[PPT] - Bootstrap approach for dissolution similarity testing, performance PowerPoint Presentation

SLIDE 1

Leslie Van Alstine May 21, 2019

Bootstrap approach for dissolution similarity testing, performance and limitations

SLIDE 2

Introduction

Outline:

Use of the f2 for dissolution profile similarity

testing and the issue with large within batch (unit-to-unit) variability

Introduction to bootstrapping as a statistical

technique

Applications of bootstrapping for dissolution

profile similarity testing

Summary of Pros/Cons of using bootstrapping

SLIDE 3

Dissolution Profile Similarity Comparison

Moore, J. W. and H. H. Flanner, 1996, "Mathematical Comparison of Dissolution Profiles“, Pharmaceutical Technology, 20 (6):64-74. 𝑔

2 = 50 × 𝑚𝑝𝑕10

100 1 + σ𝑢=1

𝑜

𝑆𝑢 − 𝑈𝑢

2

𝑜

10 20 30 40 50 60 70 80 90 100 10 20 30 40 50 60 70 80 90 100

Calculated f2 Average Difference Between Reference and Test Curves (%)

Relationship Between f2 and the Average Distance Between Curves

Most Commonly Used Test – f2

SLIDE 4

Dissolution Profile Similarity Comparison

Shortly after Moore and Flanner published their article, it was suggested that the f2 statistic might be problematic when the within batch variability was high due to there being too much uncertainty in the estimates

f

the means. 𝑔

2 = 50 × 𝑚𝑝𝑕10

100 1 + σ𝑢=1

𝑜

𝑆𝑢 − 𝑈𝑢

2

𝑜

SLIDE 5

Criteria USA EMA Brazil Canada # of time points Minimum of 3 Minimum of 3 (excluding 0) Minimum of 5 (excluding 0) Adequate sampling until 90% of drug is dissolved or an asymptote is reached. Last time point When both Reference and Test batches have reached 85% released When either the Reference or the Test batch reaches 85% released When both Reference and Test batches have reached 85% released When both Reference and Test batches have reached 85% released

Limits on variability

RSD < 20% at early time points and < 10% at all other time points RSD < 20% at first time point and < 10% at all

ther time

points RSD < 20% at early time points (first 40%) and < 10% at all others RSD < 20% at early time points and < 10% at all other time points

f2 Guidance for Immediate Release Products

Varies by Country

SLIDE 6

Alternatives to f2 when variability criteria not met

Bootstrapping as an alternative does not appear in any of the regulatory guidances.

Shah, V.P., Y. Tsong, P. Sathe and

J.P. Liu, 1998, “In Vitro Dissolution Profile Comparison – Statistics and Analysis of the Similarity Factor, f2”, Pharmaceutical Research, Vol. 15, No. 6, pp 889-896.

SLIDE 7

Bootstrapping is a statistical technique for generating an

estimate of the sampling distribution of a statistic that was introduced by Bradley Efron in 1979 (“Bootstrap Methods: Another Look at the Jacknife”; The Annals of Statistics, Vol. 7, No. 1, pp 1-26.)

Technique based on using available data to resample

from the data with replacement to generate the sampling distribution of a statistic where the theoretical distribution is complex or unknown Bootstrapped f2 – generate distribution of f2 values based

n observed data; if lower 5th percentile is greater than 50 –

declare similarity

Bootstrapping

SLIDE 8

Bootstrap Example – Confidence Interval for Sample Mean

10 5

5

Median Mean 3 2 1

1
2

1st Quartile

3.30635

Median 0.05173 3rd Quartile 2.42906 Maximum 9.52552

1.79365

2.21047

2.14477

2.32930 3.68498 6.65087 A-Squared 0.27 P-Value 0.645 Mean 0.20841 StDev 4.74127 Variance 22.47965 Skewness 0.125455 Kurtosis

0.404760

N 24 Minimum

7.88222

Anderson-Darling Normality Test 95% Confidence Interval for Mean 95% Confidence Interval for Median 95% Confidence Interval for StDev

95% Confidence Intervals

Original n=24 Generated From Normal (0,5)

A random sample of 24
bservations are taken from

a Normal distribution with mean 0 and a standard deviation of 5.

Want to construct a 95%

confidence interval about the mean

To construct a bootstrapped

confidence interval for the mean.

Sample 24 observations

with replacement from the

riginal data set.
Calculate the average for

each random sample

Do many times

BS10 BS9 BS8 BS7 BS6 BS5 BS4 BS3 BS2 BS1 Orig 15 10 5

5
10
15

Sample Set Data Values Individual Value Plot of Original Data and 10 Subsamples Done With Replacement

0.63 1.58 -1.44 -0.01 -0.50 0.94 -0.54 -1.05 -2.38 -0.24

3 2 1

1
2
3

Mean

Distribution of Averages From First 10 Bootstrap Samples

SLIDE 9

Bootstrapping Example

Repeat the process a large number of times (say, 10,000). The

resulting distribution of the sample means appears below.

For this example, the bootstrapped 95% confidence interval is

determined by identifying the points corresponding to the 2.5th and 97.5th percentiles (dashed lines below at -1.63, 2.05)

SLIDE 10

Bootstrapped f2 analysis from product transfer

Dissolution Time Points (min) Reference Sample Test Sample Mean RSD Mean RSD 15 30.3 16.1 34.8 8.5 30 55.9 15.2 53.8 8.0 45 75.6 11.9 70.8 7.2 60 89.3 8.1 85.3 5.8 90 100 2.7 98.8 2.1 Variability of reference sample at 30 and 45 minute dissolution time points is greater than that recommended by most regulatory agencies

20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0 100.0 110.0 15 30 45 60 75 90 Dissolution (% Released) Minutes

Average Dissolution Profiles - Mean ± 2 StDev

Reference Test

SLIDE 11

Bootstrapped f2 analysis from product transfer

81.6 76.8 72.0 67.2 62.4 57.6 52.8 350 300 250 200 150 100 50 Resulting f2 Value Frequency f2 = 69.5 5th percentile = 60.2

Distribution of Bootstrapped f2 Values Based on r=5,000 Results

Bootstrapped f2 5th percentile > 50

SLIDE 12

Example with large variability

Variability of test sample at multiple time points is greater than that recommended by most regulatory agencies Dissolution Time Points (min) Reference Sample Test Sample Mean RSD Mean RSD 10 47.2 13.8 37.3 28.6 15 60.9 10.0 52.7 20.0 20 70.0 8.4 64.0 13.5 30 80.6 6.1 77.8 7.2 45 89.5 3.1 88.5 3.2

10 20 30 40 50 60 70 80 90 100 5 10 15 20 25 30 35 40 45 50 Dissolution (% Released) Minutes

Average Dissolution Profiles - Mean ± 2 StDev

Reference Test

SLIDE 13

Example with large variability

Bootstrapped f2 5th percentile < 50

SLIDE 14

Summary – Bootstrapped f2 analysis

Bootstrapped f2 – is a statistically acceptable and valuable approach for comparing dissolution profiles Pros:

– well understood technique which has been around for a long time – provides a simple answer which most people can conceptualize – does not require any distributional assumptions – software is available for doing the simulations (DDSolver)

SLIDE 15

Summary – Bootstrapped f2 analysis

Bootstrapped f2 – is a statistically acceptable and valuable approach for comparing dissolution profiles Cons:

– does not address issues of biorelevance that apply to the f2 – not clear what rules should apply to time point selection – while software is available, some can be complex for non- statisticians – may be conservative???

SLIDE 16

Leslie Van Alstine May 21, 2019

Bootstrap approach for dissolution similarity testing, performance and limitations

Introduction

Outline:

testing and the issue with large within batch (unit-to-unit) variability

technique

profile similarity testing

Dissolution Profile Similarity Comparison

Dissolution Profile Similarity Comparison

Shortly after Moore and Flanner published their article, it was suggested that the f2 statistic might be problematic when the within batch variability was high due to there being too much uncertainty in the estimates

the means. 𝑔

100 1 + σ𝑢=1

𝑆𝑢 − 𝑈𝑢

𝑜

Limits on variability

f2 Guidance for Immediate Release Products

Varies by Country

Alternatives to f2 when variability criteria not met

Bootstrapping as an alternative does not appear in any of the regulatory guidances.

J.P. Liu, 1998, “In Vitro Dissolution Profile Comparison – Statistics and Analysis of the Similarity Factor, f2”, Pharmaceutical Research, Vol. 15, No. 6, pp 889-896.

estimate of the sampling distribution of a statistic that was introduced by Bradley Efron in 1979 (“Bootstrap Methods: Another Look at the Jacknife”; The Annals of Statistics, Vol. 7, No. 1, pp 1-26.)

from the data with replacement to generate the sampling distribution of a statistic where the theoretical distribution is complex or unknown Bootstrapped f2 – generate distribution of f2 values based

declare similarity

Bootstrapping

Bootstrap Example – Confidence Interval for Sample Mean

a Normal distribution with mean 0 and a standard deviation of 5.

confidence interval about the mean

confidence interval for the mean.

Bootstrapping Example

resulting distribution of the sample means appears below.

determined by identifying the points corresponding to the 2.5th and 97.5th percentiles (dashed lines below at -1.63, 2.05)

Bootstrapped f2 analysis from product transfer

Bootstrapped f2 analysis from product transfer

Example with large variability

Example with large variability

Summary – Bootstrapped f2 analysis

Bootstrapped f2 – is a statistically acceptable and valuable approach for comparing dissolution profiles Pros:

– well understood technique which has been around for a long time – provides a simple answer which most people can conceptualize – does not require any distributional assumptions – software is available for doing the simulations (DDSolver)

Summary – Bootstrapped f2 analysis

Bootstrapped f2 – is a statistically acceptable and valuable approach for comparing dissolution profiles Cons:

– does not address issues of biorelevance that apply to the f2 – not clear what rules should apply to time point selection – while software is available, some can be complex for non- statisticians – may be conservative???

Conclusion

Thank you!

Any Questions?