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Robust Bayesian sample size determination in clinical trials
Author(s) -
Brutti Pierpaolo,
De Santis Fulvio,
Gubbiotti Stefania
Publication year - 2008
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.3175
Subject(s) - prior probability , sample size determination , bayesian probability , posterior probability , posterior predictive distribution , context (archaeology) , statistics , mathematics , sensitivity (control systems) , computer science , bayesian inference , bayesian linear regression , biology , paleontology , electronic engineering , engineering
This article deals with determination of a sample size that guarantees the success of a trial. We follow a Bayesian approach and we say an experiment is successful if it yields a large posterior probability that an unknown parameter of interest (an unknown treatment effect or an effects‐difference) is greater than a chosen threshold. In this context, a straightforward sample size criterion is to select the minimal number of observations so that the predictive probability of a successful trial is sufficiently large. In the paper we address the most typical criticism to Bayesian methods—their sensitivity to prior assumptions—by proposing a robust version of this sample size criterion. Specifically, instead of a single distribution, we consider a class of plausible priors for the parameter of interest. Robust sample sizes are then selected by looking at the predictive distribution of the lower bound of the posterior probability that the unknown parameter is greater than a chosen threshold. For their flexibility and mathematical tractability, we consider classes of ε‐contamination priors. As specific applications we consider sample size determination for a Phase III trial. Copyright © 2008 John Wiley & Sons, Ltd.