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Fitting nonlinear regression models with correlated errors to individual pharmacodynamic data using SAS software

R Bender¹, L Heinemann

¹Heinrich-Heine-University Düsseldorf, Department of Metabolic Diseases and Nutrition, Germany.

Journal of Pharmacokinetics and Biopharmaceutics

|February 1, 1995

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This study introduces a method for pharmacokinetic modeling that accounts for correlated errors, improving parameter estimation accuracy. The approach utilizes time series statistical software for fitting log-normal functions to response curves.

Area of Science:

Pharmacokinetics and Pharmacodynamics
Statistical Modeling
Biostatistics

Background:

Nonlinear regression, particularly nonlinear ordinary least squares, is standard in pharmacokinetic and pharmacodynamic (PK/PD) modeling.
The common assumption of independent errors is often violated in PK/PD data, yet this is frequently overlooked.
Ignoring error correlation leads to underestimated standard deviations of parameter estimates, impacting model reliability.

Purpose of the Study:

To present a method for fitting log-normal functions to individual response curves with correlated errors.
To address the computational challenges and need for careful implementation when accommodating correlated errors.
To provide a practical approach using statistical software for time series analysis.

Main Methods:

Related Experiment Videos

Utilized SAS/ETS procedure MODEL for fitting log-normal functions to data with correlated errors.
Developed a linear weighted least squares approach for estimating initial parameters in nonlinear iterative algorithms.
Employed Monte Carlo simulations to assess the method's adequacy and compare statistical properties with standard nonlinear least squares.

Main Results:

The proposed method successfully fits log-normal functions to response curves with correlated errors.
The linear weighted least squares approach provides adequate starting values for nonlinear algorithms.
Simulations demonstrated that accommodating correlated errors yields more accurate standard deviations for parameter estimates compared to ignoring them.

Conclusions:

The developed method offers a robust approach for PK/PD modeling when error structures are non-independent.
Accurate parameter estimation is crucial for reliable PK/PD model interpretation and application.
The method, illustrated with insulin time-action profiles, is valuable for analyzing complex biological data.