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

Alessandra Spagnoli (1) , Robin Henderson (2) , Richard J. Boys (2) , Jeanine J. Houwing-Duistermaat (3)

1 Dipartimento di Scienze Statistiche
2 Epidemiology of Ageing
3 Department of Medical Statistics and Bioinformatics

We adopt a hidden state approach for the analysis of longitudinal data subject to dropout. Motivated by two applied studies, we assume 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 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.

Mots clés: Change points; Monotonic missing data; Mixed models; Random effects; State space

Domaines: Bio-informatique [q-bio.QM]; Bio-Informatique, Biologie Systémique [q-bio.QM]

Alessandra Spagnoli, Robin Henderson, Richard J. Boys, Jeanine J. Houwing-Duistermaat. A hidden Markov model for informative dropout in longitudinal response data with crisis states. Statistics and Probability Letters, 2011, ⟨10.1016/j.spl.2011.02.005⟩. ⟨hal-00746102⟩