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We propose an inferential approach for maximum likelihood estimation of thehidden Markov models for continuous responses. We extend to the case oflongitudinal observations the finite mixture model of multivariate Gaussiandistributions with Missing At Random (MAR) outcomes, also accounting forpossible dropout. The resulting hidden Markov model accounts for differenttypes of missing pattern: (i) partially missing outcomes at a given timeoccasion; (ii) completely missing outcomes at a given time occasion(intermittent pattern); (iii) dropout before the end of the period ofobservation (monotone pattern). The MAR assumption is formulated to deal withthe first two types of missingness, while to account for informative dropout weassume an extra absorbing state. Maximum likelihood estimation of the modelparameters is based on an extended Expectation-Maximization algorithm relyingon suitable recursions. The proposal is illustrated by a Monte Carlo simulationstudy and an application based on historical data on primary biliarycholangitis.

Maximum likelihood estimation of hidden Markov models for continuous longitudinal data with missing responses and dropout