Investigating non-inferiority or equivalence in time-to-event data under non-proportional hazards

Kathrin Möllenhoff () and Achim Tresch
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Kathrin Möllenhoff: Heinrich Heine University
Achim Tresch: University of Cologne

Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, 2023, vol. 29, issue 3, No 1, 483-507

Abstract: Abstract The classical approach to analyze time-to-event data, e.g. in clinical trials, is to fit Kaplan–Meier curves yielding the treatment effect as the hazard ratio between treatment groups. Afterwards, a log-rank test is commonly performed to investigate whether there is a difference in survival or, depending on additional covariates, a Cox proportional hazard model is used. However, in numerous trials these approaches fail due to the presence of non-proportional hazards, resulting in difficulties of interpreting the hazard ratio and a loss of power. When considering equivalence or non-inferiority trials, the commonly performed log-rank based tests are similarly affected by a violation of this assumption. Here we propose a parametric framework to assess equivalence or non-inferiority for survival data. We derive pointwise confidence bands for both, the hazard ratio and the difference of the survival curves. Further we propose a test procedure addressing non-inferiority and equivalence by directly comparing the survival functions at certain time points or over an entire range of time. Once the model’s suitability is proven the method provides a noticeable power benefit, irrespectively of the shape of the hazard ratio. On the other hand, model selection should be carried out carefully as misspecification may cause type I error inflation in some situations. We investigate the robustness and demonstrate the advantages and disadvantages of the proposed methods by means of a simulation study. Finally, we demonstrate the validity of the methods by a clinical trial example.

Keywords: Equivalence; Non-inferiority; Non-proportional hazards; Survival analysis; Time-to-event data (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s10985-023-09589-5

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