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Related Concept Videos

Pharmacodynamic Models: Linear Concentration–Effect Model01:15

Pharmacodynamic Models: Linear Concentration–Effect Model

The linear concentration–effect model, underpinned by the principle that pharmacological effect (E) is directly proportional to plasma drug concentration (C), emerges as a pivotal simplification of the Emax model for conditions where C is significantly less than EC50. This model portrays a linear trajectory of the concentration–effect relationship when drug levels are markedly below the EC50 threshold.Despite its inherent assumption of continuous effect augmentation with increasing drug...
Pharmacodynamic Models: Logarithmic Concentration–Effect Model01:15

Pharmacodynamic Models: Logarithmic Concentration–Effect Model

The log-linear model is a pharmacological framework used to describe the relationship between drug concentration and its effect. This model is particularly relevant when the observed effects range between 20% and 80% of the drug’s maximum effect (Emax), where a near-linear relationship is observed between the log of drug concentration and the measured effect. However, the log-linear model does not predict the maximum possible effect (Emax) or the effect at zero drug concentration, limiting its...
Mechanistic Models: Compartment Models in Individual and Population Analysis01:23

Mechanistic Models: Compartment Models in Individual and Population Analysis

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)...
Analysis Methods of Pharmacokinetic Data: Model and Model-Independent Approaches01:14

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Drug disposition in the body is a complex process and can be studied using two major approaches: the model and the model-independent approaches.
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The Integrated Rate Law: The Dependence of Concentration on Time02:39

The Integrated Rate Law: The Dependence of Concentration on Time

While the differential rate law relates the rate and concentrations of reactants, a second form of rate law called the integrated rate law relates concentrations of reactants and time. Integrated rate laws can be used to determine the amount of reactant or product present after a period of time or to estimate the time required for a reaction to proceed to a certain extent. For example, an integrated rate law helps determine the length of time a radioactive material must be stored for its...
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Model Approaches for Pharmacokinetic Data: Distributed Parameter Models

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Related Experiment Video

Updated: Jun 6, 2026

Improving Reproducibility to Meet Minimal Information for Studies of Extracellular Vesicles 2018 Guidelines in Nanoparticle Tracking Analysis
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Published on: November 17, 2021

Revisiting the relationship between reproducibility and concentration: a new, data-driven statistical model.

Stefan Ehling1, Paul Wehling2, Philip A Haselberger1

  • 1Abbott, 3300 Stelzer Road, Columbus, OH, 43219 USA.

Journal of AOAC International
|June 4, 2026
PubMed
Summary

A new model shows reproducibility relative standard deviation (RSDR) in nutritional analysis increases gradually with lower analyte concentration, outperforming the Horwitz equation for modern methods.

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Area of Science:

  • Analytical Chemistry
  • Chemometrics
  • Food Science

Background:

  • The Horwitz equation historically models reproducibility relative standard deviation (RSDR) vs. analyte concentration.
  • Modern analytical methods, especially for nutritional matrices, show better reproducibility than the Horwitz equation predicts.
  • A data-driven model is needed to reflect current analytical performance.

Purpose of the Study:

  • Develop and evaluate a new statistical model for the relationship between reproducibility standard deviation (sR) and analyte concentration (C).
  • Utilize a large dataset of 961 analyte-matrix combinations across 62 analytes.

Main Methods:

  • Reanalyzed published multi-laboratory study data.
  • Performed ordinary least squares regression on log-transformed sR and log-transformed C (mass fractions).
  • Employed an approach similar to previous dietary fiber data analysis.

Main Results:

  • A strong linear relationship (R² = 0.98) was found between log(sR) and log(C) across eight orders of magnitude.
  • RSDR increases gradually with decreasing concentration, generally below Horwitz equation predictions.
  • Deviations were mainly linked to specific analytical methods (e.g., AOAC 2014.08) and analytes.

Conclusions:

  • A linear relationship between log(sR) and log(C) effectively models reproducibility for modern analytical techniques in homogeneous nutritional matrices.
  • This empirical model accurately captures current performance but is not a method performance criterion.
  • The new model offers a more realistic representation of analytical precision compared to the Horwitz equation.