Bayesian Prediction Using Two-stage Designs In Experimental Trials

Prediction provides discipline and pragmatic importance to empirical research. Two stages design is commonly used in phase II experimental trials. This design possesses good frequentist properties and allows early termination of the trial when the interim data indicate that the experimental regimen is inefficacious. The design with the predictive probability approach provides an excellent alternative for conducting multi-stage phase II trials. It is efficient and flexible and possesses desirable statistical properties. Often, preliminary experimental information is already available as a “pilot”, where a first experience that we ask for confirmation of results. Formally, we consider the following situation: Given a first sample of data, we want to plan an experiment (or a new sample) to have good chances of getting the relief sought if the experiment is not abandoned. We propose the procedure based on the notion of satisfaction index which is a function of the p- value and we expect, given the available data to calculate an estimate of satisfaction for future data as Bayesian predictive index conditional on previous observations. To illustrate the proposed procedure, several models have been studied by choosing the prior distribution justifying the motivations of objectivity or neutrality that underlie the analysis of experimental data.