1 methods for determining similarity of exposure-response between pediatric and adult populations...
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METHODS FOR DETERMINING SIMILARITY OF EXPOSURE-RESPONSE BETWEEN PEDIATRIC AND ADULT POPULATIONS
Stella G. Machado, Ph.D.
Quantitative Methods and Research Staff
Office of Biostatistics/OPASS/CDER/FDA
CLINICAL PHARMACOLOGY SUBCOMMITTEE MEETING NOV 2003
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ACKNOWLEDGEMENTS
• Substantial contribution from my colleague Meiyu Shen
• ideas from Yi Tsong, James Hung, Donald Schuirmann, Scott Patterson, Walter Hauck and Sharon Anderson, Peter Lee, C. Naito, K. Akihiro, and many others.
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INTRODUCTION
• General method described for comparing PK/PD response curves in 2 populations:– Pediatric versus Adult populations– Other population groups, eg, ethnic region,
gender
• Exposure: dose, AUC, Cmin, etc
• Response: biomarkers, clinical endpoints
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BRIDGING PK/PD STUDIES
• Goal is to evaluate similarity in PK/PD relationships in Adult (original) and Pediatric (new) Populations– Conclude
• similarity• similarity with some dose regimen modification• lack of similarity
• Absence of precise guidance as to how this should be done
• Exploratory, not confirmatory, approaches needed
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DRUG X
• Scatter plot of Y vs. C for 2 populations
• How to establish similarity?
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0 20 40 60 80 100 120
Conc.
0
2
4
6
Res
pons
e
NewOriginal
DRUG X: New and Original populations: PD vs. PK
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STEPS IN THE STATISTICAL APPROACH
• Suppose data from Original and New Populations:
– original (adult): n0 patients, measure Y and C
– new population (pediatrics): n1 patients, measure Y
and C
– concentration measurements generally different,
unless data from concentration controlled trial
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STEPS IN THE STATISTICAL APPROACH
• PK/PD response curves:
– to establish similarity, need to compare the average shapes of response curves, taking account variability
– response curve Y depends on exposure C, and unknown parameters :
Y = f(C, )
• may have different parameters in the two populations
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0 20 40 60 80 100 120
Conc.
0
10
20
30
40
50
Res
pons
e
NewOriginal
DRUG X: PK/PD scatter plot with loess fits
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STEPS IN THE STATISTICAL APPROACH
• assess similarity between responses at all concentrations likely to be encountered
• distance between the curves – shape comparison
• account for variability of the response
• need “Equivalence” type approach, not hypothesis tests showing that the responses are not significantly different
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HYPOTHETICAL:SIMPLEST SITUATIONfocus on single exposure C
• Reduces to usual equivalence-type analysis approach
• Response metric of interest for comparison could be:
– average response at every exposure C– combination of average and variance of response at each C:
like FDA-PBE or Kullback-Liebler distance metrics
or – whole distribution at each C – Kolmogorov-Smirnov
generalization
• Choose here to look at average response
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All C’s identical, continued
• Usual equivalence-type analysis:
– can define “similarity” to be requirement that the average responses in the 2 populations, at the same C, are closely similar:
– choose “goalposts” L and U, eg 80% to 125%
– calculate 95% confidence interval for ratio of average
responses (1 / 0)
( = mean or average response)
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All C’s identical, continued
• If 95% confidence interval of ratio 1 / 0 falls entirely within
interval (L, U), then null hypothesis of lack of equivalence is
rejected.
• This corresponds to “simultaneous two one-sided test
procedure for equivalence”, carried out at level = 0.025.
• Proposal: use confidence intervals to measure “similarity”
and to quantify what was actually determined from data in
the 2 populations
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Estimation of 95% confidence interval for ratio 1 / 0
• some work required - methods in literature
• easier: use bootstrap method from observations, or computer simulation
• for decision-making, can make useful statements, such as, for example,
– “the average response to concentration C in the New Population is about 93% of that in the Original Population, and we are 95% confident that the ratio of the averages lies between 83% and 105%”
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SITUATION: MANY VALUES OF C
• First approach:
– Categorize values of C into intervals:
(C1, C2), (C2, C3), (C3, C4), etc
– For each interval, (Ci, Ci+1), estimate 95% confidence intervals for 1i / 0i and interpret.
– Interpret responses graphically, for all categories of C.
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Drug X: 95% CI’s for ratios 1/0 for concentrations: 0, 0-40, 40-60, 60-80, >80
0 20 40 60 80 100
Conc
0.5
1.0
1.5
2.0
2.5
95
% c
on
fide
nce
bo
un
ds f
or
sim
ilari
ty
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Comment on Graph
• ratios trend upwards from 1.0 as C increases: New population has greater average response than Original population
• upper limits of 95% CI’s exceed 1.25 for all exposures
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SITUATION: MANY VALUES OF C• Second approach: model-based .
Fit models: 0(C) = f(C, 0)
1(C) = f(C, 1)
Estimate the unknown parameters: ’s, variances.
Use fitted model to simulate 0(C), 1(C), for as many values of C as desired:
estimate the ratios of the average responses: 1(C)/0(C)
estimate 95% CI’s from percentiles of ratios
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EXAMPLE: Drug X
• Response transformed by square root to stabilize the variance
• Linear models were fitted separately for the two populations
• sqrt(response) = a + b * Conc +
• For each C, 5000 pairs of studies were generated 5000 estimates of 1/0, and percentiles
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DRUG X: 95% CI’s for ratios 1/0 for concentrations: 0, 20,50,70,90 via
model-based method
0 40 80 120
Conc
0.6
1.0
1.4
1.8
95
% c
on
fid
en
ce
bo
un
ds f
or
sim
ila
rity
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0 20 40 60 80 100
Conc
0.5
1.0
1.5
2.0
2.5
95%
con
fiden
ce b
ound
s fo
r si
mila
rity
DRUG X: COMPARISON OF 2 APPROACHES 95% CI’s for 1/0 from Categorized C’s (1st in pair) and Model-based
method (2nd in pair)
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Comparison of approaches
• model based method:
– less influenced by outliers– generally greater precision– both useful
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DESIGN CONSIDERATIONS for studies in New Population
• based on parameter estimates from Original Population and any prior information from New Population
• include doses likely to produce C’s in the whole range of interest
• perform simulations to assess robustness to model assumptions, variability of parameter estimates, choice of doses, to determine required number of patients needed in new population
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OCNCLUDING REMARKS
• efficacy vs. safety
• proposed method for quantifying the similarity between Original and New Populations over whole range of concentrations likely to be encountered
• applies to data from trials with different designs
• usual goalposts such as (0.8, 1.25) may not be meaningful for the drug (therapeutic range) and disease - interpretation of how much similarity is needed requires medical input.