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Cox Regression with Incomplete Covariate Measurements using the EM‐algorithm

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  • Torben Martinussen

Abstract

Ibrahim (1990) used the EM‐algorithm to obtain maximum likelihood estimates of the regression parameters in generalized linear models with partially missing covariates. The technique was termed EM by the method of weights. In this paper, we generalize this technique to Cox regression analysis with missing values in the covariates. We specify a full model letting the unobserved covariate values be random and then maximize the observed likelihood. The asymptotic covariance matrix is estimated by the inverse information matrix. The missing data are allowed to be missing at random but also the non‐ignorable non‐response situation may in principle be considered. Simulation studies indicate that the proposed method is more efficient than the method suggested by Paik & Tsai (1997). We apply the procedure to a clinical trials example with six covariates with three of them having missing values.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:scjsta:v:26:y:1999:i:4:p:479-491
    DOI: 10.1111/1467-9469.00163
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    Cited by:

    1. Torben Martinussen & Klaus K. Holst & Thomas H. Scheike, 2016. "Cox regression with missing covariate data using a modified partial likelihood method," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(4), pages 570-588, October.
    2. Richard J. Cook & Jerald F. Lawless & Bingfeng Xie, 2022. "Marker-dependent observation and carry-forward of internal covariates in Cox regression," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 28(4), pages 560-584, October.
    3. S. Eftekhari Mahabadi & M. Ganjali, 2012. "An index of local sensitivity to non-ignorability for parametric survival models with potential non-random missing covariate: an application to the SEER cancer registry data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(11), pages 2327-2348, July.
    4. Chengcheng Hu & Victor De Gruttola, 2007. "Joint Modeling of Progression of HIV Resistance Mutations Measured with Uncertainty and Failure Time Data," Biometrics, The International Biometric Society, vol. 63(1), pages 60-68, March.
    5. J. F. Lawless, 2018. "Two-phase outcome-dependent studies for failure times and testing for effects of expensive covariates," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 24(1), pages 28-44, January.
    6. 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.
    7. Amélie Detais & Jean-François Dupuy, 2011. "Maximum likelihood estimation in a partially observed stratified regression model with censored data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(6), pages 1183-1206, December.
    8. Chen, Ming-Hui & Ibrahim, Joseph G. & Shao, Qi-Man, 2009. "Maximum likelihood inference for the Cox regression model with applications to missing covariates," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2018-2030, October.

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