A unified approach to power and sample size determination for log-rank tests under proportional and nonproportional hazards
- 5 April 2021
- journal article
- research article
- Published by SAGE Publications in Statistical Methods in Medical Research
- Vol. 30 (5), 1211-1234
- https://doi.org/10.1177/0962280220988570
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.Keywords
This publication has 46 references indexed in Scilit:
- On Sample Size Calculation for Comparing Survival Curves Under General Hypothesis TestingJournal of Biopharmaceutical Statistics, 2012
- Size and power estimation for the Wilcoxon–Mann–Whitney test for ordered categorical dataStatistics in Medicine, 2011
- Sipuleucel-T Immunotherapy for Castration-Resistant Prostate CancerThe New England Journal of Medicine, 2010
- Power and sample size calculation for log‐rank test with a time lag in treatment effectStatistics in Medicine, 2009
- Tutorial in biostatistics: competing risks and multi‐state modelsStatistics in Medicine, 2006
- Evaluation of sample size and power for multi-arm survival trials allowing for non-uniform accrual, non-proportional hazards, loss to follow-up and cross-overStatistics in Medicine, 2006
- Designing complex group sequential survival trialsStatistics in Medicine, 2002
- Comparing sample size formulae for trials with unbalanced allocation using the logrank testStatistics in Medicine, 1992
- Weighted log rank type statistics for comparing survival curves when there is a time lag in the effectiveness of treatmentBiometrika, 1990
- Planning the duration of a comparative clinical trial with loss to follow-up and a period of continued observationJournal of Chronic Diseases, 1981