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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
Exposure-response in dose finding3
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
Exposure-response in dose finding4
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
Exposure-response in dose finding5
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 finding6
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 finding7
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 finding8
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 finding9
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 in dose finding10
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~|
* ),(
Exposure-response in dose finding11
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
Exposure-response in dose finding12
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%
Exposure-response in dose finding13
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
Exposure-response in dose finding14
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
Exposure-response in dose finding15
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
Exposure-response in dose finding16
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
Exposure-response in dose finding17
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
Exposure-response in dose finding18
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
Exposure-response in dose finding19
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
Exposure-response in dose finding20
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
Exposure-response in dose finding21
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
Exposure-response in dose finding22
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
Exposure-response in dose finding23
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 finding24
MED estimation – Model 2
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%
Median True 90% prob. interval
Exposure-response in dose finding25
MED estimation – Model 3
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%
Median True 90% prob. interval
Exposure-response in dose finding26
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 finding27
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
Exposure-response in dose finding28
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%
Exposure-response in dose finding29
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%
Exposure-response in dose finding30
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%
Exposure-response in dose finding31
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 finding32
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 finding33
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 finding34
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 finding35
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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