Balancing Events, Not Patients, Maximizes Power of the Logrank Test: And Other Insights on Unequal Randomization in Survival Trials

We revisit the question of what randomization ratio (RR) maximizes the power of the logrank test (LRT) in event-driven survival trials under proportional hazards (PH). By comparing three approximations of the LRT (Schoenfeld, Freedman, and Rubinstein) to empirical simulations, we find that the RR that maximizes power is the RR that balances the number of events across treatment arms at the end of the trial. This contradicts the common misconception implied by Schoenfeld's approximation that 1:1 randomization maximizes power. Besides power, we consider other factors that might influence the choice of RR (accrual, trial duration, sample size, etc.). We perform simulations to better understand how unequal randomization might impact these factors in practice. Altogether, we derive 5 insights to guide statisticians in the design of survival trials considering unequal randomization.