Design and analysis of individually randomized group-treatment trials with time to event outcomes

In a typical individually randomized group-treatment (IRGT) trial, subjects are randomized between a control arm and an experimental arm. While the subjects randomized to the control arm are treated individually, those in the experimental arm are assigned to one of clusters for group treatment. By sharing some common frailties, the outcomes of subjects in the same groups tend to be dependent, whereas those in the control arm are independent. In this paper, we consider IRGT trials with time to event outcomes. We modify the two-sample log-rank test to compare the survival data from TRGT trials, and derive its sample size formula. The proposed sample size formula requires specification of marginal survival distributions for the two arms, bivariate survival distribution and cluster size distribution for the experimental arm, and accrual period or accrual rate together with additional follow-up period. In a sample size calculation, either the cluster sizes are given and the number of clusters is calculated or the number of clusters is given at the time of study open and the required accrual period to determine the cluster sizes is calculated. Simulations and a real data example show that the proposed test statistic controls the type I error rate and the formula provides accurately powered sample sizes. Also proposed are optimal designs minimizing the total sample size or the total cost when the cost per subject is different between two treatment arms.