Power calculation for the log rank test using historical data

When planning a clinical trial that is to use the log rank test to compare survival in two groups, it is desirable to determine that the power of the test is adequate given the anticipated accrual rate and time, follow-up time, and survival functions S-1(t) and S-2(t). Often it is assumed that the ratio of the associated hazards is a constant, rho, and we want adequate power for a given value of rho. In this case S-2(t) = S-1(rho)(t), so that an assumption concerning S-1(t) is required. If a Kaplan-Meier estimate <(S)over cap (1)(t)> is available from a previous study, its use might be preferable to assuming a distribution of a particular form. In this note we show how such power calculations can be performed. Furthermore, since for any value of t, <(S)over cap (rho)(1)(t)> is a random variable, the variance of power estimates calculated using it can be estimated.