Kim Erland Vukovinsky

There are fundamental reasons why the normal distribution is a reasonable approximation in many development and manufacturing settings, but there are also practical reasons why data may not exactly follow a normal distribution. This article provides an overview of both cases. It will focus on content uniformity and provide examples of why this type of data is not necessarily normally distributed. It will also provide insight into why it is easy, even when underlying data are normal, to reject normality via standard statistical tests. The goal of this article is to increase awareness of the concept of normality within the pharmaceutical industry and detail its potential limitations.

	Statisticians frequently assume that data follow a normal distribution when developing statistical methods and performing practical data analysis. In most introductory statistics textbooks, the methods presented assume the data follow a normal distribution. Why is this distribution so heavily used?

	First, an immense amount of data from many differing fields and applications displays the approximately bell-shaped, single-peak distribution. In these cases, the data seem to center at a particular value (mean) and spread out relatively evenly on both sides of the center with most data congregating near the central value.

	The second reason that the normal distribution is used is that most statistical methods employ some level of summing or averaging of the individual data points. A useful theorem in statistics, *The Central Limit Theorem, states that sums and averages tend to follow a normal distribution, no matter what distribution the individual data values come from. For a real-life example, consider rolling a six-sided die a given number of times and take averages of the results from those rolls. Assume that a die is rolled five times, and the average of the five results (“rolls”) is collected. This process is repeated a large number of times, say 10, or 50, or 500 times. On roll 1, the result is 6, on roll 2 the result is 4, roll 3 produces a 4, roll 4 a 2, and roll 5 is a 3. The sum of these numbers is 19 and the average is 3.8. Although it is equally likely to receive a 1, 2, 3, 4, 5, or 6 from any individual roll of the die, and thus the distribution of any roll is flat or uniform (i.e., not “normal”), the distribution of the five-roll average appears to be unimodal, symmetric, and bell-shaped, approaching “normal” as the process is repeated a large number of times. 

 shows the distribution of each roll, with the resulting distribution of the average when the process is repeated 10, 50, and 500 times. Note that the uniform nature of the distribution of individual data and the “normal” appearance of the distribution of the averages hold and are easier to visualize as the sample size increases (1).

	This theorem is the main reason that statistical methods that are based on assuming a normal distribution are quite robust to departures from this assumption. In other words, even if the underlying data do not exactly follow a normal distribution, the statistical methods work reasonably well on the sums/averages that are often being analyzed statistically. For a more detailed explanation of the graphs used in 

	The final reason assuming normality is so common is that this distribution has practical properties that allow for useful interpretation of data. For example, if data are approximately normal there is a reasonable expectation of where future data should fall relative to the mean of the current data. A common tool in practical data analysis is to calculate “three sigma limits” to understand where to expect the future data to range. Almost all future data will lie within the three sigma limits of the mean since 99.7% of data from a normal distribution should be within these limits.

	What are the methods to determine normality?

	Graphical tools are one of the best ways to determine if data follow an approximate normal distribution (2, 3). They also have the additional benefit of highlighting other possible features in a set of data such as outliers. As John W. Tukey (4) said, “The greatest value of a picture is when it forces us to notice what we never expected to see.” The histogram, boxplot, and normal probability plot are three graphics that can be used when assessing the distribution of a set of data.

, left panel, shows a histogram of some typical content uniformity data. In this graph, the length of the bar shows the number of data values (x-axis) that fall in the range of the bar indicated on the y-axis. From this graph, the distribution of data looks relatively normal with perhaps a longer “tail” on the lower side of the mean than on the upper side.

, middle panel, is a boxplot of the same content uniformity data shown on the left. The data set is represented by a box and lines that extend past the top and bottom of the box. The line across the middle of the box is the median (middle value) of the data set. The top of the box is the 75th percentile (75% of the data are below the top of the box) and the bottom of the box is the 25th percentile. The box encompasses the middle 50% of the data. If the data follow an approximately normal distribution, the median should be near the center of the box and the lines extending out from the box should be roughly the same length. The difference between the 75th and 25th percentiles is called the interquartile range. The lines coming out of the box at the top and bottom extend to the largest and smallest data values that are within 1.5 times the interquartile range from the box. If there are values beyond that limit, they are plotted as individual values (stars in 

). Note that two values are plotted as stars on the bottom indicating that these values are worth investigating to make sure they are truly a part of the data distribution.

		The final graphical tool for assessing the distribution of a set of data is the normal probability plot (i.e., normal quantile plot). 

, right panel, shows the content uniformity data in a normal probability plot. The x-axis scale represents the percentiles of a normal distribution. When data are plotted against this scale, the points should fall along a straight line if the data are normally distributed. It is not essential that the data form a perfectly straight line, only that they be close. One practical approach is to imagine that the graph is on a piece of paper and that a fat pencil is placed on the graph. This fat pencil should be able to cover most of the points if the data are reasonably approximated by a normal distribution.

	Statistical methods are also available to perform a statistical hypothesis test for concluding (at a pre-determined level of statistical confidence) that the data do not follow a theoretical normal distribution. The common tests available in menu-driven statistical software are the Anderson-Darling, Shapiro-Wilk, and Kolmogorov-Smirnov tests. Each of these tests is optimal under certain data situations such as large and small sample sizes. These tests should be used with caution as several data conditions other than not following a normal distribution can cause these tests to be statistically significant (this is discussed in the next section). It is also important to remember that these statistical hypothesis tests cannot “prove” that the data are normally distributed; they can only provide evidence that a set of data does not follow a normal distribution (when the 

* associated with the test is statistically significant). If the sample size is small, these tests may not be powerful enough to detect important departures from normality. If the test is statistically significant, the test does not reveal why the data “failed” normality testing. The graphical approaches discussed above provide essential understanding of the data distribution in a way hypothesis testing can never approach as it is possible to easily find relevant features in the data (e.g., outliers, multiple peaks).

	Why might the normal distribution not always hold?

	Similar to the process of rolling a die five times, pharmaceutical manufacturing processes and the data that result from the processes are usually the combination of at least several sub-processes. In producing a tablet, the sub-processes might occur as: blend, mill, blend, roller compact, mill, and compress. These sub-processes create in-process material distributions, each of which is not necessarily normally distributed. Regardless of the individual distributions of these sub-processes, if there are several, and their variability is of similar magnitude, the final data will be normally distributed. This may seem like magic but 

 provides illustrative proof. The example distributions (Weibull, Uniform, Triangular, Beta, and Gamma) are not meant to be representative of actual manufacturing distributions; they were selected to illustrate that the mathematical principle works even when using these “non-normal” distributions. To interpret 

, assume that the pre-blend process acts on the material, producing a result that over time, would follow a Weibull distribution. The material is then passed to the mill, and the mill-blend process acts independently of the pre-blend process, and adjusts the material per a uniform distribution. The material is then passed to the roller compactor that acts independent of the previous processes and adjusts the material in a triangular fashion. The final mill creates an adjustment distributed as a beta and the compression process as gamma. If several lots would be made in this fashion, those independent data distributions would result in a normal distribution of the final product. Several hundred lots are displayed in 

. A true departure from normality may occur in a number of ways:

Number of sub-processes and/or magnitude of variation. If there are not a sufficient number of sub-processes or the magnitude of variability from one sub-process overwhelms the others, then the final result may not be normal. This might cause a skewed distribution, a distribution with thicker “tails” than a normal distribution, a bi-modal distribution, or any number of distributions. 

 displays a simulated process with a resulting distribution that is non-normal.

A non-normal distribution could occur in tablet manufacturing in several ways. For example, if in a granulated product, the particle size of the active granules is greater than the excipient particle size, then there may be segregation at the end of the batch. If the data are collected in a stratified fashion throughout the run, then the potency data will result in a skewed right distribution. Another example is when blend segregation occurs during initial discharge of the bin and/or during compression; in this case, there might be lower/higher potency values at start and/or end of run resulting in a skewed distribution or thick tails.

	These types of phenomena are studied and minimized during development, but it may not be possible to eliminate them completely. Here, process knowledge and process control are essential, not the normality of the data distribution. A process with slightly heavier tails but a narrow range of content uniformity results would certainly be more desirable to the patient than a process that follows a normal distribution but has a larger range of results. Failing a test of normality does not automatically imply poor quality product.

. In this case, the data may have been truncated due to a natural or “person-made” limit. An example of data truncation can occur as the result of weight control of tablets during compression. If the process is actively adjusting tablet weights during manufacturing, then the resulting weight data (and hence potency and other responses) will become limited and result in a truncated, non-normal, distribution. 

 displays such a result. These data will fail normality, but the result is “better than normal” and better lot quality; lot release should not be affected.

. It is best to keep the data to as many significant figures as possible for use in data analysis. When the data are subjected to high-level rounding, although the underlying data might be normal, the result may be non-normal data. This degree of rounding not only affects normality, it makes decision-making difficult. The content uniformity data in 

, original and rounded, clearly show that the uniformity results in the “tenths” place pass the Anderson-Darling normality test, but fail the test when the data are rounded to the “ones” place. The normal probability plot shows the evidence of rounding and that the underlying distribution is most likely normal given how the points surround the line evenly.

. Outliers in a dataset are another reason that a normality test can be statistically significant (i.e., have a p-value that is small, usually less than 0.05 or 0.01) even if the rest of the data is normal. The normal plot and the boxplot are excellent graphs for revealing outliers. In content uniformity, when outliers are found, it is important to determine the reason for these results or the sources of variability.

	The variability in content uniformity data can be attributed to the raw materials, the manufacturing process, and the analytical method. For example, “process-caused” outliers in potency/content uniformity data might be the result of drug substance agglomeration. The ability of a drug product to agglomerate should be studied in development and minimized in manufacturing. However, if minor agglomeration is found in the final product sample, the resulting distribution may fail normality testing and/or may intermittently have outliers that are well within the specifications. Also, “analytical method-caused” outliers could occur when content uniformity data are analyzed by near infrared (NIR). In analyzing content uniformity data by NIR, a mathematical model is developed. If there are changes to a physical property of the material that is not accounted for in the NIR model, the model will not predict well. This poor prediction might result in abnormally large observations, or outliers in the data. Such model prediction errors can typically be detected with the use of spectral matching algorithms prior to prediction of content and inform the analyst about the need for model improvement. Still, the true underlying tablet potency distribution may be unchanged and normal.

 contains developmental content uniformity data from a single compression run plotted in the order it was manufactured. The results display that the data are time-dependent or autocorrelated. This means that the current content uniformity result is somewhat dependent on what happened during the time period just before it. This time-ordered dependency is found in almost all manufacturing processes and may be induced by factors such as common raw materials, environmental conditions (relative humidity and temperature), and feedback control of the process. The data in 

 do not pass a statistical test of normality. The data cover a narrow range, 95-105% label claim, and represent excellent control of content uniformity. Failing the normality test does not imply poor quality.

. For large samples, it is possible to find very small departures from exact normality using statistical tests. The dice example from 

 clearly shows the appearance of the data as more bell-shaped, unimodal, symmetric, and “normal” as the sample size increased. Yet, one would accept the assumption of normality (p = 0.85 for Sharpiro-Wilk and p = 0.85 for Anderson-Darling) for the sample of size 10 and would reject normality (p = 0.013 for Sharpiro-Wilk and p < 0.005 for Anderson-Darling) for the sample of size 500. This is a general property of statistical hypothesis tests. All else being equal, as the sample size increases, the statistical test is able to detect increasingly small differences in the data.

	Application to content uniformity testing

	As noted in the introduction, there has been much commentary both at conferences and in the literature (5-10) on revising content uniformity tests for small sample sizes and developing content uniformity tests for large sample sizes. In these tests, there are assumptions around normality and/or testing for normality.

	How should an understanding of data distributions be used in the development of performance qualification and routine lot release criteria? As shown in the examples presented above, failing a statistical test of normality or having a process that produces data that are not normally distributed does not necessarily affect the quality of the product. As a part of continuous process verification, it is important to evaluate production data to ensure that the data are meeting expectations based on development and past production experience. It is, however, not necessary that the data follow an exact normal distribution. The examples presented provide many real world case studies of why this type of requirement should not be applied routinely.

	Knowing that production data may not be exactly normally distributed implies that the lot release or validation acceptance criteria should be developed to be robust to departures from normality. If the criteria require the assumption of normality, the test should use statistical functions such as sums and averages to improve robustness to differing data distributions. Alternatively, a nonparametric test (8, 9) (i.e., one that does not require normality) should be developed. Criteria that utilize statistical functions such as minimums/maximums and the “tails” of assumed probability distributions should be avoided (6). One reasonable approach is to provide both a parametric (assumes normal distribution) and nonparametric test such as the European Pharmacopoeia content uniformity procedures for large sample sizes (5, 10).

	Although it is reasonable to expect that the underlying content uniformity data is normal, there are several reasons why the data might not be normal or might be normal and fail a test for normality. These departures from normality do not necessarily affect the quality of the product. As a result, the distribution of the data should be understood as part of process understanding and continuous improvement. The data should not be tested for normality as part of lot release.

	It is prudent to develop lot acceptance criteria (e.g., compendial or release tests) that are robust to moderate departures from normality. Or, if testing for normality is a requirement for using the test, then there should be options for non-normal data as well.

	The authors would like to thank Stan Altan (Janssen), Anthony Carella (Pfizer), Tom Garcia (Pfizer), Jeff Hofer (Eli Lilly), Sonja Sekulic (Pfizer), and Gert Thurau (Roche) for their careful review of this document.

	1. NIST, “Engineering Statistics Handbook,” accessed Sept. 1, 2014.
	2. S. Shapiro, 

How to Test Normality and Other Distributional Assumptions

, Volume 3 (ASQC, 1990).
	3. Henry C. Thode, 

, General Chapter 2.9.47 Uniformity of dosage units using large sample sizes (EDQM, Council of Europe, 6. Strasbourg, France).
	6. M. Shen and Y. Tsong, 37 (1) Stimuli to the Revision of the USP: Bias of the USP Harmonized Test for Dose Content Uniformity.
	7. W. Hauck et. al, 38 (6) Stimuli to the Revision Process: USP Methods for Measuring Uniformity in USP.
	8. D. Sandell et al., 

, 40 (3) 337-344 (2006).
	9. J. Bergum and K. Vukovinsky, 

, 34 (11) 72-79 (2010).
	10. S. Andersen et al., 

	Lori B. Pfahler is director, Center for Mathematical Sciences, Merck Manufacturing Division, 770 Sumneytown Pike, PO Box 4, WP97-B208, West Point, PA 19486, tel.: 215.652.2967, email: Lori.Pfahler@merck.com.

	Kim Erland Vukovinsky is senior director, Pharm Science & Manufacturing Statistics, Pfizer, MS 8220-4439, Eastern Point Rd., Groton, CT 06340, tel.: 860.715.0916, email: kim.e.vukovinsky@pfizer.com.

Articles

Review challenges in the use of normality testing situations and recommendations on how to assess data distributions in the pharmaceutical development manufacturing environment

The Role of Normal Data Distribution in Pharmaceutical Development and Manufacturing

Applications of process analytical technology (PAT) for in-process and/or end-product release testing are attracting wide interest from both regulators and the pharmaceutical industry. Nondestructive measurement techniques such as near-infrared spectroscopy, together with statistical modeling of the obtained spectrum, facilitate fast and precise measures supporting the vision of improved manufacturing process understanding. Such techniques can generate a significant amount of data in real time and thereby open the possibility of improved process control and capability. In such scenarios, the added value of traditional lot-release testing based on a random sample from the batch is questioned. 

One of the potential applications of PAT is real-time evaluation of tablet content uniformity. A related issue is the choice of acceptance criteria in light of the increased sample size because the International Conference on Harmonization's (ICH) uniformity of dosage units (UDU) test is based on either 10 or 30 dosage units (1). To address this issue, the Pharmaceutical Research and Manufacturers of America (PhRMA) Chemistry, Manufacturing, and Controls (CMC) Statistics Expert Team (SET) published an alternative to the ICH test in 2006 that could be used as a batch-release specification when testing a large number of dosage units (2). This proposed test was intended as an alternative, not as a replacement, to the ICH UDU test as the official regulatory method. Through interactions with European and American regulators during the second half of 2009, questions about the PhRMA approach were raised; this feedback highlighted the need to modify the test to achieve quality equivalent to or better than the ICH UDU test across the entire test range.  

This paper provides a modified version of the test described in the PhRMA CMC SET paper. This modified test is proposed as an alternative test and not as a replacement; it is intended perform similar to or better than the ICH test with the increased sample size. In both the original and modified tests, the proportion of dosage units within 85–115% of label claim (LC) (the "coverage of 85–115% LC") is proposed as the measure of the uniformity of the batch. The acceptance criteria for these tests are based on counting the number of dosage units in the sample outside 85–115% LC and rejecting the batch if that count is too high. The acceptance criteria for these tests are meant to support effective regulatory application of PAT to processing. The tests are nonparametric; simple to implement, use, and regulate; and are applicable to large sample sizes. The modified version of the PhRMA CMC SET alternate test provides the same or better assurance as the harmonized UDU test with respect to the batch's uniformity.  

An alternative uniformity of dosage units test

The European Pharmacopoeia, Japanese Pharmacopoeia, and United States Pharmacopeia (USP) contributed to the ICH-harmonized pharmacopeial specification (e.g., 

 2.9.40) for the content UDU, which is based on either 10 or 30 dosage units. The PhRMA CMC SET proposed an alternative to the ICH test to address the issue of developing acceptance criteria for increased sample size due to PAT. The tablet-sampling procedure (e.g., one tablet every three minutes) is established before batch manufacture. The resulting sample size is determined by the sampling procedure, and is larger than 30 dosage units, more likely 100 to 500 units. The PhRMA CMC SET test, called the "Large-N" test in this paper, is a one-tiered counting test for uniformity of dosage units. The nonparametric test is based on counting the number of dosage units outside the 85–115% range of label claim and rejects the batch if that count is outside the set limit.  

) outside the target interval (85–115% LC) is binomially distributed with parameters 

 = 0.048, the quality level (QL) calculated corresponds to 95.2% coverage, associated with a 50% probability of complying with the ICH UDU test. The test translates to finding the largest integer 

 for various sample sizes. For example, if 500 units are tested and 23 or fewer results are outside 85–115% LC, the batch passes the test.  

Table I: Large-N test acceptance limit for various n.  

The test is designed to be more conservative than the ICH UDU test for all levels of batch quality where the probability of accepting a batch is less than 0.5. The acceptance limit, 

Figure 1: Large-N (various percent label claim [LC]) operating characteristic curves for n = 100 with International Conference on Harmonizations (ICH) uniformity of dosage units (UDU) test (100% LC). StDev is standard deviation. (ALL FIGURES ARE COURTESY OF THE AUTHORS) 

Figures 1 and 2 show operating characteristic (OC) curves for the Large-N test for sample sizes of 100 and 500, respectively, compared to the OC curve for the ICH UDU test when the batch mean is 100% LC. Here, the probability to accept the batch is plotted against batch standard deviation with curves varying by batch mean. If the mean is off target, the standard deviation must decrease to maintain constant coverage; this change results in the shift to the left in the curves. Also, the test is symmetric; a mean of 98% produces the same OC curve as a mean of 102%. Note that for the sample size of 500, the probability of accepting the lot under the Large-N test is slightly higher than passing the ICH UDU test for small standard deviations; this higher probability is expected because increasing the sample size results in a more discriminating test.  

Figure 2: Large-N (various percent label claim [LC]) operating characteristic curves for n = 500 with International Conference on Harmonizations (ICH) uniformity of dosage units (UDU) test (100% LC). StDev is standard deviation. 

This paper proposes a modification to the Large-N test by increasing the QL from 0.048 to 0.030. This change is demonstrated by OC curves for sample sizes from 

= 500. This modification results in a more conservative test than the Large-N test because the number of tablets allowed outside of 85–115% LC is reduced. The value of 0.030 for the QL was chosen because of its performance against the ICH UDU test's OC curve (discussed below) and because the former ICH content-uniformity test allowed 1 tablet (1/30 = 0.033) outside of the 85–115% range. Using the same QL for all sample sizes simplifies the calculation for the acceptable number of tablets. 

The modified Large-N test is as follows:   

 and round it down to the nearest integer. For example, for 

 = 250, 3.0% of the 250 tablets is 7.5, which will be rounded down to 

The batch complies if the number of tablets outside the range of 85.0–115.0% of LC is no more than 

For sample sizes of 100 to 500 tablets, the proposed alternative test is similar to or more conservative than the harmonized compendia test for UDU. A comparison of the acceptance values using the Large-N and modified Large-N test is provided in Table II.  

Table II: Acceptance values for the Large-N and Modified Large-N tests. 

Figures 3–4 show the OC curves for batch means of 96% and 100% LC and sample sizes of 100 and 500 units for the ICH UDU test, as well as the Large-N and modified Large-N tests. Sample sizes of 100 and 500 units were chosen because they cover the current typical range of sample sizes.  

Figure 3: Large-N and modified Large-N operating characteristic curves for n = 100 with International Conference on Harmonizations (ICH) uniformity of dosage units (UDU) test (batch mean = 96% and 100% label claim [LC]). StDev is standard deviation. 

The OC curves provide the probability of passing each test at various values of the batch standard deviation (SD). For example, if 100 tablets are tested from a batch with a batch mean of 96% LC (see Figure 3), then for an SD of about 6.4% LC, the probability of passing either the ICH UDU or Large-N test is about 54%, and the probability of passing the modified Large-N test is about 30%. For the same set of curves at a standard deviation of about 4.0% LC, the probability of passing either Large-N test or the ICH UDU test is more than 99.8%. Also, as can be seen in these figures, the test is sensitive to how far the batch mean is from its target (i.e., 100%).  

Figure 4: Large-N and modified Large-N operating characteristic curves for n = 500 with International Conference on Harmonizations (ICH) uniformity of dosage units (UDU) test (batch mean = 96% and 100% label claim [LC]). StDev is standard deviation. 

Coverage, or the percentage outside 85–115% LC, is a function of the average and the standard deviation of the batch. As the batch mean moves away from target, the standard deviation required to achieve the same probability of passing the test is reduced. Therefore, if a batch is produced off-target, the standard deviation needs to decrease to attain constant coverage. The figures also show that the curves become steeper as the sample size increases; this change is expected because the test becomes more discriminating as the sample size increases. For sample sizes of 100 to 500 units, these curves show that the modified Large-N test is similar to or more stringent than the ICH UDU test.  

The acceptance criteria for the Large-N and modified Large-N tests do not include a requirement for zero tolerance of tablets outside 75–125% LC, which is a requirement of the 30-sample ICH UDU test. Passing a batch using the Large-N or modified Large-N test with a zero-tolerance criterion depends on the sample size and the true proportion of tablets falling outside 75–125% LC. If the content-uniformity results follow a normal distribution, the following provides justification against a zero-tolerance rule because there is inherent control of the number of tablets outside 75–125% LC through counting the number of tablets outside 85–115%. Adding a zero-tolerance rule would act as a disincentive to collecting the larger sample size, which could result in a deterrent to process understanding.  

The modified Large-N test inherently controls the number of tablets outside 75–125% LC through controlling the number outside 85–115% LC. To evaluate the probability of tablets falling outside 75–125% LC, calculations were performed assuming that the content-uniformity results followed a normal distribution. Figure 5 shows the control of tablets outside 75–125% LC through implementation of the modified Large-N test. Note that for a sample size of 500, the probability to accept the batch approaches 0 when 0.1% of the tablets in the batch are outside 75–125% LC for the modified Large-N test, whereas the probability of passing the ICH UDU test is greater than 50%.  

Figure 5: Inherent control of the number of tablets outside 75â125% label claim. ICH UDU is the International Conference on Harmonizations uniformity of dosage units test. 

The probability of a tablet outside 75–125% LC, the number of tablets inspected until one is found outside 75–125% LC, and the number of lots until this event were calculated under several scenarios (see Table III). These probabilities were determined by 1) assuming a normal distribution that allows a 0.5%, 1%, or 3% chance of an individual tablet to fall outside 85–115% LC or 2) selecting probabilities that required no distributional assumption. For example, a batch with a mean of 98% LC and a 1% chance of a tablet falling outside 85–115% LC has a 0.001473% chance of a tablet falling outside 75–125% LC. Therefore, the expected number of inspected tablets required to find one outside 75–125% LC is (1/0.00001473) or 67,888 tablets. If 10 tablets were sampled per batch, as is the case of the ICH UDU test, then 1 tablet outside of 75–125% LC would be detected, on average, every 6789 batches. Increasing the sample size from 10 to 250 tablets tested per batch results in at least 1 tablet detected outside 75–125% LC every 272 batches. This is simply the result of the laws of probability; increasing the sample size increases the chance of obtaining a value outside of 75–125% LC and has no bearing on the true quality of the batch. The batch quality has not changed, but the batch-rejection rate would. Adding a zero-tolerance requirement for tablets outside 75–125% LC would be a disincentive to increasing the sample size, and hence a barrier to increased process understanding. Note that the probability of falling outside 75–125% LC is all that is needed for the calculation (i.e., the distribution does not matter—only the probability).  

Table III: Expected number of tablets to detect one result outside 75â125% label claim (LC).  

The modified Large-N counting test controls the percent of tablets outside 85–115% LC to no more than 3%. As the sample size increases (e.g., from 100 to 500 units), the OC curve becomes steeper, the test's discriminating ability increases, and the level of quality assurance is raised.  

The modified test maintains the beneficial properties of the original test. This test has the advantage of being mathematically simple and simple to implement, requiring only a look-up table or a simple mathematical calculation. There is 

 flexibility in selecting the sample size. Similar to the original Large-N test, this test is nonparametric, having  the benefit that the test behaves well when the underlying distribution is not normal and testing for normality is not required. 

Because this proposed test inherently controls the number of tablets outside 75–125% LC and zero tolerance on this population of tablets could create a disincentive to process understanding and future technology development, the authors recommend careful thought about additional test requirements. 

The authors wish to thank Fasheng Li, associate director of statistics–Groton at Pfizer (New York) for creating the plots used in the paper. Thank you to Tom Garcia, a research fellow for global regulatory CMC–Groton at  Pfizer and Ambarish Singh, associate director of global regulatory sciences–CMC at Bristol-Myers Squibb (New York) for reviewing the paper. 

* is an associate director of nonclinical biostatistics at Bristol-Myers Squibb, 1 Squibb Drive, New Brunswick, NJ 08903, tel. 732.227.5981, fax 732.227.3005, 

 is a director of nonclinical statistics at Pfizer. 

*To whom all correspondence should be addressed. 

Submitted: Mar. 15, 2010. Accepted: Apr. 12, 2010. 

 28 Reissue, General Chapter <905>, "Uniformity of Dosage Units," (US Pharmacopeial Convention, Rockville, MD, Oct. 2010, pp. R–86).  

The authors describe a modified version of the Large-N test used to determine content uniformity.