Motivating sample sizes in adaptive Phase I trials via Bayesian posterior credible intervals

In contrast with typical Phase III clinical trials, there is little existing methodology for determining the appropriate numbers of patients to enroll in adaptive Phase I trials. And, as stated by Dennis Lindley in a more general context, "[t]he simple practical question of 'What size of sample should I take' is often posed to a statistician, and it is a question that is embarrassingly difficult to answer." Historically, simulation has been the primary option for determining sample sizes for adaptive Phase I trials, and although useful, can be problematic and time-consuming when a sample size is needed relatively quickly. We propose a computationally fast and simple approach that uses Beta distributions to approximate the posterior distributions of DLT rates of each dose and determines an appropriate sample size through posterior coverage rates. We provide sample sizes produced by our methods for a vast number of realistic Phase I trial settings and demonstrate that our sample sizes are generally larger than those produced by a competing approach that is based upon the nonparametric optimal design.