Clinical trials usually involve sequential patient entry. When designing a clinical trial, it is often desirable to include a provision for interim analyses of accumulating data with the potential for stopping the trial early. We review Bayesian sequential clinical trial designs based on posterior probabilities, posterior predictive probabilities, and decision-theoretic frameworks. A pertinent question is whether Bayesian sequential designs need to be adjusted for the planning of interim analyses. We answer this question from three perspectives: a frequentist-oriented perspective, a calibrated Bayesian perspective, and a subjective Bayesian perspective. We also provide new insights into the likelihood principle, which is commonly tied to statistical inference and decision making in sequential clinical trials. Some theoretical results are derived, and numerical studies are conducted to illustrate and assess these designs.
Phase I trials investigate the toxicity profile of a new treatment and identify the maximum tolerated dose for further evaluation. Most phase I trials use a binary dose-limiting toxicity endpoint to summarize the toxicity profile of a dose. In reality, reported toxicity information is much more abundant, including various types and grades of adverse events. Building upon the i3+3 design (Liu et al., 2020), we propose the Ti3+3 design, in which the letter “T” represents “total” toxicity. The proposed design takes into account multiple toxicity types and grades by computing the toxicity burden at each dose. The Ti3+3 design aims to achieve desirable operating characteristics using a simple statistics framework that utilizes“toxicity burden interval” (TBI). Simulation results show that Ti3+3 demonstrates comparable performance with existing more complex designs.