Bayesian models for discrete censored sampling and dose finding.

We first consider the problem of discrete censored sampling. Censored binomial data may lead to irregular likelihood functions and problems with statistical inference. We consider a Bayesian approach to inference for censored binomial problems and compare it to non-Bayesian methods. We include examples and a simulation study in which we compare point estimation, interval coverage, and interval width for Bayesian and non-Bayesian methods. The continual reassessment method (CRM) is a Bayesian design often used in Phase I cancer clinical trials. It models the toxicity response of the patient as a function of administered dose using a model that is updated as data accrues. The CRM does not take into consideration the relationship between the toxicity response and the proportion of the administered drug that is absorbed by targeted tissue. Not accounting for this discrepancy can yield misleading conclusions about the maximum tolerated dose to be used in subsequent Phase II trials. We will examine, through simulation, the effect that disregarding the level of bioavailability has on the performance of the CRM.