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Title: Using factor copula functions to model the association structure in right-censored survival data Authors:  Roel Braekers - Hasselt University (Belgium) [presenting]
Abstract: In clustered right-censored survival data, both frailty and copula models are commonly used to describe the association between different lifetimes. Within the copula models, we use factor copula functions to model the structure between the different event times in a cluster. This new methodology allows for clusters to have variable sizes ranging from small to large and allows for intracluster dependence to be flexibly modeled by any parametric family of bivariate copulas. In this way, we encompass a wide range of dependence structures. The incorporation of covariates (possibly time-dependent) in the margins is also supported. We propose three estimation procedures: both a one- and two-stage parametric method and a two-stage semiparametric method where marginal survival functions are estimated by using a Cox proportional hazards model. For the parameter estimators, we prove that they are consistent and asymptotically normally distributed, and assess their finite sample behavior with simulation studies. Furthermore, we illustrate the proposed methods on a data set containing the time to the first insemination after calving in dairy cattle clustered in herds of different sizes.