Most stable sample size determination in clinical trials

This paper is devoted to robust Bayes sample size determination under the quadratic loss function. The idea behind the proposed approach is that the smaller a chosen posterior functional, the more robust the posterior inference. Such desired posterior functional has been taken, in the literature, as the range of posterior mean over a class of priors but we show that dealing with the posterior mean is not the only method leading to an optimal sample size. To provide an alternative approach, we propose implementing most stable rules into the context of sample size determination. We discuss properties of the desired most stable estimate and provide some examples in the normal model. We then compare the proposed approach with that of a recent global robustness study from both numerical and theoretical aspects. We illustrate the practical utility of our proposed method by analyzing a real data set.