Joint Model of Clustered Failure Time Data with Informative Cluster Size

Abstract

In this article, we propose an estimation procedure to estimate parameters of joint model when there exists a relationship between cluster size and clustered failure times of subunits within a cluster. We use a joint random effect model of clustered failure times and cluster size. To investigate the possible association, two submodels are connected by a common latent variable. The EM algorithm is applied for the estimation of parameters in the models. Simulation studies are performed to assess the finite sample properties of the estimators. Also, sensitivity tests show the influence of the misspecification of random effect distributions. The methods are applied to a lymphatic filariasis study for adult worm nests.

Keywords:

• EM algorithm
• Informative cluster size
• Joint model
• Random effects

Mathematics Subject Classification:

• 62N02
• 62J22

Acknowledgments

This work was partly supported by by the Sookmyung Women's University Research Grants 2011 (Y.-J. Kim), the Korea Research Foundation Grant funded by the Korean Government (MOEHRD, Basic Research Promotion Fund: KRF-2008-313-C00148 (J. W. Lee)).

Notes

SE is the empirical standard error calculated from 600 parameter estimates;

SEM is the mean of the 600 estimated standard errors of the parameters;

CP is the empirical coverage probability of the estimated 95 % confidence interval.