Precision of the reportable value-Statistical optimization of the number of replicates

In pharmaceutical analysis, the precision of the reportable value, i.e. the result which is to be compared to the specification limit(s), is relevant for the suitability of the analytical procedure. Using the variance contributions determined in precision studies addressing the levels injection/system precision, repeatability, and intermediate precision, the number of the corresponding replications for analysis/injection, sample preparation, and series/runs can be varied to improve the precision of the mean (reportable) value (Ermer, Agut, J.Chromatogr. A, 1353 (2014) 71-77). However, this calculation will provide only information on the gain for the precision of the calculated reportable value itself. These so-called point estimators have uncertainty associated with them which can be quantified using statistical confidence intervals. Commonly used statistical equations only allow one to calculate confidence intervals for the intermediate precision of the reportable value, which requires that the routine replication strategy must be defined before starting the precision study. In this paper, statistical models are presented that allow optimizing efficiently the replication strategy with respect to the confidence interval of the precision based on the Satterthwaite approximation posterior, i.e. using the results from the precision study without prior knowledge, as for the point estimate. It is further proposed to simplify the model by including only significant variance contributions larger than 20% of the total variation. The advantage of this minimizing the level of nesting is that the upper precision bound will tighten as the level of nesting decreases. This is important as 90% upper confidence bounds are often up to 2 or 3 times the point estimate, even for a larger number of four runs in the precision study. Four models each have been developed both for a 2-fold balanced nested design representing a complete intermediate precision study, and for a 1-fold balanced nested design using injection/system precision from an independent source. An Excel spreadsheet that performs all the calculations in this paper as well as the appropriate model selection is available from the authors. Due to the usually rather low number of series/runs in precision studies, the uncertainty of the reportable value precision is often dominated by the factor runs. For a statistical evaluation of the precision of the reportable value (in case of three precision levels), the authors recommend a minimum of six runs, two preparations per run, and two injections/analyses per preparation, in order to provide sufficient precision of the variance estimates. However, a risk-based approach is recommended for the decision to apply a statistical evaluation of the precision of the reportable value. In case of low patient risk such as for an assay of a well-characterized drug substance with tightly controlled manufacturing and analytical variability dominating the specification range, a point estimator will usually be adequate to demonstrate the suitability of the analytical procedure.