Addressing issues in sparseness, ecological bias and formulation of the adjacency matrix in bayesian spatio temporal analysis of disease counts

School of Mathematical Sciences Queensland University of Technology Addressing Issues in Sparseness, Ecological Bias and Formulation of the Adjacency Matrix in Bayesian Spatio-temporal Analysis of Disease Counts Arul Earnest B.Soc.Sc (Hons) in Statistics, National University of Singapore MSc in Medical Statistics, London School of Hygiene and Tropical Medicine, University of London A thesis submitted for the degree of Doctor of Philosophy in the Faculty of Science and Technology, Queensland University of Technology according to QUT requirements Principal Supervisor: Professor Kerrie Mengersen Associate Supervisors: Associate Professor Geoff Morgan Professor Tony Pettitt 2010 KEYWORDS Spatial, autoregressive, disease mapping, CAR model, birth defects, ecological bias, neighbourhood weight matrix, forecasting, priors, Bayesian, MCMC, joint modeling i ABSTRACT The main objective of this PhD was to further develop Bayesian spatio-temporal models (specifically the Conditional Autoregressive (CAR) class of models), for the analysis of sparse disease outcomes such as birth defects The motivation for the thesis arose from problems encountered when analyzing a large birth defect registry in New South Wales The specific components and related research objectives of the thesis were developed from gaps in the literature on current formulations of the CAR model, and health service planning requirements Data from a large probabilistically-linked database from 1990 to 2004, consisting of fields from two separate registries: the Birth Defect Registry (BDR) and Midwives Data Collection (MDC) were used in the analyses in this thesis The main objective was split into smaller goals The first goal was to determine how the specification of the neighbourhood weight matrix will affect the smoothing properties of the CAR model, and this is the focus of chapter Secondly, I hoped to evaluate the usefulness of incorporating a zero-inflated Poisson (ZIP) component as well as a sharedcomponent model in terms of modeling a sparse outcome, and this is carried out in chapter The third goal was to identify optimal sampling and sample size schemes designed to select individual level data for a hybrid ecological spatial model, and this is done in chapter Finally, I wanted to put together the earlier improvements to the CAR model, and along with demographic projections, provide forecasts for birth defects at the SLA level Chapter describes how this is done ii For the first objective, I examined a series of neighbourhood weight matrices, and showed how smoothing the relative risk estimates according to similarity by an important covariate (i.e maternal age) helped improve the model’s ability to recover the underlying risk, as compared to the traditional adjacency (specifically the Queen) method of applying weights Next, to address the sparseness and excess zeros commonly encountered in the analysis of rare outcomes such as birth defects, I compared a few models, including an extension of the usual Poisson model to encompass excess zeros in the data This was achieved via a mixture model, which also encompassed the shared component model to improve on the estimation of sparse counts through borrowing strength across a shared component (e.g latent risk factor/s) with the referent outcome (caesarean section was used in this example) Using the Deviance Information Criteria (DIC), I showed how the proposed model performed better than the usual models, but only when both outcomes shared a strong spatial correlation The next objective involved identifying the optimal sampling and sample size strategy for incorporating individual-level data with areal covariates in a hybrid study design I performed extensive simulation studies, evaluating thirteen different sampling schemes along with variations in sample size This was done in the context of an ecological regression model that incorporated spatial correlation in the outcomes, as well as accommodating both individual and areal measures of covariates Using the Average Mean Squared Error (AMSE), I showed how a simple random sample of 20% of the iii SLAs, followed by selecting all cases in the SLAs chosen, along with an equal number of controls, provided the lowest AMSE The final objective involved combining the improved spatio-temporal CAR model with population (i.e women) forecasts, to provide 30-year annual estimates of birth defects at the Statistical Local Area (SLA) level in New South Wales, Australia The projections were illustrated using sixteen different SLAs, representing the various areal measures of socio-economic status and remoteness A sensitivity analysis of the assumptions used in the projection was also undertaken By the end of the thesis, I will show how challenges in the spatial analysis of rare diseases such as birth defects can be addressed, by specifically formulating the neighbourhood weight matrix to smooth according to a key covariate (i.e maternal age), incorporating a ZIP component to model excess zeros in outcomes and borrowing strength from a referent outcome (i.e caesarean counts) An efficient strategy to sample individual-level data and sample size considerations for rare disease will also be presented Finally, projections in birth defect categories at the SLA level will be made iv TABLE OF CONTENTS 1.1 1.2 1.3 1.4 INTRODUCTION Primary research aims and motivation Content and scope of thesis Structure of thesis List of publications and conferences arising from thesis 1 10 2.1 2.2 2.2.1 2.2.2 2.2.3 2.3 2.4 DATA Summary Sources of data Birth defects Births and maternal characteristics Areal-level indices of socio-economic status Definition and classification of birth defects Spatial and temporal trends of birth defects in New South Wales, Australia 12 12 12 12 13 14 16 18 3.1 3.2 3.3 3.3.1 3.3.2 3.3.3 3.3.4 3.3.5 LITERATURE REVIEW Summary Spatial analysis of birth defects Risk factors for birth defects Maternal age at delivery Maternal smoking during pregnancy Socio-economic indicators Maternal diabetes mellitus Common risk factors for caesarean section rates/ spatial variation 21 21 22 25 25 26 28 30 31 4.1 4.2 4.3 4.4 4.5 4.6 4.7 4.8 4.9 CONDITIONAL AUTOREGRESSIVE (CAR) MODEL Summary Spatial epidemiology Disease mapping Geographical correlation studies Formulation of the CAR model Comparison of single disease CAR models Studies that have applied CAR models Studies that have compared single disease CAR models Comparison of multiple disease CAR models 33 33 34 35 40 41 43 55 64 67 5.1 5.2 5.3 5.4 CAR MODELLING ISSUES Summary Bayesian Theory Markov chain Monte Carlo (MCMC) MCMC Convergence 74 74 74 76 77 v 5.5 5.6 5.7 5.8 5.9 5.10 Specifying the hyperprior distribution Conjugate priors and improper priors Sensitivity analysis on priors Model selection techniques for spatial models Modifiable Areal Unit Problem (MAUP) Boundary analysis 78 81 82 85 87 89 6.1 6.2 6.3 6.4 6.5 6.6 NEIGHBOURHOOD WEIGHT MATRIX SPECIFICATION Background Aims Methods Results Discussion Conclusion 93 97 102 102 111 114 118 7.1 7.2 7.3 7.4 7.5 MODELLING SPARSE DISEASE COUNTS Introduction Methods Results Discussion Conclusion 127 130 133 138 141 145 STRATEGIES FOR COMBINING AREAL WITH INDIVIDUAL 160 DATA Introduction 164 Ecological bias 166 Addressing ecological bias 167 Sampling techniques and sample size 168 Methods 171 Data 171 Statistical model 172 Model comparison 175 Simulation 176 Example 178 Results 179 Discussion 181 Conclusion 185 8.1 8.1.1 8.1.2 8.1.3 8.2 8.2.1 8.2.2 8.2.3 8.2.4 8.2.5 8.3 8.4 8.5 9.1 9.2 9.3 9.4 9.5 9.6 FORECASTING BIRTH DEFECTS AT THE SMALL AREA 197 LEVEL Introduction 201 Aim 204 Methods 204 Results 210 Discussion 212 Conclusion 214 vi 10 10.1 10.1 10.2 10.3 232 232 233 236 239 CONCLUSION Summary of results Implications of research Limitations Directions for future research 243 REFERENCES vii STATEMENT OF ORIGINAL AUTHORSHIP "The work contained in this thesis has not been previously submitted to meet requirements for an award at this or any other higher education institution To the best of my knowledge and belief, the thesis contains no material previously published or written by another person except where due reference is made” Arul Earnest 26th February 2010 viii ACKNOWLEDGEMENTS I would like to thank my principal supervisor, Professor Kerrie Mengersen, from Queensland University of Technology (QUT), for her unlimited guidance and supervision throughout the course of my PhD candidature I am indebted to her for introducing the field of Bayesian statistics to me My appreciation also goes out to Professor Tony Pettitt for facilitating the smooth flow of my PhD studies I would also like to express my gratitude to my associate supervisor, Associate Professor Geoff Morgan, from the Northern Rivers University Department of Rural Health (University of Sydney) for constantly providing input on my PhD, in particular the epidemiological, study design and clinical implication aspects of the thesis I have certainly enjoyed the numerous thought-provoking discussions we had in his office in Lismore I am equally indebted to Professor John Beard, director of Ageing and Lifecourse at the World Health Organisation, who was my previous supervisor I would like to credit him with providing me with the opportunity to start on this PhD studies, and also for his generous advice and guidance on the manuscripts resulting from this thesis My sincere gratitude goes to Dr Lee Taylor and Dr David Muscatello from the New South Wales Department of Health for providing me with useful advice on the data upon which this thesis is built on, and also valuable opinion on the practical applications resulting from this thesis I would like to show my appreciation to the internal review panel from QUT and the external examiners, whose comments and suggestions have strengthened the quality of this thesis Most importantly, I would like to thank my family members, especially my 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