Asymptotic normality of semiparametric estimators in the Cox model with nonignorable missing covariate

Let T denote a random duration until some event of interest. In the Cox model lambda(T)(t) e(betaz(t)), if the value of Z at event time is unobserved, Dupuy and Mesbah (Lifetime Data Analysis 8 (2002) 99-115) have proposed to estimate the parameters beta and Lambda(T)(t) = integral(0)(t) lambda(T)(s) ds by maximizing a likelihood obtained from a joint model for survival and the longitudinal covariate data. We show that the estimators derived from this joint likelihood are asymptotically normally distributed. To cite this article: J.-F Dupuy et al., C. R. Acad. Sci. Paris, Ser. I336 (2003). (C) 2003 Academie des sciences/Editions scientifiques et medicales Elsevier SAS. All rights reserved.