2013/06/07 by Francesco Bartolucci, Bartolucci, Francesco, Alessio Farcomeni +1
Mathematics · #FOS: Mathematics #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1306.1678
arxiv created 2013/06/07 · arxiv updated 2013/06/10
Latent Markov (LM) models represent an important tool of analysis of longitudinal data when response variables are affected by time-varying unobserved heterogeneity, which is accounted for by a hidden Markov chain. In order to avoid bias when using a model of this type in the presence of informative drop-out, we propose an event-history (EH) extension of the LM approach that may be used with multivariate longitudinal data, in which one or more outcomes of a different nature are observed at each time occasion. The EH component of the resulting model is referred to the interval-censored drop-out, and bias in LM modeling is avoided by correlated random effects, included in the different model components, which follow a common Markov chain. In order to perform maximum likelihood estimation of the proposed model by the Expectation-Maximization algorithm, we extend the usual backward-forward recursions of Baum and Welch. The algorithm has the same complexity of the one adopted in cases of non-informative drop-out. Standard errors for the parameter estimates are derived by using the Oakes' identity. We illustrate the proposed approach through an application based on data coming from a medical study about primary biliary cirrhosis in which there are two outcomes of interest, the first of which is continuous and the second is binary.