Multilevel joint frailty model for hierarchically clustered binary and survival data

Hierarchical data arise when observations are clustered into groups. Multilevel models are practically useful in these settings, but these models are elusive in the context of hierarchical data with mixed multivariate outcomes. In this article, we consider binary and survival outcomes and assume the hierarchical structure is induced by clustering of both outcomes within patients and clustering of patients within hospitals which frequently occur in multicenter studies. We introduce a multilevel joint frailty model that analyzes the outcomes simultaneously to jointly estimate their regression parameters and explicitly model within-patient correlation between the outcomes and within-hospital correlation separately for each outcome. Estimation is facilitated by a computationally efficient residual maximum likelihood method that further predicts cluster-specific frailties for both outcomes and circumvents the formidable challenges induced by multidimensional integration that complicates the underlying likelihood. The performance of the model and estimation procedure is investigated via extensive simulation studies. The practical utility of the model is illustrated through simultaneous modeling of disease-free survival and binary endpoint of platelet recovery in a multicenter allogeneic bone marrow transplantation dataset that motivates this study.

Analysis of clustered competing risks data using subdistribution hazard models with multivariate frailties

Competing risks data often exist within a center in multi-center randomized clinical trials where the treatment effects or baseline risks may vary among centers. In this paper, we propose a subdistribution hazard regression model with multivariate frailty to investigate heterogeneity in treatment effects among centers from multi-center clinical trials. For inference, we develop a hierarchical likelihood (or h-likelihood) method, which obviates the need for an intractable integration over the frailty terms. We show that the profile likelihood function derived from the h-likelihood is identical to the partial likelihood, and hence it can be extended to the weighted partial likelihood for the subdistribution hazard frailty models. The proposed method is illustrated with a dataset from a multi-center clinical trial on breast cancer as well as with a simulation study. We also demonstrate how to present heterogeneity in treatment effects among centers by using a confidence interval for the frailty for each individual center and how to perform a statistical test for such heterogeneity using a restricted h-likelihood.