A resampling‐based test for two crossing survival curves

• Published in: Pharmaceutical statistics : the journal of the pharmaceutical industry Vol. 19; no. 4; pp. 399 - 409
• Main Authors: Liu, Tiantian, Ditzhaus, Marc, Xu, Jin
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Inc 01-07-2020; Wiley Subscription Services, Inc
• Subjects: area between curves; Asymptotic methods; Bootstrap method; conditional bootstrap test; Kaplan‐Meier estimator; log‐rank test; nonproportional hazard; Survival analysis; Wilcoxon test; Wilcoxon test; conditional bootstrap test; nonproportional hazard; area between curves; Kaplan-Meier estimator; log-rank test
• ISSN: 1539-1604; 1539-1612
• DOI: 10.1002/pst.2000

Summary
The area between two survival curves is an intuitive test statistic for the classical two‐sample testing problem. We propose a bootstrap version of it for assessing the overall homogeneity of these curves. Our approach allows ties in the data as well as independent right censoring, which may differ between the groups. The asymptotic distribution of the test statistic as well as of its bootstrap counterpart are derived under the null hypothesis, and their consistency is proven for general alternatives. We demonstrate the finite sample superiority of the proposed test over some existing methods in a simulation study and illustrate its application by a real‐data example.