Calibration and Stability Analysis with a Simple Mixed Linear Model When the Experiment Is of a Split-Plot Type

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Abstract
A typical calibration problem in bioassay involves several known concentrations of an analyte, with replicate determinations of the analyte at each level of concentration. A straight-line regression between the replicate determinations of the analyte and the known concentrations is sought. Common practice in this situation is to obtain several determinations of one analyte at each consecutive concentration level, instead of running the experiment in a completely randomized fashion. A proper model for this type of calibration experiment is a simple mixed linear model with two sources of variation: between analyte concentrations, and within analyte concentrations (model A). However, a practitioner may use a model based on the average determination at each concentration of analyte (model B), or helshe may adopt a model that assumes a completely independent error structure (model C) to fit a straight line. The purpose of this article is to compare the analysis based on models B and C to the supposedly correct analysis based on model A. It is shown that the statistical analysis based on model B is equivalent to the one based on model A except for the estimation of individual variance components, Simulated data sets generated from model A under various parameter value combinations are analyzed to provide the summary of pelformance for both models B and C and to point out the shortcomings of the usual practices based on model C. Application to pharmaceutical stability analysis is also given.