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

Bootstrap approach for dissolution similarity testing, performance and limitations Leslie Van Alstine May 21, 2019

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

Dissolution Profile Similarity Comparison Most Commonly Used Test – f 2 Moore, J. W. and H. H. Flanner, 1996, 100 " Mathematical Comparison of 𝑔 2 = 50 × 𝑚𝑝𝑕 10 Dissolution Profiles “, Pharmaceutical 2 𝑜 1 + σ 𝑢=1 𝑆 𝑢 − 𝑈 𝑢 Technology , 20 (6):64-74. 𝑜 Relationship Between f2 and the Average Distance Between Curves 100 90 80 70 60 Calculated f2 50 40 30 20 10 0 0 10 20 30 40 50 60 70 80 90 100 Average Difference Between Reference and Test Curves (%)

Dissolution Profile Similarity Comparison 100 𝑔 2 = 50 × 𝑚𝑝𝑕 10 2 𝑜 1 + σ 𝑢=1 𝑆 𝑢 − 𝑈 𝑢 𝑜 Shortly after Moore and Flanner published their article, it was suggested that the f 2 statistic might be problematic when the within batch variability was high due to there being too much uncertainty in the estimates of the means.

f 2 Guidance for Immediate Release Products Varies by Country Criteria USA EMA Brazil Canada # of time points Minimum of 3 Minimum of 3 Minimum of 5 Adequate (excluding 0) (excluding 0) sampling until 90% of drug is dissolved or an asymptote is reached. Last time point When both When either the When both When both Reference and Reference or the Reference and Reference and Test batches Test batch Test batches Test batches have reached reaches 85% have reached have reached 85% released released 85% released 85% released RSD < 20% at RSD < 20% at RSD < 20% at RSD < 20% at Limits on early time first time point early time early time variability points and < and < 10% at all points (first points and < 10% at all other other time 40%) and < 10% 10% at all other time points points at all others time points

Alternatives to f 2 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, f 2 ”, Pharmaceutical Research, Vol. 15, No. 6, pp 889-896.

Bootstrapping • 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 f 2 – generate distribution of f 2 values based on observed data; if lower 5th percentile is greater than 50 – declare similarity

Bootstrap Example – Confidence Interval for Sample Mean  A random sample of 24 observations are taken from a Normal distribution with Original n=24 Generated From Normal (0,5) Distribution of Averages From First 10 Bootstrap Samples Individual Value Plot of Original Data and 10 Subsamples Done With Replacement mean 0 and a standard 15 Anderson-Darling Normality Test A-Squared 0.27 deviation of 5. P-Value 0.645 10 Mean 0.20841  Want to construct a 95% StDev 4.74127 Variance 22.47965 5 Skewness 0.125455 confidence interval about Kurtosis -0.404760 Data Values N 24 the mean Minimum -7.88222 0 1st Quartile -3.30635 Median 0.05173  -5 0 5 10 To construct a bootstrapped 3rd Quartile 2.42906 -5 Maximum 9.52552 95% Confidence Interval for Mean confidence interval for the -1.79365 2.21047 -10 95% Confidence Interval for Median -3 -2 -1 0 1 2 3 mean. -2.14477 2.32930 Mean 95% Confidence Intervals 95% Confidence Interval for StDev • -15 Sample 24 observations -0.63 1.58 -1.44 -0.01 -0.50 0.94 -0.54 -1.05 -2.38 -0.24 Mean 3.68498 6.65087 Orig BS1 BS2 BS3 BS4 BS5 BS6 BS7 BS8 BS9 BS10 Median with replacement from the Sample Set -2 -1 0 1 2 3 original data set. • Calculate the average for each random sample • Do many times

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 2.5 th and 97.5 th percentiles (dashed lines below at -1.63, 2.05)

Bootstrapped f 2 analysis from product transfer Dissolution Time Reference Sample Test Sample Variability of reference Points (min) Mean RSD Mean RSD sample at 30 and 45 minute dissolution 15 30.3 16.1 34.8 8.5 time points is greater 30 55.9 15.2 53.8 8.0 than that 45 75.6 11.9 70.8 7.2 recommended by most regulatory 60 89.3 8.1 85.3 5.8 agencies 90 100 2.7 98.8 2.1 Average Dissolution Profiles - Mean ± 2 StDev 110.0 Reference Test 100.0 90.0 80.0 Dissolution (% Released) 70.0 60.0 50.0 40.0 30.0 20.0 0 15 30 45 60 75 90 Minutes

Bootstrapped f 2 analysis from product transfer Distribution of Bootstrapped f2 Values Based on r=5,000 Results 5th percentile = 60.2 f2 = 69.5 350 300 250 Frequency 200 150 100 50 0 52.8 57.6 62.4 67.2 72.0 76.8 81.6 Resulting f2 Value Bootstrapped f 2 5 th percentile > 50

Example with large variability Dissolution Time Reference Sample Test Sample Variability of test Points (min) sample at multiple Mean RSD Mean RSD time points is greater 10 47.2 13.8 37.3 28.6 than that 15 60.9 10.0 52.7 20.0 recommended by most regulatory 20 70.0 8.4 64.0 13.5 agencies 30 80.6 6.1 77.8 7.2 45 89.5 3.1 88.5 3.2 Average Dissolution Profiles - Mean ± 2 StDev 100 Reference Test 90 80 70 Dissolution (% Released) 60 50 40 30 20 10 0 5 10 15 20 25 30 35 40 45 50 Minutes

Example with large variability Bootstrapped f 2 5 th percentile < 50

Summary – Bootstrapped f 2 analysis Bootstrapped f 2 – 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 f 2 analysis Bootstrapped f 2 – is a statistically acceptable and valuable approach for comparing dissolution profiles Cons : – does not address issues of biorelevance that apply to the f 2 – 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?