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A hidden Markov model for informative dropout in longitudinal response data with crisis states

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  • Spagnoli, Alessandra
  • Henderson, Robin
  • Boys, Richard J.
  • Houwing-Duistermaat, Jeanine J.

Abstract

We adopt a hidden state approach for the analysis of longitudinal data subject to dropout. Motivated by two applied studies, we assume that subjects can move between three states: stable, crisis, dropout. Dropout is observed but the other two states are not. During a possibly transient crisis state both the longitudinal response distribution and the probability of dropout can differ from those for the stable state. We adopt a linear mixed effects model with subject-specific trajectories during stable periods and additional random jumps during crises. We place the model in the context of Rubin's taxonomy and develop the associated likelihood. The methods are illustrated using the two motivating examples.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:7:p:730-738
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    References listed on IDEAS

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    1. Geert Molenberghs & Caroline Beunckens & Cristina Sotto & Michael G. Kenward, 2008. "Every missingness not at random model has a missingness at random counterpart with equal fit," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(2), pages 371-388, April.
    2. Peter Diggle & Daniel Farewell & Robin Henderson, 2007. "Analysis of longitudinal data with drop‐out: objectives, assumptions and a proposal," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 56(5), pages 499-550, November.
    3. 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.
    4. Chantal Guihenneuc-Jouyaux & Sylvia Richardson & Ira M. Longini Jr., 2000. "Modeling Markers of Disease Progression by a Hidden Markov Process: Application to Characterizing CD4 Cell Decline," Biometrics, The International Biometric Society, vol. 56(3), pages 733-741, September.
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    Cited by:

    1. Antonello Maruotti, 2015. "Handling non-ignorable dropouts in longitudinal data: a conditional model based on a latent Markov heterogeneity structure," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 84-109, March.

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