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Confidence and Prediction in Linear Mixed Models: Do Not Concatenate the Random Effects. Application in an Assay Qualification Study

Version 2 2020-08-21, 18:12
Version 1 2020-06-02, 16:08
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posted on 2020-08-21, 18:12 authored by Bernard G. Francq, Dan Lin, Walter Hoyer

Abstract–In the pharmaceutical industry, all analytical methods must be shown to deliver unbiased and precise results. In an assay qualification or validation study, the trueness, accuracy, and intermediate precision are usually assessed by comparing the measured concentrations to their nominal levels. Trueness is assessed by using Confidence Intervals (CIs) of mean measured concentration, accuracy by Prediction Intervals (PIs) for a future measured concentration, and the intermediate precision by the total variance. ICH and USP guidelines alike request that all relevant sources of variability must be studied, for example, the effect of different technicians, the day-to-day variability or the use of multiple reagent lots. Those different random effects must be modeled as crossed, nested, or a combination of both; while concatenating them to simplify the model is often taken place. This article compares this simplified approach to a mixed model with the actual design. Our simulation study shows an under-estimation of the intermediate precision and, therefore, a substantial reduction of the CI and PI. The power for accuracy or trueness is consequently over-estimated when designing a new study. Two real datasets from assay validation study during vaccine development are used to illustrate the impact of such concatenation of random variables.

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