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Maximum likelihood inference for the Cox regression model with applications to missing covariates

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  • Chen, Ming-Hui
  • Ibrahim, Joseph G.
  • Shao, Qi-Man

Abstract

In this paper, we carry out an in-depth theoretical investigation for existence of maximum likelihood estimates for the Cox model [D.R. Cox, Regression models and life tables (with discussion), Journal of the Royal Statistical Society, Series B 34 (1972) 187-220; D.R. Cox, Partial likelihood, Biometrika 62 (1975) 269-276] both in the full data setting as well as in the presence of missing covariate data. The main motivation for this work arises from missing data problems, where models can easily become difficult to estimate with certain missing data configurations or large missing data fractions. We establish necessary and sufficient conditions for existence of the maximum partial likelihood estimate (MPLE) for completely observed data (i.e., no missing data) settings as well as sufficient conditions for existence of the maximum likelihood estimate (MLE) for survival data with missing covariates via a profile likelihood method. Several theorems are given to establish these conditions. A real dataset from a cancer clinical trial is presented to further illustrate the proposed methodology.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:9:p:2018-2030
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    References listed on IDEAS

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    2. Chen M-H. & Ibrahim J.G. & Shao Q-M., 2004. "Propriety of the Posterior Distribution and Existence of the MLE for Regression Models With Covariates Missing at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 421-438, January.
    3. Ming-Hui Chen & Joseph G. Ibrahim & Qi-Man Shao, 2006. "Posterior propriety and computation for the Cox regression model with applications to missing covariates," Biometrika, Biometrika Trust, vol. 93(4), pages 791-807, December.
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    10. Amy H. Herring & Joseph G. Ibrahim & Stuart R. Lipsitz, 2004. "Non‐ignorable missing covariate data in survival analysis: a case‐study of an International Breast Cancer Study Group trial," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(2), pages 293-310, April.
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    2. Lubomír Štěpánek & Filip Habarta & Ivana Malá & Ladislav Štěpánek & Marie Nakládalová & Alena Boriková & Luboš Marek, 2023. "Machine Learning at the Service of Survival Analysis: Predictions Using Time-to-Event Decomposition and Classification Applied to a Decrease of Blood Antibodies against COVID-19," Mathematics, MDPI, vol. 11(4), pages 1-27, February.
    3. Peter A. F. Fraser‐Mackenzie & Tiejun Ma & Ming‐Chien Sung & Johnnie E. V. Johnson, 2019. "Let's Call it Quits: Break‐Even Effects in the Decision to Stop Taking Risks," Risk Analysis, John Wiley & Sons, vol. 39(7), pages 1560-1581, July.

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