A nonparametric relative treatment effect for direct comparisons of censored paired survival outcomes

TL;DR

This paper introduces a nonparametric method for comparing two treatments in censored paired survival data, providing a new estimator of relative treatment effect along with hypothesis testing and confidence intervals.

Contribution

It develops a novel estimand-driven approach using competing risks techniques for censored paired data, including resampling-based inference methods.

Findings

The proposed test shows good power in simulations.

The method effectively compares treatments in censored paired survival data.

Application to diabetic retinopathy data demonstrates practical utility.

Abstract

A very classical problem in statistics is to test the stochastic superiority of one distribution to another. However, many existing approaches are developed for independent samples and, moreover, do not take censored data into account. We develop a new estimand-driven method to compare the effectiveness of two treatments in the context of right-censored survival data with matched pairs. With the help of competing risks techniques, the so-called relative treatment effect is estimated. It quantifies the probability that the individual undergoing the first treatment survives the matched individual undergoing the second treatment. Hypothesis tests and confidence intervals are based on a studentized version of the estimator, where resampling-based inference is established by means of a randomization method. In a simulation study, we found that the developed test exhibits good power, when compared to competitors which are actually testing the simpler null hypothesis of the equality of both marginal survival functions. Finally, we apply the methodology to a well-known benchmark data set from a trial with patients suffering from with diabetic retinopathy.