Comparison of Quantile Regression Curves with Censored Data

TL;DR

This paper introduces a new statistical test for comparing conditional quantile curves with censored data, applicable to independent and paired samples, with proven asymptotic properties and validated through simulations and real data application.

Contribution

It develops a novel test for comparing censored quantile curves, including bootstrap-based critical value approximation and performance evaluation against existing methods.

Findings

Test performs well for small and moderate sample sizes.

Bootstrap procedure effectively approximates critical values.

Application to diabetic retinopathy data demonstrates practical utility.

Abstract

This paper proposes a new test for the comparison of conditional quantile curves when the outcome of interest, typically a duration, is subject to right censoring. The test can be applied both in the case of two independent samples and for paired data, and can be used for the comparison of quantiles at a fixed quantile level, a finite set of levels or a range of quantile levels. The asymptotic distribution of the proposed test statistics is obtained both under the null hypothesis and under local alternatives. We describe a bootstrap procedure in order to approximate the critical values, and present the results of a simulation study, in which the performance of the tests for small and moderate sample sizes is studied and compared with the behavior of alternative tests. Finally, we apply the proposed tests on a data set concerning diabetic retinopathy.