A pseudo-partial likelihood method for semiparametric survival regression with covariate errors

David M. Zucker*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

42 Scopus citations


This article presents an estimator for the regression coefficient vector in the Cox proportional hazards model with covariate error. The estimator is obtained by maximizing a likelihood-type function similar to the Cox partial likelihood. The likelihood function involves the cumulative baseline hazard function, for which a simple estimator is substituted. The method is capable of handling general covariate error structures; it is not restricted to the independent additive error model. It can be applied to studies with either an external or internal validation sample, and also to studies with replicate measurements of the surrogate covariate. The estimator is shown to be consistent and asymptotically normal, and an estimate of the asymptotic covariance matrix is derived. Some extensions to general transformation survival models are indicated. Simulation studies are presented for a setup with a single error-prone binary covariate and a setup with a single error-prone normally distributed covariate. These simulation studies show that the method typically produces estimates with low bias and confidence intervals with accurate coverage rates. Efficiency results relative to fully parametric maximum likelihood are also presented. The method is applied to data from the Framingham Heart Study.

Original languageAmerican English
Pages (from-to)1264-1277
Number of pages14
JournalJournal of the American Statistical Association
Issue number472
StatePublished - Dec 2005

Bibliographical note

Funding Information:
David M. Zucker is Associate Professor, Department of Statistics, Hebrew University, Mt. Scopus, 91905 Jerusalem, Israel (E-mail: mszucker@mscc. huji.ac.il). The author thanks Donna Spiegelman for stimulating his interest in the area and for helpful input. The author also thanks the associate editor and referees for helpful comments leading to substantial improvements in the article. Finally, the author thanks the U.S. National Heart, Lung, and Blood Institute (NHLBI) for providing data from the Framingham Heart Study (FHS), which was conducted and supported by the NHLBI in collaboration with the FHS investigators. The article was not prepared in collaboration with the FHS investigators and does not necessarily reflect the opinions or views of the FHS or the NHLBI.


  • Cox model
  • Errors in variables
  • Proportional hazards
  • Proportional odds


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