ROBUST HIERARCHICAL BAYES MEmODOLOGY FOR CLINICAL STUDIFS

MELISSA GROUT SMITH. Robust Hierarchical Bayes Methodology for Clinical Studies (Under the joint direction of Drs. Clarence E. Davis and Richard 1. Smith.) Outlier observations can have an adverse effect on statistical inference. Identification and elimination of such observations are one option, however, dealing with outliers in this manner has many drawbacks. An alternative approach is to utilize statistical methods that are robust to outliers. Robustness is a desirable property of statistical estimators because it ensures that the estimator reflects the pattern in the majority of the data, without being too sensitive to a handful of outliers. In this dissertation robust methodology for constructing empirical Bayes confidence intervals is presented. Three different robust models are proposed: a variance inflation model, a location-shift model and a heavy-tailed model. These three general types of models are described within a hierarchical Bayes framework and are applied in two separate contexts. In the first, we apply the robust methodologies to the normal means problem, and in the second we apply them to the modelling of longitudinal data by random-effects models. The Gibbs sampler is used for analysis of these complex models. Four alternative types of confidence intervals are proposed and evaluated. The proposed methodology incorporates heavy-tailed or contamination-type distributions into a hierarchical model of the data. These distributions allow the possibility of outliers and are hypothesized to make the resulting inference more robust to outliers. Specifically, for robust linear random-effects models, the random errors and random effects are modelled by heavier-tailed alternatives to the normal distribution, such as the variance inflation distribution or the t distribution. The proposed techniques are illustrated using longitudinal data from a clinical study of cholesterol-lowering in the elderly. In addition, we compare the techniques via simulation studies, which show that the interval estimates from the variance inflation and heavy-tailed