Topics in Bayesian inference : induced priors, proof loading for combination drugs, and distribution of archaeological skeletal assemblages.

Abstract

Many illnesses are often treated with a combination of drugs. These combinations can be more effective than using any of the component drugs individually, but may lead to increased safety concerns. Prior to human trials with the combination, what can be said about efficacy and/or safety of the combination? An experimental design known as proof loading allows us to obtain preliminary estimates about the joint probability of an adverse event, without exposing patients to the combination drug. We propose a Bayesian distribution-free approach to proof loading as a possible solution to this problem. Our proof-loading model requires the specification of prior distributions. As we shall see, the priors are conditional and induce a prior on the joint probability of an adverse event. We consider this problem of induced priors more generally, examining several examples in the literature as well as our own prior structure. We offer a straight-forward protocol for handling induced priors. As an applied chapter, we propose a Bayesian model for studying distributions of bone types in archaeological bone assemblages. Anthropologists are interested in the evenness of an assemblage of bones across bone types. Based on the evenness of the distribution, hypotheses can be formed about the species of the hunter and what kind of transport strategy was required. We compare our method to a current method in examples and in a small-scale simulation study. Here again the issue of induced priors becomes important.