Evaluating and quantifying benefit of
exposure-response modeling for dose finding
José Pinheiro and Chyi-Hung Hsu
Novartis Pharmaceuticals
PAGE Satellite Meeting – Saint Petersburg – June 23, 2009
Collaboration with PhRMA Working Group on Adaptive Dose-Ranging Studies
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
Exposure-response in dose finding
2
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 postapproval 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
Exposure-response in dose finding
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Response
What is the problem?
Selected
doses
Dose
• True DR model unknown
• Current practice:
− Few doses
− Pairwise comparisons
“dose vs. placebo“
− Sample size based on
power to detect DR
Exposure-response in dose finding
Large uncertainty about the DR
curve and the final dose estimate
4
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
Exposure-response in dose finding
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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)
Exposure-response in dose finding
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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
Exposure-response in dose finding
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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 in dose finding
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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
E
AUC h
SS , ij
,
 ij  E 0  max
h
h
EC  AUC
50
SS , ij
E0 is placebo response, Emax is max effect, EC50 is
AUCss giving 50% of Emax, h is Hill coefficient
Exposure-response in dose finding
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Exposure-Response model (cont.)
 Conditional on μij, response yij has log-normal distr.
log ( yij ) | 
ij
~
N ( log ( ),  y 2 )
ij
σy ≈ coeff. of variation (CV) – intrinsic PD variability
 Clearance assumed log-normally distributed

log CLij  ~ N log(TVCL),  CL2

σCL– intrinsic PK variability
 In practice, CLij measured with error: observed value
*

log CLij  | CLij ~



N log(CLij ),  U 2

σU – measurement error variability
Exposure-response in dose finding
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ER models: E0=20, Emax=100, σy=10%
0
5
10
15
EC50 = 5, h = 4
EC50 = 10, h = 8
EC50 = 5, h = 0.5
EC50 = 10, h = 2
20
25
140
120
100
80
60
Response
40
20
140
120
100
80
60
40
20
0
5
10
Exposure-response in dose finding
15
20
25
Exposure (AUCss)
11
PK and measurement variability on CL
0
 Impact of σCL
5
10
30%
CL
CL
15
50%
CL
70%
0.25
Density
0.20
0.15
0.10
0.05
0.00
0
 Impact of σU
5
10
15
0
5
10
15
CL
(σCL =50%)
U
20%
U
40%
U
60%
40
Observed CL
20
10
5
2
1
0.5
Exposure-response in dose finding
1
2
3
5
10
20
1
2
3
5
True CL
10
20
1
2
3
5
10
20
12
PD and measurement variability on response
Measurement
 σy=10%
Total
0
5
10
15
U
20%
U
40%
U
60%
U
80%
20
25
140
120
100
80
60
Response
40
20
140
120
100
80
60
40
20
0
Exposure-response in dose finding
5
10
15
20
25
Observed exposure (AUCss)
13
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
E
dh
 ij  E 0  hmax i h ,
ED
d
50, ij
i
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


2
log(ED50,ij ) ~ N log(TVCL)log(EC50 ),  CL
.
Exposure-response in dose finding
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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
dh
i ,
 i  E 0  max
ED h  d h
50 i
E
median response depends on dose only, not varying
with subject
Exposure-response in dose finding
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DR models: E0=20, Emax=100, σy=10%
DR
0
20
40
60
80
Total
100
0
20
40
60
80
30%
EC50 = 5, h = 4
30%
EC50 = 10, h = 8
30%
EC50 = 5, h = 0.5
30%
EC50 = 10, h = 2
50%
EC50 = 5, h = 4
50%
EC50 = 10, h = 8
50%
EC50 = 5, h = 0.5
50%
EC50 = 10, h = 2
CL
CL
CL
100
CL
140
120
100
80
60
40
20
CL
CL
CL
CL
140
Response
120
100
80
60
40
20
70%
CL
EC50 = 5, h = 4
70%
CL
EC50 = 10, h = 8
70%
CL
EC50 = 5, h = 0.5
70%
CL
EC50 = 10, h = 2
140
120
100
80
60
40
20
0
20in dose
40 finding
60
80
Exposure-response
100
0
Dose
20
40
60
80
100
16
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.
2
2 1/ 2
with pars. log(TVCL) and  C   CL   U  - 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)
Exposure-response in dose finding
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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  arg min d Pr(  (d )   (0)   | data)  p
 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.
Exposure-response in dose finding
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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:
Model
EC50
h
1
5
4
2
10
8
3
5
0.5
4
10
2
 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
Exposure-response in dose finding
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Simulation ER models: E0=20, Emax=100, σy=10%
0
5
10
15
20
Model 1: EC50 = 5, h = 4
Model 2: EC50 = 10, h = 8
Model 3: EC50 = 5, h = 0.5
Model 4: EC50 = 10, h = 2
25
120
100
80
60
Response
40
20
120
100
80
60
40
20
0
5
Exposure-response in dose finding
10
15
20
25
Exposure (AUCss)
20
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
Model
1
2
3
4
30%
33
62
66
72
σCL
50%
36
69
74
80
70%
40
76
82
89
 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)
Exposure-response in dose finding
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MED estimation – Model 1
Median
True
0
Y
CL
10%
30%
20
40
Y
CL
60
90% prob. interval
80
DR
10%
50%
Y
CL
10%
70%
60
50
40
MED estimate (mg)
30
20
10
Y
CL
20%
30%
Y
CL
20%
50%
Y
CL
20%
70%
60
50
40
30
20
10
0
20
40
Exposure-response in dose finding
60
80
DR
0
U (%)
20
40
60
80
DR
22
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%
Exposure-response in dose finding
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MED estimation – Model 2
Median
True
0
Y
CL
20
40
10%
30%
CL
20%
30%
CL
Y
60
90% prob. interval
80
DR
10%
50%
CL
20%
50%
CL
Y
10%
70%
100
90
80
MED estimate (mg)
70
60
Y
CL
Y
Y
20%
70%
100
90
80
70
60
0
20
40
Exposure-response
in dose
finding
60
80
DR
0
U (%)
20
40
60
80
DR
24
MED estimation – Model 3
Median
True
0
Y
CL
10%
30%
20
40
Y
CL
60
90% prob. interval
80
DR
10%
50%
Y
CL
10%
70%
100
90
80
MED estimate (mg)
70
60
50
Y
CL
20%
30%
Y
CL
20%
50%
Y
CL
20%
70%
100
90
80
70
60
50
0
20
40
Exposure-response in dose finding
60
80
DR
0
U (%)
20
40
60
80
DR
25
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.
Exposure-response in dose finding
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Evaluating estimation of DR profile
 Performance metric: average relative prediction error (ARPE)
100 k

ARPE
 (d i )   (d i ) /  (d i )

k i 1


(
d
)

(d i )
where
i denotes the median response for dose di and
its estimate
 Relative errors calculated at doses used in trial (k = 5)
Exposure-response in dose finding
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ARPE – Model 1
0
Y
CL
10%
30%
20
40
Y
CL
60
80
DR
10%
50%
Y
CL
10%
70%
20
Avg relative prediction error (%)
15
10
Y
CL
20%
30%
Y
CL
20%
50%
Y
CL
20%
70%
20
15
10
0
20
40
Exposure-response in dose finding
60
80
DR
0
U (%)
20
40
60
80
DR
28
ARPE – Model 2
0
Y
CL
20
40
10%
30%
CL
20%
30%
CL
Y
60
80
DR
10%
50%
CL
20%
50%
CL
Y
10%
70%
45
40
Avg relative prediction error (%)
35
30
25
Y
CL
Y
Y
20%
70%
45
40
35
30
25
0
20
40
Exposure-response in dose finding
60
80
DR
0
U (%)
20
40
60
80
DR
29
ARPE – Model 3
0
Y
CL
10%
30%
20
40
Y
CL
60
80
DR
10%
50%
Y
CL
10%
70%
20
18
Avg relative prediction error (%)
16
14
12
Y
CL
20%
30%
Y
CL
20%
50%
Y
CL
20%
70%
20
18
16
14
12
0
20
40
Exposure-response in dose finding
60
80
DR
0
U (%)
20
40
60
80
DR
30
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%.
Exposure-response in dose finding
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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
Exposure-response in dose finding
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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
Exposure-response in dose finding
33
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.
Exposure-response in dose finding
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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.
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