Large%20sample%20dose%20content%20uniformity%20test:%20parametric%20and%20nonparametric%20(counting)

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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

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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

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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

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Indifferent zone

• M

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Harmonized USP DCU for small n
Step 1, 10 tablets
Step 2, additional 20 tablets
No
Yes
Fail
Yes
Pass
Pass
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EU option 1 for large n100
Take n tablets, Xi, i1,2,,n
No
Fail
Yes
6
Pass
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EU option 2 for large n100
Take n tablets, Xi, i1,2,,n
No
Fail
Yes
Pass
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EU Option 2 acceptable number of individual units
c1 outside (10.15) and c2 outsides (10.25)
n c1 c2
100 3 0
123 3 0
150 3 0
176 5 1
196 6 1
.
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PTIT_matchUSP90
Take n tablets, Xi, i1,2,,n
No
Fail
Yes
Pass
9
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EU option 1 and PTIT_matchUSP90

• EU Option 1

• 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
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EU option 1 and PTIT_matchUSP90

• EU Option 1

• PTIT_matchUSP90

• Formula for K
• Confidence level 1-a0.95
• Each tail probability (1-p(n))/2
• For n30, p82.04,

• Formula for K
• Confidence level
• Center Coverage

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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
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Normal on target product, mean100
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Normal off target product, mean102
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Mixed normal on target overall mean
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Mixed normal off target overall mean
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Bias of EU Option 1
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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 n300.
• the PTIT_macthUSP90 has zero passing probability
  for n100.

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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 Acceptance probability
Sample size, n EU option 2 PTIT_USPmatch90
100 0.6458 0
150 0.5276 0
200 0.6047 0
300 0.455 0
500 0.3509 0
1000 0.2075 0
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EU Option 2 and PTIT_matchUSP90for 2 special
cases
Case Sample size, n Passing probability Passing probability
Case Sample size, n EU Option 2 PTIT_matchUSP90
Xi is 100 with 97 probability, and 50 with 3 probability. 100 0.641 0.196
Xi is 100 with 97 probability, and 50 with 3 probability. 150 0.523 0.172
Xi is 90 with 97 probability, and 50 with 3 probability. 100 0.648 0.045
Xi is 90 with 97 probability, and 50 with 3 probability. 150 0.530 0.012
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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)

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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.
• gt50 probability to pass the EU Option 2
• About 1 probability to pass PTIT_matchUSP90

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References

• USP Pharmacopoeia 2015
• European Pharmacopoeia 7.7
• European Pharmacopoeia 8.1
• 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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Thank you!