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

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 that 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.