SID: A Novel Class of Nonparametric Tests of Independence for Censored Outcomes

TL;DR

This paper introduces the survival independence divergence (SID), a new nonparametric metric for testing independence between right-censored outcomes and covariates, capable of detecting nonlinear dependence.

Contribution

The paper develops the SID metric using a counting process approach, establishes its asymptotic properties, and proposes a bootstrap method for hypothesis testing.

Findings

SID tests are highly competitive with existing methods.

The proposed tests effectively detect various nonlinear dependencies.

Asymptotic properties of the estimators are rigorously established.

Abstract

We propose a new class of metrics, called the survival independence divergence (SID), to test dependence between a right-censored outcome and covariates. A key technique for deriving the SIDs is to use a counting process strategy, which equivalently transforms the intractable independence test due to the presence of censoring into a test problem for complete observations. The SIDs are equal to zero if and only if the right-censored response and covariates are independent, and they are capable of detecting various types of nonlinear dependence. We propose empirical estimates of the SIDs and establish their asymptotic properties. We further develop a wild bootstrap method to estimate the critical values and show the consistency of the bootstrap tests. The numerical studies demonstrate that our SID-based tests are highly competitive with existing methods in a wide range of settings.