NONLINEAR PERPENDICULAR LEAST-SQUARES REGRESSION IN PHARMACODYNAMICS

Currently available software for nonlinear regression does not account for errors in both the independent and the dependent variables. In ph armacodynamics, measurement errors are involved in the drug concentrat ions as well as in the effects. Instead of minimizing the sum of squar ed vertical errors (OLS), a Fortran program was written to find the cl osest distance from a measured data point to the tangent line of an es timated nonlinear curve and to minimize tile sum of squared perpendicu lar distances (PLS). A Monte Carlo simulation was conducted with the s igmoidal E-max model to compare the OLS and PLS methods. The area betw een the true pharmacodynamic relationship and the fitted curve was com pared as a measure of goodness of fit. The PLS demonstrated an improve ment over the OLS by 20.8% with small differences in the parameter est imates when the random noise level had a standard deviation of five fo r both concentration and effect. Consideration of errors in both conce ntrations and effects with the PLS could lead to a more rational estim ation of pharmacodynamic parameters. (C) 1997 John Wiley & Sons, Ltd.