Using non-inferiority test of proportions in design of randomized non-inferiority trials with time-to-event endpoint with a focus on low-event-rate setting

Background/aims For cancers with low incidence, low event rates, and a time-to-event endpoint, a randomized non-inferiority trial designed based on the logrank test can require a large sample size with significantly prolonged enrollment duration, making such a non-inferiority trial not feasible. This article evaluates a design based on a non-inferiority test of proportions, compares its required sample size to the non-inferiority logrank test, assesses whether there are scenarios for which a non-inferiority test of proportions can be more efficient, and provides guidelines in usage of a non-inferiority test of proportions. Methods This article describes the sample size calculation for a randomized non-inferiority trial based on a non-inferiority logrank test or a non-inferiority test of proportions. The sample size required by the two design methods are compared for a wide range of scenarios, varying the underlying Weibull survival functions, the non-inferiority margin, and loss to follow-up rate. Results Our results showed that there are scenarios for which the non-inferiority test of proportions can have significantly reduced sample size. Specifically, the non-inferiority test of proportions can be considered for cancers with more than 80% long-term survival rate. We provide guidance in choice of this design approach based on parameters of the Weibull survival functions, the non-inferiority margin, and loss to follow-up rate. Conclusion For cancers with low incidence and low event rates, a non-inferiority trial based on the logrank test is not feasible due to its large required sample size and prolonged enrollment duration. The use of a non-inferiority test of proportions can make a randomized non-inferiority Phase III trial feasible.