Random-Effect Models in Nonlinear Regression with Applications to Bioassay

Abstract

SUMMARY Transformation and weighting techniques are applied to dose-response curve models. In particular, weighting methods derived from a controlled-variable, random-effect model and a closely related random-coefficient model are studied. These two models correspond to additive and multiplicative effects of variations in the dose, and both lead to variance components proportional to the square of the derivative of the response function with respect to dose. When the dose-response curve is nonlinear in dose, the variance components are typically identifiable even without replicate measurements of dose. In a bioassay example the fit of a logistic model is studied. The transform-both-sides technique with a power transformation is shown to give a vast improvement in fit, compared to the analysis with no transformation and no weighting, and it also gives considerably better estimates of the parameters in the logistic function. For the data set studied, a significant further improvement in the fit is possible by use of the random-effect models.