A new flexible dependence measure for semi-competing risks.

Semi-competing risks data are often encountered in chronic disease follow-up studies that record both nonterminal events (e.g., disease landmark events) and terminal events (e.g., death). Studying the relationship between the nonterminal event and the terminal event can provide insightful information on disease progression. In this article, we propose a new sensible dependence measure tailored to addressing such an interest. We develop a nonparametric estimator, which is general enough to handle both independent right censoring and left truncation. Our strategy of connecting the new dependence measure with quantile regression enables a natural extension to adjust for covariates with minor additional assumptions imposed. We establish the asymptotic properties of the proposed estimators and develop inferences accordingly. Simulation studies suggest good finite-sample performance of the proposed methods. Our proposals are illustrated via an application to Denmark diabetes registry data.