Covariate measurement errors in frailty models for clustered survival data

Abstract

SUMMARY We propose a new class of frailty measurement error models for clustered survival data when covariates are measured with error. We show that the induced hazard function conditional on the observed covariates also follows a frailty model but of a more complicated form. We study the asymptotic bias in regression coefficients and variance components when measurement error is ignored, and the impact of censoring on this asymptotic bias. We show that the naive estimator of the regression coefficient is attenuated and the naive estimator of the variance component is inflated when measurement error is ignored. As the censoring proportion increases, the asymptotic bias in the former becomes larger, but the asymptotic bias in the latter interestingly becomes smaller. We develop a structural approach for parameter estimation using the nonparametric maximum likelihood method, where the baseline hazard is estimated nonparametrically. We prove model identifiability and the existence of the nonparametric maximum likelihood estimators. An EM algorithm is developed for calculating the nonparametric maximum likelihood estimates. The method is applied to the western Kenya parasitaemia data and its performance is evaluated through simulations.