Flexible association modelling and prediction with semi‐competing risks data

Abstract

AbstractSemi‐competing risks data involve a non‐terminal event time, such as time to disease progression, and a terminal event time such as time to death. Existing methods for handling semi‐competing risks data often assume that the underlying association between the two event times follows a pre‐specified copula with unknown association parameters, which often correspond to the strength of association. In this article we propose a flexible association model that does not require pre‐specifying a copula. Therefore our methods facilitate a convenient and robust evaluation of the underlying association pattern, as well as the association strength. Furthermore the proposed association model leads to a robust estimator for the conditional survival probability of the terminal event given the non‐terminal event. The methods were also extended to handle left‐truncation. Both the association and survival estimators were shown to feature desirable asymptotic properties and satisfactory numerical performance. Our methods were successfully applied to a diabetes data set to study the association between time to diabetic nephropathy and time to death, and to predict the mortality rate given the onset time of nephropathy. The Canadian Journal of Statistics 44: 361–374; 2016 © 2016 Statistical Society of Canada