Nonlinear perpendicular least-squares regression in pharmacodynamics

✍ Scribed by Hui C. Ko; William J. Jusko; William F. Ebling

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 199 KB
• Volume: 18
• Category: Article
• ISSN: 0142-2782
• DOI: 10.1002/(sici)1099-081x(199711)18:8<711::aid-bdd55>3.0.co;2-x

✦ Synopsis

Currently available software for nonlinear regression does not account for errors in both the independent and the dependent variables. In pharmacodynamics, measurement errors are involved in the drug concentrations as well as in the eects. Instead of minimizing the sum of squared vertical errors (OLS), a Fortran program was written to ®nd the closest distance from a measured data point to the tangent line of an estimated nonlinear curve and to minimize the sum of squared perpendicular distances (PLS). A Monte Carlo simulation was conducted with the sigmoidal E max model to compare the OLS and PLS methods. The area between the true pharmacodynamic relationship and the ®tted curve was compared as a measure of goodness of ®t. The PLS demonstrated an improvement over the OLS by 20´8% with small dierences in the parameter estimates when the random noise level had a standard deviation of ®ve for both concentration and eect. Consideration of errors in both concentrations and eects with the PLS could lead to a more rational estimation of pharmacodynamic parameters.