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Statistical modelling issues arising from PK/PD bridging in paediatrics The Trileptal Example Jerry R. Nedelman, Modeling and Simulation, Novartis Workshop on Modelling in Paediatric Drug Development and Use 14 April 2008 Outline

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SLIDE 1

Statistical modelling issues arising from PK/PD bridging in paediatrics

The Trileptal Example Jerry R. Nedelman, Modeling and Simulation, Novartis Workshop on Modelling in Paediatric Drug Development and Use 14 April 2008

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SLIDE 2

2 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Outline

Background Pediatric Decision Tree The problem: “observational data”, potential confounding The solution: diagnostics for confounding Lessons learned

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SLIDE 3

3 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Outline

Background Pediatric Decision Tree The problem: “observational data”, potential confounding The solution: diagnostics for confounding Lessons learned

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4 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Background: Trileptal

Oxcarbazepine Anti-epileptic Activity primarily through active metabolite MHD “PK” refers to MHD concentrations “PD” refers to seizure rates

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5 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Goal

☑

Children

☑ ☑

Adults Monotherapy Adjunctive therapy

Background: Initial approval status in the U.S.

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SLIDE 6

6 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Goal

☑

Children

☑ ☑

Adults Monotherapy Adjunctive therapy

Background: Available data PK/PD PK/PD PK/PD PK

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SLIDE 7

7 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Goal

☑

Children

☑ ☑

Adults Monotherapy Adjunctive therapy

Background: Bridging strategy PK/PD PK/PD PK/PD PK

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SLIDE 8

8 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Outline

Background Pediatric Decision Tree The problem: “observational data”, potential confounding The solution: diagnostics for confounding Lessons learned

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SLIDE 9

9 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Pediatric Decision Tree

Reasonable to assume (pediatrics vs adults) similar disease progression? similar response to intervention?

Pediatric Study Decision Tree

Is there a PD measurement** that can be used to predict efficacy? NO

  • Conduct PK studies
  • Conduct safety/efficacy trials*

NO

  • Conduct PK studies to

achieve levels similar to adults

  • Conduct safety trials

YES Reasonable to assume similar concentration-response (C-R) in pediatrics and adults? YES TO BOTH

  • Conduct PK/PD studies to get

C-R for PD measurement

  • Conduct PK studies to achieve

target concentrations based on C-R YES

  • Conduct safety trials

NO

http://www.fda.gov/cder/guidance/5341fnl.htm
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SLIDE 10

10 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Pediatric Decision Tree

Reasonable to assume (pediatrics vs adults) similar disease progression? similar response to intervention?

Pediatric Study Decision Tree

Is there a PD measurement** that can be used to predict efficacy? NO

  • Conduct PK studies
  • Conduct safety/efficacy trials*

NO

  • Conduct PK studies to

achieve levels similar to adults

  • Conduct safety trials

YES Reasonable to assume similar concentration-response (C-R) in pediatrics and adults? YES TO BOTH

  • Conduct PK/PD studies to get

C-R for PD measurement

  • Conduct PK studies to achieve

target concentrations based on C-R YES

  • Conduct safety trials

NO

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SLIDE 11

11 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Pediatric Decision Tree: Bridging (1)

Reasonable to assume (pediatrics vs adults) similar disease progression? similar response to intervention?

Pediatric Study Decision Tree

  • Conduct PK studies to

achieve levels similar to adults

  • Conduct safety trials

YES Reasonable to assume similar concentration-response (C-R) in pediatrics and adults? YES TO BOTH

Goal

☑

Children

☑ ☑

Adults Monotherapy Adjunctive therapy Goal

☑

Children

☑ ☑

Adults Monotherapy Adjunctive therapy

PK/PD PK/PD PK/PD PK

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SLIDE 12

12 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Pediatric Decision Tree: Bridging (2)

Reasonable to assume (pediatrics vs adults) similar disease progression? similar response to intervention?

Pediatric Study Decision Tree

  • Conduct PK studies to

achieve levels similar to adults

  • Conduct safety trials

YES Reasonable to assume similar concentration-response (C-R) in pediatrics and adults? YES TO BOTH

Goal

☑

Children

☑ ☑

Adults Monotherapy Adjunctive therapy Goal

☑

Children

☑ ☑

Adults Monotherapy Adjunctive therapy

PK/PD PK/PD PK/PD PK

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13 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Pediatric Decision Tree: Burden of proof

Reasonable to assume similar concentration-response (C-R) in pediatrics and adults?

Goal

☑

Children

☑ ☑

Adults Monotherapy Adjunctive therapy Goal

☑

Children

☑ ☑

Adults Monotherapy Adjunctive therapy

PK/PD PK/PD PK/PD PK

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SLIDE 14

14 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Pediatric Decision Tree: But first …

Reasonable to assume similar concentration-response (C-R) in pediatrics and adults?

Are the estimated PK/PD (C-R) relationships acceptable in the first place?

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SLIDE 15

15 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Outline

Background Pediatric Decision Tree The problem: “observational data”, potential confounding The solution: diagnostics for confounding Lessons learned

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16 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Observational vs Experimental

“Relationship”: Input Output Experimental study: Input controlled by investigator

  • Usually assigned randomly to experimental units
  • E.g., dose-controlled trial, concentration-controlled trial

Observational study: Input not controlled by investigator

  • E.g., PK PD in a dose-controlled trial
  • PK is an output as well as an input
  • For PK/PD purposes, a dose-controlled trial is an observational study

What can go wrong with observational PK/PD? ….

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17 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Concentration-controlled PK/PD PK/PD data and least-squares model fit, assuming concentration controlled trial, with 3 concentrations, at each of which patients divide evenly into two groups of high and low responders

Efficacy vs Concentration

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

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18 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Dose-controlled PK/PD, scenario 1 Suppose that in a dose-controlled trial, patients who have higher concentrations at a given dose also have higher efficacy at a given concentration, and lower goes with lower

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

Efficacy vs Concentration Concentration vs Dose

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SLIDE 19

19 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Dose-controlled PK/PD, scenario 1 Suppose that in a dose-controlled trial, patients who have higher concentrations at a given dose also have higher efficacy at a given concentration, and lower goes with lower

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

Efficacy vs Concentration Concentration vs Dose B

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SLIDE 20

20 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Dose-controlled PK/PD, scenario 1 Suppose that in a dose-controlled trial, patients who have higher concentrations at a given dose also have higher efficacy at a given concentration, and lower goes with lower

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

Efficacy vs Concentration Concentration vs Dose B C

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SLIDE 21

21 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Dose-controlled PK/PD, scenario 1 Suppose that in a dose-controlled trial, patients who have higher concentrations at a given dose also have higher efficacy at a given concentration, and lower goes with lower

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

Efficacy vs Concentration Concentration vs Dose B C D A

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SLIDE 22

22 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Dose-controlled PK/PD, scenario 1 Suppose that in a dose-controlled trial, patients who have higher concentrations at a given dose also have higher efficacy at a given concentration, and lower goes with lower

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

Efficacy vs Concentration Concentration vs Dose B C D A

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SLIDE 23

23 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Dose-controlled PK/PD, scenario 1 The least-squares fit to the resulting data is a biased (confounded) estimate of the true PK/PD relationship

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

Efficacy vs Concentration Concentration vs Dose B C D A

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SLIDE 24

24 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Dose-controlled PK/PD, scenario 2 Suppose that in a dose-controlled trial, patients who have higher concentrations at a given dose are equally likely to have high or low efficacy at a given concentration, and the same for patients with lower concentrations

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

Efficacy vs Concentration Concentration vs Dose

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SLIDE 25

25 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Dose-controlled PK/PD, scenario 2 Suppose that in a dose-controlled trial, patients who have higher concentrations at a given dose are equally likely to have high or low efficacy at a given concentration, and the same for patients with lower concentrations

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

Efficacy vs Concentration Concentration vs Dose B1,C1 B2,C2

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SLIDE 26

26 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Dose-controlled PK/PD, scenario 2 Suppose that in a dose-controlled trial, patients who have higher concentrations at a given dose are equally likely to have high or low efficacy at a given concentration, and the same for patients with lower concentrations

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

Efficacy vs Concentration Concentration vs Dose B1,C1 B2,C2 D1 D2 A2 A1

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27 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Dose-controlled PK/PD, scenario 2 The least-squares fit to the resulting data is an unbiased (unconfounded) estimate of the true PK/PD relationship

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

Efficacy vs Concentration Concentration vs Dose B1,C1 B2,C2 D1 D2 A2 A1

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28 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Summary

If the relationship of PK to PD is not independent of the

relationship of dose to PK, then the estimated PK/PD relationship may be confounded.

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29 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Trileptal adjunctive pediatric PK/PD

Trough Concentration % Change in Seizure Freq (Transformed) 20 40 60 80 100 3 4 5 6

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30 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

… or Trileptal adjunctive pediatric PK/PD ???

Trough Concentration % Change in Seizure Freq (Transformed) 20 40 60 80 100 3 4 5 6

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31 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Confounding or not – how do you know?

You never do for certain Scientific reasoning may argue for implausibility of

confounding

Skeptic response: “There are more things in heaven and

earth, Horatio, than are dreamt of in your philosophy”*

Some diagnostics can be reassuring

*Hamlet, Act I, Scene V

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32 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Outline

Background Pediatric Decision Tree The problem: “observational data”, potential confounding The solution: diagnostics for confounding Lessons learned

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SLIDE 33

33 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Concentration vs Dose Efficacy vs Concentration

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

A C B D Residuals plot

  • 0.4
  • 0.2

0.0 0.2 0.4 Conc vs Dose Residual

  • 4
  • 2

2 4 Eff vs Conc Residual

Residuals for Scenario 1, bias in PK/PD

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34 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Concentration vs Dose Efficacy vs Concentration

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

A C B D Residuals plot

  • 0.4
  • 0.2

0.0 0.2 0.4 Conc vs Dose Residual

  • 4
  • 2

2 4 Eff vs Conc Residual

  • 0.5

Residuals for Scenario 1, bias in PK/PD

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SLIDE 35

35 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Concentration vs Dose Efficacy vs Concentration

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

A C B D Residuals plot

  • 0.4
  • 0.2

0.0 0.2 0.4 Conc vs Dose Residual

  • 4
  • 2

2 4 Eff vs Conc Residual

  • 0.5
  • 5

Residuals for Scenario 1, bias in PK/PD

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SLIDE 36

36 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Concentration vs Dose Efficacy vs Concentration

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

A C B D Residuals plot

  • 0.4
  • 0.2

0.0 0.2 0.4 Conc vs Dose Residual

  • 4
  • 2

2 4 Eff vs Conc Residual

C

  • 0.5
  • 5

Residuals for Scenario 1, bias in PK/PD

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SLIDE 37

37 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Concentration vs Dose Efficacy vs Concentration

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

A C B D Residuals plot

  • 0.4
  • 0.2

0.0 0.2 0.4 Conc vs Dose Residual

  • 4
  • 2

2 4 Eff vs Conc Residual

C A B D

  • 0.5
  • 5

Residuals for Scenario 1, bias in PK/PD

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SLIDE 38

38 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Concentration vs Dose Efficacy vs Concentration

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

A C B D Residuals plot

  • 0.4
  • 0.2

0.0 0.2 0.4 Conc vs Dose Residual

  • 4
  • 2

2 4 Eff vs Conc Residual

C A B D

  • 0.5
  • 5

Residuals for Scenario 1, bias in PK/PD When the dose-controlled study causes confounding in the PK/PD relationship, the residuals exhibit correlation.

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SLIDE 39

39 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Concentration vs Dose Efficacy vs Concentration

50 100 150 200 250 Dose

1 2 3

Concentration

A B C D

Residuals for Scenario 2, no bias in PK/PD

Residuals plot

When the dose-controlled study does not cause confounding in the PK/PD relationship, the residuals do not exhibit correlation.

1 2 3 Concentration 5 10 15 20 25 30 35 Efficacy

A1 A2 B1,C1 B2,C2 D1 D2

  • 0.4
  • 0.2

0.0 0.2 0.4 Conc vs Dose Residual

  • 4
  • 2

2 4 Eff vs Conc Residual

(A2,C2) (A1,C1) (B2,D2) (B1,D1)

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40 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

No correlations were observed

  • 60
  • 40
  • 20

20 40 60 Concentration Residuals (x)

  • 2
  • 1

1 2 Efficacy Residuals (y) correlation = 0.069 p-value = 0.23

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SLIDE 41

41 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Diagnostics for confounding

Examine correlations of residuals Rubin-causal-model sensitivity analysis Instrumental-variables regression See Statistics in Medicine 2007; 26:290-308

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SLIDE 42

42 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Outline

Background Pediatric Decision Tree The problem: “observational data”, potential confounding The solution: diagnostics for confounding Lessons learned

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SLIDE 43

43 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Lesson learned

When the stakes are high, modeling is held to a high

standard

Prospective validation of models is important

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44 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008

Acknowledgements

Donald B. Rubin, Lewis B. Sheiner David Aitken, Deborah Bennett, Joseph D’Souza, Hai Jing,

Mary Ann Karolchyk, James Lee, Peter Mesenbrink, William Sallas, Werner Schmidt, Greg Sedek, Claire Souppart, Mara Stiles, Yvonne Sturm, Audrey Wong, Rocco Zaninelli

FDA reviewers and pharmacometricians