Visualizing hypothesis tests in survival analysis under anticipated delayed effects

• Published in: Pharmaceutical statistics : the journal of the pharmaceutical industry Vol. 23; no. 6; pp. 870 - 883
• Main Authors: Jiménez, José L., Barrott, Isobel, Gasperoni, Francesca, Magirr, Dominic
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Inc 01.11.2024; Wiley Subscription Services, Inc
• Subjects: Data Interpretation, Statistical; delayed effects; Humans; Models, Statistical; Proportional Hazards Models; pseudo‐value; Randomized Controlled Trials as Topic - methods; Randomized Controlled Trials as Topic - statistics & numerical data; Research Design; score; Survival Analysis; survival test; Time Factors; visualization; score; visualization; pseudo‐value; delayed effects; survival test
• ISSN: 1539-1604; 1539-1612; 1539-1612
• DOI: 10.1002/pst.2393

What can be considered an appropriate statistical method for the primary analysis of a randomized clinical trial (RCT) with a time‐to‐event endpoint when we anticipate non‐proportional hazards owing to a delayed effect? This question has been the subject of much recent debate. The standard approach is a log‐rank test and/or a Cox proportional hazards model. Alternative methods have been explored in the statistical literature, such as weighted log‐rank tests and tests based on the Restricted Mean Survival Time (RMST). While weighted log‐rank tests can achieve high power compared to the standard log‐rank test, some choices of weights may lead to type‐I error inflation under particular conditions. In addition, they are not linked to a mathematically unambiguous summary measure. Test statistics based on the RMST, on the other hand, allow one to investigate the average difference between two survival curves up to a pre‐specified time point τ—a mathematically unambiguous summary measure. However, by emphasizing differences prior to τ, such test statistics may not fully capture the benefit of a new treatment in terms of long‐term survival. In this article, we introduce a graphical approach for direct comparison of weighted log‐rank tests and tests based on the RMST. This new perspective allows a more informed choice of the analysis method, going beyond power and type I error comparison.