Statistical modelling issues arising from PK/PD bridging in … · The problem: “observational data”, potential confounding ... Statistical Modelling Issues Arising from PK/PD

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


Outline

Background




Lessons learned


Background: Trileptal

Oxcarbazepine

Anti-epileptic

Activity primarily through active metabolite MHD

“PK” refers to MHD concentrations

“PD” refers to seizure rates


Goal☑Children

☑☑Adults

MonotherapyAdjunctive therapy

Background: Initial approval status in the U.S.


Goal☑Children

☑☑Adults


Background: Available data

PK/PDPK/PD

PK/PD PK


Goal☑Children

☑☑Adults


Background: Bridging strategy

PK/PDPK/PD

PK/PD PK


Outline

Background




Lessons learned



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



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


Is there a PD measurement**that can be used to predictefficacy?

NO

•Conduct PK studies•Conduct safety/efficacy trials*

NO


YES


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


Pediatric Decision Tree: Bridging (1)




YES


YES TO BOTH

Goal☑Children

☑☑Adults


Goal☑Children

☑☑Adults


PK/PDPK/PD

PK/PD PK


Pediatric Decision Tree: Bridging (2)




YES


YES TO BOTH

Goal☑Children

☑☑Adults


Goal☑Children

☑☑Adults


PK/PDPK/PD

PK/PD PK


Pediatric Decision Tree: Burden of proof


Goal☑Children

☑☑Adults


Goal☑Children

☑☑Adults


PK/PDPK/PD

PK/PD PK


Pediatric Decision Tree: But first …


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


Outline

Background




Lessons learned


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? ….


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


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




50 100 150 200 250Dose

12

3C

once

ntra

tion

A

B C

D

1 2 3Concentration

510

1520

2530

35

Effi

cacy


B




50 100 150 200 250Dose

12

3C

once

ntra

tion

A

B C

D

1 2 3Concentration

510

1520

2530

35

Effi

cacy


B

C




50 100 150 200 250Dose

12

3C

once

ntra

tion

A

B C

D

1 2 3Concentration

510

1520

2530

35

Effi

cacy


B

C

D

A




50 100 150 200 250Dose

12

3C

once

ntra

tion

A

B C

D

1 2 3Concentration

510

1520

2530

35

Effi

cacy


B

C

D

A



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


B

C

D

A



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





50 100 150 200 250Dose

12

3C

once

ntra

tion

A

B C

D

1 2 3Concentration

510

1520

2530

35

Effi

cacy


B1,C1

B2,C2




50 100 150 200 250Dose

12

3C

once

ntra

tion

A

B C

D

1 2 3Concentration

510

1520

2530

35

Effi

cacy


B1,C1

B2,C2

D1

D2

A2

A1



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


B1,C1

B2,C2

D1

D2

A2

A1


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.


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


… 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


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


Outline

Background




Lessons learned


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



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


-4-2

02

4Ef

fvs

Con

cR

esid

ual

-0.5




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


-4-2

02

4Ef

fvs

Con

cR

esid

ual

-0.5

-5




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


-4-2

02

4Ef

fvs

Con

cR

esid

ual

C

-0.5

-5




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


-4-2

02

4Ef

fvs

Con

cR

esid

ual

C

A

B

D

-0.5

-5




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


-4-2

02

4Ef

fvs

Con

cR

esid

ual

C

A

B

D

-0.5

-5


When the dose-controlled study causes confounding in the PK/PD relationship, the residuals exhibit correlation.



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


-4-2

02

4E

ff vs

Con

c R

esid

ual (A2,C2)

(A1,C1)

(B2,D2)

(B1,D1)


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


Diagnostics for confounding

Examine correlations of residuals

Rubin-causal-model sensitivity analysis

Instrumental-variables regression

See Statistics in Medicine 2007; 26:290-308


Outline

Background




Lessons learned


Lesson learned

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

Prospective validation of models is important


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

Documents

Statistical modelling issues arising from PK/PD bridging in … · The problem: “observational data”, potential confounding ... Statistical Modelling Issues Arising from PK/PD