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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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Physiological and compartmental models are valuable tools used in studying biological systems. These models rely on differential equations to maintain mass balance within the system, ensuring an accurate representation of the dynamic processes at play.
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This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
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Mechanistic models play a crucial role in algorithms for numerical problem-solving, particularly in nonlinear mixed effects modeling (NMEM). These models aim to minimize specific objective functions by evaluating various parameter estimates, leading to the development of systematic algorithms. In some cases, linearization techniques approximate the model using linear equations.
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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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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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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Bayesian model selection for multilevel models using integrated likelihoods.

Tom Edinburgh1, Ari Ercole2, Stephen Eglen1

  • 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, United Kingdom.

Plos One
|February 15, 2023
PubMed
Summary
This summary is machine-generated.

This study introduces a new Bayesian method for selecting the best multilevel linear model. The approach improves estimation consistency by reducing the dimensionality of sampling algorithms, making model comparison more reliable.

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Area of Science:

  • Statistics
  • Computational Statistics
  • Bayesian Inference

Background:

  • Multilevel linear models are essential for analyzing stratified data.
  • Model selection in complex hierarchical structures is challenging.
  • Bayesian model comparison using Bayes factors is standard but often computationally intractable.

Purpose of the Study:

  • To present a practical Bayesian framework for estimating log model evidence.
  • To improve the consistency and efficiency of model evidence estimation.
  • To demonstrate the application of the method on hierarchical data.

Main Methods:

  • Intermediate marginalization over non-variance parameters to reduce sampling dimensionality.
  • Application of Monte Carlo sampling techniques for estimation.
  • Illustration using simulated multilevel data and real-world radon concentration data.

Main Results:

  • The proposed method yields more consistent estimates of log model evidence.
  • Reduced dimensionality enhances the performance of Monte Carlo sampling.
  • The framework is shown to be effective in practice for hierarchical data.

Conclusions:

  • The presented method offers a robust approach to Bayesian model selection for multilevel data.
  • Intermediate marginalization is a key technique for improving computational efficiency.
  • The framework is validated on both simulated and real-world datasets.