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Model Approaches for Pharmacokinetic Data: Distributed Parameter Models01:06

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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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Survival analysis is a statistical method used to study time-to-event data, where the "event" might represent outcomes like death, disease relapse, system failure, or recovery. A unique feature of survival data is censoring, which occurs when the event of interest has not been observed for some individuals during the study period. This requires specialized techniques to handle incomplete data effectively.
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Parametric survival analysis models survival data by assuming a specific probability distribution for the time until an event occurs. The Weibull and exponential distributions are two of the most commonly used methods in this context, due to their versatility and relatively straightforward application.
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Bayesian hierarchical modeling: an introduction and reassessment.

Myrthe Veenman1, Angelika M Stefan2, Julia M Haaf3

  • 1Leiden University, Wassenaarseweg 52, Leiden, Netherlands. myrthe.veenman@gmail.com.

Behavior Research Methods
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Summary

Psychologists are increasingly using Bayesian hierarchical models for repeated-measures designs. This guide offers best practices for model specification, interpretation, and common pitfalls, enhancing the use of these powerful statistical tools.

Keywords:
brmsrstanBayes factorMultilevelTutorial

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Area of Science:

  • Psychology
  • Statistics
  • Computational Statistics

Background:

  • Bayesian hierarchical modeling is gaining traction in psychology due to user-friendly tools.
  • These models effectively capture inter- and intraindividual variability, ideal for repeated-measures data.
  • Existing guidance often lacks comprehensive coverage of practical implementation and potential issues.

Purpose of the Study:

  • To provide psychologists with practical guidance on Bayesian hierarchical modeling.
  • To detail best practices for model specification, prior sensitivity analysis, and interpretation.
  • To highlight common pitfalls in model fitting and evaluation, including Bayes factor calculation.

Main Methods:

  • Review and synthesis of best practices in Bayesian hierarchical modeling.
  • Emphasis on prior specification, prior sensitivity analysis, and Bayes factor computation.
  • Demonstration of state-of-the-art software: Stan and brms.

Main Results:

  • A comprehensive overview of best practices for applying Bayesian hierarchical models in psychological research.
  • Identification of common challenges and strategies for overcoming them during model fitting and evaluation.
  • Practical examples using Stan and brms to illustrate key concepts.

Conclusions:

  • Bayesian hierarchical modeling offers significant advantages for analyzing psychological data, particularly repeated measures.
  • Adherence to best practices in specification, prior handling, and model evaluation is crucial for reliable results.
  • This guide aims to empower psychologists to effectively utilize Bayesian hierarchical models for robust scientific inquiry.