Efficient error determination in sequential clinical trial design

Many clinical trials involve a sequential stopping rule to specify the conditions under which a study might be terminated earlier before its planned completion. The most important issue in the design stage is to determine common operating characteristics such as Type I and Type II error rates, for which crude Monte Carlo simulation methods are widely adopted. However, it is well known that crude Monte Carlo may lead to large variabilities in resultant estimates and excessive waste of computational resources. In this article, we propose an efficient importance sampling approach for determining Type I and Type II error rates in both fully sequential and group sequential clinical trial designs with either immediate responses or survival endpoints. The approach is insensitive to the underlying statistics of interest, and can be easily built into a general algorithm to evaluate error rates, determine sample sizes, test statistical hypotheses, and construct confidence intervals. Our simulation results on a hypotensive agent trial and a modified Beta-Blocker Heart Attack Trial indicate that the proposed approach is not only superior to the crude Monte Carlo method, but may also provide many-fold savings in simulation cost.