In Vitro Dissolution Profile Comparison for Highly Variable Dissolution Data: Biased-Corrected and Accelerated (BCA) Bootstrap Methodology for f2

1. In Vitro Dissolution Profile Comparison for Highly Variable
Dissolution Data:
Biased-Corrected and Accelerated (BCA) Bootstrap
Methodology for f2
November 16
Loan Pham, Ph.D.
Pharmacokinetic Specialist
Camargo Pharmaceutical Services
9825 Kenwood Road, Suite 203
Cincinnati, OH 45242

2. The relative standard deviation (RSD) for each analysis should be
not more than (NMT) 20% at early time points (eg, 15 min)
The RSD should be NMT 10% for all other points
Introduction
When variability exceeds the f2 rules,
other statistical models should be
considered.
o Biased-Corrected and Accelerated (BCA)
Bootstrap

3. Tablet 5 min 10 min
15
min 20 min 30 min
1 8 39 63 78 89
2 14 49 72 83 91
3 19 32 74 83 90
4 19 54 75 85 91
5 20 53 73 83 90
6 15 50 71 82 90
7 16 52 73 80 88
8 21 53 74 83 90
9 6 36 59 73 87
10 6 27 61 76 87
11 5 56 78 86 92
12 16 47 70 81 89
Mean 13.8 45.7 70.3 81.1 89.5
SD 5.9 9.7 6.0 3.8 1.6
%RSD 43.2 21.2 8.5 4.7 1.8
Tablet 5 min 10 min 15 min 20 min 30 min
1 12 52 67 86 89
2 14 49 72 88 91
3 19 32 74 86 90
4 19 54 75 85 91
5 22 56 73 82 90
6 15 50 71 82 90
7 22 55 73 86 88
8 21 53 74 83 90
9 6 36 59 85 87
10 6 27 61 84 87
11 5 56 78 86 92
12 16 47 70 88 89
Mean 14.8 47.3 70.6 85.1 89.5
SD 6.3 10.0 5.6 2.0 1.6
%RSD 42.8 21.1 8.0 2.4 1.8
Introduction
Example of individual dissolution data from the Test and Reference Batches

4. 1. The Non-parametric Bootstrap Method is used for BCA bootstrapped
f2
2. The Parametric Bootstrap Method
o Resampling
o Random sampling with replacement,
o Same size (n=12) with the original dissolution
dataset
o Utilize information from the observed
sample to generate numbers from a
defined distribution, and we do the re-
sampling from that numbers.
Introduction

5. Example of a random non-parametric bootstrap sample:
Reference Batch Test Batch
2 × tablet 1 1 × tablet 2
4 × tablet 5 3 × tablet 5
2 × tablet 8 1 × tablet 8
4× tablet 9 1 × tablet 9
4 × tablet 10
2 × tablet 12
N = 12 N = 12
Introduction

6. • SAS®
• SAS code was written to calculate bias-corrected
and accelerated (BCA) CI:
o Bias-corrected: corrects potential systematic
underestimation or overestimation of the
estimate, f2.
o Accelerated: corrects potential influence of
each individual record on the estimate, f2.
BCA Bootstrap f2 Methodology

7. The SAS code was written to perform the
following steps:
1. Generate N bootstrap samples (eg,
N=1000)
2. Calculate f2 values from N bootstrap
samples.
3. Calculate bias-corrected and accelerated
(bca) 90% CI intervals:
a. Calculate the bias correction statistic
to correct for the potential skewed
distribution of f2 derived from the
bootstrap samples.
b. Calculate lower and upper bounds of
the 90% confidence interval
BCA Bootstrap f2 Methodology
To declare similarity between test and reference dissolution profiles, the
lower bound of the 90% CI  50.
Lower 90% CI (BCA): 44.24

8. o Useful alternative to inference based on ‘parametric’
assumptions.
Non-Parametric Bootstrapping Method Advantages:
BCA Bootstrap f2 Methodology
Non-Parametric Bootstrapping Method Disadvantages:
o Assumes that the data is a random sample.
o Depends on the sample being representative.
o Requires efficient programming techniques.

9. Lower bound of 90% BCA f2: 54.56
Original f2: 57.24
• Original f2 = 57.24
• RSD = 35%
• Bootstrap n = 1000
• 90% BCA CI: 54.56 – 62.07
Example 1

10. Example 2
• RSD = 172.6%
• Original f2 = 55.55
• Lower 90% Percentile CI: 43
• Lower 90% BCA CI: 49.8
Bootstrap n = 10000

11. • Non-parametric bootstrapping:
o No assumptions on distribution
o Accurate BCA CI of f2
o A robust and reliable approach
Conclusions

12. References
1. Shah VP, Tsong Y, Sathe P, Liu JP. In vitro dissolution profile comparison—
statistics and analysis of the similarity factor, f2. Pharm Res. 1998;15(6):889–
96.
2. Nancy Barker. A Practical Introduction to the bootstrap using the SAS
system.
3. Ocana J, Frutos G, Sanchez P. Using the similarity factor f2 in practice: a
critical revision and suggestions for its standard error estimation.
Chemometr Intell Lab Syst. 2009;99(1):49–56.
4. FDA. NDA 204412 Clinical Pharmacology Review in Summary Basis of
Approval (SBA) for Delzicol (mesalamine) Capsules. 2013.
5. Ruth E. Stevens, Vivian Gray, Angelica Dorantes, Lynn Gold, Loan Pham.
Scientific and Regulatory Standards for Assessing Product Performance
Using the Similarity Factor, f2 AAPS J. 2015 Mar; 17(2): 301–306. Published
online 2015 Feb 12. doi: 10.1208/s12248-015-9723-y PMCID: PMC4365094

13. Acknowledgments
Ly Nguyen, MS
University of Buffalo; School of Pharmacy
and Pharmaceutical Sciences
Lynn Gold, PhD
Camargo Pharmaceutical Services