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Statistical Approaches for Particle Size Distribution Data David Christopher Schering-Plough Research Institute PQRI and INFTG Workshop Demonstrating Bioequivalence of Locally Acting Orally Inhaled Drug Products March 9-10, 2009 Hyatt Regency Bethesda Bethesda, MD Acknowledgements Walter Hauck Ziqing Pan David Christopher – PQRI BE Workshop, March 9-10, 2009 2 Outline • Brief overview of cascade impactor (CI) and particle size distribution (PSD) profiles • Comparison of three statistical approaches: – Chi-square – f2 Similarity Factor – Multivariate Bioequivalence (MVBE) • Discussion of how a statistical test may correctly meet some objectives (e.g., unbiasedness, scaled to reference variability, etc.) but fail to have enough power to detect differences of practical importance. • Discussion of difficulty in establishing a "target" (i.e., consensus on profiles that are, or are not equivalent) against which the performance of a statistical test can be judged. David Christopher – PQRI BE Workshop, March 9-10, 2009 3 Cascade Impactor Particle Size Distribution Profile Mass Recovery Reference Product Actuator Stem Deposition Site David Christopher – PQRI BE Workshop, March 9-10, 2009 4 Cascade Impactor Particle Size Distribution Profile Mass Recovery Test Product Deposition Site David Christopher – PQRI BE Workshop, March 9-10, 2009 5 Example Test / Reference PSD Profiles Mass Recovery 30 CI runs each for Test (Red) and Reference (Blue) Products Deposition Site David Christopher – PQRI BE Workshop, March 9-10, 2009 6 PQRI Profile Comparisons WG Realistic Scenarios • WG developed an approach to simulate realistic PSD profiles, including inter-site correlations • Created 55 scenarios to cover a broad range of PSD profile differences seen in real products • Used these 55 realistic scenarios to evaluate the performance characteristics of the Chi-square Ratio Test • f2 and multivariate PBE (MVBE) also evaluated against these scenarios David Christopher – PQRI BE Workshop, March 9-10, 2009 7 Profile Examples from PQRI Profile Comparisons WG David Christopher – PQRI BE Workshop, March 9-10, 2009 8 Chi-Square Ratio Test • FDA proposal requires 30 CI runs for Test and 30 CI runs for Reference • Calculates Chi-square ratio as an overall measure of “distance” between Test and Reference PSD profiles, scaled to Reference product variability • Uses re-sampling to create a distribution of these ratios • Uses the 95th percentile of this distribution as the test statistic • Smaller means more similar David Christopher – PQRI BE Workshop, March 9-10, 2009 9 Sample mean and confidence interval Chi-Square Ratio Test 1. Calculate Chi-sq Ratio of the kth triplet 2 2 R(Chi )k =Ss Ws[ds(test, ref)] /es(test, ref) 2. Calculate mean Ch-sq Ratio of K triplets Determining the equivalence limit, 2 R(Chi ) = (1/K) Si=1 to K (Chi-sq ratio(i)), q (=7.66) through simulation (using K = number of test/ref1/ref2 triplets (e.g. K=30) Albuterol MDI) 3. Repeat the steps M times and 1. calculate sample mean of K Generate n = 1000 per product (10 lots, 100 ratios of Chi-sq distance canisters/lot) Calculation of Chi-sq and Chi-sq Ratio (based on Anderson Cascade ^E(R) = (1/M) Sm=1 to MRm 2. Real data mean and %CV used in Impactor) simulations. Same between-lot and withinU Product lot (between-canister) variability at each ST & 4. The 95% upper confidence bound for the E(R), R is the ACT stage. Two type of %CV (i.e. low and high) empirical upper 95 percentile among the M Rm„s Product Low ST & ACT 20 Test #1 ST1 Throat Ref ST0 14.28 ST2 U ST1 ST2 38.26 1.83 2.06 2.24 #2 10 Ref30 47.51 20 20 19.22 20 10 10 10 10 5 Ref=(ref #1+ref #2)/2 18.89 46.91 D(test, ref) 4.61 8.65 was simulated from Es =(test+ ref)/2 16.59 42.59 D2 / Es 1.28 1.76 Chi-sq (test:ref) = 13.25 3. Deposition in the stage lognormal dist. 4. Standardized to total =100. D(ref1, ref2) ST3 ST4 0.66 d-sq/ave(ref1, ref2) .023 Chi-sq(ref1,ref2) = 0.70 2.03 20 ST5 ST6 7.56 17.97 13.11 1.59 7.11 2.44 0.82 7.15 2.01 20 0.83 20 9.06 10.21 18.56 ST4 46.32 ST5 2.15 ST6 0.43 0.92 ST3 ST7 9.11 12.00 5. Compare R with q (pre-given). BE if R < q 10 (e.g. =7.66). High 5 15 U Throat ST0 10 10 10 2.09 0.63 0.87 9.08 11.10 ST7 0.51 0.82 0.94 7.13 2.23 0.88 0.26 1.43 1.37 1.52 6.87 5.97 0.64 0.37 1.96 1.34 1.56 8.32 14.54 10.12 1.91 0.70 0.03 1.52 1.20 0.28 3.24 3.53 0.21 0.19 1.19 0.12 0.39 0.08 0.05 .030 .006 .249 .008 .0002 1.79 0.04 0.43 0.12 .288 .0002 .083 .016 Chi-sq Ratio = 18.83 (the smaller the better) Based on Albuterol MDI data and simulations Profile Analysis of Cascade Impactor Data: Proposed FDA Approach, Yi Tsong, Ph.D. (2000) http://www.fda.gov/ohrms/dockets/ac/00/slides/3609s1e/index.htm David Christopher – PQRI BE Workshop, March 9-10, 2009 10 f2 (or Similarity Factor) • Developed for comparing dissolution profiles, but could potentially be applied to PSD profiles • A population measure for assessing the similarity of two profiles • Based on squared differences of cumulative distribution of Test and Reference • Requires ordering of deposition sites – straightforward for inside impactor sites – how to treat outside impactor sites? • No Reference product variability scaling • In dissolution testing, similarity factor of 50 or greater indicates “similar” profiles • Shah V, Tsong Y, Sathe P, Liu JP, In vitro Dissolution Profile Comparison – Statistics and Analysis of the Similarity Factor, f2, Pharmaceutical Research, Vol 15, No. 6, 1998. David Christopher – PQRI BE Workshop, March 9-10, 2009 11 Multivariate PBE (MVBE) • Generalizes univariate PBE, including Reference product variability scaling • Originally developed with in vitro bioequivalence in mind; e.g., treating four measures of spray pattern together in a single test rather than as four separate tests • Shown statistically valid for dimensions up to 8 (not studied for >8) • Would be better suited for cases where difference is on most stages rather than on just 1 or 2 • Chervoneva I, Hyslop T, Hauck WW. A multivariate test for population bioequivalence. Statistics in Medicine 26:1208-23;2007. David Christopher – PQRI BE Workshop, March 9-10, 2009 12 How Do We Judge Performance? • How consistently did the method agree with the true answer? • Must know what the true answer is • Not simple… David Christopher – PQRI BE Workshop, March 9-10, 2009 13 Realistic Scenarios: Example Profiles Proportion of WG who judged profiles equivalent 0.79 Scenario 2a R Total Mass = 113.43 R ISM = 58.85 T Total Mass = 112.54 T ISM = 56.42 “Minimal” differences in impactor-sized profiles between Reference and Test CI Deposition Sites Blue Line = Reference (R), Red Line = Test (T) David Christopher – PQRI BE Workshop, March 9-10, 2009 ISM Sites 14 Realistic Scenarios: Example Profiles Proportion of WG who judged profiles equivalent 0.50 Scenario 2b R Total Mass = 115.52 R ISM = 57.61 T Total Mass = 118.24 T ISM = 57.74 More pronounced differences in impactor-sized profiles between Reference and Test CI Deposition Sites Blue Line = Reference (R), Red Line = Test (T) David Christopher – PQRI BE Workshop, March 9-10, 2009 ISM Sites 15 Realistic Scenarios: Example Profiles Proportion of WG who judged profiles equivalent 0.21 Scenario 2c R Total Mass = 115.77 R ISM = 57.42 T Total Mass = 114.89 T ISM = 56.04 Very visible differences in impactor-sized profiles between Reference and Test CI Deposition Sites Blue Line = Reference (R), Red Line = Test (T) David Christopher – PQRI BE Workshop, March 9-10, 2009 ISM Sites 16 Chi-square Ratio Test 95th Percentile Box-Whisker Plot of 95th Percentile Higher Variability Lower Variability Scenarios David Christopher – PQRI BE Workshop, March 9-10, 2009 17 Chi-square Ratio Test 95th Percentile Box-Whisker Plot of 95th Percentile Vcrit=7.66 Vcrit=2.75 Scenarios David Christopher – PQRI BE Workshop, March 9-10, 2009 18 Chi-square Ratio Test 95th Percentile Box-Whisker Plot of 95th Percentile 0.79 Equiv. 0.21 Equiv. Vcrit=7.66 Vcrit=2.75 Scenarios David Christopher – PQRI BE Workshop, March 9-10, 2009 19 Chi-square Ratio Test 95th Percentile 0.07 Equiv. Box-Whisker Plot of 95th Percentile Vcrit=7.66 1.00 Equiv. Vcrit=2.75 Scenarios David Christopher – PQRI BE Workshop, March 9-10, 2009 20 Vcrit= 50 David Christopher – PQRI BE Workshop, March 9-10, 2009 21 Vcrit= 50 David Christopher – PQRI BE Workshop, March 9-10, 2009 22 David Christopher – PQRI BE Workshop, March 9-10, 2009 23 Conclusions • All three approaches generally agree in rank order for the lower variability profiles – MVBE may be more sensitive to differences in variability • No approach seems to be able to consistently discriminate among differences likely to be of practical importance • Difficult to evaluate performance when there is no clear consensus on “truth” David Christopher – PQRI BE Workshop, March 9-10, 2009 24