Finite Mixtures of Hidden Markov Models for Longitudinal Responses Subject to Drop out |
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Authors: | Maria Francesca Marino Marco Alfò |
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Institution: | 1. Dipartimento di Statistica, Informatica, Applicazioni, Università degli Studi di Firenze;2. mariafrancesca.marino@unifi.it;4. Dipartimento di Scienze Statistiche, “Sapienza” Università di Roma |
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Abstract: | AbstractDrop out is a typical issue in longitudinal studies. When the missingness is non-ignorable, inference based on the observed data only may be biased. This paper is motivated by the Leiden 85+ study, a longitudinal study conducted to analyze the dynamics of cognitive functioning in the elderly. We account for dependence between longitudinal responses from the same subject using time-varying random effects associated with a heterogeneous hidden Markov chain. As several participants in the study drop out prematurely, we introduce a further random effect model to describe the missing data mechanism. The potential dependence between the random effects in the two equations (and, therefore, between the two processes) is introduced through a joint distribution specified via a latent structure approach. The application of the proposal to data from the Leiden 85+ study shows its effectiveness in modeling heterogeneous longitudinal patterns, possibly influenced by the missing data process. Results from a sensitivity analysis show the robustness of the estimates with respect to misspecification of the missing data mechanism. A simulation study provides evidence for the reliability of the inferential conclusions drawn from the analysis of the Leiden 85+ data. |
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Keywords: | Latent Markov models informative missingness sensitivity analysis random effects repeated observations |
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