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Large sample results for frequentist multiple imputation for Cox regression with missing covariate data

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  • Frank Eriksson

    (University of Copenhagen)

  • Torben Martinussen

    (University of Copenhagen)

  • Søren Feodor Nielsen

    (Copenhagen Business School)

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.

Suggested Citation

  • Frank Eriksson & Torben Martinussen & Søren Feodor Nielsen, 2020. "Large sample results for frequentist multiple imputation for Cox regression with missing covariate data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(4), pages 969-996, August.
    • Handle: RePEc:spr:aistmt:v:72:y:2020:i:4:d:10.1007_s10463-019-00716-4
    DOI: 10.1007/s10463-019-00716-4
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    References listed on IDEAS

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    1. Qi, Lihong & Wang, C.Y. & Prentice, Ross L., 2005. "Weighted Estimators for Proportional Hazards Regression With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1250-1263, December.
    2. Chen H.Y., 2002. "Double-Semiparametric Method for Missing Covariates in Cox Regression Models," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 565-576, June.
    3. Torben Martinussen, 1999. "Cox Regression with Incomplete Covariate Measurements using the EM‐algorithm," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(4), pages 479-491, December.
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