The Heaven and The Earth, The Beneficent, The Merciful, Who has created Man, The Pen, The Knowledge and What the Pen writes, The All-knowing for bestow His honour and favour on me. I would like to specially thank my supervisors Prof. Temesgen Zewotir and Prof. Shaun Ramroop for their guidance, encouragement and their positive words through- out my work. Many thanks to Prof. Henry Mwambi for his encouragements, semi- nars, workshops and training young statisticians across Africa continent. I would like to thank the Federal University of Technology, Minna for giving me the study leave and the fellowship support from the Tertiary Education Trust (TET) Fund, Abuja that enable me undertake my PhD in South Africa. Special thanks to Prof. MGM Kolo (Dean Postgraduate School, FUT Minna) for being such a good friend and a friend of my family for his guidance, encouragement and his prompt interventions in time of difficulties. I am also thankful to my colleagues and friends in the School of Agriculture and Agricultural Technology, FUT-Minna: Dr(s): ST. Yusuf, MT Salaudeen, LY Bello, E. Daniya, Haruna Ibrahim, US Saba, MA Ojo, A. Saidu, Amina(Mrs) and Hajiya Rakiya for their support and prayer. I am also grateful to Senior Colleagues for their encouragement and good gesture: Prof. Oladiran, Prof. AS Gana, Prof. ET. Tsado, Prof.T. Ijaiya, Prof. KM Baba, Prof. R. Kolo (Dean , SAAT), Prof. Sadiku, Prof. Adama, Prof. Abdullah Bala (Vice Chancellor), Prof. Osunde and other senior colleagues in the School of Agriculture(SAAT) for placing responsibility on me. I am also indebted to Dr. Ezra Gayawan for introducing the BayesX software program- ming to me. I appreciate you all for your constant prayers and encouragement. I would like to thank my friends and colleagues at University of KwaZulu-Natal for their support and assistance: Dr. Elfas Okango(Kenya) for his assistance