statistical approaches for particle size distribution...
TRANSCRIPT
Statistical Approaches for
Particle Size Distribution Data
David ChristopherSchering-Plough Research Institute
PQRI and INFTG WorkshopDemonstrating Bioequivalence of Locally Acting Orally Inhaled
Drug Products
March 9-10, 2009
Hyatt Regency Bethesda
Bethesda, MD
David Christopher – PQRI BE Workshop, March 9-10, 2009 2
Acknowledgements
Walter Hauck
Ziqing Pan
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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.
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Cascade Impactor Particle Size
Distribution Profile
Deposition Site
Mass
Recovery
Actuator
Stem
Reference
Product
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Cascade Impactor Particle Size
Distribution Profile
Deposition Site
Mass
Recovery Test
Product
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Deposition Site
Mass
Recovery
Example Test / Reference PSD
Profiles
30 CI runs each for Test (Red)
and Reference (Blue) Products
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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
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Profile Examples from PQRI Profile Comparisons WG
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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
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Sample mean and confidence interval
1. Calculate Chi-sq Ratio of the kth triplet
R(Chi2)k =Ss Ws[ds(test, ref)]
2/es(test, ref)
2. Calculate mean Ch-sq Ratio of K triplets
R(Chi2) = (1/K) Si=1 to K (Chi-sq ratio(i)),
K = number of test/ref1/ref2 triplets (e.g. K=30)
3. Repeat the steps M times and calculate sample mean of Kratios of Chi-sq distance
^E(R) = (1/M) Sm=1 to MRm
4. The 95% upper confidence bound for the E(R), RU is the
empirical upper 95 percentile among the M Rm„s
5. Compare RU with q (pre-given). BE if R
U < q (e.g. =7.66).
Determining the equivalence limit,
q (=7.66) through simulation(using
Albuterol MDI)
1. Generate n = 1000 per product (10 lots, 100canisters/lot)
2. Real data mean and %CV used insimulations. Same between-lot and within-lot (between-canister) variability at eachstage. Two type of %CV (i.e. low and high)
Product ST & ACT Throat ST0 ST1 ST2 ST3 ST4 ST5 ST6 ST7
Low 20 10 30 20 20 20 10 20 20 20
High 10 5 15 10 10 10 5 10 10 10
3. Deposition in the stage was simulated fromlognormal dist.
4. Standardized to total =100.
Calculation of Chi-sq and Chi-sqRatio (based on Anderson CascadeImpactor)
Product ST &
ACT
Throat ST0 ST1 ST2 ST3 ST4 ST5 ST6 ST7
Test 14.28 38.26 1.83 2.06 2.24 7.56 17.97 13.11 1.59 0.51
Ref #1 18.56 46.32 2.15 0.43 0.92 9.11 12.00 7.11 2.44 0.82
Ref #2 19.22 47.51 2.03 0.82 0.83 9.06 10.21 7.15 2.01 0.94
Ref=(ref #1+ref #2)/2 18.89 46.91 2.09 0.63 0.87 9.08 11.10 7.13 2.23 0.88
D(test, ref) 4.61 8.65 0.26 1.43 1.37 1.52 6.87 5.97 0.64 0.37
Es =(test+ ref)/2 16.59 42.59 1.96 1.34 1.56 8.32 14.54 10.12 1.91 0.70
D2
/ Es
1.28 1.76 0.03 1.52 1.20 0.28 3.24 3.53 0.21 0.19
Chi-sq (test:ref) = 13.25
D(ref1, ref2) 0.66 1.19 0.12 0.39 0.08 0.05 1.79 0.04 0.43 0.12
d-sq/ave(ref1, ref2) .023 .030 .006 .249 .008 .0002 .288 .0002 .083 .016
Chi-sq(ref1,ref2) = 0.70
Chi-sq Ratio = 18.83 (the smaller the better)
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
Based on Albuterol MDI data and simulations
Chi-Square Ratio Test
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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.
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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.
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How Do We Judge Performance?
• How consistently did the method agree
with the true answer?
• Must know what the true answer is
• Not simple…
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Scenario 2a
“Minimal” differences in
impactor-sized profiles
between Reference and Test
R Total Mass = 113.43
R ISM = 58.85
T Total Mass = 112.54
T ISM = 56.42
CI Deposition Sites
ISM SitesBlue Line = Reference (R), Red Line = Test (T)
Realistic Scenarios:
Example Profiles
Proportion of WG
who judged profiles
equivalent
0.79
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More pronounced differences in
impactor-sized profiles between
Reference and Test
ISM Sites
R Total Mass = 115.52
R ISM = 57.61
T Total Mass = 118.24
T ISM = 57.74Scenario 2b
CI Deposition Sites
Blue Line = Reference (R), Red Line = Test (T)
Realistic Scenarios:
Example Profiles
Proportion of WG
who judged profiles
equivalent
0.50
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Very visible differences in
impactor-sized profiles
between Reference and Test
R Total Mass = 115.77
R ISM = 57.42
T Total Mass = 114.89
T ISM = 56.04
ISM Sites
Scenario 2c
CI Deposition Sites
Blue Line = Reference (R), Red Line = Test (T)
Realistic Scenarios:
Example Profiles
Proportion of WG
who judged profiles
equivalent
0.21
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Box-Whisker Plot of 95th Percentile
95
thP
erc
en
tile
Scenarios
Chi-square Ratio Test
Lower Variability
Higher Variability
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Box-Whisker Plot of 95th Percentile
95
thP
erc
en
tile
Scenarios
Vcrit=7.66
Vcrit=2.75
Chi-square Ratio Test
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Box-Whisker Plot of 95th Percentile
95
thP
erc
en
tile
Scenarios
Vcrit=7.66
Vcrit=2.75
Chi-square Ratio Test
0.79
Equiv. 0.21
Equiv.
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Box-Whisker Plot of 95th Percentile
95
thP
erc
en
tile
Scenarios
Vcrit=7.66
Vcrit=2.75
Chi-square Ratio Test0.07
Equiv.
1.00
Equiv.
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Vcrit= 50
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Vcrit= 50
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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”