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Statistical modelling issues arising from PK/PD bridging in paediatrics
The Trileptal ExampleJerry R. Nedelman, Modeling and Simulation, NovartisWorkshop on Modelling in Paediatric Drug Development and Use14 April 2008
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
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
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
5 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008
Goal☑Children
☑☑Adults
MonotherapyAdjunctive therapy
Background: Initial approval status in the U.S.
6 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008
Goal☑Children
☑☑Adults
MonotherapyAdjunctive therapy
Background: Available data
PK/PDPK/PD
PK/PD PK
7 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008
Goal☑Children
☑☑Adults
MonotherapyAdjunctive therapy
Background: Bridging strategy
PK/PDPK/PD
PK/PD PK
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
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 predictefficacy?
NO
•Conduct PK studies•Conduct safety/efficacy trials*
NO
•Conduct PK studies toachieve levels similar to adults•Conduct safety trials
YES
Reasonable to assume similarconcentration-response (C-R)in pediatrics and adults?
YES TO BOTH
•Conduct PK/PD studies to getC-R for PD measurement•Conduct PK studies to achievetarget concentrations based on C-R
YES
•Conduct safety trials
NO
http://www.fda.gov/cder/guidance/5341fnl.htm
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 predictefficacy?
NO
•Conduct PK studies•Conduct safety/efficacy trials*
NO
•Conduct PK studies toachieve levels similar to adults•Conduct safety trials
YES
Reasonable to assume similarconcentration-response (C-R)in pediatrics and adults?
YES TO BOTH
•Conduct PK/PD studies to getC-R for PD measurement•Conduct PK studies to achievetarget concentrations based on C-R
YES
•Conduct safety trials
NO
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 toachieve levels similar to adults•Conduct safety trials
YES
Reasonable to assume similarconcentration-response (C-R)in pediatrics and adults?
YES TO BOTH
Goal☑Children
☑☑Adults
MonotherapyAdjunctive therapy
Goal☑Children
☑☑Adults
MonotherapyAdjunctive therapy
PK/PDPK/PD
PK/PD PK
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 toachieve levels similar to adults•Conduct safety trials
YES
Reasonable to assume similarconcentration-response (C-R)in pediatrics and adults?
YES TO BOTH
Goal☑Children
☑☑Adults
MonotherapyAdjunctive therapy
Goal☑Children
☑☑Adults
MonotherapyAdjunctive therapy
PK/PDPK/PD
PK/PD PK
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 similarconcentration-response (C-R)in pediatrics and adults?
Goal☑Children
☑☑Adults
MonotherapyAdjunctive therapy
Goal☑Children
☑☑Adults
MonotherapyAdjunctive therapy
PK/PDPK/PD
PK/PD PK
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 similarconcentration-response (C-R)in pediatrics and adults?
Are the estimated PK/PD (C-R) relationships acceptable in the first place?
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
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? ….
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
510
1520
2530
35
Effi
cacy
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 250Dose
12
3C
once
ntra
tion
A
B C
D
1 2 3Concentration
510
1520
2530
35
Effi
cacy
Efficacy vs Concentration Concentration vs Dose
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 250Dose
12
3C
once
ntra
tion
A
B C
D
1 2 3Concentration
510
1520
2530
35
Effi
cacy
Efficacy vs Concentration Concentration vs Dose
B
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 250Dose
12
3C
once
ntra
tion
A
B C
D
1 2 3Concentration
510
1520
2530
35
Effi
cacy
Efficacy vs Concentration Concentration vs Dose
B
C
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 250Dose
12
3C
once
ntra
tion
A
B C
D
1 2 3Concentration
510
1520
2530
35
Effi
cacy
Efficacy vs Concentration Concentration vs Dose
B
C
D
A
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 250Dose
12
3C
once
ntra
tion
A
B C
D
1 2 3Concentration
510
1520
2530
35
Effi
cacy
Efficacy vs Concentration Concentration vs Dose
B
C
D
A
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 250Dose
12
3C
once
ntra
tion
A
B C
D
1 2 3Concentration
510
1520
2530
35
Effi
cacy
Efficacy vs Concentration Concentration vs Dose
B
C
D
A
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 250Dose
12
3C
once
ntra
tion
A
B C
D
1 2 3Concentration
510
1520
2530
35
Effi
cacy
Efficacy vs Concentration Concentration vs Dose
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 250Dose
12
3C
once
ntra
tion
A
B C
D
1 2 3Concentration
510
1520
2530
35
Effi
cacy
Efficacy vs Concentration Concentration vs Dose
B1,C1
B2,C2
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 250Dose
12
3C
once
ntra
tion
A
B C
D
1 2 3Concentration
510
1520
2530
35
Effi
cacy
Efficacy vs Concentration Concentration vs Dose
B1,C1
B2,C2
D1
D2
A2
A1
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 250Dose
12
3C
once
ntra
tion
A
B C
D
1 2 3Concentration
510
1520
2530
35
Effi
cacy
Efficacy vs Concentration Concentration vs Dose
B1,C1
B2,C2
D1
D2
A2
A1
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.
29 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008
Trileptal adjunctive pediatric PK/PD
Trough Concentration
% C
hang
e in
Sei
zure
Fre
q (T
rans
form
ed)
0 20 40 60 80 100
34
56
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
% C
hang
e in
Sei
zure
Fre
q (T
rans
form
ed)
0 20 40 60 80 100
34
56
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
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
33 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008
Concentration vs DoseEfficacy vs Concentration
50 100 150 200 250Dose
12
3C
once
ntra
tion
A
B C
D
1 2 3Concentration
510
1520
2530
35
Effi
cacy
A
C
B
D
Residuals plot
-0.4 -0.2 0.0 0.2 0.4Conc vs Dose Residual
-4-2
02
4Ef
fvs
Con
cR
esid
ual
Residuals for Scenario 1, bias in PK/PD
34 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008
Concentration vs DoseEfficacy vs Concentration
50 100 150 200 250Dose
12
3C
once
ntra
tion
A
B C
D
1 2 3Concentration
510
1520
2530
35
Effi
cacy
A
C
B
D
Residuals plot
-0.4 -0.2 0.0 0.2 0.4Conc vs Dose Residual
-4-2
02
4Ef
fvs
Con
cR
esid
ual
-0.5
Residuals for Scenario 1, bias in PK/PD
35 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008
Concentration vs DoseEfficacy vs Concentration
50 100 150 200 250Dose
12
3C
once
ntra
tion
A
B C
D
1 2 3Concentration
510
1520
2530
35
Effi
cacy
A
C
B
D
Residuals plot
-0.4 -0.2 0.0 0.2 0.4Conc vs Dose Residual
-4-2
02
4Ef
fvs
Con
cR
esid
ual
-0.5
-5
Residuals for Scenario 1, bias in PK/PD
36 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008
Concentration vs DoseEfficacy vs Concentration
50 100 150 200 250Dose
12
3C
once
ntra
tion
A
B C
D
1 2 3Concentration
510
1520
2530
35
Effi
cacy
A
C
B
D
Residuals plot
-0.4 -0.2 0.0 0.2 0.4Conc vs Dose Residual
-4-2
02
4Ef
fvs
Con
cR
esid
ual
C
-0.5
-5
Residuals for Scenario 1, bias in PK/PD
37 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008
Concentration vs DoseEfficacy vs Concentration
50 100 150 200 250Dose
12
3C
once
ntra
tion
A
B C
D
1 2 3Concentration
510
1520
2530
35
Effi
cacy
A
C
B
D
Residuals plot
-0.4 -0.2 0.0 0.2 0.4Conc vs Dose Residual
-4-2
02
4Ef
fvs
Con
cR
esid
ual
C
A
B
D
-0.5
-5
Residuals for Scenario 1, bias in PK/PD
38 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008
Concentration vs DoseEfficacy vs Concentration
50 100 150 200 250Dose
12
3C
once
ntra
tion
A
B C
D
1 2 3Concentration
510
1520
2530
35
Effi
cacy
A
C
B
D
Residuals plot
-0.4 -0.2 0.0 0.2 0.4Conc vs Dose Residual
-4-2
02
4Ef
fvs
Con
cR
esid
ual
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.
39 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008
Concentration vs DoseEfficacy vs Concentration
50 100 150 200 250Dose
12
3C
once
ntra
tion
A
B C
D
Residuals for Scenario 2, no bias in PK/PD
Residuals plotWhen the dose-controlled study does not cause confounding in the PK/PD relationship, the residuals do not exhibit correlation.
1 2 3Concentration
510
1520
2530
35
Effi
cacy
A1
A2
B1,C1
B2,C2
D1
D2
-0.4 -0.2 0.0 0.2 0.4Conc vs Dose Residual
-4-2
02
4E
ff vs
Con
c R
esid
ual (A2,C2)
(A1,C1)
(B2,D2)
(B1,D1)
40 | Statistical Modelling Issues Arising from PK/PD Bridging in Paediatrics | Jerry R. Nedelman | 14 April 2008
No correlations were observed
-60 -40 -20 0 20 40 60
Concentration Residuals (x)
-2-1
01
2
Effic
acy
Res
idua
ls (y
)correlation = 0.069
p-value = 0.23
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
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
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
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
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