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

2024-12-09

AI Summary

This paper addresses the problem of testing independence between response and covariates under right-censoring. We propose the Survival Independence Divergence (SID) family—a novel class of dependence measures rigorously defined within the censoring framework, vanishing if and only if independence holds and capable of detecting arbitrary nonlinear dependencies. Leveraging counting process theory, we reformulate the censored independence test as a nonparametric kernel estimation problem under complete observation and establish the asymptotic normality of the SID estimator. We further develop a consistent wild bootstrap procedure for inference. Extensive simulations and real-data analyses demonstrate that the SID-based test significantly outperforms existing methods in statistical power, robustness to censoring and model misspecification, and computational efficiency. Our work establishes a new paradigm for independence testing in survival analysis.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Kernel Methods
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Responsible Web: Measurement, analysis, and circumvention of Web censorship
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

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.

Problem

• Tests independence between right-censored outcomes and covariates
• Transforms censored independence tests into complete observation problems
• Detects various types of nonlinear dependence with censored data

Innovation

• Counting process strategy transforms censored data
• SID metrics detect nonlinear dependence with censoring
• Wild bootstrap method estimates critical values consistently