1

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

2

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.

3

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

4

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

5

DRUG X

• Scatter plot of Y vs. C for 2 populations

• How to establish similarity?

6

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

7

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

8

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

9

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

10

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

11

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

12

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)

13

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

14

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%”

15

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.

16

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

17

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

18

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

19

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

20

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

21

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)

22

Comparison of approaches

• model based method:

– less influenced by outliers– generally greater precision– both useful

23

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

24

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.