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Review
. 2025 May;44(10-12):e70101.
doi: 10.1002/sim.70101.

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

Godwin Yung  1 , Kaspar Rufibach  2 , Marcel Wolbers  2 , Ray Lin  1 , Yi Liu  3
Affiliations
Review

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

Godwin Yung et al. Stat Med. 2025 May.

Abstract

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.

Keywords: proportional hazards; randomization ratio; survival study; time‐to‐event.

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References

    1. D. Schoenfeld, “The Asymptotic Properties of Nonparametric Tests for Comparing Survival Distributions,” Biometrika 68 (1981): 316–319.
    1. S. J. Pocock, “Allocation of Patients to Treatment in Clinical Trials,” Biometrics 35 (1979): 183–197.
    1. A. L. Avins, “Can Unequal Be More Fair? Ethics, Subject Allocation, and Randomised Clinical Trials,” Journal of Medical Ethics 24 (1998): 401–408.
    1. J. C. Dumville, S. Hahn, J. N. Miles, and D. J. Torgerson, “The Use of Unequal Randomisation Ratios in Clinical Trials: A Review,” Contemporary Clinical Trials 27, no. 1 (2006): 1–12, https://doi.org/10.1016/j.cct.2005.08.003.
    1. S. P. Hey and J. Kimmelman, “The Questionable Use of Unequal Allocation in Confirmatory Trials,” Neurology 82 (2014): 77–79.

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