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Dupuy, Jean-François; Grama, Ion; Mesbah, Mounir

Asymptotic theory for the Cox model with missing time-dependent covariate. (English) Zbl 1092.62100

Ann. Stat. 34, No. 2, 903-924 (2006).
Summary: 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. 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.

Cited in 12 Documents

MSC:

62N02 Estimation in survival analysis and censored data
62G20 Asymptotic properties of nonparametric inference
62N01 Censored data models
62G05 Nonparametric estimation
62E20 Asymptotic distribution theory in statistics

Keywords:

time-dependent Cox model; survival data; missing time-dependent covariate; maximum likelihood estimation; consistency
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References:

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