Optimal Sample Size for Evidence and Consensus in Phase III Clinical Trials

Design and analysis of clinical trials imply decisions that often involve multiple parties. We focus here on one of the main design issues in phase III trials, that is the choice of the sample size, that influences the final probability of success of the experiment, i.e. showing evidence of superiority of a new treatment over the standard one. Bayesian Statistics allows one to exploit pre-experimental information and uncertainty that can be translated into probability distributions for the effects-difference parameter. Sometimes sources of prior knowledge can be in striking contrast (skeptimism vs optimism), possibly leading to divergent final post-experimental conclusions. We propose a sample size criterion that controls not only the achievement of minimal evidence of superiority but also posterior consensus. The method is illustrated for trials involving binary outcomes with normal approximation for the log odds ratio with application to a comparative study of two interventions for diabetic patients with coronary artery disease.