Optimal continuous sequential boundaries for monitoring toxicity in clinical trials: a restricted search algorithm

Continuous monitoring of severe adverse experiences can ensure the timely termination of a clinical trial if the therapy is shown to be harmful. In this paper we present methods for choosing a stopping rule for continuous monitoring of toxicity in small trials. They are especially useful for small phase II trials of about 30 patients for monitoring a binary toxicity event that is observed relatively quickly compared to the efficacy outcome. In 1987 Goldman described an algorithm for computing the exact type I error rate (alpha) and power (1-beta) of a specified discrete stopping boundary for sequential monitoring of a study with a fixed maximum number of patients (N) to be enrolled on the experimental therapy. Only an upper boundary was used since trials are only terminated for an excess frequency of toxicity and not for a low rate. By repeated use of this algorithm a stopping rule can be identified which has nearly the chosen level of (alpha) and a reasonable power depending on the design parameters of the study. The work reported here embeds this earlier algorithm as a subroutine in a larger FORTRAN program which searches all boundaries that fulfil constraints on size and power, as specified by the user. The search is restricted so that only those boundaries with size in a small neighbourhood of the chosen alpha are examined and displayed if the power is above a set minimum. These restrictions reduce the number of boundaries examined to only 0.4 per cent of all possible boundaries, thus reducing running time to a practical few seconds. Many such boundaries exist, the one with the largest power can then be chosen for monitoring the trial. The average sample number (ASN) and the expected relative loss (ERL) are also computed. The criterion for choosing may also be based on small ASN or low ERL in addition to power and appropriate alpha.