A unified approach to power and sample size determination for log-rank tests under proportional and nonproportional hazards. (May 2021)

• Record Type: Journal Article
• Authors: Tang, Yongqiang
• Is Part Of: Statistical methods in medical research. Volume 30:Number 5(2021)
• Page Start: 1211
• Page End: 1234
• Publication Date: 2021-05
• Subjects: Cure fraction -- data maturity -- delayed effect -- exponentiated-Weibull distribution -- local alternatives -- maximum combination test -- noninferiority trial -- treatment switching; Medicine -- Research -- Statistical methods -- Periodicals; Research -- Periodicals; Review Literature -- Periodicals; Statistics -- methods -- Periodicals; Médecine -- Recherche -- Méthodes statistiques -- Périodiques; 610.727
• DOI: 10.1177/0962280220988570
• Languages: English
• ISSNs: 0962-2802

Abstract

Log-rank tests have been widely used to compare two survival curves in biomedical research. We describe a unified approach to power and sample size calculation for the unweighted and weighted log-rank tests in superiority, noninferiority and equivalence trials. It is suitable for both time-driven and event-driven trials. A numerical algorithm is suggested. It allows flexible specification of the patient accrual distribution, baseline hazards, and proportional or nonproportional hazards patterns, and enables efficient sample size calculation when there are a range of choices for the patient accrual pattern and trial duration. A confidence interval method is proposed for the trial duration of an event-driven trial. We point out potential issues with several popular sample size formulae. Under proportional hazards, the power of a survival trial is commonly believed to be determined by the number of observed events. The belief is roughly valid for noninferiority and equivalence trials with similar survival and censoring distributions between two groups, and for superiority trials with balanced group sizes. In unbalanced superiority trials, the power depends also on other factors such as data maturity. Surprisingly, the log-rank test usually yields slightly higher power than the Wald test from the Cox model under proportional hazards in simulations. We consider various nonproportional hazards patterns induced by delayed effects, cure fractions, and/or treatment switching. Explicit power formulae are derived for the combination test that takes the maximum of two or more weighted log-rank tests to handle uncertain nonproportional hazards patterns. Numerical examples are presented for illustration.