On Frequentist and Bayesian Sequential Clinical Trial Designs

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 frequentist and Bayesian sequential clinical trial designs with a focus on their fundamental and philosophical differences. Frequentist designs utilize repeated significance testing or conditional power to make early stopping decisions. The majority of frequentist designs are concerned with controlling the overall type I error rate of falsely rejecting the null hypothesis at any analysis. On the other hand, Bayesian designs utilize posterior or posterior predictive probabilities for decision-making. The prior and threshold values in a Bayesian design can be chosen to either achieve desirable frequentist operating characteristics or reflect the investigator's subjective belief. We also comment on the likelihood principle, which is commonly tied with statistical inference and decision-making in sequential clinical trials. A single-arm trial example with normally distributed outcomes is used throughout to illustrate some frequentist and Bayesian designs. Numerical studies are conducted to assess these designs.