In Vitro Dissolution Profile Comparison for Highly Variable Dissolution Data:

Biased-Corrected and Accelerated (BCA) Bootstrap Methodology for f2

November 16Loan Pham, Ph.D.

Pharmacokinetic Specialist

Camargo Pharmaceutical Services9825 Kenwood Road, Suite 203

Cincinnati, OH 45242

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

Tablet 5

min 10

min 15

min 20 min 30

min 1 8 39 63 78 892 14 49 72 83 913 19 32 74 83 904 19 54 75 85 915 20 53 73 83 906 15 50 71 82 907 16 52 73 80 888 21 53 74 83 909 6 36 59 73 87

10 6 27 61 76 8711 5 56 78 86 9212 16 47 70 81 89

Mean 13.8 45.7 70.3 81.1 89.5SD 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 86 892 14 49 72 88 913 19 32 74 86 904 19 54 75 85 915 22 56 73 82 906 15 50 71 82 907 22 55 73 86 888 21 53 74 83 909 6 36 59 85 87

10 6 27 61 84 8711 5 56 78 86 9212 16 47 70 88 89

Mean 14.8 47.3 70.6 85.1 89.5SD 6.3 10.0 5.6 2.0 1.6

%RSD 42.8 21.1 8.0 2.4 1.8

IntroductionExample of individual dissolution data from the Test and Reference Batches

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

Example of a random non-parametric bootstrap sample:

Reference Batch

Test Batch

2 × tablet 1 1 × tablet 24 × tablet 5 3 × tablet 52 × tablet 8 1 × tablet 84× tablet 9 1 × tablet 9

4 × tablet 102 × tablet 12

N = 12 N = 12

Introduction

• SAS®

• SAS code was written to calculate bias-corrected and accelerated (BCA) CI:

oBias-corrected: corrects potential systematic underestimation or overestimation of the estimate, f2.

oAccelerated: corrects potential influence of each individual record on the estimate, f2.

BCA Bootstrap f2 Methodology

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

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.

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

Example 2

• RSD = 172.6%• Original f2 = 55.55• Lower 90% Percentile CI:

43• Lower 90% BCA CI: 49.8

Bootstrap n = 10000

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

Conclusions

References1. 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

Acknowledgments

Ly Nguyen, MSUniversity of Buffalo; School of Pharmacy and Pharmaceutical SciencesLynn Gold, PhDCamargo Pharmaceutical Services