Index and prevision of satisfaction in exponential models for clinical trials

Abstract

This paper deals with a Bayesian predictive approach applied to a frequentist statistical test. The methodology is useful in two-steps testing procedures, such as those considered in the clinical trial context. We review the Bayesian predictive procedure for monitoring experiments and the notion of index of satisfaction. We applied this procedure to a family of limited indices of satisfaction. These indices generalize the rudimentary index of satisfaction considered by Grouin (1994) and the interest of these indices of satisfaction could be in the concept of ‘‘prevision of satisfaction’’ for a future sample, given the data in hand. Given the posterior distribution derived from the available data, the ‘‘prevision of satisfaction’’ is defined like the predictive expectation of the index of satisfaction for the future sample (the interpretation of the index being left to the ‘‘expert’’). The procedure is introduced in the case of a two-step trial, where the result of the first step is used to decide if the experiment will be continued. We consider different cases of the application of the proposed procedure with a conjugate prior. The computations and the simulation results concern an inferential problem, related to the Gaussian model.