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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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    1. Vivekananda Roy & James P. Hobert, 2007. "Convergence rates and asymptotic standard errors for Markov chain Monte Carlo algorithms for Bayesian probit regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 607-623, September.
    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.
    4. Traci Leong & Stuart R. Lipsitz & Joseph G. Ibrahim, 2001. "Incomplete covariates in the Cox model with applications to biological marker data," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(4), pages 467-484.
    5. J. G. Ibrahim & S. R. Lipsitz & M.‐H. Chen, 1999. "Missing covariates in generalized linear models when the missing data mechanism is non‐ignorable," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 173-190.
    6. Ming‐Hui Chen & Joseph G. Ibrahim, 2001. "Maximum Likelihood Methods for Cure Rate Models with Missing Covariates," Biometrics, The International Biometric Society, vol. 57(1), pages 43-52, March.
    7. J. G. Booth & J. P. Hobert, 1999. "Maximizing generalized linear mixed model likelihoods with an automated Monte Carlo EM algorithm," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 265-285.
    8. 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.
    9. Lan Huang & Ming-Hui Chen & Joseph G. Ibrahim, 2005. "Bayesian Analysis for Generalized Linear Models with Nonignorably Missing Covariates," Biometrics, The International Biometric Society, vol. 61(3), pages 767-780, September.
    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.
    11. Amy H. Herring & Joseph G. Ibrahim & Stuart R. Lipsitz, 2002. "Frailty Models with Missing Covariates," Biometrics, The International Biometric Society, vol. 58(1), pages 98-109, March.
    12. Herring A. H & Ibrahim J. G, 2001. "Likelihood-Based Methods for Missing Covariates in the Cox Proportional Hazards Model," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 292-302, March.
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    2. 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.
    3. Mário de Castro & Ming‐Hui Chen & Yuanye Zhang & Anthony V. D'Amico, 2020. "A Bayesian multi‐risks survival (MRS) model in the presence of double censorings," Biometrics, The International Biometric Society, vol. 76(4), pages 1297-1309, December.

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