Preliminary testing in a class of simple non-linear mixed models to improve estimation accuracy

Abstract

In applied research hypothetical information about the parameters in a stochastic model sometimes can be generated from theory or previous studies. Replacing unknown parameters by constants might increase the estimation accuracy. This is especially apparent when replacing parameters in non-linear expressions. The problem is how to handle the uncertainty of the hypothetical information. Here, a pretest procedure will be examined for an unknown exponent of the explanatory variable in a simple non-linear mixed model. The optimal pretest sizes for some parameter settings are found for a minimax regret criterion based on Mean-Squared-Error. The optimal test sizes were found to be approximately valid also for the case where no subject specific components are present. The examined class of models is useful for modelling concentration-time data for drugs with rapid absorption, and a small-sample example is given to illustrate the potential gain in estimation accuracy of the pretest approach in pharmacokinetics.