Mixed hidden Markov quantile regression models for longitudinal data with possibly incomplete sequences

Statistical Methods in Medical Research
Maria Francesca MarinoMarco Alfò

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.

References

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Citations

Jul 31, 2018·Biometrical Journal. Biometrische Zeitschrift·Giorgio E MontanariFrancesco Bartolucci
Jan 13, 2018·Multivariate Behavioral Research·Jingheng CaiXinyuan Song
Jul 30, 2020·Statistical Methods in Medical Research·Hefei LiuBaoxue Zhang
Jan 1, 2019·Journal of Applied Statistics·Huijuan MaHaoda Fu
Oct 17, 2018·Statistics in Medicine·Francesco Bartolucci, Alessio Farcomeni
Jun 23, 2021·Multivariate Behavioral Research·Antonello MaruottiMatteo Rizzolli

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Software Mentioned

lqmHMM

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