Influence of Random Effects Incorporated in the Analysis of Pharmacological Data Based on a Four-parameter Logistic Model

In the later phases of selecting candidate chemicals for drug development, pharmacological experiments are conducted using animal organs or human peripheral blood cells. In these experiments, data analysis is often performed on the basis of mixed-effect models so that the individuality effect can be incorporated in the dose-response relationship. This paper studied the influence of the incorporation of random effects on parameters in a logistic model intended for analysis, with the assumption that the dose-response relationship is really described by a four-parameter logistic model. Using Monte-Carlo simulation experiments, we compared the performances of eight models in which various mixed-effects were incorporated. In each of the eight analysis models, five methods of calculation, namely, the standard two-stage method (STS), first-order approximation method (FOA), Laplacian approximation method (LAP), Monte Carlo integration method (MCI), and Gaussian quadrature method (GAU), were applied to the simulation data. The eight analysis models and five estimation methods were compared, using estimability and the deviation of estimates from the true value as the criteria. The results revealed the analysis model incorporating the random effect on only the maximum response to be the best. The results also indicated that the FOA, LAP, MCI, and GAU methods had almost the same performances for this analysis model. The authors recommend LAP as the preferred method because of the simplicity of its calculation.