Monitoring of sequential trials using a robust Bayesian stopping rule

In this paper we consider a method for monitoring a clinical trial whose patients are sequentially evaluated for response. We focus on a parameter representing treatment effect. Adopting a Bayesian approach we suggest to update progressively prior information on this unknown quantity: in particular, we monitor the trend of the posterior probability that the parameter is larger than a minimally clinical relevant value, as responses are collected. The trial is terminated with success as soon as this probability exceeds a prefixed threshold; if this does not happen before a preplanned maximum sample size is reached, the treatment is declared ineffective. Hence, the sample size is a random variable associated to the chosen stopping rule. With a simulation study we show that the expected sample size is always smaller than the preplanned optimal sample size and we illustrate an application to compare the sequential and the non sequential procedure. Finally, a robust version of the sequential criterion is proposed in which a single prior distribution is replaced by a suitable class of prior distributions.