## Out-of-Specification Sample-Size Confusion

Precedents set in the historic Barr case continue to raise questions over suitable sample-size criteria.
Dec 02, 2011

 Lynn D. Torbeck
The sample size needed to investigate an out-of-specification (OOS) result continues to be a point of contention within the pharmaceutical industry. The following quotes from the US vs. Barr Laboratories case, which covered OOS issues, provide good background to the discussion (1):

"... the number of retests performed before a firm concludes that an unexplained out of specification result is invalid or that a product is unacceptable is a matter of scientific judgment."

"Nevertheless, retesting cannot continue ad infinitum. Because such a practice is not scientifically valid ..."

"Such a conclusion cannot be based on 3 of 4 or 5 of 6 passing results, but possibly 7 of 8."

" ... retesting determinations will vary on a case by case basis, a necessary corollary of which is that an inflexible retesting rule, designed to be applied in every circumstance, is inappropriate."

The specific question here is: "How big should the sample be?" and it is the most commonly asked question of a professional statistician. The truth is that there is no simple answer because it depends on the information available. There are at least four possible approaches:

• Scientific estimate
• Seven out of eight as in the Barr case
• Statistical formula with historical estimates
• Statistical formula with sample.

Scientific estimate

One approach to determine the sample size would be to ask a trained analyst with industry experience to use his or her best scientific judgment to determine what would be an adequate sample size to select. Prior to the Barr case this was (and still is in some places) the standard operating procedure. Although this has scientific basis in the fact that the best person available uses all information to estimate a size, the fact that different people would not get the same number is not scientific. However, the Barr case quotes would seem to support this approach.

Seven out of eight

As in the Barr case, the seven out of eight rule is used by some companies in the absence of any other available information. However, so far there is little statistical justification for seven versus any other value. Some companies choose nine only so they can say they have improved upon the Barr criteria.