Discussion of results outside 75–125%
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 75–125% 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 75–125% 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 a priori 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.