Estimation for frailty measurement error Cox models based on profile likelihood and Bayes methods

Abstract

We study a class of frailty Cox models with measurement error in covariates for right censored clustered data. Based on the corrected profile likelihood and Bayes estimation, we construct estimators of the regression coefficients, baseline hazard and frailties in the models, which can reduce the dimension of estimated parameters and make the computation feasible. Numerical results show that frailty measurement error Cox model (FMCM) is more competitive and of good adaptivity than frailty Cox model (FCM) and measurement error Cox model (MCM) in terms of bias and mean square error.

Keywords:

• Cox model
• Frailty
• Measurement error
• Profile likelihood

Acknowledgement

We thank the Editor-in-Chief and the referees for their helpful comments and suggestions that have led to improvements of this paper. This work is supported by the Research Projects of Humanities and Social Science of Ministry of Education of China (17YJA910003) and Intelligent Plant Factory of Zhejiang Province Engineering Lab.