Confidence and Prediction in Linear Mixed Models: Don’t Concatenate the Random Effects. Application in an Assay Qualification Study

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 of mean measured concentration, accuracy by Prediction Intervals 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, e.g. 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 paper 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 confidence and prediction intervals. 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.