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Statistica Sinica 14(2004), 885-905





PROPORTIONAL HAZARDS REGRESSION MODELS WITH

UNKNOWN LINK FUNCTION AND TIME-DEPENDENT

COVARIATES


Wei Wang


Harvard University


Abstract: Proportional hazards regression models assume that the covariates affect the survival time through a link function and an index which is a linear function of the covariates. We study the situation when the link is unspecified and some covariates are time-dependent. Due to the nature of irregular designs, oftentimes the history of the time-dependent covariates is not observable. We propose a two-stage approach to account for the missingness. In the first stage, we impute the missing time-dependent covariates using functional data analysis methods. In the second stage, we perform a two-step iterative algorithm to estimate the unknown link function. Asymptotic properties are derived for the non-parametric estimated link function when time-dependent covariates history is observable. The approach is illustrated through several simulations and a data set of a prostate cancer clinical trial.



Key words and phrases: Functional data analysis, non-parametric smoothing, proportional hazards regression, time-dependent covariates.


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