Semi-parametric inferences for association with semi-competing risks data

In many biomedical studies, it is of interest to assess dependence between bivariate failure time data. We focus here on a special type of such data, referred to as semi-competing risks data. In this article, we develop methods for making inferences regarding dependence of semi-competing risks data across strata of a discrete covariate Z. A class of rank statistics for testing constancy of association across strata are proposed; its asymptotic properties are also derived. We develop a novel re-sampling-based technique for calculating the variances of the proposed test statistics. In addition, we develop methods for combining test statistics for assessing marginal effects of Z on the dependent censoring variable as well as its effects on association. The finite-sample properties of the proposed methodology are assessed using simulation studies, and they are applied to data from a leukaemia transplantation study.