Modelling multivariate failure time data using additive risk frailty model

Abstract

As a viable alternative to the proportional hazards model, the additive risks model examines excess risk and provides a flexible tool of modeling multivariate failure time data. We propose a class of additive risk models for the analysis of competing risks and semi-competing risks data. First, we consider the additive risk approach for competing risks data by modeling both the cause-specific and sub-distribution hazards. Secondly, we suggest an additive risk frailty model for semi-competing risks data. Frailties are used to model the dependence between the terminal and non-terminal events and covariate effects are examined by excess risk given the frailty. Splines are used to model the conditional baseline hazard nonparametrically. Finally, the extension to the more general additive-multiplicative model is discussed. In all cases, we investigate theoretical and numerical properties of the estimators. Simulation studies and real medical examples are used to illustrate the practical utilities of the proposed methodology.