Nonlinear perpendicular least-squares regression in pharmacodynamics

Area of Science:

• Pharmacodynamics
• Biostatistics
• Computational Biology

Background:

• Current nonlinear regression software often fails to account for measurement errors in both independent (e.g., drug concentration) and dependent (e.g., effect) variables.
• Pharmacodynamic modeling frequently encounters errors in both concentration and effect data, impacting parameter estimation accuracy.

Purpose of the Study:

• To introduce and evaluate a novel nonlinear regression method, perpendicular least squares (PLS), that addresses errors in both variables.
• To compare the performance of PLS against the traditional ordinary least squares (OLS) method in pharmacodynamic modeling.

Main Methods:

• Developed a Fortran program implementing PLS, minimizing the sum of squared perpendicular distances from data points to the fitted nonlinear curve.
• Utilized a Monte Carlo simulation with the sigmoidal Emax model to compare OLS and PLS methods.
• Assessed goodness of fit by measuring the area between the true pharmacodynamic relationship and the fitted curve.

Main Results:

• The PLS method demonstrated a 20.8% improvement over OLS in goodness of fit.
• Parameter estimates showed only small differences between OLS and PLS when random noise (standard deviation of five) affected both concentration and effect.
• PLS provides a more robust estimation of pharmacodynamic parameters when errors exist in both measured variables.

Conclusions:

• Perpendicular least squares (PLS) offers a more rational and accurate approach to nonlinear regression in pharmacodynamics by considering errors in both drug concentrations and effects.
• This improved method can lead to more reliable parameter estimates, enhancing the understanding of drug-effect relationships.