Download Statistical Approaches for Particle Size Distribution Data

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