Evaluation of Validation Dissolution Test Results Using Lower

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Evaluation of Validation
Dissolution Test Results Using
Lower Probability Bound
Distribution Charts
Pramote Cholayudth
INTRODUCTION
The concept of using probability charts in the article
entitled “Evaluation of Validation Content Uniformity
Test Results Using Probability Distribution Charts,”
published in the Journal of Validation Technology (JVT)
(1), is applicable by its title to the content uniformity
test—one of the critical quality attributes (CQAs) in
process validation of oral solid dosage forms (e.g.,
tablets and capsules). Another important CQA in such
a validation exercise is the dissolution test. The approach to compute the probability of passing the test
was introduced, in addition to computing the probability for content uniformity test, by J.S. Bergum in
1990 (2) using the SAS program and developed into
a Microsoft Excel (MS Excel) program by the author
in 2006 (3).
To provide an alternative to computation of the
probability of passing the dissolution test by the MS
Excel program, this article introduces an approach of
using the lower probability bound distribution charts,
constructed using Bergum’s method, for evaluation
of validation dissolution test results. The approach is
similar to that described in the previously-mentioned
JVT article.
USP TEST ACCEPTANCE CRITERIA
The USP dissolution test is summarized in Table I.
[
For more Author
information,
go to ivthome.com
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PROBABILITY OF PASSING THE
DISSOLUTION TEST
Based on Bergum’s method described in “Using the Bergum
Method and MS Excel to Determine the Probability of Passing the USP Dissolution Test” (3), the probability formulae are illustrated in Tables II and III. Readers can either
copy the formulae in the tables to construct a two-sheet
MS Excel file for computing the probability or download
the MS Excel file from www.ivthome.com/JVTSummer.
The computed probability values (in Table II) are the
lower bounds, because the upper bound (UB) for the
standard deviation (SD) and the lower bound (LB) for
the mean are used for the computation. Using the MS
Excel program, the lower probability bound distribution
charts for various sample means and standard deviations
(SDs) can be constructed, and their example is illustrated
in Figure 1. Figure 2 is identical to Figure 1, except that
the difference values between the sample means and the
Q value are plotted instead of the mean values (the formula is derived in Appendix 1). Now the new chart can
be applied to any Q value, which becomes the advantage
for construction of the probability charts with “Mean-Q”
values on the X-axis in this article.
From the two figures, all the curves are overlapping at
the 100% probability level. To reduce the difficulty of
identifying the probability results at about 100%, another
chart is constructed for initial evaluation, as illustrated
in Figure 3 (reproduced from page 4 of Appendix 2).
ABOUT THE AUTHOR
Pramote Cholayudth is a validation consultant to Biolab in Thailand and executive director of Valitech, a wellestablished GMP and validation service firm to the pharmaceutical industry. He is a guest speaker on process validation
to the industry organized by local FDA. He can be contacted by e-mail at cpramote2000@yahoo.com.
VALIDATION TECHNOLOGY [SUMMER 2008]
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P R A M O T E C H O L AY U D T H
Table I: Dissolution test acceptance criteria.
Stage #
Test Sample Size
Acceptance Criteria
Stage 1 (S1)
Test 6 units.
Pass if each unit is not less than Q+5%.
Stage 2 (S2)
Test 6 additional units.
Pass if mean of 12 units (S1+S2) is not less than Q%
and no unit is less than Q-15%.
Stage 3 (S3)
Test 12 additional units.
Pass if mean of 24 units (S1+S2+S3) is not less than
Q% and not more than two units are less than Q-15%
and no unit is less than Q-25%.
Where Q is the amount of dissolved active ingredient specified in the individual monograph, expressed as a percentage of the labeled content (LC) of the dosage unit, e.g., Q = 80% LC.
Table II: Microsoft Excel formula sheet1.
Excel Sheet1
A
B
C
80
1
Q Value (% LC)
80
2
Joint Confidence Level (%)
95
3
Sample Size (n)
20
4
Sample Mean (% LC)
84.00
5
Sample SD (% LC)
Lower (0.95^0.5)x100 % Conf. Limit –
Mean
3.00
6
7
Upper (0.95^0.5)x100 % Conf. Limit - SD
8
Probability of Passing USP Test
9
Sampling Plan #
D
82.09
86.27
4.38
4.33
99.03%
100.00%
Plan 1
Plan 2
E
For sampling plan 1, follow column B.
B1: Q Value (entry data)
B2: Joint Confidence Level (entry data) = (0.95^0.5)x(0.95^0.5) = 0.95 = 95%
B3: Sample Size (entry data)
B4: Sample Mean (entry data)
B5: Sample SD (entry data)
B6 =B4-B7*NORMSINV(1-(1-(B2/100)^0.5))/B3^0.5
B7 =B5*((B3-1)/(CHIINV((B2/100)^0.5,B3-1)))^0.5
B8 =MAX((1-NORMSDIST(((B1+5)-B6)/B7))^6,(1-NORMSDIST(((B1-15)-B6)/B7))^12+(1-NORMSDIST((12^0.5)*(B1-B6)/B7))-1,(1NORMS DIST(((B1-15)-B6)/B7))^24+COMBIN(24,1)*(1-NORMSDIST(((B1-15)-B6)/B7))^23*(NORMSDIST(((B1-15)-B6)/B7)NORMSDIST(((B1-25)-B6)/B7))+COMBIN(24,2)*(1-NORMSDIST(((B1-15)-B6)/B7))^22*(NORMSDIST(((B1-15)-B6)/B7)-NORMSDIST(((B1-25)-B6)/B7))^2+(1-NORMSDIST((24^0.5)*(B1-B6)/B7))-1) (Reproduced from references [3, 4])
For sampling plan 2, follow column C and Table III. Plan 2 is, for example, 6x3 (6 units/locationx3 locations).
C6 =Sheet2!D9-NORMSINV(1-(1-0.95^(1/3))/2)*Sheet2!D12
C7 =Sheet2!D13
The formula for C8 is the same as B8, replace B1, B6 & B7 with C1, C6 & C7, respectively.
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Table III: Microsoft Excel formula sheet2.
Excel Sheet2
A
B
1
C
D
6 units/location x 3 locations
E
F
n
6
G
H
Unit #
2
Loc # 1
Loc # 2
Loc # 3
L
3
nxL
18
3
1
100.30
99.00
103.80
4
2
100.90
101.40
100.50
5
3
101.30
100.60
97.50
6
4
101.90
103.20
100.60
7
5
101.60
100.80
99.00
8
6
100.90
103.20
102.90
9
Sample Mean
101.08
10
Within-location SD (SE)
1.68
11
Between-location SD (SM)
0.81
12
95% Upper Bound – SM
6.20
13
95% Upper Bound – SD
4.33
B3-D8 is the entry data area.
D9 =AVERAGE(B3:D8)
D10 =((SUM(DEVSQ(B3:B8),DEVSQ(C3:C8),DEVSQ(D3:D8)))/((F1-1)*F2))^0.5
D11 =((DEVSQ(B3:D8)-(SUM(DEVSQ(B3:B8),DEVSQ(C3:C8),DEVSQ(D3:D8))))/(F2-1))^0.5
D12 =(D11^2*(F2-1)/CHIINV(0.95^(1/3),(F2-1)))^0.5 (linked to Sheet1)
D13 =(IF((D10*((F1-1)*F2)/CHIINV(0.95^(1/3),((F1-1)*F2)))>=(D11*(F2-1)/CHIINV(0.95^(1/3),(F2-1))),(D10*((F1-1)*F2)/CHIINV(0.95^(1/3),((F11)*F2))),(2/3)*(D10*((F1-1)*F2)/CHIINV(0.95^(1/3),((F1-1)*F2)))+(1/3)*(D11*(F2-1)/CHIINV(0.95^(1/3),(F2-1)))))^0.5 (linked to Sheet1)
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P R A M O T E C H O L AY U D T H
Figure 1: Probability distributions for dissolution test (with Q value).
Figure 2: Probability distributions for dissolution test (without Q value).
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Figure 3: Probability distributions at 100% level (Page 4 of Appendix 2).
About 2.7
Figure 4: Probability distributions (Page 6 of Appendix 2).
Approx. 100%
SD= 1.4
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P R A M O T E C H O L AY U D T H
HOW TO USE THE PROBABILITY CHARTS
Several probability charts are provided in Appendix 2.
The table of contents for Appendix 2 assists practitioners in determining the probability result. Once the validation dissolution test results (sampling plan 1: meanQ, SD, & n and sampling plan 2: mean-Q, SE, SM, &
n) are obtained, one may determine if the probability
result is 100% using the initial evaluation charts in the
early pages of the Appendix 2. If the actual mean-Q result is greater than the determined result, the answer
is 100% probability. If the actual mean-Q result is less
than the determined result, continue with determining on the probability charts in the following pages of
Appendix 2.
For example, if one has a dissolution result – meanQ = 2.4 and SD = 1.4 for sampling plan 1 data of n =
1x20 = 20 (5), the initial evaluation using Figure 3
(page 4 of Appendix 2) shows that at the point SD =
1.4, the mean-Q value is about 2.7. This implies that
the dissolution results with SD = 1.4 and mean-Q at
2.7 or greater will generate the probability result exactly at 100% (i.e., determining on the other charts is
not necessary). In the given example the mean-Q is
2.4; therefore, one has to continue to determine on
Figure 4 (reproduced from page 6 of Appendix 2) and
the probability result is found to be approximately
100%. Page 6 may be printed out, marked as illustrated
in Figure 4, and attached to the validation report as
supporting documentation.
Sampling plan 2 data are required to compute the
sample mean, SE, and SM using the formulae in Table
III and use the three computed parameters (including
mean-Q) for determination of the probability result.
is accomplished. Please note that it is a requirment of
the US Food and Drug Administration that any software that is used to determine quality attributes of a
medical device or drug, even off-the-shelf software such
as MS Excel and SAS, must be validated for its intended
use prior to implementation. In other words, the company that chooses to use the calculations in this paper
within an MS Excel program must independently verify the inputs and outputs, and document this activity, prior to implementation.
REFERENCES
1. Cholayudth, P., “Evaluation of Validation Content Uniformity Test Results Using Probability Distribution Charts,”
Journal of Validation Technology, Volume 14, No. 3, Spring
2008.
2. J. S. Bergum, “Constructing Acceptance Limits for Multiple Stage Tests,” Drug Development and Industrial Pharmacy, 16 (14), Marcel Dekker, Inc, 1990, pp. 2153-2166.
3. Cholayudth, P., “Using the Bergum Method and MS Excel
to Determine the Probability of Passing the USP Dissolution Test,” Pharmaceutical Technology, Volume 30, Number 1, January 2006, www.pharmtech.com.
4. Cholayudth, P., “Application of Probability of Passing
Multiple Stage Tests in Benchmarking and Validation of
Processes” Journal of Validation Technology, Volume 13, No.
4, August 2007.
5. Pluta, P., “Keep in Step with Confidence; Keep in Step
through Benchmarking” Journal of Validation Technology,
Volume 12, No. 1, November 2005.
6. “Chapter <711> Dissolution,” in United States Pharmacopeia 30–National Formulary 25 (US Pharmacopeial Convention, Rockville, MD, 2007). JVT
CONCLUSION
The concept of using probability charts will help validation practitioners and QA/QC personnel involved
visualize the integrated views of the lower probability
bound distributions, and also understand the influence of sample mean location and variability (SD, SE,
and SM) on the probability of passing the USP dissolution test. To provide a complete validation documentation, a completed (drawing & notes are taken) copy
of the page (in Appendix 2) with the probability chart
matching the validation dissolution result should be
prepared and attached. To use the probability charts
accurately one should realize which sampling plan (1
or 2) is being used and then use the correct chart. Sampling plan 1 (e.g., 1x20 or 1x30) is recommended so
that a more simple evaluation of the validation data
ARTICLE ACRONYM LISTING
CQAs
LB
LC
MS
Q
SD
SE
Sigma
SM
UB
USP
Critical Quality Attributes
Lower Bound
Label Claim
Microsoft
Q value (The amount of dissolved active ingredient
specified in the individual monograph, expressed
as a percentage of the labeled content of the
dosage unit) [6]
Standard Deviation (for a Sample)
Square Root of Mean Square Error
Population Standard Deviation
Standard Deviation of Location Means
Upper Bound
United States Pharmacopeia
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APPENDIX 1: EXCEL FORMULAE
Table IV: Probability of passing dissolution test (with Q value).
Probability as a function of Mu and Sigma
=MAX((1-NORMSDIST(((Q+5)-Mu)/Sigma))^6,(1-NORMSDIST(((Q-15)-Mu)/Sigma))^12+(1-NORMSDIST((12^0.5)*(QMu)/Sigma))-1,(1-NORMSDIST(((Q-15)-Mu)/Sigma))^24+COMBIN(24,1)*(1-NORMSDIST(((Q-15)Mu)/Sigma))^23*(NORMSDIST(((Q-15)-Mu)/Sigma)-NORMSDIST(((Q-25)-Mu)/Sigma))+COMBIN(24,2)*(1-NORMSDIST(((Q-15)-Mu)/Sigma))^22*(NORMSDIST(((Q-15)-Mu)/Sigma)-NORMSDIST(((Q-25)-Mu)/Sigma))^2+(1-NORMSDIST
((24^0.5)*(Q-Mu)/Sigma))-1) *
* Reproduced from [3, 4], Mu (m) = Lower Bound (LB) for Mean, Sigma (s) = Upper Bound (UB) for standard deviation (SD)
Table V: Probability of passing dissolution test (with Mean-Q value).
Probability as a function of Mean-Q, Sigma, and n (modified from Table IV)
=MAX((1-NORMSDIST((-(Mu-Q)+5)/Sigma))^6,(1-NORMSDIST((-(Mu-Q)-15)/Sigma))^12+(1-NORMSDIST((12^0.5)*((Mu-Q))/Sigma))-1,(1-NORMSDIST((-(Mu-Q)-15)/Sigma))^24+COMBIN(24,1)*(1-NORMSDIST((-(Mu-Q)15)/Sigma))^23*(NORMSDIST((-(Mu-Q)-15)/Sigma)-NORMSDIST((-(Mu-Q)-25)/Sigma))+COMBIN(24,2)*(1-NORMSDIST((-(Mu-Q)-15)/Sigma))^22*(NORMSDIST((-(Mu-Q)-15)/Sigma)-NORMSDIST((-(Mu-Q)-25)/Sigma))^2+(1-NORMSDI
ST((24^0.5)*(-(Mu-Q))/Sigma))-1)
=MAX((1-NORMSDIST((-(Mean-Sigma*Z/n^0.5-Q)+5)/Sigma))^6,(1-NORMSDIST((-(Mean-Sigma*Z/n^0.5-Q)15)/Sigma))^12+(1-NORMSDIST((12^0.5)*(-(Mean-Sigma*Z/n^0.5-Q))/Sigma))-1,(1-NORMSDIST((-(MeanSigma*Z/n^0.5-Q)-15)/Sigma))^24+COMBIN(24,1)*(1-NORMSDIST((-(Mean-Sigma*Z/n^0.5-Q)15)/Sigma))^23*(NORMSDIST((-(Mean-Sigma*Z/n^0.5-Q)-15)/Sigma)-NORMSDIST((-(Mean-Sigma*Z/n^0.5-Q)-25)/
Sigma))+COMBIN(24,2)*(1-NORMSDIST((-(Mean-Sigma*Z/n^0.5-Q)-15)/Sigma))^22*(NORMSDIST((-(MeanSigma*Z/n^0.5-Q)-15)/Sigma)-NORMSDIST((-(Mean-Sigma*Z/n^0.5-Q)-25)/Sigma))^2+(1-NORMSDIST((24^0.5)*((Mean-Sigma*Z/n^0.5-Q))/Sigma))-1)
=MAX((1-NORMSDIST((-(Mean-Q)-Sigma*Z/n^0.5+5)/Sigma))^6,(1-NORMSDIST((-(Mean-Q)-Sigma*Z/n^0.515)/Sigma))^12+(1-NORMSDIST((12^0.5)*(-(Mean-Q)-Sigma*Z/n^0.5)/Sigma))-1,(1-NORMSDIST((-(Mean-Q)Sigma*Z/n^0.5-15)/Sigma))^24+COMBIN(24,1)*(1-NORMSDIST((-(Mean-Q)-Sigma*Z/n^0.5-15)/Sigma))^23*(NORMSDIST((-(Mean-Q)-Sigma*Z/n^0.5-15)/Sigma)-NORMSDIST((-(Mean-Q)-Sigma*Z/n^0.5-25)/Sigma))+COMBIN(24,2)*(1NORMSDIST((-(Mean-Q)-Sigma*Z/n^0.5-15)/Sigma))^22*(NORMSDIST((-(Mean-Q)-Sigma*Z/n^0.5-15)/Sigma)NORMSDIST((-(Mean-Q)-Sigma*Z/n^0.5-25)/Sigma))^2+(1-NORMSDIST((24^0.5)*(-(Mean-Q)Sigma*Z/n^0.5)/Sigma))-1)
Mu = Lower Bound for Mean = (Sample) Mean-Sigma*NORMSINV(1-(1-(0.95)^0.5))/n^0.5 = Mean-Sigma*Z/n^0.5,
Sigma = Upper Bound for SD, n = Sample Size
APPENDIX 2: PROBABILITY CHARTS
Appendix 2 is available for download at www.ivthome.com/JVTSummer. Probability charts provided in Appendix
2 are presented in order of sampling plan types and overall sample sizes. All the charts are constructed on 95% joint
confidence level. The charts on pages 4 and 5 are recommended for initial evaluation and followed by the following pages (as appropriate) as described in the article. For test results outside the provided charts, please contact
cpramote2000@yahoo.com.
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