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A note on fitting one-compartment models: non-linear least squares versus linear least squares using transformed

A J Bailer1, C J Portier

  • 1Department of Mathematics and Statistics, Miami University, Oxford, OH 45056.

Journal of Applied Toxicology : JAT
|August 1, 1990
PubMed
Summary

This study compares two methods for analyzing drug concentrations in one-compartment systems: non-linear regression and log-transformed linear regression. It highlights how data point selection impacts parameter estimation in pharmacokinetic modeling.

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Area of Science:

  • Pharmacokinetics
  • Mathematical Modeling
  • Biostatistics

Background:

  • Drug concentrations in one-compartment systems are often modeled using single exponential functions.
  • Accurate parameter estimation is crucial for understanding drug behavior in the body.

Purpose of the Study:

  • To compare non-linear least-squares regression and log-transformed linear least-squares regression for estimating parameters of single exponential models.
  • To analyze the influence of data points on parameter estimation in pharmacokinetic modeling.

Main Methods:

  • Non-linear least-squares regression applied to original concentration-time data.
  • Logarithmic transformation of concentration-time data followed by linear least-squares regression.
  • Analysis of data point influence and comparison of weighted vs. unweighted regression models.

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Main Results:

  • Log-transformed linear regression provides an approximation to weighted regression on the original scale.
  • Different fitting methods yield varying parameter estimates and data point influence.
  • An illustrative example demonstrates discrepancies between log-transformed and original-scale data fitting.

Conclusions:

  • Both non-linear and log-transformed linear regression are viable for pharmacokinetic modeling, but differ in their assumptions and results.
  • Understanding data point influence is critical for accurate parameter estimation.
  • The choice of method impacts the interpretation of drug concentration-time profiles.