Semiparametric Estimation in a Joint Model for Event Time Data and Longitudinal Measurements

• Activity Number: 379
• Type: Topic Contributed
• Date/Time: Thursday, August 15, 2002 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Jean-François Dupuy*+ and Ion Grama and Mounir Mesbah
• Affiliation(s): University of South Brittany and University of South Brittany and Université de Bretagne-Sud
• Keywords: Time-dependent Cox model ; Missing data ; Semi-parametric likelihood ; Asymptotic properties

Abstract

The relationship between a time-dependent covariate and a failure time process can be assessed using the Cox model. A frequently encountered problem in practice, however, is the occurence of missing covariate data. Dupuy and Mesbah (to appear in Lifetime Data Analysis, 2002) have proposed a joint modeling approach to the problem of Cox regression with a time-dependent covariate, when the value of the covariate at failure time is not observed.

Estimation in this joint model is conducted by maximization of a full likelihood for the covariate process and the time-to-failure data. A Markov model is assumed for the covariate process. Direct maximization of this likelihood is not possible because the baseline hazard is not specified. A semi-parametric likelihood is obtained by constraining the cumulative baseline hazard to be a step function with jumps at the observed distinct failure times. We prove existence of maximum likelihood estimators of the parameters of the joint model, based on this semi-parametric likelihood. Relying on techniques based on empirical process theory, we show that these estimators are consistent and asymptotically normally distributed.