Correlated random effects models for clustered survival data

Abstract: Frailty models are frequently used to analyse clustered survival data in medical contexts. The frailties, or random effects, are used to model the association between individual survival times within clusters. Analysis of survival times of related individuals is typically complicated because follow up on an event type of interest is censored by events of secondary interest. Treating such competing events as independent may yield an incorrect analysis when the random effects associated with other event types are dependent of the event type of interest. We study two related inferential procedures for dependent data where the frailties of the type specific hazards may be correlated between competing event types. Routine registers offer possibilities to study covariate effects on survival times for rare diseases, for which large cohorts are required. However, the vast amount of data and the clustering of related individuals pose statistical challenges. In the first paper we adapt maximum likelihood methods for semiparametric transformation regression models to a cohort register subsampling design. This approach drastically reduces the computing times with a minor loss of efficiency, and results in practically useful estimation procedures. In the second paper we propose an estimator of covariate effects based on the observed intensities, where the nonparametric baseline hazards are profiled out. Thereby we reduce the problem to finite dimensions, where e.g. the covariance matrix is more directly estimated. A set of frailty structures for paired competing risks data based on sums of gamma variables is investigated through simulations. We establish the asymptotic properties of the estimators and present consistent covariance estimators. Worked examples are provided for illustration.