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Title: Survival analysis under non-proportional hazards: Investigating non-inferiority or equivalence in time-to-event data Authors:  Kathrin Moellenhoff - Heinrich Heine University Düsseldorf (Germany) [presenting]
Achim Tresch - (Germany)
Abstract: Time-to-event outcomes are frequently observed in medical research, for instance, in the area of oncology or cardiovascular diseases. A commonly addressed issue is the comparison of a test to a reference treatment regarding survival. For this purpose, an analysis based on Kaplan-Meier curves, followed by a log-rank test, is still the most popular approach. In case of addressing non-inferiority or equivalence, extensions of the log-rank test are used. Using one of these approaches, a direct interpretation is obtained by summarizing the treatment effect in one single parameter, given by the hazard ratio of the two treatments, assumed to be constant over time. However, in numerous trials, hazards are non-proportional, and these approaches suffer from a loss of power. We propose a parametric framework to assess equivalence or non-inferiority for survival data. Assuming various time-to-event distributions, we first derive pointwise confidence bands for both, the hazard ratio and the difference in the survival curves. Second, we perform a test addressing non-inferiority and equivalence by directly comparing the survival functions at certain time points or over an entire time interval. We demonstrate the validity of the approach even in settings where sample sizes are small.