Restricted survival benefit with right-censored data

Abstract

The hazard ratio is widely used to quantify treatment effects. However, it may be difficult to interpret for patients and practitioners, especially when the hazard ratio is not constant over time. Alternative measures of the treatment effects have been proposed such as the difference of the restricted mean survival times, the difference in survival proportions at some fixed follow-up time, or the net chance of a longer survival. In this paper, we propose the restricted survival benefit (RSB), a quantity that can incorporate multiple useful measurements of treatment effects. Hence, it provides a framework for a comprehensive assessment of the treatment effects. We provide estimation and inference procedures for the RSB that accommodate censored survival outcomes, using methods of the inverse-probability-censoring-weighted $U$ -statistic and the jackknife empirical likelihood. We conduct extensive simulation studies to examine the numerical performance of the proposed method, and we analyze data from a randomized Phase III clinical trial (SWOG S0777) using the proposed method.

Keywords: $$U$$ -statistic; inverse probability censoring weighting; jackknife empirical likelihood; restricted survival benefit.

Figure 1

Type I error and power of testing the hypothesis of “no treatment effect” under independent censoring for θ₁ = E{(T₁ Λ τ) − (T₀ Λ τ)}: difference of restricted mean survival time. AN: test based on the asymptotic normality; JELR: jackknife empirical likelihood ratio test. Logrank: logrank test; Uno et al. (2014): test based on the asymptotic normality of the estimator in Uno et al. (2014).

Figure 2

Type I error and power of testing the hypothesis of “no treatment effect” under dependent censoring for θ₁ = E{(T₁ Λ τ) − (T₀ Λ τ)}: difference of restricted mean survival time. AN: test based on the asymptotic normality; JELR: jackknife empirical likelihood ratio test. Logrank: logrank test; Uno et al. (2014): test based on the asymptotic normality of the estimator in Uno et al. (2014).