Download presentation_5-22-2015-10-57-4.counting procedure and dose

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
1
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:
M  98.5% if X  98.5%.;
M  101.5% if X  101.5%;
M  X otherwise.
•
M  X  K  s  15
83.5%  X  K  s  X  K  s  113.5% if X  98.5%.;
86.5%  X  K  s  X  K  s  116.5% if X  101.5%;
K  s  15 otherwise.
4
Harmonized USP DCU for small n
Step 1, 10 tablets
Step 2, additional 20 tablets
M  X  K  s  15%
No outside (0.75 M, 1.25M)
K  2.4
M  X  K  s  15%
No outside (0.75 M, 1.25M)
K  2.0
No
Yes
Pass
Fail
Yes
5
Pass
EU option 1 for large n≥100
Take n tablets, {Xi}, i=1,2,…,n
M  X  K  s  15%
n
&  I  X i  1  0.25M   c 2.
i 1
Here, K  Z 1 
2
n  1/ n
,   0.84,   0.91.
 2 n  1
No
Fail
Yes
Pass
6
EU option 2 for large n≥100
Take n tablets, {Xi}, i=1,2,…,n
n
 I X
i 1
i
 1  0.15  c1
n
&  I  X i  1  0.25  c 2.
i 1
No
Fail
Yes
Pass
7
EU Option 2 acceptable number of
individual units c1 outside (1±0.15) and c2
outsides (1±0.25)
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}, i=1,2,…,n
100%  X  K  s  15%
1  Pn 
 X  Ks
Here, K : Pr 
f x :  ,  dx 
  1
2 
 
2
1
f x :  ,   
e  x    2 2
2 


No
Fail
Yes
Pass
9
EU option 1 and PTIT_matchUSP90
EU Option 1
• Two-sided tolerance
interval
PTIT_matchUSP90
• Two one-sided tolerance
interval
– Control probability within
(85,115)%
• Two-sided hypothesis
H 0 : Pr L  X  U   P
H 1 : Pr L  X  U   P
P
– Control probability each tail
outside (85,115)%
•
Two one-sided hypothesis
H 0 : Pr  X  L   1  Pn  / 2  Pr X  U   1  Pn  / 2
H 1 : Pr  X  L   1  Pn  2  Pr  X  U   1  Pn  2
(1-P)/2
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EU option 1 and PTIT_matchUSP90
EU Option 1
• Formula for K
– K  Z 1
2
n  1/ n
 2 n  1
– Confidence level:   0.84
– Center Coverage:   0.91
PTIT_matchUSP90
• Formula for K
–
K  tn 1,1 (Z1 p ( n ) n ) / n
2
– Confidence level: 1-α=0.95
– Each tail probability: (1-p(n))/2
– For n=30, p=82.04%,
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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, mean=100%
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Normal: off target product, mean=102%
14
Mixed normal: on target overall mean
15
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 n=300.
• the PTIT_macthUSP90 has zero passing probability for
n≥100.
18
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
100
150
200
300
500
1000
Acceptance probability
EU option 2 PTIT_USPmatch90
0.6458
0
0.5276
0
0.6047
0
0.455
0
0.3509
0
0.2075
0
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EU Option 2 and PTIT_matchUSP90
for 2 special cases
Case
Sample size, n Passing probability
EU Option 2 PTIT_matchUSP90
Xi is 100 with 97%
probability, and 50
with 3%
probability.
Xi is 90 with 97%
probability, and 50
with 3%
probability.
100
150
0.641
0.523
0.196
0.172
100
150
0.648
0.530
0.045
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.
– >50% 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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