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Population Pharmacodynamic Modeling Using the Sigmoid Emax Model: Influence of Inter-individual Variability on the
Johannes H Proost1,2, Douglas J Eleveld3, Michel M R F Struys3,4
1Department of Anesthesiology, University Medical Center Groningen, University of Groningen, Hanzeplein 1, 9713 GZ, Groningen, the Netherlands. j.h.proost@umcg.nl.
The steepness of drug concentration-effect relationships is influenced by inter-individual variability (IIV). Population modeling may underestimate this steepness, impacting drug effect predictions.
Area of Science:
- Pharmacology
- Mathematical Modeling
- Biostatistics
Background:
- Drug concentration-effect relationships are often modeled empirically.
- The sigmoid Emax model is commonly used to describe these relationships.
- Inter-individual variability (IIV) in model parameters can affect predictions.
Purpose of the Study:
- To investigate the relationship between concentration-effect steepness and IIV in sigmoid Emax model parameters.
- To assess the accuracy of population modeling in estimating IIV.
- To derive and validate an equation for population-predicted concentration-effect steepness.
Main Methods:
- Simulated multiple data sets with varying model parameters and IIV.
- Analyzed data using Excel Solver and NONMEM.
- Derived an empirical equation relating population steepness (γ*) to individual steepness (γ) and IIV.
- Validated the equation for binary and continuous data.
Main Results:
- The tested study design had insufficient precision for estimating IIV in C50 and γ.
- Population estimates of steepness (γ*) were significantly lower than simulated individual steepness (γ).
- The population-predicted concentration-effect relationship (γ*) is less steep than individual relationships (γ).
Conclusions:
- Population modeling may underestimate the steepness of concentration-effect relationships due to IIV.
- The derived equation (Eq. (11)) describes population-predicted steepness (γ*) based on individual steepness (γ) and IIV.
- Population-predicted drug effect, using γ*, represents the average effect or probability of effect at a given concentration.
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