Sample size calculation for the log-rank tests for multi-arm trials with a control

Suppose that there are KK experimental arms and a control arm in a study with survival as the primary endpoint. We consider a Dunnett-type testing procedure to discover the experimental arms that have longer survival distributions than the control arm using the log-rank statistic. In order to adjust for the multiplicity of the testing procedure, a Dunnett-type test controls the family-wise error rate (FWER). We derive the sample size required for a given parameter setting on the FWER level, power, survival distributions of the K+1K+1 arms, accrual period (or accrual rate), and additional follow-up period. Through simulations, derived sample sizes are shown to accurately maintain the power. The proposed method is applied to a real clinical trial.