Smaller sample sizes for phase II trials based on exact tests with actual error rates by trading-off their nominal levels of significance and power

Abstract

Background: Sample sizes for single-stage phase II clinical trials in the literature are often based on exact (binomial) tests with levels of significance (alpha (α) <5% and power >80%). This is because there is not always a sample size where α and power are exactly equal to 5% and 80%, respectively. Consequently, the opportunity to trade-off small amounts of α and power for savings in sample sizes may be lost.

Methods: Sample-size tables are presented for single-stage phase II trials based on exact tests with actual levels of significance and power. Trade-off in small amounts of α and power allows the researcher to select from several possible designs with potentially smaller sample sizes compared with existing approaches. We provide SAS macro coding and an R function, which for a given treatment difference, allow researchers to examine all possible sample sizes for specified differences are provided.

Results: In a single-arm study with P(0) (standard treatment)=10% and P(1) (new treatment)=20%, and specified α=5% and power=80%, the A'Hern approach yields n=78 (exact α=4.53%, power=80.81%). However, by relaxing α to 5.67% and power to 77.7%, a sample size of 65 can be used (a saving of 13 patients).

Interpretation: The approach we describe is especially useful for trials in rare disorders, or for proof-of-concept studies, where it is important to minimise the trial duration and financial costs, particularly in single-arm cancer trials commonly associated with expensive treatment options.