Les plans bayésiens dans les essais expérimentaux.

Abstract

The work presented in this thesis relates to the methodological problems which arise in the context of experimental tests, we have exposed the methods of the sequential analysis setting up to use it in the evaluation of experimental designs which allows to arrive at effective experimental plans. We are considering the use of the assurance method in the planning of clinical trials : In the assurance method, which is an alternative to the power calculation, we calculate the probability that a clinical trial will lead to a positive result, via eliciting a priori probability distribution about the pertinent treatment effect. In this work, we are interested to Bayesian prediction modeling to evaluate a satisfaction index after a first stage of experiment in order to decide to stop at the second stage or continue. We apply this method to Poisson and Gamma distributed outcomes in many fields such as reliability or survival analysis for early termination due to either futility or efficacy. We look at two kinds of decisions making : an hybrid Bayesian-frequentist or a full Bayesian approach. This work also made it possible to determine the effective sample size of an a priori parameter in a Bayesian model.