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

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”

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

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 2002 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

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)

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 https://www.fda.gov/regulatory-information/search-fda-guidance-documents/exposure-response-relationships-study-design-data-analysis-and-regulatory-applications

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, 685-692.

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 )

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

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 https://www.accessdata.fda.gov/drugsatfda_docs/nda/2003/021014_S003_TRILEPTAL%20TABLETS_BIOPHARMR.pdf

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 ) https://www.accessdata.fda.gov/drugsatfda_docs/nda/2003/021014_S003_TRILEPTAL%20TABLETS_BIOPHARMR.pdf

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 -0.0099 𝜷 𝟐,𝑷 -0.0024 -0.0174 β 3,𝐴 0.0031 β 3,𝑃 σA 0.67 σP

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 -0.0102 (-0.0116, -0.0088) -0.0081 (-0.0098, -0.0065) (-0.0099, -0.0064) -0.0105 (-0.0131, -0.0080) -0.0035 (-0.0064, -0.0007) -0.0166 (-0.0190, -0.0142) β 3,𝑖 0.0035 (0.0022, 0.0049) 0.0018 (0.0001, 0.0035) 0.0017 (0.0000, 0.0033) 0.0047 (0.0022, 0.0072) 0.0036 (0.0007, 0.0065) 0.0033 (0.0007, 0.0058) 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 -0.0102 (-0.0116, -0.0088) -0.0081 (-0.0098, -0.0064) -0.081 (-0.0099, -0.0064) -0.0105 (-0.0131, -0.0079) -0.0035 (-0.0063,- 0.0007) -0.0166 (-0.0190, -0.0142) β 3,𝑖 0.0035 (0.0022, 0.0049) 0.0018 (0.0001, 0.0035) 0.0017 (-0.000, 0.0033) 0.0047 (0.0022, 0.0072) 0.0036 (0.0007, 0.0065) 0.0033 (0.0007, 0.0058) σi 0.651 (0.611, 0.696) 0.706 (0.663, 0.755) 0.682 (0.640, 0.728) 0.661 (0.724, 0.7980 0.720 (0.670,0.793) 0.638 (0.5824, 0.7032)

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

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

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]

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.

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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

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 https://www.fda.gov/regulatory-information/search-fda-guidance-documents/exposure-response-relationships-study-design-data-analysis-and-regulatory-applications