Review Articles

Log-rank and stratified log-rank tests

Ting Ye ,

Department of Biostatistics, University of Washington, Seattle, WA, USA

Jun Shao ,

School of Statistics, East China Normal University, Shanghai, People's Republic of China; Department of Statistics, University of Wisconsin, Madison, WI, USA

jshao@wisc.edu

Yanyao Yi

Global Statistical Sciences, Eli Lilly and Company, Indianapolis, IN, USA

Pages | Received 03 Feb. 2023, Accepted 20 Sep. 2023, Published online: 05 Oct. 2023,
  • Abstract
  • Full Article
  • References
  • Citations

In randomized clinical trials with right-censored time-to-event outcomes, the popular log-rank test without adjusting for baseline covariates is asymptotically valid for treatment effect under simple randomization of treatments but is too conservative under covariate-adaptive randomization. The stratified log-rank test, which adjusts baseline covariates in the test procedure by stratification, is asymptotically valid regardless of what treatment randomization is applied. In the literature, however, under simple randomization there is no affirmative conclusion about whether the stratified log-rank test is asymptotically more powerful than the unstratified log-rank test. In this article we show when the stratified and unstratified log-rank tests aim for the same null hypothesis and that, under simple randomization, the stratified log-rank test is asymptotically more powerful than the unstratified log-rank test in the region of alternative hypothesis that is specified by a Cox proportional hazards model. We also provide some discussion about why we do not have an affirmative conclusion in general.

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To cite this article: Ting Ye, Jun Shao & Yanyao Yi (05 Oct 2023): Log-rank and stratified log-rank tests, Statistical Theory and Related Fields, DOI: 10.1080/24754269.2023.2263720 To link to this article: https://doi.org/10.1080/24754269.2023.2263720