Hierarchical models in medical research

This thesis describes and develops the use of hierarchical models in medical research from both a classical and Bayesian perspective. Hierarchical models are appropriate when observations are clustered into larger units within a data set, which is a common occurence in medical research. The use and versatility of hierarchical models is shown through a number of examples, with the aim of developing improved and more appropriate methods of analysis. The examples are real data sets and present real problems in terms of statistical analysis.;The data sets presented include two data sets involved with longitudinal data where repeated measurements are clustered within individuals. One data set has repeated blood pressure measurements taken on pregnant women and the other consists of repeated peak expiratory flow measurements taken on asthmatic children. Bayesian and classical analyses are compared. A number of issues are explored including the modelling of complex mean profiles, interpretation and quantification of variance components and the modelling of heterogeneous within-subject variances. Other data sets are concerned with meta-analysis, where individuals are clustered within studies. The classical and Bayesian frameworks are compared and one data set investigates the potential to combine estimates from different study types in order to estimate the attributable risk. One of the meta-analysis data sets included individual patient data, where there is a substantial amount of missing covariate data. For this data set models that incorporate individuals with incomplete data when modelling survival times for children with Neuroblastoma are developed.;This thesis thus demonstrates that hierarchical models are of great importance in analysing data in medical research. In many situations a Bayesian analysis provides a number of advantages over classical models especially when introducing realistic complexity that would be hard to incorporate using classical methodology.