Asymptotic theory for the Cox model with missing time-dependent covariate

Jean-François Dupuy, Ion Grama, Mounir Mesbah
2006 Annals of Statistics  
The relationship between a time-dependent covariate and survival times is usually evaluated via the Cox model. Time-dependent covariates are generally available as longitudinal data collected regularly during the course of the study. A frequent problem, however, is the occurence of missing covariate data. A recent approach to estimation in the Cox model in this case jointly models survival and the longitudinal covariate. However, theoretical justification of this approach is still lacking. In
more » ... is paper we prove existence and consistency of the maximum likelihood estimators in a joint model. The asymptotic distribution of the estimators is given along with a consistent estimator of the asymptotic variance.
doi:10.1214/009053606000000038 fatcat:7mn4sbqecbbfhg4wmzrjpobiuq