1. 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

2. 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

3. 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

4. Indifferent zone M:

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

6. 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

7. 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

8. 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 …. …

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

10. 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

11. 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:

12. 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

13. Normal: on target product, mean=100%

14. Normal: off target product, mean=102%

15. Mixed normal: on target overall mean

16. Mixed normal: off target overall mean

17. Bias of EU Option 1

18. 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.

19. 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

20. 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

21. 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%)

22. 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

23. 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)
Meiyu Shen and Yi Tsong, Bias Of The United States Pharmacopeia Harmonized Test For Dose Content Uniformity, United States Pharmacopeia forum, January 2011

24. Thank you!