# Volume III - 4.7 Statistics Applied to Drug Analysis

Orientation and Training

Food and Drug Administration

**III-04**

**Section 4 - Basic Statistics and Presentation**

10-01-03

1-31-13

- 4.7.1 Introduction
- 4.7.2 USP Guidance on Significant Figures and Rounding
- 4.7.3 Additional Guidance in the USP
- 4.7.4 References

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.