This module computes the sample size and power of the logrank test for equality of survival distributions under very general assumptions. The parameterization can be in terms of hazard rates, median survival time, proportion surviving, and mortality (proportion dying). Accrual time, follow-up time, loss during follow up, noncompliance, and time-dependent hazard rates are other parameters that can be set.

A clinical trial is often employed to test the equality of survival distributions for two treatment groups. For example, a researcher might wish to determine if Beta-Blocker A enhances the survival of newly diagnosed myocardial infarction patients over that of the standard Beta-Blocker B. The question being considered is whether the pattern of survival is different.

The two-sample t-test is not appropriate for two reasons. First, the data consist of the length of survival (time to failure), which is often highly skewed, so the usual normality assumption cannot be validated. Second, since the purpose of the treatment is to increase survival time, it is likely (and desirable) that some of the individuals in the study will survive longer than the planned duration of the study. The survival times of these individuals are then said to be censored. These times provide valuable information, but they are not the actual survival times. Hence, special methods have to be employed which use both regular and censored survival times.

The logrank test is one of the most popular tests for comparing two survival distributions. It is easy to apply and is usually more powerful than an analysis based simply on proportions. It compares survival across the whole spectrum of time, not just at one or two points. This module allows the sample size and power of the logrank test to be analyzed under very general conditions.

Power and sample size calculations for the logrank test have been studied by several authors. This PASS module uses the method of Lakatos (1988) because of its generality. This method is based on a Markov model that yields the asymptotic mean and variance of the logrank statistic under very general conditions.