Failure time regression with continuous covariates measured with error

Abstract

We consider failure time regression analysis with an auxiliary variable in the presence of a validation sample. We extend the nonparametric inference procedure of Zhou and Pepe to handle a continuous auxiliary or proxy covariate. We estimate the induced relative risk function with a kernel smoother and allow the selection probability of the validation set to depend on the observed co-variates. We present some asymptotic properties for the kernel estimator and provide some simulation results. The method proposed is illustrated with a data set from an on-going epidemiologic study.