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Maximum Likelihood Methods for Cure Rate Models with Missing Covariates

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  • Ming‐Hui Chen
  • Joseph G. Ibrahim

Abstract

Summary. We propose maximum likelihood methods for parameter estimation for a novel class of semi‐parametric survival models with a cure fraction, in which the covariates are allowed to be missing. We allow the covariates to be either categorical or continuous and specify a parametric distribution for the covariates that is written as a sequence of one‐dimensional conditional distributions. We propose a novel EM algorithm for maximum likelihood estimation and derive standard errors by using Louis's formula (Louis, 1982, Journal of the Royal Statistical Society, Series B44, 226–233). Computational techniques using the Monte Carlo EM algorithm are discussed and implemented. A real data set involving a melanoma cancer clinical trial is examined in detail to demonstrate the methodology.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:biomet:v:57:y:2001:i:1:p:43-52
    DOI: 10.1111/j.0006-341X.2001.00043.x
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    References listed on IDEAS

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    1. Joseph G. Ibrahim & Ming-Hui Chen & Stuart R. Lipsitz, 1999. "Monte Carlo EM for Missing Covariates in Parametric Regression Models," Biometrics, The International Biometric Society, vol. 55(2), pages 591-596, June.
    2. Jane C. Lindsey & Louise M. Ryan, 1993. "A Three‐State Multiplicative Model for Rodent Tumorigenicity Experiments," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 42(2), pages 283-300, June.
    3. 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.
    4. W. R. Gilks & P. Wild, 1992. "Adaptive Rejection Sampling for Gibbs Sampling," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 41(2), pages 337-348, June.
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    Citations

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    Cited by:

    1. Elizabeth R. Brown & Joseph G. Ibrahim, 2003. "Bayesian Approaches to Joint Cure-Rate and Longitudinal Models with Applications to Cancer Vaccine Trials," Biometrics, The International Biometric Society, vol. 59(3), pages 686-693, September.
    2. Morbiducci, Marta & Nardi, Alessandra & Rossi, Carla, 2003. "Classification of "cured" individuals in survival analysis: the mixture approach to the diagnostic-prognostic problem," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 515-529, January.
    3. Qingxia Chen & Joseph G. Ibrahim, 2006. "Semiparametric Models for Missing Covariate and Response Data in Regression Models," Biometrics, The International Biometric Society, vol. 62(1), pages 177-184, March.
    4. N. Balakrishnan & M. V. Koutras & F. S. Milienos & S. Pal, 2016. "Piecewise Linear Approximations for Cure Rate Models and Associated Inferential Issues," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 937-966, December.
    5. 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.
    6. 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.
    7. Rodrigues, Josemar & Balakrishnan, N. & Cordeiro, Gauss M. & de Castro, Mário, 2011. "A unified view on lifetime distributions arising from selection mechanisms," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3311-3319, December.
    8. Lee, Min Cherng & Mitra, Robin, 2016. "Multiply imputing missing values in data sets with mixed measurement scales using a sequence of generalised linear models," Computational Statistics & Data Analysis, Elsevier, vol. 95(C), pages 24-38.

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