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.
