Optimal Sample Sizes and Go/No-Go Decisions for Phase II/III Development Programs Based on Probability of Success

In the course of late-stage drug development, a phase II/III clinical development program faces a series of sample size planning and decision problems: the simultaneous sample sizes determination (SSD) across phase II and phase III trials at the program planning stage, the go/no-go decisions after phase II data have been observed, and the SSD of phase III trials incorporating phase II data. Conventionally, SSD are carried out on a trial-by-trial basis and independent of one another even though the trials are within the same program; and the go/no-go decisions are made based on the p-values, point estimates, and confidence intervals which may be, at times, ambiguous for decision making. In a combined empirical Bayesian and frequentist framework, this article proposes a probability of success (POS) function to allow an integrated approach to the SSD and go/no-go decision problems for a phase II/III program in which both the phase II and III trials share a common, normally distributed response variable. For the first time, optimal sample sizes can be determined simultaneously for a phase II/III program using the proposed POS function. As the POS function includes the conventional power function as a special case, it enjoys broader applications including SSD of phase II trials and that of phase III trials incorporating phase II data-neither of which can be handled as readily using the conventional power function.