title: Mixed hidden Markov quantile regression models for longitudinal data with possibly incomplete sequences.
abstract: Quantile regression provides a detailed and robust picture of the distribution of a response variable, conditional on a set of observed covariates. Recently, it has be been extended to the analysis of longitudinal continuous outcomes using either time-constant or time-varying random parameters. However, in real-life data, we frequently observe both temporal shocks in the overall trend and individual-specific heterogeneity in model parameters. A benchmark dataset on HIV progression gives a clear example. Here, the evolution of the CD4 log counts exhibits both sudden temporal changes in the overall trend and heterogeneity in the effect of the time since seroconversion on the response dynamics. To accommodate such situations, we propose a quantile regression model, where time-varying and time-constant random coefficients are jointly considered. Since observed data may be incomplete due to early drop-out, we also extend the proposed model in a pattern mixture perspective. We assess the performance of the proposals via a large-scale simulation study and the analysis of the CD4 count data.
authors.affiliation: 1 Department of Political Science, University of Perugia, Perugia, Italy.
authors.forename: Maria Francesca
authors.initials: MF
authors.lastname: Marino
authors.affiliation: 2 Department of Social Statistics and Demography, Southampton Statistical Sciences Research Institute, Southampton University, Southampton, UK.
authors.forename: Nikos
authors.initials: N
authors.lastname: Tzavidis
authors.affiliation: 3 Department of Statistics, Sapienza University of Rome, Rome, Italy.
authors.forename: Marco
authors.initials: M
authors.lastname: Alfò
mesh_terms: D000465:Algorithms; D018791:CD4 Lymphocyte Count / Q000706:statistics & numerical data; D003627:Data Interpretation, Statistical; D015658:HIV Infections / Q000378:metabolism; D006801:Humans; D016013:Likelihood Functions; D008137:Longitudinal Studies; D008390:Markov Chains; D012044:Regression Analysis
keywords: Latent Markov models; informative drop-out; latent drop-out classes; missing data; mixed models; non-parametric maximum likelihood