Sequential designs with small samples: Evaluation and recommendations for normal responses

Sequential monitoring is a well-known methodology for the design and analysis of clinical trials. Driven by the lower expected sample size, recent guidelines and published research suggest the use of sequential methods for the conduct of clinical trials in rare diseases. However, the vast majority of the developed and most commonly used sequential methods relies on asymptotic assumptions concerning the distribution of the test statistics. It is not uncommon for trials in (very) rare diseases to be conducted with only a few decades of patients and the use of sequential methods that rely on large-sample approximations could inflate the type I error probability. Additionally, the setting of a rare disease could make the traditional paradigm of designing a clinical trial (deciding on the sample size given type I and II errors and anticipated effect size) irrelevant. One could think of the situation where the number of patients available has a maximum and this should be utilized in the most efficient way. In this work, we evaluate the operational characteristics of sequential designs in the setting of very small to moderate sample sizes with normally distributed outcomes and demonstrate the necessity of simple corrections of the critical boundaries. We also suggest a method for deciding on an optimal sequential design given a maximum sample size and some (data driven or based on expert opinion) prior belief on the treatment effect.