Cumulative incidence association models for bivariate competing risks data

Summary.  Association models, like frailty and copula models, are frequently used to analyse clustered survival data and to evaluate within‐cluster associations. The assumption of non‐informative censoring is commonly applied to these models, though it may not be true in many situations. We consider bivariate competing risk data and focus on association models specified for the bivariate cumulative incidence function (CIF), which is a non‐parametrically identifiable quantity. Copula models are proposed which relate the bivariate CIF to its corresponding univariate CIFs, similarly to independently right‐censored data, and accommodate frailty models for the bivariate CIF. Two estimating equations are developed to estimate the association parameter, permitting the univariate CIFs to be estimated either parametrically or non‐parametrically. Goodness‐of‐fit tests are presented for formally evaluating the parametric models. Both estimators perform well with moderate sample sizes in simulation studies. The practical use of the methodology is illustrated in an analysis of dementia associations.