Evaluating benefit of exposure-response modeling for dose finding - - PowerPoint PPT Presentation

José Pinheiro and Chyi-Hung Hsu

Johnson & Johnson PRD Novartis Pharmaceuticals

2010 Rutgers Biostatistics Day – Rutgers University – April 16, 2010

Collaboration with PhRMA Working Group on Adaptive Dose-Ranging Studies

Evaluating benefit of exposure-response modeling for dose finding

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Exposure-response in dose finding

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

• f doses, via pairwise hypothesis testing ⇒

inefficient and inaccurate

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Exposure-response in dose finding

What is the problem?

Response Dose

Selected doses

• 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

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Exposure-response in dose finding

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

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Exposure-response in dose finding

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 , max h ij SS AUC h EC h ij SS AUC E ij

E

+ + =

μ

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Exposure-response in dose finding

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

( )

σ CL

ij

TVCL log N CL log

2 ~

), (

⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ) 2 ), ( ( ~ | ) (

σ μ μ

y ij

ij ij

log N y log

( )

σ U

ij ij

CL log N CL CL log

ij

2 ~ | *

), (

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛

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Exposure-response in dose finding

PK and measurement variability on CL

Impact of σCL Impact of σU

(σCL =50%)

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Exposure-response in dose finding

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 In practice, model is fitted assuming ED50 is fixed

, , 50 max h i d h ij ED h i d E ij

E

+ + =

μ

, 50 max h i d h ED h i d E i

E

+ + =

μ

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Exposure-response in dose finding

DR models: E0=20, Emax=100, σy=10%

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Exposure-response in dose finding

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.

p data d MED

d

≥ Δ ≥ − = ) | ) ( ) ( Pr( min arg μ μ

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Exposure-response in dose finding

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

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Exposure-response in dose finding

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

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Exposure-response in dose finding

MED estimation – Model 1

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Exposure-response in dose finding

MED estimation – Model 2

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Exposure-response in dose finding

MED Performance of ER vs. DR

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 σU increases: up to 20%, still superior to DR, but same, or worse for σU = 40%; DR better than ER for σU > 40%. Performance of DR worsens with increase in σCL - dose decreases its predictive power for the response. Bias of ER MED estimate decreases with σCL 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 σU, DR deterioration with σCL also more severe. ER only competitive with DR σU ≤ 20%

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Exposure-response in dose finding

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

1 i k i i i

d d d k ARPE μ μ μ

∑

=

− = )

) (

i

d μ ) (

i

d μ )

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Exposure-response in dose finding

ARPE – Model 1

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Exposure-response in dose finding

ARPE – Model 2

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Exposure-response in dose finding

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%.

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Exposure-response in dose finding

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

• btained, overestimating intrinsic PK variability; gets worse as

σU increases

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Exposure-response in dose finding

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.

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Exposure-response in dose finding

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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BACK-UP

Exposure-response in dose finding

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Exposure-response in dose finding

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

• ther DF methods, quantifying potential gains

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

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Exposure-response in dose finding

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

• f 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)

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Exposure-response in dose finding

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

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Exposure-response in dose finding

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

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Exposure-response in dose finding

ER models: E0=20, Emax=100, σy=10%

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Exposure-response in dose finding

PD and measurement variability on response

σy=10%

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Exposure-response in dose finding

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

• bserved 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 / 1 2 2 U CL C

σ σ σ + =

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Exposure-response in dose finding

MED estimation – Model 3

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Exposure-response in dose finding

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 (σY) has much greater impact in performance than in models 1 and 2 – substantial variability increase, not much change in bias, when σY 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.

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Exposure-response in dose finding

ARPE – Model 3

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Exposure-response in dose finding

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