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William R. Porter R4P3 Pharmaceutics Abbott Laboratories, Abbott Park, IL Uncertain Standards with Standard Uncertainties
Midwest Biopharmaceutical Statistics Workshop, Muncie IN, May 18-20, © 2009 Abbott Background In 2007, the USP Reference Standards Expert Committee Subcommittee on Certified Reference Standards issued a Stimuli article in Pharmaceutical Forum that proposed establishing procedures for upgrading USP reference materials (RMs) so that they may be labeled as Certified Reference Materials (CRMs) according to ISO 9001 and requirements. The most notable change would be the assignment of specified uncertainties to RMs. The concept, widely recognized in the universe of other standards- setting organizations as a necessary and proper procedure for the certification of reference standards, is a foreign concept in the world of pharmacopoeial testing and measurement. The ostensible motive for this recommendation is to bring USP into compliance with ISO requirements for Reference Standards.
Midwest Biopharmaceutical Statistics Workshop, Muncie IN, May 18-20, © 2009 Abbott Standard Uncertainties The concept of uncertainty in measurement is an old one. In the 1963 National Bureau of Standards Handbook 91 Experimental Statistics, author Mary Gibbons Natrella devoted an entire chapter (Chapter 23) on “Expression of the Uncertainties of Final Results.” –This chapter clearly differentiates estimates of systematic error from estimates of imprecision and establishes that BOTH sources of error must be included in a statement of uncertainty. Numerous textbooks on Analytical Chemistry stress that a numerical result, stated without an associated estimate of its uncertainty, is of no utility. Prior to 1980, uncertainties were classified as due to either “random” errors or “systematic” bias, as exemplified in Natrella’s detailed exposition.
Midwest Biopharmaceutical Statistics Workshop, Muncie IN, May 18-20, © 2009 Abbott Outdated and Impractical Splitting of Measurement Deviations In the old way of treating uncertainties, efforts are made to estimate sources of bias and a correction is applied to the result. Whatever systematic errors that cannot be accounted for and then lumped in with the errors arising from random variation. Type B errors are difficult to estimate. Type B errors were not even reported!
Midwest Biopharmaceutical Statistics Workshop, Muncie IN, May 18-20, © 2009 Abbott Standard Uncertainties: The New Way The concept of uncertainty has changed over time. In 1980, the Comité International des Poids et Mesures (CIPM) recommended reclassifying estimates of uncertainty into two categories: –A: Uncertainty estimates determined using statistical methods on the basis of repeated measurements, and –B: Uncertainty estimates determined using other means. These concepts replace the older notions of “random” and “systematic” error. –Some components of “systematic” error introduce variation that rightly should be combined with statistical estimates of variation obtained from assessment of precision. –Other components of “systematic” error can be estimated as central tendencies that can be applied as corrections to the measured value.
Midwest Biopharmaceutical Statistics Workshop, Muncie IN, May 18-20, © 2009 Abbott Modern and Practical Way of Dealing with Measurement Uncertainties Measurement uncertainty describes a range of possible values. The classical concept of “error” describes the difference between the measured value and the “true” value. The goal of uncertainty estimation is to construct boundaries within which the “true” value is likely to lie, taking into account both uncertainties arising from random as well as systematic deviations.
Midwest Biopharmaceutical Statistics Workshop, Muncie IN, May 18-20, © 2009 Abbott Determining Measurement Uncertainty Non-Statistically Many systematic sources of uncertainty cannot be estimated from repeated measurements. Possible sources of information: Previous measurement data Experience with the sample and the measurement technique being used e.g., control charts for similar processes e.g., historical data for other products using similar or identical components Information quoted by the manufacturer of the instrument or equipment used e.g., design specifications & tolerances Data based on calibrations or certificates e.g., an assigned uncertanty for a CRM e.g., stated tolerance for ASTM calibrated volumetric glassware Uncertainties taken from manuals e.g., stated tolerances for device, such as an electronic pipettor
Midwest Biopharmaceutical Statistics Workshop, Muncie IN, May 18-20, © 2009 Abbott Calculation of the Measurement Uncertainty A multi-step process is used… Specify the measurand. Identify uncertainty sources. Quantify uncertainty components. Convert to standard uncertainties –Treat as if they were standard deviations for statistically-evaluated processes. –Triangular and rectangular distributions are used instead of Gaussian distributions. Triangular distributions are used for processes with target values and tolerance limits, e.g., volumetric dilutions. Rectangular distributions are used for processes with only tolerance limits, e.g., weighing on a digital balance. Calculate combined uncertainty.
Midwest Biopharmaceutical Statistics Workshop, Muncie IN, May 18-20, © 2009 Abbott Identification of Sources of Uncertainty Requires a Detailed Process Map All unit operations must be identified, with inputs and outputs. A mathematical model of the process, incorporating all inputs, is required. Any relationship to Lean Six Sigma process improvement strategies is NOT coincidental. It’s the same DMAIC (Define- Measure-Analyze-Improve- Control) process. Ishikawa Fishbone Diagram
Midwest Biopharmaceutical Statistics Workshop, Muncie IN, May 18-20, © 2009 Abbott ISO Guide 98: Guide to Expression of Uncertainty in Measurement The ISO Guide provides the legal basis for the new scheme for uncertainty estimation. It’s not easy to read, nor does it give much practical guidance. USP cites this guide as the proposed authority for implementing the assignment of uncertainties to USP reference standards, if USP adopts this concept.
Midwest Biopharmaceutical Statistics Workshop, Muncie IN, May 18-20, © 2009 Abbott QUAM 2000 The EURACHEM/CITAC guide, “Quantifying Uncertainty in Chemical Measurement” provides highly detailed instructions on how to perform a step-by-step evaluation of measurement uncertainty according to the 1980 CIPM recommendations. Available online at: This is the “practical guide” to uncertainty estimation, and is far more detailed than the NIST guide. It implements ISO Guide 98. Training materials are available in: M Rösslein, B Wampfler, Training Concepts and Teaching Materials in B. Neidhart, W. Wegscheider (Eds.) Quality in Chemical Measurements. (ISBN ). –PowerPoint slides are available!
Midwest Biopharmaceutical Statistics Workshop, Muncie IN, May 18-20, © 2009 Abbott So, How Does This Affect USP? The USP states: A dosage form shall be formulated with the intent to provide 100 percent of the quantity of each ingredient declared on the label. The tolerances and limits stated in the Definitions in the monographs for Pharmacopeial articles allow for analytical error, for unavoidable variations in manufacturing and compounding, and for deterioration to an extent considered acceptable under practical condition. Generally, Reference Standards used in assays are labeled with three significant figures and standards used in limit tests with two significant figures. Reference Standards having multiple applications in different methodologies may require separate assay-specific assignments. The assigned value is labeled without any associated uncertainty. Proposed change!
Midwest Biopharmaceutical Statistics Workshop, Muncie IN, May 18-20, © 2009 Abbott What Will Change? Under the proposal published in PF, the USP labeling of reference standards would include both a “standard uncertainty” and an “expanded uncertainty” assignment in the Certificate of Analysis that will accompany the potency factor. Certified Content Value:Standard Uncertainty ± Expanded Uncertainty ±
Midwest Biopharmaceutical Statistics Workshop, Muncie IN, May 18-20, © 2009 Abbott What Does All This Mean? “Standard Uncertainties” function in the same manner as “standard errors” in propagation-of-error calculations using root-mean- square variance calculations. The USP subcommittee proposes to use “3 sigma” limits for “Expanded Uncertainties.” y = p+q-r+... y = p q...
Midwest Biopharmaceutical Statistics Workshop, Muncie IN, May 18-20, © 2009 Abbott How Does This Affect Monograph Limits? Examples are cited in the PF article (Table 2): “Certified” Value (mg/mg) Total Expanded Uncertainty (mg/mg) Monograph Acceptance Criteria Uncertainty as Percentage of Monograph Assay Range CRM %–102.0%3% CRM %–102.0%3% CRM %–102.0%10% CRM %–102.0%2% CRM –1030 µg/mg13%
Midwest Biopharmaceutical Statistics Workshop, Muncie IN, May 18-20, © 2009 Abbott What About In-house Standards? The fun begins… Nothing in the current proposal precludes the establishment of in- house reference standards. Pharmaceutical companies already do this for biologics, which use WHO CRMs that have stated uncertainties. –Usually, the uncertainty of the CRM exceeds the added uncertainty of the in-house standard, so that, although the total combined uncertainty (in-house + WHO CRM) is greater than the uncertainty of the WHO CRM alone, the percentage increase in the standard uncertainty is generally small. –The standard uncertainty of a CRM includes contributions from interlaboratory differences in precision as well as interlaboratory differences in systematic deviations (bias). –For small molecules, expanded uncertainties of CRMs will likely contribute only a minor source of overall (process + measurement + calibration) uncertainty.
Midwest Biopharmaceutical Statistics Workshop, Muncie IN, May 18-20, © 2009 Abbott What Impact Will This Have? For starters, pharmaceutical company personnel will need training on the modern concept of uncertainty estimation. Training materials are available. Workflow analysis of analytical procedures will be required. –Lean Six Sigma opportunity. Documentation will need to be revised. $$$, time estimates are needed.
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