On a Type of Probability Stopping Rule for Toxicity Study

Abstract

In early phase cancer clinical trials where toxicity events follow independent and identical Bernoulli distributions indexed by patients, the Bayesian stopping rule has been used for continuous monitoring of toxicity along with an affordable maximum sample size (N). This article studies some properties of an heuristic procedure where the trial will stop at the first time that the posterior probability that the toxicity rate (p) is greater than a threshold (η) is greater than certain probability threshold (τ). Specifically, we study the pattern formed by stopping times and regions, recursive stopping probability computation, and toxicity rate estimation. Some relevant theoretical results are given. The presented results are potentially useful for guiding toxicity clinical trial designs.