Note on the role of the placebo group in the short‐term and long‐term hazard ratio model

Abstract

We read with interest the paper, "Improving testing and description of treatment effect in clinical trials with survival outcomes" by Yang 1 and related papers "Semiparametric analysis of short-term and long-term hazard ratios with two-sample survival data" and "Improved logrank-type tests for survival data using adaptive weights" published by Yang and Prentice. 2,3 Alternatives to the absence of treatment effect on survival are most commonly framed within the proportional hazards model structure. When broader alternatives of nonproportional hazards nature are of interest, it is known that the high efficiency of the log-rank test can be lost. One test that focuses on this issue is the test of Yang and Prentice, 3 based on the short-term and long-term hazard ratio model. The authors argue that the test is able to detect departures from a null hypothesis of no effect against quite broad alternatives. We recall the model on which this test is based and the test itself. Theoretical work and simulations appear to show the test to work well. However, it is important to underline that the test can only be used when the placebo group is clearly defined. Failing to correctly identify which group is the placebo group can have serious consequences and lead to erroneous conclusions. The results may not be interpretable. In situations where we wish to compare Treatment A with Treatment B, neither of which can be considered to correspond unambiguously to the placebo group, our advice would be to avoid this test altogether. We give two examples before concluding that the validity of this test hinges crucially upon a clear and sharp definition of the placebo group.