A hidden Markov model for continuous longitudinal data with missing responses and dropout

• Published in: Biometrical journal Vol. 65; no. 5; pp. e2200016 - n/a
• Main Authors: Pandolfi, Silvia, Bartolucci, Francesco, Pennoni, Fulvia
• Format: Journal Article
• Language: English
• Published: Germany Wiley - VCH Verlag GmbH & Co. KGaA 01.06.2023
• Subjects: Algorithms; Cholangitis; expectation‐maximization algorithm; forward–backward recursion; Independent variables; latent Markov model; Longitudinal studies; Markov analysis; Markov chains; missing values; Monte Carlo simulation; prediction; prediction; latent Markov model; expectation-maximization algorithm; forward-backward recursion; missing values
• ISSN: 0323-3847; 1521-4036; 1521-4036
• DOI: 10.1002/bimj.202200016

We propose a hidden Markov model for multivariate continuous longitudinal responses with covariates that accounts for three different types of missing pattern: (I) partially missing outcomes at a given time occasion, (II) completely missing outcomes at a given time occasion (intermittent pattern), and (III) dropout before the end of the period of observation (monotone pattern). The missing‐at‐random (MAR) assumption is formulated to deal with the first two types of missingness, while to account for the informative dropout, we rely on an extra absorbing state. Estimation of the model parameters is based on the maximum likelihood method that is implemented by an expectation‐maximization (EM) algorithm relying on suitable recursions. The proposal is illustrated by a Monte Carlo simulation study and an application based on historical data on primary biliary cholangitis.