A Positive Stable Frailty Model for Clustered Failure Time Data with Covariate-Dependent Frailty
Version of Record online: 1 JUN 2010
© 2010, The International Biometric Society
Volume 67, Issue 1, pages 8–17, March 2011
How to Cite
Liu, D., Kalbfleisch, J. D. and Schaubel, D. E. (2011), A Positive Stable Frailty Model for Clustered Failure Time Data with Covariate-Dependent Frailty. Biometrics, 67: 8–17. doi: 10.1111/j.1541-0420.2010.01444.x
- Issue online: 14 MAR 2011
- Version of Record online: 1 JUN 2010
- Received December 2008. Revised March 2010. Accepted March 2010.
- Bridge distribution;
- Clustered failure times;
- Covariate-dependent frailty;
- Cox model;
- Positive stable frailty;
- Shared frailty
Summary In this article, we propose a positive stable shared frailty Cox model for clustered failure time data where the frailty distribution varies with cluster-level covariates. The proposed model accounts for covariate-dependent intracluster correlation and permits both conditional and marginal inferences. We obtain marginal inference directly from a marginal model, then use a stratified Cox-type pseudo-partial likelihood approach to estimate the regression coefficient for the frailty parameter. The proposed estimators are consistent and asymptotically normal and a consistent estimator of the covariance matrix is provided. Simulation studies show that the proposed estimation procedure is appropriate for practical use with a realistic number of clusters. Finally, we present an application of the proposed method to kidney transplantation data from the Scientific Registry of Transplant Recipients.