A Bayesian approach to Meta-Regression: The relationship between Body Mass Index and all-cause mortality

This thesis presents a Bayesian approach to Meta-Regression and Individual Patient Data (IPD) Meta-analysis. The focus of the research is on establishing the relationship between Body Mass Index (BMI) and all-cause mortality. This has been an area of continuing interest in the medical and public health communities and no concensus has been reached on what the optimal weight for individuals is. Standards are usually specified in terms of body mass index (BMI = wtkgheigh tm2 ) which is associated with body fat percentage. Many studies in the literature have modelled the relationship between BMI and mortality and reported a variety of relationships including U-shaped, J-shaped and linear curves.;Another area which is explored briefly is that of Individual Patient Data meta-analysis. A Frailty model or Random Effects Proportional Hazards Survival model approach is proposed to carry out IPD meta-regression and come up with a single estimated relationship between BMI and mortality, adjusting for the variation between studies.;The aim of my research was to use statistical methods to determine whether we can combine these diverse results an obtain single estimated relationship, using which one can find the point of minimum mortality and establish reasonable ranges for optimal BMI or how we can best examine the reasons for the heterogeneity of results. Commonly used techniques of Meta-analysis and Meta-regression are explored and a problem with the estimation procedure in the multivariate setting is presented. A Bayesian approach using Hierarchical Generalized Linear Mixed Model is suggested and implemented to overcome this drawback of standard estimation techniques.