Three-component cure rate model for nonproportional hazards alternative in the design of randomized clinical trials

Abstract

Cure rate models have been extensively studied and widely used in time-to-event data in cancer clinical trials. Although cure rate models based on the generalized exponential distribution have been developed, they have not been used in the design of randomized cancer clinical trials, which instead have relied exclusively on two-component exponential cure rate model with a proportional hazards (PH) alternative. In some studies, the efficacy of the experimental treatment is expected to emerge some time after randomization. Since this does not conform to a PH alternative, such studies require a more flexible model to describe the alternative hypothesis. In this article, we report the study design of a phase III clinical trial of acute myeloid leukemia using a three-component exponential cure rate model to reflect the alternative hypothesis. A newly developed power calculation program that does not require PH assumption was used. Using a custom-made three-component cure rate model as an alternative hypothesis, the proposed sample size was 409, compared with a sample size of 209 under the assumption of exponential distribution and 228 under the PH alternative. A simulation study was performed to present the degree of power loss when the alternative hypothesis is not appropriately specified. The power calculation program used in this study is for a single analysis and does not account for group sequential tests in phase III trials. However, the loss in power is small, and this was handled by inflating the sample size by 5%. Misspecification of the alternative hypothesis can result in a seriously underpowered study. We report examples of clinical trials that required a custom-made alternative hypothesis to reflect a later indication of experimental treatment efficacy. The proposed three-component cure rate model could be very useful for specifying non-PH alternative.