When designing a cancer clinical trial, it is usual to assume an exponential distribution for a time-to-event outcome such as overall survival (OS). OS is often expressed as the sum of progression-free survival (PFS) and survival post-progression (SPP), each of which is assumed to be exponentially distributed. Then, OS does not follow an exponential distribution any more but a gamma or hypo-exponential distribution. In this study, we derived a sample size calculation formula for comparing OS between two treatment arms using the log-rank test for OS following a gamma or hypo-exponential distribution. We conducted a simulation study to evaluate the sample size and power calculation based on the gamma or hypo-exponential distribution. We found that we could reduce the sample sizes considerably compared to when assuming an exponential distribution for OS.
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