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A correlated random effects model for non-homogeneous Markov processes with nonignorable missingness

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  • Chen, Baojiang
  • Zhou, Xiao-Hua

Abstract

Life history data arising in clusters with pre-specified assessment time points for patients often feature incomplete data since patients may choose to visit the clinic based on their needs. Markov process models provide a useful tool describing disease progression for life history data. The literature mainly focuses on time homogeneous process. In this paper we develop methods to deal with non-homogeneous Markov process with incomplete clustered life history data. A correlated random effects model is developed to deal with the nonignorable missingness, and a time transformation is employed to address the non-homogeneity in the transition model. Maximum likelihood estimate based on the Monte-Carlo EM algorithm is advocated for parameter estimation. Simulation studies demonstrate that the proposed method works well in many situations. We also apply this method to an Alzheimer’s disease study.

Suggested Citation

  • Chen, Baojiang & Zhou, Xiao-Hua, 2013. "A correlated random effects model for non-homogeneous Markov processes with nonignorable missingness," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 1-13.
    • Handle: RePEc:eee:jmvana:v:117:y:2013:i:c:p:1-13
    DOI: 10.1016/j.jmva.2013.01.009
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    References listed on IDEAS

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    1. Richard J. Cook & Grace Y. Yi & Ker-Ai Lee & Dafna D. Gladman, 2004. "A Conditional Markov Model for Clustered Progressive Multistate Processes under Incomplete Observation," Biometrics, The International Biometric Society, vol. 60(2), pages 436-443, June.
    2. Richard J. Cook & Leilei Zeng & Ker-Ai Lee, 2008. "A Multistate Model for Bivariate Interval-Censored Failure Time Data," Biometrics, The International Biometric Society, vol. 64(4), pages 1100-1109, December.
    3. Rafael Pérez‐Ocón & Juan Eloy Ruiz‐Castro & M. Luz Gámiz‐Pérez, 2001. "Non‐homogeneous Markov models in the analysis of survival after breast cancer," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 50(1), pages 111-124.
    4. Burton Singer & Seymour Spilerman, 1976. "Some Methodological Issues in the Analysis of Longitudinal Surveys," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 5, number 4, pages 447-474, National Bureau of Economic Research, Inc.
    5. R. A. Hubbard & L. Y. T. Inoue & J. R. Fann, 2008. "Modeling Nonhomogeneous Markov Processes via Time Transformation," Biometrics, The International Biometric Society, vol. 64(3), pages 843-850, September.
    6. William B. Goggins & Dianne M. Finkelstein & Alan M. Zaslavsky, 1999. "Applying the Cox Proportional Hazards Model When the Change Time of a Binary Time-Varying Covariate Is Interval Censored," Biometrics, The International Biometric Society, vol. 55(2), pages 445-451, June.
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    Cited by:

    1. Giorgos Bakoyannis, 2021. "Nonparametric analysis of nonhomogeneous multistate processes with clustered observations," Biometrics, The International Biometric Society, vol. 77(2), pages 533-546, June.
    2. Jane M. Lange & Rebecca A. Hubbard & Lurdes Y. T. Inoue & Vladimir N. Minin, 2015. "A joint model for multistate disease processes and random informative observation times, with applications to electronic medical records data," Biometrics, The International Biometric Society, vol. 71(1), pages 90-101, March.
    3. Saligrama Agnihothri & Leon Cui & Mohammad Delasay & Balaraman Rajan, 2020. "The value of mHealth for managing chronic conditions," Health Care Management Science, Springer, vol. 23(2), pages 185-202, June.

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