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Title: A non-homogeneous hidden Markov model for partially observed longitudinal responses Authors:  Maria Francesca Marino - University of Florence (Italy) [presenting]
Marco Alfo - University La Sapienza, Rome (Italy)
Abstract: Dropout represents a typical issue in longitudinal studies. If the mechanism that generates the missing data is non-ignorable, inference based only on the observed data may be severely biased. Therefore, it is worth to define a model that describes the dropout process and links this auxiliary model to the main one, entailing the longitudinal responses. A frequent strategy is based on using individual-specific random coefficients that help capture sources of unobserved heterogeneity and introduce a reasonable structure of dependence between the longitudinal and the missing data process. In this way, we model dependence within and between profiles from the same subject using two different, but correlated, sets of random coefficients. For the longitudinal outcome, we consider time-varying (discrete) random coefficients that evolve over time according to a non-homogeneous hidden Markov chain. The aim is to capture differential (possibly non-smooth) dynamics in the individual longitudinal profiles. For the missing data indicator, we consider time-constant (discrete) random coefficients to represent the effect of the individual-specific propensity to stay into the study. Dependence between profiles is described by an upper-level latent class variable that allows to connect the two sets of random coefficients.