A general class of quasi-independence tests for left-truncated right-censored data

TL;DR

This paper introduces a unified class of statistical tests for assessing quasi-independence in left-truncated and right-censored survival data, enhancing existing methods with new test statistics and demonstrating their effectiveness.

Contribution

It proposes a general framework for quasi-independence testing that unifies and extends existing methods, including new statistics like a conditional Spearman's rank correlation.

Findings

The proposed tests are asymptotically normal.

New tests show improved power under certain alternatives.

The framework encompasses existing methods and introduces novel statistics.

Abstract

In survival studies, classical inferences for left-truncated data require quasi-independence, a property that the joint density of truncation time and failure time is factorizable into their marginal densities in the observable region. The quasi-independence hypothesis is testable; many authors have developed tests for left-truncated data with or without right-censoring. In this paper, we propose a class of test statistics for testing the quasi-independence which unifies the existing methods and generates new useful statistics such as conditional Spearman's rank correlation coefficient. Asymptotic normality of the proposed class of statistics is given. We show that a new set of tests can be powerful under certain alternatives by theoretical and empirical power comparison.