Randomized two-stage optimal design for interval-censored data

Interval-censored data occur in a study where the exact event time of each participant is not observed but it is known to be within a certain time interval. Multiple tests were proposed for such data, including the logrank test by Sun, the proportional hazard test by Finkelstein, and the Wilcoxon-type test by Peto and Peto. We propose sample size calculations based on these tests for a parallel one-stage or two-stage design. When the proportional hazard assumption is met, the proportional hazard test and the logrank test need smaller sample sizes than the Wilcoxon-type test, and the sample size savings are substantial. But this trend is reversed when the proportional hazard assumption does not hold, and the sample size savings using the Wilcoxon-type test are sizable. An example from a lung cancer clinical trial is used to illustrate the application of the proposed sample size calculations.