Estimation of pharmacokinetic parameters by orthogonal regression: comparison of four algorithms

The contribution of non-linear orthogonal regression for estimation of individual pharmacokinetic parameters when drug concentrations and sampling times are subject to error was studied. The first objective was to introduce and compare four numerical approaches that involve different degrees of approximation for parameter estimation by orthogonal regression. The second objective was to compare orthogonal with non-orthogonal regression. These evaluations were based on simulated data sets from 300 'subjects', thereby enabling precision and accuracy of parameter estimates to be determined. The pharmacokinetic model was a one-compartment open model with first-order absorption and elimination rates. The inter-individual coefficients of variation (CV) of the pharmacokinetic parameters were in the range 33-100%. Eight measurement-error models for times and concentrations (homo- or heteroscedastic with constant CV) were considered. Accuracy of the four algorithms was very close in almost all instances (typical bias, 1-4%). Precision showed three expected trends: root mean squared error (RMSE) increased when the residual error was larger or the number of observations was smaller, and it was highest for the absorption rate constant and common error variance. Overall, RMSE ranged from 5 to 40%. It was found that the simplest algorithm for othogonal regression performed as well as the more complicated approaches. Errors in sampling time resulted in an increased bias and imprecision in individual parameter estimates (especially for k(a) in our example) and in common error variance when the estimation method did not take into account these errors. In this situation, use of orthogonal regression resulted in smaller bias and better precision.