1. Assessing similarity of curves: An application in assessing similarity between pediatric and adult exposure-response curves
July 31, 2019
Yodit Seifu, Merck Life Sciences
Co-Authors: Mathangi Gopalakrishnan, University of Maryland; Junshan Qiu, FDA/CDER; Junjing Lin, AbbVie; Margaret Gamalo-Siebers, Eli Lilly

2. Quick overview
There are significant challenges to pediatric drug development
Under ‘certain” condition pediatric approval can be achieved via PK/PD (exposure response) study and a safety study
The objective of the PK/PD study is to establish ‘similar’ exposure response
We present a method for objectively assessing ‘similarity”

3. Outline of presentation
Regulatory background
Motivation of the problem
Statistical measure of similarity
Frequentist method
Bayesian method
Conclusion/Summary

4. Regulatory background: Pediatric drug development
Pediatric Research Equity Act (PREA) of 2003:
Requires new NDAs/BLAs (new active ingredient, indication, dosage, dosing regimen, or new route of administration) to contain a pediatric assessment unless the applicant has obtained a waiver or deferral
Even with this act, pediatric labeling is lagging behind. Between and 2008, the FDA approved 142 NMEs*;
105/142 (74%) were deemed to have potential pediatric use
43/105 (41%) had pediatric information in the labeling
*NME: new molecular entity
JAMA, May 9, 2012—Vol 307, No. 18

5. Regulatory background: Extrapolation in the context of pediatric drug development
PREA Legislation wording on extrapolation:
“If the course of the disease and the effects of the drug are sufficiently similar in adults and pediatric patients, the Secretary may conclude that pediatric effectiveness can be extrapolated from adequate and well-controlled studies in adults, usually supplemented with other information obtained in pediatric patients, such as pharmacokinetic studies. “
FDA has provided guidance on when such extrapolation can be used to meet the PREA requirement
FDA Guidance document: Exposure-Response Relationships — Study Design, Data Analysis, and Regulatory Applications (April 2003)

6. Partial Extrapolation
Framework for Extrapolation: FDA Guidance document: Exposure-Response Relationships — Study Design, Data Analysis, and Regulatory Applications
Reasonable to assume (children vs adults)
Similar disease progression? √
Similar response to intervention? √
YES NO
Reasonable to assume similar exposure-response (ER) in pediatrics and adults?
Conduct PK study (dose ranging)
Conduct Safety/efficacy trials NO
Full Extrapolation
YES
Is there a PD measurement that can be used to predict efficacy in children?
Conduct PK studies to achieve levels similar to adults
Conduct safety trials
Partial Extrapolation
YES
Conduct PK/PD studies to get E-R for PD measurement
Conduct PK studies to achieve target exposure based on E-R
Conduct Safety trials

7. Motivation: Assessment of similarity of E-R between adult and pediatric patients (dapagliflozin study in patients with type 2 diabetes mellitus)
Parkinson J et al (2016), Comparison of the exposure-response relationship of dapagliflozin in adult and paediatric patients with type 2 diabetes mellitus. Diabetes, Obesity and Metabolism, 18,

8. Proposed method: Quantitative graphical assessment of similarity in E-R functions
Model:
Adult E-R function at exposure x and with covariate z:
m(x, z, β 𝐴 ) and associated frequentist estimate m(x, z, β 𝐴 )
Pediatric E-R function at exposure x and with covariate z:
m(x, z, β 𝑃 ) and associated frequentist estimate m(x, z, β 𝑃 )
Unit free similarity measure
Similarity assessment measure: (m(x, z, β 𝐴 ) - m(x, z, β 𝑃 ))/ m(x, z, β 𝐴 )
Estimate of the measure (frequentist): (m(x, z, β 𝐴 ) - m(x, z, β 𝑃 ))/ m(x, z, β 𝐴 )

9. Estimating the similarity assessment measure
Frequentist Method
Fieller’s formula can be used to construct point-wise Confidence Interval
The estimate and associated Confidence Interval can be plotted to objectively assess similarity
Bayesian method
Bayesian computation method can be used to sample from the posterior distribution of the regression parameters
These samples can be used to construct posterior distribution of the percentage difference at a given exposure (x) and can be used to construct point-wise Credible Interval

10. Example : Trileptal (Oxcarbazepine); A drug indicated for seizures
Approved as adjunctive therapy in adult and pediatric patients based on Phase 3 trials
Approved as monotherapy for adult patients based on Phase 3 trial
For the pediatric monotherapy approval, the exposure-response relationship was explored between adults and pediatric patients via a model
Similarity assessed qualitatively and quantitatively

11. Example: Trileptal (Oxcarbazepine)
Similarity of the Trileptal exposure (concentration)-response (Percent change from baseline (PCB) in seizure frequency) relationship between adult and pediatric patients was assessed via simulations
Exposure-response data was generated using the model below
Model
log(PCB+110) = 𝜷 𝟏,𝒊 + 𝜷 𝟐,𝒊 × Cmin +
𝜷 𝟑,𝒊 × Cmin (log(baseline seizure frequency) -2.5) + ϵij
where i=A, P and ϵij~ N(0, σi2 )

12. Simulation Parameters
10/12/2019
Simulation Parameters
Parameter
(adults)
Adults
(Pediatrics)
Pediatrics
Ist
simulation
2nd simulation
3rd simulation
same as adult parameter
75% reduction in E-R slope
75% increase in E-R slope
β 1,𝐴
4.54
β 1,𝑃
β 2,𝐴
𝜷 𝟐,𝑷
β 3,𝐴
0.0031
β 3,𝑃 σA
0.67 σP

13. Frequentist Regression Parameter Estimates
10/12/2019
Frequentist Regression Parameter Estimates
Parameter
Adults
Estimate (95% Confidence intervals)
Pediatrics
Ist simulation
2nd simulation
3rd simulation
same as adult parameter
75% reduction in E-R slope
75% increase in E-R slope
β 1,𝑖
4.550
(4.472, 4.628)
4.546
(4.462, 4.630)
4.467
(4.386, 4.548)
4.574
(4.450, 4.698)
4.580
(4.462, 4.700)
4.540
(4.434, 4.646)
β 2,𝑖
( , )
( , )
( , )
( , )
( , )
( , )
β 3,𝑖
0.0035
(0.0022, )
0.0018
(0.0001, )
0.0017
(0.0000, )
0.0047
(0.0022, )
0.0036
(0.0007, )
0.0033
(0.0007, )
Posterior distribution of Parameters (vague and indep. priors)
Parameter
Adults
Median (95% Credible intervals)
Pediatrics
1st simulation
2nd simulation
3rd simulation
same as adult parameter
75% reduction in E-R slope
75% increase in E-R slope
β 1,𝑖
4.550
(4.471, 4.628)
4.546
(4.462, 4.629)
4.467
(4.386, 4.548)
4.574
(4.450, 4.697)
4.580
(4.462, 4.699)
4.540
(4.434, 4.646)
β 2,𝑖
( , )
( , )
-0.081
( , )
( , )
( , )
( , )
β 3,𝑖
0.0035
(0.0022, )
0.0018
(0.0001, )
0.0017
(-0.000, )
0.0047
(0.0022, )
0.0036
(0.0007, )
0.0033
(0.0007, ) σi
0.651
(0.611, 0.696)
0.706
(0.663, 0.755)
0.682
(0.640, 0.728)
0.661
(0.724,
0.720
(0.670,0.793)
0.638
(0.5824, )

14. Estimated functions: (m(x, z, β 𝐴 ) - m(x, z, β 𝑃 ))/ m(x, z, β 𝐴 ) when baseline log(seizure) = 3.28

15. Posterior Dist: (m(x, z, β 𝐴 ) - m(x, z, β 𝑃 ))/ m(x, z, β 𝐴 ) when baseline log(seizure) = 3.28

16. 10/12/2019
Comparison of similarity measure: Bayesian versus frequentist estimation
Measure of similarity
Statistical method
Cmin region where similarity criteria is met
[0, 192]
same
75% reduction
75% increase
Percentage difference within +/- 30%
95% Credible Interval
[0, 132]
[0, 128]
95% Confidence interval
Percentage difference within +/- 40%
[0, 164]
[0, 160]

17. Conclusion/Summary
An objective quantitative assessment of similarity of E-R curves proposed.
A percentage difference of the pediatric E-R from the adult E-R, can be evaluated and associated confidence interval/credible interval can be generated.
Demonstrated via a regression example.
This methodology can be used to design pediatric PK-PD studies.
In cases where there are prior information, the Bayesian methodology may have advantage over the frequentist method.

18. Thank You

19. Back UP slides

20. 10/12/2019
Distribution of simulated covariate data: log(baseline seizure frequency)
Adults
Pediatrics
Simulation category
Ist
simulation
2nd simulation
3rd
same as adult parameter
75% reduction in E-R slope
75% increase in E-R slope
min
1.609
1.666
1.611
1.629
1.624
1.617
Median
3.309
3.310
3.367
3.186
3.341
3.323
max
3.908
3.912
3.909
3.910
3.905

21. Why is there interest in showing similarity of exposure-response functions?
Assume the disease progression and response to intervention is similar between adult and the pediatric population
Assume there is no adequate information on similarity (between adult and the pediatric pop) in exposure-response (E-R)
Allowed Path:
Identify a PD measurement that can be used to predict efficacy.
Conduct pediatric and adult PK/PD (E-R) study
Similarity of adult and pediatric patients E-R is used to select the pediatric dose
Conduct pediatric safety trial at the selected dose