Essentials in Tolerance Design and Setting Specification Limits

This article provides an overview of methods for setting specification limits and acceptance criteria for drug release testing, systems suitability/validity for analytical methods, process limits for in-process control and monitoring, and process limits for cell culture, purification, and other unit operations including raw materials and reagents. It is recommended that limits are set early in drug development (Phase I) and refined in latter phases (Phase II and III) as data becomes more available. The International Council for Harmonization (ICH) defines a specification in Q6B Specifications: Test Procedures and Acceptance Criteria for Biotechnological/Biological Products (1) as: “a list of tests, references to analytical procedures, and appropriate acceptance criteria which are numerical limits, ranges, or other criteria for the tests described. It establishes the set of criteria to which a drug substance, drug product or materials at other stages of its manufacture should conform to be considered acceptable for its intended use. ‘Conformance to specification’ means that the drug substance and drug product, when tested according to the listed analytical procedures, will meet the acceptance criteria. Specifications are critical quality standards that are proposed and justified by the manufacturer and approved by regulatory authorities as conditions of approval.”

In addition, ICH Q8 Pharmaceutical Development points out the following application areas for specification limits:

• Specifications are linked to preclinical and clinical studies.

• Specifications are linked to analytical procedures.

• Specifications are linked to a manufacturing process.

• Specifications should account for the stability of drug substance and drug product. 

ICH Q8 (2) says the following regarding critical quality attributes (CQAs), distributions, and limits: “A CQA is a physical, chemical, biological, or microbiological property or characteristic that should be within an appropriate limit, range, or distribution to ensure the desired product quality.”

Systematic drug development
Systematic drug development can be routinely characterized by three basic activities: system design, the method by which the product is synthesized, formulated, processed and measured; parameter design, the critical attributes or parameters and targets that achieve all CQAs; and tolerance design, the acceptable range for each critical attribute or parameter that will assure all CQAs will be within limits without out-of-specification (OOS) events. Tolerance design is the focus of this paper and discussion. A tolerance is the distance from the upper specification limit (USL) to the lower specification limit (LSL). When a tolerance is defined, there is a clear target. For a one-sided specification, the goal is to maximize or minimize performance (i.e., purity or impurity) and there is no clear target; therefore, margin is measured rather than tolerance. Margin is defined as the distance from the mean performance to the nearest specification limit (see
Figure 1).
 

Figure 1: Systematic drug development. [Courtesy of author]

Figure 1: Systematic drug development. [Courtesy of author]

Setting tolerances and limits
The following are six methods typically used for setting limits, listed in order of preference; the first method being most desirable and the last method is least desirable:

• Set specification limits based on transfer functions and associated margin analysis. Limits have a clear link to clinical pharmacokinetic (PK) studies or linked from CQAs to unit operations.

• Set specification limits based on statistical distributions and analysis.

• Set tolerances based on a worst-case margin analysis.

• Set tolerances based on a percentage of the mean (±10% or ±20%).

• Guess at tolerances and set arbitrary limits.

• No tolerances and no targets, quality levels are vague or undefined.

Ideally, all limits should be based on a transfer function, correlation, or model. It expresses the relationship of how variation in the factor (X) transmits variation onto the response (Y). Limits are used as part of the control plan to control the variation in the product, process, or assay. Statistical distributions are also a valid approach to limit setting; however, it requires that there are no adverse outcomes linked to the parameter of interest. It is reasoned that if the variation of the product, process, method, or raw materials does not result in poor or adverse outcomes, then the variation present in the samples data must be acceptable. When adverse outcomes are linked to a parameter, statistical distributions should not be used to set limits. Tolerance design should begin with all CQAs for release testing of drug substance and drug product and then flow down to all unit operations, assays/analytical methods, formulation, raw materials, and equipment settings. Where possible CQAs and drug attributes should be linked to PK clinical studies, a sound scientific rationale, and/or prior knowledge.

Guidance on setting limits
ICH Q6B 2.6 further states (1), “Appropriate statistical analysis should be applied, when necessary, to quantitative data reported. The methods of analysis, including justification and rationale, should be described fully. These descriptions should be sufficiently clear to permit independent calculation of the results presented.”

Statistical tools such as SAS or SAS/JMP are recommended when setting limits. Excel or other spreadsheet tools lack a robust set of tools for setting limits and incorrectly assume normal distributions when they are often nonnormal.

Risk and setting limits
There is a direct relationship between limit setting and risk. ICH Q9 Quality Risk Management (3) suggests using risk as a consideration in product development. The wider the interval, the greater the amount of transmitted variation on the Y response, thus wider intervals should only be used when the risk of OOS or clinical risk is medium to low.

Table I provides the statistical basis for the interval in K sigma and likelihood of failure and resulting OOS levels. In general, K sigma design margin of 1 or even 1.5 is desirable where possible. OOS in parts per million (PPM) should be targeted at 100 or less for every CQA.

Table I: Probability and risk table for setting limits. OOS is out of specification. PPM is parts per million.

Table I: Probability and risk table for setting limits. OOS is out of specification. PPM is parts per million.

Tolerance interval approach
Tolerance intervals were developed to provide a correction for limited sample sizes and scales the interval of risk based on three considerations: sample size, confidence interval, and proportion of the population to be described. The National Institute for Standards and Technology (NIST) (4) defines a tolerance interval as, “There is also a way to cover a fixed proportion of the population with a stated confidence. Such an interval is called a tolerance interval. The endpoints of a tolerance interval are called tolerance limits. An application of tolerance intervals to manufacturing involves comparing specification limits prescribed by the client with tolerance limits that cover a specified proportion of the population.”
 

• Tolerance intervals should be used under the following conditions:

• No transfer function is available and/or possible.

• No adverse or unacceptable results are associated with the parameter or response.

• Sample size is less than 30, tolerance intervals should not be used when n³ than 30 as they will be too tight and fail to correct for n. Use K sigma when n³30.

• Sample data are stable (use a control chart or regression analysis to evaluate stability).

• Distribution is either normal or nonnormal.

The tolerance interval procedure is as follows:

• Make sure you have a representative sample of the population of interest.

• Confirm there are no compendial limits or requirements specified by guidance. If so, use the compendial limits.

• Outlier removal precedes distribution fitting and evaluation, Grubbs, or Dixon’s Q test.

• Determine the distribution that best fits the data, normal, or nonnormal distribution, use a goodness of fit or Akaike’s Information Criterion Corrected (AICc) functions to determine the best fit.

• Avoid using Johnson or lognormal distributions when fitting nonnormal tolerance intervals as they are set limits excessively wide. Normal, Gamma, Weibull, Normal Mixture are preferred and should all work well to set limits.

• Use Table I to determine the risk and associated tolerance interval and margin.

• Use a K Factor calculator (5) to determine K for the interval (n, confidence and population) (see Table II).

• Set specifications using K Sigma to define the limits.

• Compare results to compendial or historical limits for the drug attribute or process parameter.

Table II: K factor calculation.

Table II: K factor calculation.

Tolerance Interval Example
In regards to % HMW tolerance interval example n=12, see Figures 2–4 for the determination of the limits.

Figure 2: Fitting the normal cuve and setting the tolerance interval. [Courtesy of author]

Figure 2: Fitting the normal cuve and setting the tolerance interval. [Courtesy of author]

K Sigma approach
K sigma approach is similar in every way to a tolerance interval except it uses the K sigma value from Table I and does not correct for sample size, confidence interval, nor proportion of the population. There is no need for sample size correction once the sample size is 30 or more.

Figure 3: Setting the K value and type of limit. [Courtesy of author]

Figure 3: Setting the K value and type of limit. [Courtesy of author]

Figure 4: One sided 95/999 tolerance interval for %HMW. [Courtesy of author]

Figure 4: One sided 95/999 tolerance interval for %HMW. [Courtesy of author]

DOE or regression transfer function
A transfer function (see Figure 5) is the best way of predicting the influence of how changes in X influence the change in the response. Transfer functions may be generated based on a designed experiment and fitting a model to the data or by other regression techniques.
The following is the procedure setting limits using a transfer function and a statistical package such as SAS/JMP:

• Using a structured designed experiment, generate the transfer function or model equation.

• Load the model into a profiler and use the profiler to set limits.

• Optimize the settings to achieve excellent results in the response and set the target.

• Turn on the simulator function to set limits.

• Determine one sigma variation for each factor at the optimal set point. If not using a normal sources of error, add the parameters of the curve being used.

• Add the root mean squared error to the analysis to account for analytical/measurement error and or other sources of variation not explained by the model.

• Define the likely distribution of the X parameter. If processing to target, use a normal truncated distribution. If processing to range, use a uniform distribution.

• Restrict the range of X at the set point until all responses indicate a PPM of <100 per parameter. This is done for all critical process parameters, method parameters, etc.

Figure 5: Transfer function. [Courtesy of author]

Figure 5: Transfer function. [Courtesy of author]

Time zero limits versus product lifecycle limits due to stability
To set limits for product lifecycle, the following procedure is recommended (Figure 6):

• Determine tolerance intervals or K sigma limits for the time zero data.

• From the stability data, determine the rate of change per month or unit of time.

• Use the following equation to determine the product lifecycle limit. Time Zero Specification Limit + Rate*Number of time points. In most cases, only one limit is modified due to the direction of change.

Figure 6: Simulation to set limits on the response. OOS is out of specification. PPM is parts per million. [Courtesy of author]

Figure 6: Simulation to set limits on the response. OOS is out of specification. PPM is parts per million. [Courtesy of author]

Conclusion
Setting limits and acceptance criteria are critical elements of drug development and an important part of the control plan. Transfer functions, tolerance intervals, and K sigma intervals are key methods to make sure the approach to setting specification limits is statistically rigorous, scientifically sound, and defendable to regulatory reviewers.

References
1. ICH, Q6B Specifications: Test Procedures and Acceptance Criteria for Biotechnological/Biological Products (ICH, March 1999).
2. ICH, Q8 Pharmaceutical Development (ICH, August 2009).
3. ICH, Q9 Quality Risk Management (ICH, June 2006).
4. NIST, Engineering Handbook, www.itl.nist.gov/div898/handbook
5. QbD Consulting, Tools and Templates, http://qualitybydesignconsulting.com/tools/index.php

Article DetailsBioPharm International
Vol. 29, No. 6
Pages: 41–45

Citation
When referring to this article, please cite it as T. Little, "Essentials in Tolerance Design and Setting Specification Limits," BioPharm International29 (6) 2016.