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Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
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Mechanistic models are utilized in individual analysis using single-source data, but imperfections arise due to data collection errors, preventing perfect prediction of observed data. The mathematical equation involves known values (Xi), observed concentrations (Ci), measurement errors (εi), model parameters (ϕj), and the related function (ƒi) for i number of values. Different least-squares metrics quantify differences between predicted and observed values. The ordinary least...
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Longitudinal studies are also widely used in other medical and social science fields. For instance, in cardiovascular research, they can monitor patients' health over decades to identify risk factors for heart disease, such as high cholesterol or smoking, and evaluate the long-term effectiveness of preventive measures. Similarly, in mental health studies, researchers might follow individuals from adolescence into adulthood to understand the development and progression of conditions like...
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Generalized linear mixed hidden semi-Markov models in longitudinal settings: A Bayesian approach.

Saiedeh Haji-Maghsoudi1, Jan Bulla2,3, Majid Sadeghifar4

  • 1Department of Biostatistics, School of Public Health, Hamadan University of Medical Sciences, Hamadan, Iran.

Statistics in Medicine
|February 15, 2021
PubMed
Summary

This study introduces generalized linear mixed hidden semi-Markov models (GLM-HSMMs) for analyzing longitudinal data with complex dependencies. These models effectively handle time-varying unobserved heterogeneity and various response types, improving data analysis in fields like occupational health.

Keywords:
Bayesian estimationMonte Carlo Newton-Raphsongeneralized linear modelshidden Markov modelshidden semi-Markov models

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Area of Science:

  • Statistics
  • Biostatistics
  • Longitudinal Data Analysis

Background:

  • Hidden Markov and semi-Markov models (H(S)MMs) offer flexibility in modeling data with latent structures.
  • Generalized linear mixed models (GLMMs) are suitable for analyzing categorical and count-type longitudinal data.
  • Existing models may not fully capture time-varying unobserved heterogeneity in longitudinal responses.

Purpose of the Study:

  • To propose a novel statistical model, generalized linear mixed hidden semi-Markov models (GLM-HSMMs).
  • To integrate the strengths of H(S)MMs and GLMMs to handle complex longitudinal data.
  • To develop an estimation algorithm for the proposed GLM-HSMMs.

Main Methods:

  • Development of the GLM-HSMM framework, incorporating state-dependent random effects.
  • Parameter estimation using a Monte Carlo Newton-Raphson (MCNR)-like algorithm.
  • Application and validation through an occupational health case study and simulation studies.

Main Results:

  • The proposed GLM-HSMMs effectively model time-varying unobserved heterogeneity and diverse response types.
  • The MCNR-like algorithm provides a viable method for parameter estimation in these complex models.
  • The model demonstrates applicability in real-world scenarios, such as occupational health count data analysis.

Conclusions:

  • GLM-HSMMs offer a powerful and flexible approach for analyzing complex longitudinal data.
  • The proposed methodology enhances the analysis of data with latent dynamics and mixed effects.
  • The study validates the model's utility and the estimation algorithm's performance.