Applicability of sample size calculations based on a comparison of proportions for use with the logrank test

The asymptotic relative efficiency of a test of proportions versus the logrank test is calculated for various clinical trial designs that are used to compare the survival of two treatment groups. The asymptotic relative efficiency is shown to be a reasonable guide to the relative sample sizes required for the logrank and proportions test. It is shown that the efficiency of the proportions test is near 1.0 for designs corresponding to typical studies of cardiovascular disease, for which the duration of the experiment is short compared to mean survival. This result is of practical importance, because sample size calculations based on the comparison of proportions are available to cover many contingencies, including a delay in the onset of full treatment effectiveness, whereas similar calculations have not been published for the logrank statistic. On the other hand, the efficiency of the proportions test can drop to 72% or less for trials in which the accrual period exceeds the mean survival, as is often the case in trials to treat cancer. In such cases, sample size calculations for the proportions test would be [(1/0.72) - 1] = 39% larger than required for the logrank test. Thus, power calculations specifically tailored to the logrank test should be used for studies with a duration comparable to mean survival, if one intends to employ the logrank statistic.