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Related Concept Videos

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving01:29

Mechanistic Models: Compartment Models in Algorithms for Numerical Problem Solving

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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Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

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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 squares (OLS)...
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One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation

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Pharmacodynamic Models: Emax Drug–Concentration Effect Model01:18

Pharmacodynamic Models: Emax Drug–Concentration Effect Model

The Emax drug-concentration effect model is central to pharmacodynamics in drug discovery and development. This model is predicated on the receptor occupancy theory, which posits that the effect of a drug is directly related to the number of receptors occupied by the drug and the resultant complex formation.The model describes the reversible interaction between a drug (C) and a receptor (R) to form a drug-receptor complex (RC). The kinetics of this interaction are quantified by an equation that...
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Optimizing growth media enhances microbial proliferation and maximizes product yield. Statistical experimental design methodologies provide structured and reproducible approaches, offering progressively higher levels of robustness and efficiency.The One-Factor-at-a-Time (OFAT) MethodThe One-Factor-at-a-Time (OFAT) method involves adjusting a single variable while keeping all others constant. However, it cannot detect interactions between variables, often leading to suboptimal outcomes when...
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Development of an Individual-Tree Basal Area Increment Model using a Linear Mixed-Effects Approach
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Published on: July 3, 2020

Nonlinear Random Effects Mixture Models: Maximum Likelihood Estimation via the EM Algorithm.

Xiaoning Wang1, Alan Schumitzky, David Z D'Argenio

  • 1Department of Biomedical Engineering, University of Southern California, Los Angeles, CA 90089, USA.

Computational Statistics & Data Analysis
|September 17, 2009
PubMed
Summary
This summary is machine-generated.

This study introduces a new statistical model for analyzing complex biological data, improving the identification of genetic variations affecting drug responses. The method enhances precision without simplifying the model, offering a flexible approach for pharmacokinetic/pharmacodynamic research.

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Area of Science:

  • Pharmacometrics
  • Statistical Modeling
  • Population Pharmacokinetics/Pharmacodynamics

Background:

  • Identifying genetic polymorphisms influencing pharmacokinetic/pharmacodynamic (PK/PD) phenotypes is crucial for personalized medicine.
  • Existing methods may involve model linearization, potentially losing information or introducing bias.
  • Finite mixture structures within nonlinear random effects models offer a powerful framework for capturing heterogeneity in PK/PD data.

Purpose of the Study:

  • To develop and evaluate a novel nonlinear random effects mixture model for identifying PK/PD phenotype polymorphisms.
  • To implement an expectation-maximization (EM) algorithm using sampling-based methods for maximum likelihood estimation.
  • To demonstrate the model's feasibility and performance through a detailed simulation study.

Main Methods:

  • Developed a nonlinear random effects model incorporating finite mixture structures.
  • Employed an EM algorithm for maximum likelihood estimation.
  • Utilized sampling-based methods for the expectation step, enabling an analytically tractable maximization step without model linearization.

Main Results:

  • The proposed estimation approach is feasible and performs well, as illustrated by a detailed simulation study.
  • The method avoids model linearization, preserving model complexity.
  • Estimation precision can be controlled by adjusting the sampling process.

Conclusions:

  • The developed nonlinear random effects mixture model provides a robust and flexible approach for PK/PD phenotype analysis.
  • The sampling-based EM algorithm facilitates estimation without compromising model structure.
  • Future applications to diverse population PK/PD problems are warranted.