Evaluating Risk-Based Specifications for Pharmaceuticals - Pharmaceutical Technology

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Evaluating Risk-Based Specifications for Pharmaceuticals
The author discusses the purpose of analysis and testing and the implications for specifications and their underlying statistical distribution.


Pharmaceutical Technology
Volume 37, Issue 7, pp. 54-60


Figure 3: Conventional specification from a customer perspective. OOS refers to out of specification. LSL refers to lower specification limit. USL refers to upper specification limit.
The nature of specifications
The nature of a specification depends upon the type of data and their inherent mathematical distribution. In this article, the discussion is confined to continuous data where normal distribution may be assumed. This assumption has been shown to be well founded for traditional chemical analytical testing (12).


Figure 4: Taguchi quality loss function. LSL refers to lower specification limit. USL refers to upper specification limit.
The conventional view of fixed-limit specification is generally known as the "voice of the customer," or in the case of pharmaceuticals, the "voice of the regulator" (see Figure 3); this approach is from Western countries. In Japan, particularly in the engineering and electronics industries, the Taguchi approach to quality loss (13) is often adopted, whereby only at the target is the loss zero (see Figure 4). This approach is widely used in Six Sigma and Lean Sigma quality initiatives. The "voice of the process," on the other hand, is for the majority of continuous analytical measurements described by normal distribution. Two parameters define this distribution: namely a measure of its location denoted by the arithmetic mean (i.e., the average) and a measure of its dispersion (i.e., the standard deviation).


Figure 5: Reportable value (RV) and a normal distribution.
The necessity to control both parameters is recognized in FDA's OOS guidance (5), whereby the reportable result or value is controlled as well as the range of individuals as a measure of dispersion. The analytical reportable value is represented by a distribution around the best estimate found (see Figure 5). There is a fundamental incompatibility of the voice of the customer and the voice of the process. The problem with near-the-limit OOS results is indicated in Figure 6.


Figure 6: Conventional voice of the customer issues with out-of-specification (OOS) results. LSL is lower specification limit; USL is upper specification limit.
In Figure 6, there are two analytical reportable values lying close to the lower specification limit. The reportable value (indicated by the red "X") is conventionally OOS, and the reportable value (indicated by the green "X") is not. From a statistical viewpoint, given measurement uncertainty in the reportable value, it is likely that both are within the known variability of the test procedure. FDA, in its final OOS guidance, says, in such cases (5):

...where a series of assay results (to produce a single reportable result) are required by the test procedure and some of the individual results are OOS, some are within specification, and all are within the known variability of the method, the passing results are no more likely to represent the true value for the sample than the OOS results. For this reason, a firm should err on the side of caution and treat the reportable average of these values as an OOS result, even if that average is within specification.


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