Evaluating and quantifying benefit of exposure-response modeling for dose finding José Pinheiro and Chyi-Hung Hsu Novartis Pharmaceuticals PAGE Satellite

Evaluating and quantifying benefit of exposure-response modeling for dose finding

José Pinheiro and Chyi-Hung HsuNovartis Pharmaceuticals

PAGE Satellite Meeting – Saint Petersburg – June 23, 2009

Collaboration with PhRMA Working Group on Adaptive Dose-Ranging Studies

Exposure-response in dose finding2

Outline

Motivation

Background: PhRMA Adaptive Dose-Ranging Studies WG

Dose-exposure-response modeling framework

Estimation of target doses and dose-response profiles under dose- and exposure-response modeling

Simulation study to compare DR- and ER-based estimation

Conclusions


Motivation

Poor understanding of (efficacy and safety) dose response: pervasive problem in drug development

Indicated by both FDA and Industry as one of the root causes of late phase attrition and post-approval problems – at the heart of industry’s pipeline problem

Currently “Phase III view” of dose finding: focus on dose selection out of fixed, generally small number of doses, via pairwise hypothesis testing inefficient and inaccurate


What is the problem?

Res

pons

e

Dose

Selecteddoses

• True DR model unknown

• Current practice:−Few doses−Pairwise

comparisons “dose vs. placebo“

−Sample size based on power to detect DR

Large uncertainty about the DR curve and the final dose

estimate


PhRMA Adaptive Dose-Ranging Studies WG

• One of 10 WGs formed by PhRMA to address key drivers of poor performance in pharma industry

• Goals:- Investigate and develop designs and methods for efficient learning of

efficacy and safety DR profiles benefit/risk profile

- Evaluate operational characteristics of different designs and methods (adaptive and fixed) to make recommendations on their use

- Increase awareness about adaptive and model-based DF approaches, promoting their use, when advantageous

How: comprehensive simulation study comparing ADRS to other DF methods, quantifying potential gains

Results and key recommendations from first round of evaluations published in Bornkamp et al, 2007


PhRMA ADRS WG: key conclusions

Detecting DR is much easier than estimating it

Sample sizes for DF studies are typically not large enough for accurate dose selection and estimation of dose response profile

Adaptive dose-ranging and model-based methods can lead to substantial gains over traditional pairwise testing approaches (especially for estimating DR and selecting dose)


Key recommendations

Adaptive, model-based dose-ranging methods should be routinely considered in Phase II

Sample size calculations for DF studies should take into account precision of estimated dose; when resulting N not feasible, consider ≥ 2 doses in Ph. III

PoC and dose selection should, when feasible, be combined in one seamless trial

To be further explored:- Value of exposure-response (ER) modeling

- Additional adaptive, model-based methods

- Impact of dose selection in Phase III


Goals of this presentation

Describe statistical framework for evaluating and quantifying benefit of ER modeling for estimating target dose(s) and dose-response (DR)

Present and discuss results from simulation study investigating:- reduction in response-uncertainty, related to inter-subject

variation, by switching the focus from dose-response (DR) to exposure-response (ER, PK-PD) models

- impact of intrinsic PK variability and uncertainty about PK information on the relative benefits of ER vs. DR modeling for dose finding

Preliminary investigations leading to collaborative work with ADRS WG


Exposure-Response model

Parallel groups – k doses: d1< …< dk, d1 = placebo

Exposure represented by steady-state area under the concentration curve AUCss,ij = di/CLij

CLij is clearance of patient j in dose group i

Sigmoid-Emax model for median response μij

E0 is placebo response, Emax is max effect, EC50 is AUCss giving 50% of Emax, h is Hill coefficient

,

,50

,max0 h

ijSSAUChEC

hijSS

AUCE

ij E


Exposure-Response model (cont.)

Conditional on μij, response yij has log-normal distr.

σy ≈ coeff. of variation (CV) – intrinsic PD variability

Clearance assumed log-normally distributed

σCL– intrinsic PK variability

In practice, CLij measured with error: observed value

σU – measurement error variability

CLij TVCLlogNCLlog 2~ ),(

)2

),((~|)( yij ijijlogNylog

Uijij CLlogNCLCLlogij

2~|

* ),(


ER models: E0=20, Emax=100, σy=10%

Exposure (AUCss)

Res

pons

e 20

40

60

80

100

120

140

EC50 = 5, h = 4

0 5 10 15 20 25

EC50 = 10, h = 8

0 5 10 15 20 25

EC50 = 5, h = 0.5

20

40

60

80

100

120

140

EC50 = 10, h = 2


PK and measurement variability on CL

Impact of σCL

CL

De

nsi

ty

0.00

0.05

0.10

0.15

0.20

0.25

0 5 10 15

CL 30%

0 5 10 15

CL 50%

0 5 10 15

CL 70%

Impact of σU

(σCL =50%)

True CL

Ob

serv

ed

CL

0.5

1

2

5

10

20

40

1 2 3 5 10 20

U 20%

1 2 3 5 10 20

U 40%

1 2 3 5 10 20

U 60%


PD and measurement variability on response σy=10%

Observed exposure (AUCss)

Res

pons

e 20

40

60

80

100

120

140

U 20%

0 5 10 15 20 25

U 40%

0 5 10 15 20 25

U 60%

20

40

60

80

100

120

140

U 80%

Measurement Total


Dose-Response model

Dose derived from exposure as di = CLij AUCss,ij

Sigmoid-Emax ER model for median response μij can be re-expressed as a mixed-effects DR model

E0, Emax, and h defined as in ER model and ED50,ij = CLij EC50 is the (subject-specific) dose at which 50% of the max effect is attained

From distributional assumptions of ER model

,

,50

max0 h

idh

ijED

hidE

ij E

.),()()( 250~

,50 CLijEClogTVCLlogNEDlog


Dose-Response model (cont.)

Typical value of ED50: TVED50 = TVCL×EC50

DR model accommodates intrinsic inter-subject (PK) variation by allowing ED50 to vary with patient

Not estimable (under frequentist approach) unless multiple observations per patient available

In practice, model is fitted assuming ED50 is fixed

median response depends on dose only, not varying with subject

,

50

max0 h

idhED

hidE

i E


DR models: E0=20, Emax=100, σy=10%

Dose

Res

pons

e

20

40

60

80

100

120

140

EC50 = 5, h = 4CL 30%

0 20 40 60 80 100

EC50 = 10, h = 8CL 30%

EC50 = 5, h = 0.5CL 30%

0 20 40 60 80 100

EC50 = 10, h = 2CL 30%

EC50 = 5, h = 4CL 50%

EC50 = 10, h = 8CL 50%

EC50 = 5, h = 0.5CL 50%

20

40

60

80

100

120

140

EC50 = 10, h = 2CL 50%

20

40

60

80

100

120

140

0 20 40 60 80 100

EC50 = 5, h = 4CL 70%

EC50 = 10, h = 8CL 70%

0 20 40 60 80 100

EC50 = 5, h = 0.5CL 70%

EC50 = 10, h = 2CL 70%

DR Total


Model estimation

Bayesian methods used to estimate both ER and DR models, and target dose (frequentist methods could also be used)

Measurement error incorporated in ER model by assuming observed CL as realizations from (marginal) lognormal distr. with pars. log(TVCL) and - note that σCL and σU are confounded

Model with fixed ED50 used for direct DR estimation

Indirect DR estimation can be obtained from fitted ER model, using TVED50 = TVCL×EC50 to estimate ED50 – remaining parameters are the same

Non-informative priors typically assumed for all model parameters, but informative priors can (and should) be used when information available (e.g., previous studies, drugs in same class, etc)

2/122UCLC


Target dose

Criteria for dose selection typically a combination of statistical significance (e.g., superior to placebo) and clinical relevance (e.g., minimal effect)

Use a Bayesian definition for the minimum effective dose (MED) – smallest dose producing a clinically relevant improvement Δ over placebo, with (posterior) probability of at least 100p%

MED depends on median DR profile μ(d) and intrinsic PK variability σCL

Alternative target dose: EDx – dose producing x% of maximum (median) effect with at least 100p% prob.

pdatadMED d )|)0()(Pr(minarg


Simulation study

Goal: quantify relative performance of ER vs. DR modeling for dose selection and DR characterization under various scenarios – identify key drivers

120 scenarios considered – combinations of: Sig-Emax ER models (4), all with E0=20 and Emax=100:

intrinsic PK variability (3): σCL = 30%, 50%, and 70%

PK measurement error var. (5): σU = 0%, 20%, 40%, 60%, and 80%

PD variability (2): σy = 10% and 20%

Basic design: parallel groups with 5 doses: 0, 25, 50, 75, and 100 mg – 150 patients total (30/dose)

Typical value of clearance: TVCL = 5

Model 1 2 3 4EC50 5 10 5 10h 4 8 0.5 2


Simulation ER models: E0=20, Emax=100, σy=10%

Exposure (AUCss)

Res

pons

e 20

40

60

80

100

120

Model 1: EC50 = 5, h = 4

0 5 10 15 20 25

Model 2: EC50 = 10, h = 8

0 5 10 15 20 25

Model 3: EC50 = 5, h = 0.5

20

40

60

80

100

120

Model 4: EC50 = 10, h = 2


Simulation study (cont.) MED estimation:

clinically relevant difference: Δ = 60 posterior probability threshold: p = 0.7 Estimates truncated at 101 mg (if > 100 mg)

True MED values: depend on model and σCL

Non-informative priors for all parameters in Bayesian modeling

1,000 simulations used for each of 120 scenarios

Bayesian estimation using MCMC algorithm in LinBUGS implementation of OpenBUGS 3.0.2 (linux cluster)

σCL

Model 30% 50% 70%

1 33 36 40

2 62 69 76

3 66 74 82

4 72 80 89


MED estimation – Model 1

U (%)

ME

D e

stim

ate

(mg)

10

20

30

40

50

60

CL 30% Y 10%

0 20 40 60 80 DR

CL 50% Y 10%

CL 70% Y 10%

0 20 40 60 80 DR

CL 30% Y 20%

CL 50% Y 20%

0 20 40 60 80 DR

10

20

30

40

50

60

CL 70% Y 20%

Median True 90% prob. interval


MED Performance of ER vs. DR – model 1

Under 0% PK measurement error, ER provides substantial gains over DR - smaller bias (≈ 0 for ER) and variability.

MED estimation performance of ER deteriorates as U increases: up to 20%, still superior to DR, but same, or worse for U = 40%; DR better than ER for U > 40%.

Performance of DR worsens with increase in CL - dose decreases its predictive power for the response.

Bias of ER MED estimate decreases with CL from 30% to 50%, but increases (and changes sign) from 50% to 70%. Its variation is not much affected.

ER and DR MED estimates variability ↑ with σY, but not much

Model 2: estimation features magnified: ER performance worsens more dramatically with U, DR deterioration with σCL also more severe. ER only competitive with DR U ≤ 20%



U (%)

ME

D e

stim

ate

(mg) 60

70

80

90

100

CL 30% Y 10%

0 20 40 60 80 DR

CL 50% Y 10%

CL 70% Y 10%

0 20 40 60 80 DR

CL 30% Y 20%

CL 50% Y 20%

0 20 40 60 80 DR

60

70

80

90

100

CL 70% Y 20%




U (%)

ME

D e

stim

ate

(mg)

50

60

70

80

90

100

CL 30% Y 10%

0 20 40 60 80 DR

CL 50% Y 10%

CL 70% Y 10%

0 20 40 60 80 DR

CL 30% Y 20%

CL 50% Y 20%

0 20 40 60 80 DR

50

60

70

80

90

100

CL 70% Y 20%



ER vs. DR MED Performance – model 3

DR underestimates MED; ER overestimates it with increased σU (as in the previous two models). Bias gets worse with increase in σCL. Because of the high bias associated with DR, ER estimation is competitive up to 40% values of σU.

PD variability (Y) has much greater impact in performance than in models 1 and 2 – substantial variability increase, not much change in bias, when Y increases from 10% to 20%.

Overall, not enough precision in MED estimates under either method, even for ER with σU = 0%.

Poor choice of dose/exposure range (not allowing proper estimation of Emax parameter) partly explains bad performance.


Evaluating estimation of DR profile

Performance metric: average relative prediction error (ARPE)

where denotes the median response for dose di and its estimate

Relative errors calculated at doses used in trial (k = 5)

)(/)()(100

1i

k

iii ddd

kARPE

)( id )( id


ARPE – Model 1

U (%)

Avg

rel

ativ

e pr

edic

tion

erro

r (%

)

10

15

20

CL 30% Y 10%

0 20 40 60 80 DR

CL 50% Y 10%

CL 70% Y 10%

0 20 40 60 80 DR

CL 30% Y 20%

CL 50% Y 20%

0 20 40 60 80 DR

10

15

20

CL 70% Y 20%


ARPE – Model 2

U (%)

Avg

rel

ativ

e pr

edic

tion

erro

r (%

)

25

30

35

40

45

CL 30% Y 10%

0 20 40 60 80 DR

CL 50% Y 10%

CL 70% Y 10%

0 20 40 60 80 DR

CL 30% Y 20%

CL 50% Y 20%

0 20 40 60 80 DR

25

30

35

40

45

CL 70% Y 20%


ARPE – Model 3

U (%)

Avg

rel

ativ

e pr

edic

tion

erro

r (%

)

12

14

16

18

20

CL 30% Y 10%

0 20 40 60 80 DR

CL 50% Y 10%

CL 70% Y 10%

0 20 40 60 80 DR

CL 30% Y 20%

CL 50% Y 20%

0 20 40 60 80 DR

12

14

16

18

20

CL 70% Y 20%


DR profile estimation – highlights

Model 1: DR prediction performance parallels that for MED estimation:

- ER performance deteriorates as σU increases

- DR modeling gets worse with increase in σCL

- PD variability has a modest impact on the overall performance.

ER better than DR for σU ≤ 60%, and up to 80% when σCL = 70%.

ARPE relatively small: ≤22% for all scenarios considered.

Model 2: ARPE nearly doubles, compared to model 1, with ER performance deteriorating more dramatically with σU.

DR modeling quite competitive with ER modeling for σCL = 30% and moderately competitive for σCL = 50%.


DR profile estimation – highlights (cont.)

Model 3: ARPE shows different pattern, being similar for ER and DR and not varying much with σU or σCL

Possibly due to less pronounced DR relationship

PD variability has more impact on performance than other sources of variation

Overall, prediction errors are not too large (≤ 20%)

ARPE plots for Model 4, and corresponding conclusions, are similar to those for Model 2


Conclusions

ER modeling for dose selection and DR estimation can produce substantial gains in performance compared to direct DR modeling

Relative performance of two approaches highly depends on: • intrinsic PK variability

• accuracy of the exposure measurements (i.e., the measurement error).

Advantage of ER over DR increases with intrinsic PK variability, if observed exposure is reasonably accurate

As PK measurement error increases, DR becomes preferable to ER, especially for dose selection.

Partly explained by use of Bayesian MED definition: can not separate estimation of σCL from σU combined estimate obtained, overestimating intrinsic PK variability; gets worse as σU increases


Conclusions (cont.)

Likewise, if σCL is high, dose is poor predictor of response and ER methods have greater potential to produce gains

Performance driver of ER modeling (σU) can be improved via better technology (e.g., PK models, bioassays), while σCL, which dominates DR performance, is dictated by nature

Choice of dose range also important performance driver for both ER and DR – difficult problem, as optimal range depends on unknown model(s). Adaptive dose-finding designs can provide a better compromise, with caveats

Impact of model uncertainty also to be investigated to extend results presented here. “Right” model (sigmoid-Emax) assumed known in simulations, but would not in practice. Extensions of MCP-Mod DR method proposed by Bretz, Pinheiro, and Branson (2005) to ER modeling could be considered.


References

Bornkamp et al., (2007) Innovative Approaches for Designing and Analyzing Adaptive Dose-Ranging Trials (with discussion). Journal of Biopharmaceutical Statistics, 17(6), 965-995

Bretz F, Pinheiro J, Branson M. (2005). Combining multiple comparisons and modeling techniques in dose-response studies. Biometrics. 61, 738-748.

Documents

Evaluating and quantifying benefit of exposure-response modeling for dose finding José Pinheiro and Chyi-Hung Hsu Novartis Pharmaceuticals PAGE Satellite