Abstract
The hazard ratio is widely used to measure or to summarize the magnitude of treatment effects, but it is justifiably difficult to interpret in a meaningful way to patients and perhaps for clinicians as well. In addition, it is most meaningful when the hazard functions are approximately proportional over time. We propose a new measure, termed personalized chance of longer survival. The measure, which quantifies the probability of living longer with one treatment over the another, accounts for individualized characteristics to directly address personalized treatment effects. Hence, the measure is patient focused, which can be used to evaluate subgroups easily. We believe it is intuitive to understand and clinically interpretable in the presence of nonproportionality. Furthermore, because it estimates the probability of living longer by some fixed amount of time, it encodes the probabilistic part of treatment effect estimation. We provide nonparametric estimation and inference procedures that can accommodate censored survival outcomes. We conduct extensive simulation studies, which characterize performance of the proposed method, and data from a large randomized Phase III clinical trial (SWOG S0819) are analyzed using the proposed method.