An extension of the Cox–Czanner divergence measure to residual lifetime distributions with applications

Abstract

A time-dependent divergence measure is proposed to compare the survival functions of two lifetime random variables. It is shown that the proposed measure ranges between (Formula presented.) and for the proportional hazards case has the metric properties. Several properties of the divergence measure are investigated, among others, it is shown that the divergence between two survival functions does not depend on time if and only if they follow the proportional hazards model. The measure is also examined for various other well-known survival models such as the proportional odds model. The estimation of the suggested divergence measure for survival data is also discussed, and the asymptotic normal distribution of the resulting estimator is established. The proposed estimation is evaluated via simulation and further employed to compare the effects of two treatment groups on the overall survival times of kidney cancer patients. © 2020 Informa UK Limited, trading as Taylor & Francis Group.