P22: The Use of Mitigated Fractions as a Generalized Metric for Survival Analysis of Non-Proportional Hazards

The hazard ratio has long been considered to be the gold standard in estimating treatment effects for survival data. However, the hazard ratio relies on the proportional hazards assumption, which has been shown to not always hold, and is especially suspect for cancer immunotherapies. In these cases, the hazard ratio is not interpretable and is unable to meaningfully describe the magnitude of a treatment effect. As an alternative, we propose an adaptation of the Mann-Whitney Wilcoxon statistic called the Mitigated Fraction (MF) for evaluating survival data. The MF has been circulating in the literature under various names (Siev, 2005), and the Wilcoxon statistic has been proposed for use in survival analysis before under the name of Gehan's U (1965). We differ from Gehan in that we use the version of MF for censored data proposed by Zhang, et al. (2020), which corrects for censoring through the use of the Kaplan-Meier estimator. This results in the MF being a non-parametric estimator of the risk difference between two treatment groups which can also be regarded as a generalized metric, since it does not rely on the proportional hazards assumption, but still has a 1:1 relation to the hazard ratio when the assumption holds. To support our proposal, we provide an explanation of the formulation of the MF for survival data, some of its properties, and a power analysis on simulated data that shows that the MF's ability to detect treatment effects is comparable to that of the restricted mean survival time and the difference in median survival.

Survival Analysis

Non-Proportional Hazards

Non-Parametric Analysis

Immunotherapies

Pairwise Comparisons 

Clinical Trial Design (e.g., Innovative/Complex Design, Estimands, Master Protocol)

ASA Biopharmaceutical Section Regulatory-Industry Statistics Workshop 2023