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

•Statistical models are presented that allow optimizing the replication strategy for the number of routine injections, sample preparations, and runs defined for the reportable value.•Confidence bounds can be tightened by including only variance contributions greater than 20% of the total variation.•...

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Bibliographic Details
Published in:Journal of pharmaceutical and biomedical analysis 2019-01, Vol.162, p.149-157
Main Authors: Burdick, Richard K., Ermer, Joachim
Format: Article
Language:English
Subjects:
Confidence interval on variance components
Data Accuracy
Data Interpretation, Statistical
Intermediate precision
Measurement systems analysis
Models, Statistical
Repeatability
Reproducibility of Results
Research Design - statistics & numerical data
Satterthwaite approximation
System precision
Technology, Pharmaceutical - methods
Technology, Pharmaceutical - statistics & numerical data
Uncertainty
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Summary:•Statistical models are presented that allow optimizing the replication strategy for the number of routine injections, sample preparations, and runs defined for the reportable value.•Confidence bounds can be tightened by including only variance contributions greater than 20% of the total variation.•Models have been developed for both a complete intermediate precision study, and a study where injection precision comes from an independent source.•An Excel spreadsheet that performs all the calculations is available from the authors.•A precision study is recommened with a minimum of six runs, two preparations per run, and two injections per preparation, in order to provide sufficient precision of the variance estimates. 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 es
ISSN:0731-7085
1873-264X
DOI:10.1016/j.jpba.2018.08.062