ANOVA - a robust statistical tool for determining intermediate precision in analytical method validation

In the pharmaceutical industries, validation of analytical methods is a critical process that confirms the reliability and appropriateness of a method for its intended application. Method validation assures that the results consistently meet predefined precision, accuracy, and reproducibility criteria. The precision expresses, under the specified conditions, the closeness of agreement between a series of measurements from several samplings of the same homogenous sample. Usually, precision is discussed at three levels: repeatability, intermediate precision, and reproducibility. Repeatability expresses the precision under the same operating conditions over a short interval, whereas reproducibility expresses the precision between laboratories. Within-labs variations are expressed by intermediate precision. Other validation parameters such as accuracy, specificity, detection limit, quantitation limit, range, linearity, and robustness are not discussed here, as they fall beyond the scope of this article.

Repeatability and reproducibility are expressed in terms of standard deviation (SD) and are dependent on concentrations of analytes. According to USP (United States Pharmacopeia), a precision study provides information on the method variability. Hence, the study should include the components of ‘between run’ and ‘within-run’ variability. USP suggests that each run should be independent of the others and determine confidence intervals of the mean to interpret the data. ICH (International Council for Harmonisation) does not define intermediate precision conditions of measurement, however, the International Vocabulary of Metrology (VIM)  provides a useful definition: “a set of conditions that includes the same measurement procedure, same location and replicate measurements on the same or similar objects over an extended period, but may include other conditions involving changes”.

Robustness and ruggedness
Two other terms generally used in analytical method validation closely related to intermediate precision are robustness and ruggedness. These terms can be confusing. Guidance document-validation of analytical methods of Indian Pharmacopoeia Commission equated intermediate precision with ruggedness. The ICH defines ruggedness as the degree to which an analytical method's test results are reproducible when analyzed under a variety of conditions. Eurachem considers ruggedness as a synonym for robustness and defines it as a measure of how well a method can produce reproducible results when conditions vary between laboratories, analysts, instruments, or reagents. The ICH treats both ruggedness and robustness as synonyms, as the Eurachem treats them. However, the USP distinguishes between robustness and ruggedness. The USP defines ruggedness as - “the ruggedness of an analytical method is the degree of reproducibility of test results obtained by the analysis of the same sample under a variety of normal test conditions, such as different labs, different analysts, different instruments, different lots of reagents, different elapsed assay times, different assay temperatures, different days, etc.” This definition is equivalent to that of intermediate precision. The USP definition of robustness is - “the robustness of an analytical procedure is a measure of its capacity to remain unaffected by small, but deliberate variations in method parameters and provides an indication of its reliability during normal usage”. This definition equals to ICH definition of it.

Intermediate precision
Intermediate precision estimates are most commonly determined within laboratories but may also be determined by interlaboratory study. ICH recommends establishing the effects of random events (days, environmental conditions, analysts, reagents, calibration, equipment, etc.) on the precision of the analytical procedure. The ICH emphasizes the justification of tested variations on understanding analytical procedures and risk assessment is fundamental to effective method validation. A risk-based approach to analytical method validation is a strategic way to focus resources and attention on the most critical factors that could affect the performance of the analytical procedure. However, studying these effects individually is not necessary. According to ISO 5725:1986, for selecting factors for variation, the larger effects should be varied where possible.

Krause in his book titled, ‘Validation of Analytical Methods for Biopharmaceuticals - A Guide to Risk-based Validation and Implementation Strategies’, stated that intermediate precision represents the to-be-expected laboratory reliability at any given day, and reflects the true relationship between process capability and analytical capability. Intermediate precision results can be generated as a full or partial factorial design by analytical chemists, days, instruments, and other critical factors as identified during the analytical method development studies.

According to the guidance document of the Indian Pharmacopoeia Commission on validation of analytical methods, ‘Intermediate precision (within-laboratory variation) will be demonstrated by two analysts, using two HPLC systems on different days and evaluating the relative percent purity data across three concentration levels (50%, 100%, and 150%) that cover the analyte assay method range 80% to 120%’. To ensure the precision of a method for major analytes, the Relative Standard Deviation (RSD) should be =2%. For low-level impurities, RSD of 5-10% is acceptable. Japan has specific requirements for intermediate precision. For assay and quantitative impurities, the analysis may be carried out by the prescribed method, on six occasions at least three analyses per occasion. Routinely industries determine intermediate precision using two HPLCs, by two analysts at three concentrations. Determining intermediate precision solely based on per cent RSD has certain disadvantages.  In the new edition of Eurachem Guide “The Fitness for Purpose of Analytical Methods – A Laboratory Guide to Method Validation and Related Topics” analysis of variance (ANOVA) is proposed as an alternative way to simultaneously determine intermediate precision and repeatability in a validation study. ANOVA offers several advantages for assessing intermediate precision in a method validation study. An example of analysing intermediate precision data using one-way ANOVA is given in (Table 1). For studying intermediate precision, the Indian Pharmacopoeia Commission (Guidance document-validation of analytical methods) encourages using an experimental design.

Determining intermediate precision using ANOVA
Table 1 provides data on the area under the curve (AUC) of an active pharmaceutical ingredient using three different HPLCs - HPLC-1, 2 & 3.