### Abstract

This article deals with parameter estimation in the Cox proportional hazards model when covariates are measured with error. We consider both the classical additive measurement error model and a more general model which represents the mis-measured version of the covariate as an arbitrary linear function of the true covariate plus random noise. Only moment conditions are imposed on the distributions of the covariates and measurement error. Under the assumption that the covariates are measured precisely for a validation set, we develop a class of estimating equations for the vector-valued regression parameter by correcting the partial likelihood score function. The resultant estimators are proven to be consistent and asymptotically normal with easily estimated variances. Furthermore, a corrected version of the Breslow estimator for the cumulative hazard function is developed, which is shown to be uniformly consistent and, upon proper normalization, converges weakly to a zero-mean Gaussian process. Simulation studies indicate that the asymptotic approximations work well for practical sample sizes. The situation in which replicate measurements (instead of a validation set) are available is also studied.

Original language | English (US) |
---|---|

Pages (from-to) | 637-655 |

Number of pages | 19 |

Journal | Scandinavian Journal of Statistics |

Volume | 29 |

Issue number | 4 |

State | Published - Dec 2002 |

Externally published | Yes |

### Fingerprint

### Keywords

- Censoring
- Corrected score
- Mismeasured covariates
- Partial likelihood
- Proportional hazards
- Survival data

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Scandinavian Journal of Statistics*,

*29*(4), 637-655.

**Cox regression with covariate measurement error.** / Hu, Chengcheng; Lin, D. Y.

Research output: Contribution to journal › Article

*Scandinavian Journal of Statistics*, vol. 29, no. 4, pp. 637-655.

}

TY - JOUR

T1 - Cox regression with covariate measurement error

AU - Hu, Chengcheng

AU - Lin, D. Y.

PY - 2002/12

Y1 - 2002/12

N2 - This article deals with parameter estimation in the Cox proportional hazards model when covariates are measured with error. We consider both the classical additive measurement error model and a more general model which represents the mis-measured version of the covariate as an arbitrary linear function of the true covariate plus random noise. Only moment conditions are imposed on the distributions of the covariates and measurement error. Under the assumption that the covariates are measured precisely for a validation set, we develop a class of estimating equations for the vector-valued regression parameter by correcting the partial likelihood score function. The resultant estimators are proven to be consistent and asymptotically normal with easily estimated variances. Furthermore, a corrected version of the Breslow estimator for the cumulative hazard function is developed, which is shown to be uniformly consistent and, upon proper normalization, converges weakly to a zero-mean Gaussian process. Simulation studies indicate that the asymptotic approximations work well for practical sample sizes. The situation in which replicate measurements (instead of a validation set) are available is also studied.

AB - This article deals with parameter estimation in the Cox proportional hazards model when covariates are measured with error. We consider both the classical additive measurement error model and a more general model which represents the mis-measured version of the covariate as an arbitrary linear function of the true covariate plus random noise. Only moment conditions are imposed on the distributions of the covariates and measurement error. Under the assumption that the covariates are measured precisely for a validation set, we develop a class of estimating equations for the vector-valued regression parameter by correcting the partial likelihood score function. The resultant estimators are proven to be consistent and asymptotically normal with easily estimated variances. Furthermore, a corrected version of the Breslow estimator for the cumulative hazard function is developed, which is shown to be uniformly consistent and, upon proper normalization, converges weakly to a zero-mean Gaussian process. Simulation studies indicate that the asymptotic approximations work well for practical sample sizes. The situation in which replicate measurements (instead of a validation set) are available is also studied.

KW - Censoring

KW - Corrected score

KW - Mismeasured covariates

KW - Partial likelihood

KW - Proportional hazards

KW - Survival data

UR - http://www.scopus.com/inward/record.url?scp=0036901081&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036901081&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0036901081

VL - 29

SP - 637

EP - 655

JO - Scandinavian Journal of Statistics

JF - Scandinavian Journal of Statistics

SN - 0303-6898

IS - 4

ER -