Varying-association copula models for multivariate survival data

Abstract

To accommodate possible changes in the correlation structure of multivariate survival data, a class of varying‐association copula models is developed. The proposed model enables the association parameter to vary nonlinearly over an exposure variable, which greatly enhances the flexibility of copula models. A two‐stage estimation procedure is developed to obtain the estimators for the regression and correlation parameters. The first stage estimates the regression parameters based on the marginal proportional hazards model for each event type, and the second stage applies the B‐spline technique to estimate the varying‐association parameter by maximizing the plugged‐in likelihood function. The consistency and asymptotic normality of the proposed estimators are established, and simulation studies are conducted to examine the finite‐sample performance of our method. A real data example from the Framingham Heart Study is used to illustrate this approach. The Canadian Journal of Statistics 46: 556–576; 2018 © 2018 Société statistique du Canada