Balancing events, not patients, maximizes power of the logrank test: and other insights on unequal randomization in survival trials

TL;DR

This paper demonstrates that balancing the number of events across treatment arms, rather than patients, maximizes the power of the logrank test in survival trials, challenging common assumptions about equal randomization.

Contribution

It provides new insights and six practical guidelines for optimizing randomization ratios in survival trials, based on comparisons of theoretical approximations and empirical simulations.

Findings

Balancing events maximizes logrank test power.

Equal patient randomization is not always optimal.

Unequal randomization impacts trial factors like duration and sample size.

Abstract

We revisit the question of what randomization ratio (RR) maximizes power of the logrank test in event-driven survival trials under proportional hazards (PH). By comparing three approximations of the logrank test (Schoenfeld, Freedman, Rubinstein) to empirical simulations, we find that the RR that maximizes power is the RR that balances 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 6 insights to guide statisticians in the design of survival trials considering unequal randomization.