Large Sample Results for Frequentist Multiple Imputation for Cox Regression with Missing Covariate Data

Frank Eriksson, Torben Martinussen, Søren Feodor Nielsen

Research output: Contribution to journalJournal articleResearchpeer-review

Abstract

Incomplete information on explanatory variables is commonly encountered in studies of possibly censored event times. A popular approach to deal with partially observed covariates is multiple imputation, where a number of completed data sets, that can be analyzed by standard complete data methods, are obtained by imputing missing values from an appropriate distribution. We show how the combination of multiple imputations from a compatible model with suitably estimated parameters and the usual Cox regression estimators leads to consistent and asymptotically Gaussian estimators of both the finite-dimensional regression parameter and the infinite-dimensional cumulative baseline hazard parameter. We also derive a consistent estimator of the covariance operator. Simulation studies and an application to a study on survival after treatment for liver cirrhosis show that the estimators perform well with moderate sample sizes and indicate that iterating the multiple-imputation estimator increases the precision.
Original languageEnglish
JournalAnnals of the Institute of Statistical Mathematics
Number of pages28
ISSN0020-3157
DOIs
Publication statusPublished - 4 Apr 2019

Bibliographical note

Epub ahead of print. Published online: April 4, 2019

Keywords

  • Asymptotic distribution
  • Coarsened data
  • Semiparametric
  • Survival
  • Variance estimator

Cite this

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abstract = "Incomplete information on explanatory variables is commonly encountered in studies of possibly censored event times. A popular approach to deal with partially observed covariates is multiple imputation, where a number of completed data sets, that can be analyzed by standard complete data methods, are obtained by imputing missing values from an appropriate distribution. We show how the combination of multiple imputations from a compatible model with suitably estimated parameters and the usual Cox regression estimators leads to consistent and asymptotically Gaussian estimators of both the finite-dimensional regression parameter and the infinite-dimensional cumulative baseline hazard parameter. We also derive a consistent estimator of the covariance operator. Simulation studies and an application to a study on survival after treatment for liver cirrhosis show that the estimators perform well with moderate sample sizes and indicate that iterating the multiple-imputation estimator increases the precision.",
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Large Sample Results for Frequentist Multiple Imputation for Cox Regression with Missing Covariate Data. / Eriksson, Frank; Martinussen, Torben; Nielsen, Søren Feodor.

In: Annals of the Institute of Statistical Mathematics, 04.04.2019.

Research output: Contribution to journalJournal articleResearchpeer-review

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KW - Variance estimator

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