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Cox regression with missing covariate data using a modified partial likelihood method

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Listed:
  • Torben Martinussen

    (University of Copenhagen)

  • Klaus K. Holst

    (University of Copenhagen)

  • Thomas H. Scheike

    (University of Copenhagen)

Abstract

Missing covariate values is a common problem in survival analysis. In this paper we propose a novel method for the Cox regression model that is close to maximum likelihood but avoids the use of the EM-algorithm. It exploits that the observed hazard function is multiplicative in the baseline hazard function with the idea being to profile out this function before carrying out the estimation of the parameter of interest. In this step one uses a Breslow type estimator to estimate the cumulative baseline hazard function. We focus on the situation where the observed covariates are categorical which allows us to calculate estimators without having to assume anything about the distribution of the covariates. We show that the proposed estimator is consistent and asymptotically normal, and derive a consistent estimator of the variance–covariance matrix that does not involve any choice of a perturbation parameter. Moderate sample size performance of the estimators is investigated via simulation and by application to a real data example.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:lifeda:v:22:y:2016:i:4:d:10.1007_s10985-015-9351-y
    DOI: 10.1007/s10985-015-9351-y
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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. Zucker, David M., 2005. "A PseudoPartial Likelihood Method for Semiparametric Survival Regression With Covariate Errors," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1264-1277, December.
    3. C. Y. Wang & Hua Yun Chen, 2001. "Augmented Inverse Probability Weighted Estimator for Cox Missing Covariate Regression," Biometrics, The International Biometric Society, vol. 57(2), pages 414-419, June.
    4. 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.
    5. Xu, Qiang & Paik, Myunghee Cho & Luo, Xiaodong & Tsai, Wei-Yann, 2009. "Reweighting Estimators for Cox Regression With Missing Covariates," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1155-1167.
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