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Markov Chains with Measurement Error: Estimating the ‘True’ Course of a Marker of the Progression of Human Immunodeficiency Virus Disease

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  • Glen A. Satten
  • Ira M. Longini

Abstract

A Markov chain is a useful way of describing cohort data Longitudinal observations of a marker of the progression of the human immunodeficiency virus (HIV), such as CD4 cell count, measured on members of a cohort study, can be analysed as a continuous time Markov chain by categorizing the CD4 cell counts into stages. Unfortunately, CD4 cell counts are subject to substantial measurement error and short timescale variability. Thus, fitting a Markov chain to raw CD4 cell count measurements does not determine the transition probabilities for the true or underlying CD4 cell counts; the measurement error results in a process that is too rough. Assuming independent measurement errors, we propose a likelihood‐based method for estimating the 'true'or underlying transition probabilities. The Markov structure allows efficient calculation of the likelihood by using hidden Markov model methodology. As an example, we consider CD4 cell count data from 430 HIV‐infected participants in the San Francisco Men's Health Study by categorizing the marker data into seven stages; up to 17 observations are available for each individual. We find that including measurement error both produces a significantly better fit and provides a model for CD4 progression that is more biologically reasonable.

Suggested Citation

  • Glen A. Satten & Ira M. Longini, 1996. "Markov Chains with Measurement Error: Estimating the ‘True’ Course of a Marker of the Progression of Human Immunodeficiency Virus Disease," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 45(3), pages 275-295, September.
  • Handle: RePEc:bla:jorssc:v:45:y:1996:i:3:p:275-295
    DOI: 10.2307/2986089
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    Cited by:

    1. Joost van Rosmalen & Mehlika Toy & James F. O’Mahony, 2013. "A Mathematical Approach for Evaluating Markov Models in Continuous Time without Discrete-Event Simulation," Medical Decision Making, , vol. 33(6), pages 767-779, August.
    2. Hirji, Karim F. & Johnson, Timothy D., 1999. "Exact inference on stratified two-stage Markov chain models," Computational Statistics & Data Analysis, Elsevier, vol. 31(2), pages 159-186, August.
    3. Villacorta, Pablo J. & Verdegay, José L., 2016. "FuzzyStatProb: An R Package for the Estimation of Fuzzy Stationary Probabilities from a Sequence of Observations of an Unknown Markov Chain," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 71(i08).
    4. D. L. Hawkins & Chien-Pai Han, 2000. "Estimating Transition Probabilities from Aggregate Samples Plus Partial Transition Data," Biometrics, The International Biometric Society, vol. 56(3), pages 848-854, September.
    5. Ardo van den Hout & Ekaterina Ogurtsova & Jutta Gampe & Fiona Matthews, 2014. "Investigating healthy life expectancy using a multi-state model in the presence of missing data and misclassification," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 30(42), pages 1219-1244.
    6. Paul S. Albert, 1999. "A Mover–Stayer Model for Longitudinal Marker Data," Biometrics, The International Biometric Society, vol. 55(4), pages 1252-1257, December.
    7. Vernon T. Farewell & Li Su & Christopher Jackson, 2019. "Partially hidden multi-state modelling of a prolonged disease state defined by a composite outcome," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(4), pages 696-711, October.
    8. Ardo Hout & Graciela Muniz-Terrera, 2019. "Hidden three-state survival model for bivariate longitudinal count data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 25(3), pages 529-545, July.
    9. repec:jss:jstsof:38:i08 is not listed on IDEAS
    10. Spagnoli, Alessandra & Henderson, Robin & Boys, Richard J. & Houwing-Duistermaat, Jeanine J., 2011. "A hidden Markov model for informative dropout in longitudinal response data with crisis states," Statistics & Probability Letters, Elsevier, vol. 81(7), pages 730-738, July.

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