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| Other Laboratory Operations Food and Drug Administration |
| DOCUMENT NO.: III-04 | VERSION NO.:1.2 | Section 4 - Basic Statistics and Presentation | EFFECTIVE DATE: 10/01/2003 | REVISED: 06/27/2008 |
4.7 Statistics Applied to Drug Analysis
Chemists in ORA laboratories may have to analyze a wide range of human and
animal drugs in a number of different dosage forms, and using differing analytical
methods. Statistical evaluation of the analytical results is important for
making regulatory decisions.
4.7.1 Introduction
Drug analysis, as well as most analysis performed in the ORA laboratory, relies
on the statistical concepts defined above. In addition, there are references
in the United States Pharmacopeia (USP) and other official references with
which the drug analyst should be familiar.
4.7.2 USP Guidance on Significant Figures and Rounding
Under GENERAL NOTICES, the USP has several references, either direct or implied,
to statistics, reporting of results and maintaining precision during an analysis.
The drug analyst should be thoroughly familiar with the "Significant Figures
and Tolerances" section of the USP. Highlights of this section are summarized
as follows:
- Numerical limits specified in a monograph include the extremes
of the values and all values in between, but no values outside these limits.
This statement should be applied after proper rounding of numerical results.
If, for example, a properly rounded result is found to lie exactly at the
extreme of a limit (e.g. limits 98.0-102.0% of declared; found 102.03%, rounded
to 102.0%) then the monograph limits are met. If the result lies outside
the numerical limits (e.g. 98.0-102.0% of declared; found 102.05%, rounded
to 102.1%), then the monograph limits are not met.
- Numerical result should be reported to the same number of decimal
places as the limit expression stated in the monograph. For example, if limits
are stated as 90.0-110.0% of declared, report results to 1 decimal place
(e.g. 98.3%, 101.8%), after applying USP rounding rules.
- The USP has slightly different rounding rules than those commonly
encountered, as discussed earlier in section 4.3.1. The difference is when
a value ends in 5. USP rounding conventions are as follows:
- Retain only one extra digit to the right of the rightmost digit of
the monograph limit expression
- If the extra digit is less than 5, drop the digit.
- If the extra digit is greater than 5, drop it and increase the previous
digit by one
- If the extra digit is exactly five, then drop it and (always) increase
the previous digit by one.
- An explicit statement is made for titrimetric procedures: essentially
all factors, such as weights of analyte, should be measured with precision
commensurate with the equivalence statement given in the monograph. Examples
in the significant figures section above illustrate the importance of this
for all analytical work.
- There is a table given in SIGNIFICANT FIGURES AND TOLERANCES that
gives examples of USP conventions for rounding, reporting, and comparison
of results with compendial limits. This should be reviewed and thoroughly
understood by all ORA drug analysts. A few additional examples are given
in the following table:
Compendial Requirement |
Unrounded Result |
Rounded Result |
Conforms? (Y/N) |
Assay not less than 95.0 And
not more than 105.0%of Declared |
94.95% |
95.0% |
Y |
94.94% |
94.9% |
N |
105.65% |
105.7% |
N |
Limit Test LTE 0.2% |
0.24% |
0.2% |
Y |
0.25% |
0.3% |
N |
4.7.3 Additional Guidance in the USP
Also under GENERAL NOTICES, TESTS AND ASSAYS, is additional guidance. An important
section is "Test Results, Statistics, and Standards," which is
of particular regulatory significance. Important points to understand include:
- USP compendial instructions or guidelines are not to be applied "statistically," meaning
the conformance or non-conformance of a product is determined by a single
test which may be applied to any portion of a sample, at any time throughout
its stated shelf life. The monograph limits are chosen so that inherent uncertainty
in the method is taken into account, and system suitability tests verify
that the analytical system is reliable; therefore "any specimen tested
as directed in the monograph complies"( FDA's practice, nonetheless,
is to perform a check analysis to confirm non-compliance with a monograph
limits).
- To emphasize the "singlet determination" viewpoint
of the USP, the following statement is made: "Repeats, replicates,
statistical rejection of outliers, or extrapolations of results to larger
populations are neither specified nor proscribed by the compendia."
Finally, under GENERAL NOTICES, TESTS AND ASSAYS, the "Procedures" section
includes some guidance that should be understood by the ORA Laboratory drug
analyst:
- Weights and volumes of test substances and reference standards may
be adjusted proportionately, provided that such adjustments do not adversely
affect the accuracy of the procedure.
- Similarly, when a method calls for a standardized solution of a
known concentration, a solution of a different concentration, molarity, or
normality may be used, provided allowance is made for the differing concentration,
and the error of measurement is not thereby increased.
- Monographs often use expressions such as "25.0 mL" for
volumetric measurements. This is not to be taken literally. In practice,
volumes used quantitatively (i.e. the measurement will be used in a quantitative
calculation) should be measured to the higher precision specified in "Volumetric
Apparatus <31>" of the USP. This generally means that class A
flasks, burets, and pipets are to be used, and with proper analytical technique
employed. Similarly for weights: "25.0 mg" means that the weighing
should be performed with a high precision balance meeting standards set forth
in "Weights and Balances <41>."
4.7.4 References
(Current Ed.). U. S. Pharmacopeia and national formulary. Rockville,
MD: United States Pharmacopeial Convention, Inc.
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