Large sample dose content uniformity test: parametric and nonparametric (counting) Meiyu Shen, PhD Collaborators: Xiaoyu Dong, Ph.D., Yi Tsong, PhD Office of Biostatistics, CDER, FDA * This presentation contains opinions of the authors that do not represent the official position of U.S. Food and Drug Administration

Outline Purpose of uniformity of dosage unit Harmonized USP dose content uniformity test with a small sample Large n dose content uniformity test EU methods Option 1: Parametric method Option 2: Nonparametric method (Counting method) Two one-sided tolerance interval method Comparison between the EU method and the two one-sided tolerance interval method Conclusion

Uniformity of dosage unit The purpose of uniformity of dosage unit The degree of uniformity in the amount of the drug substance among dosage units. Demonstrated by one of the follows Dose content uniformity (focus here) based on the assay of the individual content of drug substance(s) in a number of dosage units Weight variation

Indifferent zone M:

Harmonized USP DCU for small n Step 1, 10 tablets Step 2, additional 20 tablets No Yes Fail Yes Pass Pass

Take n tablets, {Xi}, i=1,2,…,n EU option 1 for large n≥100 Take n tablets, {Xi}, i=1,2,…,n No Fail Yes 6 Pass

Take n tablets, {Xi}, i=1,2,…,n EU option 2 for large n≥100 Take n tablets, {Xi}, i=1,2,…,n No Fail Yes Pass 7

EU Option 2 acceptable number of individual units c1 outside (1±0 EU Option 2 acceptable number of individual units c1 outside (1±0.15) and c2 outsides (1±0.25) n c1 c2 100 3 123 150 176 5 1 196 6 …. …

Take n tablets, {Xi}, i=1,2,…,n PTIT_matchUSP90 Take n tablets, {Xi}, i=1,2,…,n No Fail Yes Pass 9

EU option 1 and PTIT_matchUSP90 Two-sided tolerance interval Control probability within (85,115)% Two-sided hypothesis Two one-sided tolerance interval Control probability each tail outside (85,115)% Two one-sided hypothesis P (1-P)/2

EU option 1 and PTIT_matchUSP90 Formula for K Confidence level: 1-α=0.95 Each tail probability: (1-p(n))/2 For n=30, p=82.04%, Formula for K Confidence level: Center Coverage:

K values of EU Option 1 and PTIT_matchUSP90 Sample size PTIT_matchUSP90 EU Option 1 100 2.0475 2.15 1000 2.2321 2.27

Normal: on target product, mean=100%

Normal: off target product, mean=102%

Mixed normal: on target overall mean

Mixed normal: off target overall mean

Bias of EU Option 1

Special distribution Assume the individual tablet dose content is distributed as a uniform distribution in the range from 85% to 115% with 97% probability and a value 84% with 3% probability. The probability of passing USP harmonized DCU is 3.72% for a sample size of 30 tablets. Comparison of EU Option 2 and PTIT_matchUSP90 in next table EU Option 2 has 45.5% probability to pass the DCU test when n=300. the PTIT_macthUSP90 has zero passing probability for n≥100.

EU Option 2 and PTIT_matchUSP90 Xi: a uniform distribution in the range from 85% to 115% with 97% probability and a value 84% with 3% probability Sample size, n Acceptance probability EU option 2 PTIT_USPmatch90 100 0.6458 150 0.5276 200 0.6047 300 0.455 500 0.3509 1000 0.2075

EU Option 2 and PTIT_matchUSP90 for 2 special cases Sample size, n Passing probability EU Option 2 PTIT_matchUSP90 Xi is 100 with 97% probability, and 50 with 3% probability. 100 0.641 0.196 150 0.523 0.172 Xi is 90 with 97% probability, and 50 with 3% probability. 0.648 0.045 0.530 0.012

Conclusion A large difference in acceptance probability between EU option 1 and PTIT_matchUSP90 when the batch mean is off-target. Larger passing probability for EU Option 1 than PTIT_matchUSP90 No much difference in acceptance probability between EU option 1 and PTIT_matchUSP90 when the batch mean is on-target. Bias of EU Option 1 EU Option 1 has higher probability of passing the off-target product than that of passing the on-target mean product for a given coverage within (85%, 115%)

Conclusion (continued) EU Option 2 Issue with a large variability for a mixture of 97% probability of distributing uniformly with (85%, 115%) and 3% probability of being 84%) using a sample of 200 60% probability to pass EU Option 2 0% probability to pass PTIT_matchUSP90 3% probability to pass USP harmonized Issue with a location shift of the mean product The same probability to pass the EU Option 2 for 97% population with 100% content and 97% population with 90% content. Off target product: 97% population with 90% content using a sample of 150. >50% probability to pass the EU Option 2 About 1% probability to pass PTIT_matchUSP90

References USP Pharmacopoeia 2015 European Pharmacopoeia 7.7 Meiyu Shen, Yi Tsong, Xiaoyu Dong, Statistical Properties of Large Sample Tests for Dose Content Uniformity, Therapeutic Innovation & Regulatory Science, 2014, Vol. 48(5) 613-622 Meiyu Shen and Yi Tsong, Bias Of The United States Pharmacopeia Harmonized Test For Dose Content Uniformity, United States Pharmacopeia forum, January 2011

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