Estimating the correlation between semi-competing risk survival endpoints

Time-to-event, bivariate, semi-competing risk data occur when a terminal event can censor a non-terminal event, but not vice versa. There are potential correlations between these endpoints as they are measured on the same individual. However, traditional methods to estimate the correlations cannot be used directly due to the censoring of time-to-event endpoints. We develop methods using a copula-based approach to study the dependence structures between the two survival endpoints. We use a variety of copulas to estimate the correlation between endpoints and to acknowledge different dependence structures. The estimated association parameter in the copula function is transformed into Spearman's rank correlation coefficient. We conduct a simulation study to evaluate the estimation from the proposed models along with the effects of misspecification of the copula functions and survival distributions. The proposed methods are applied to two real-life data sets.