1. 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

2. 2 Exposure-response in dose finding 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

3. 3 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 of doses, via pairwise hypothesis testing  inefficient and inaccurate

4. 4 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

5. 5 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 other DF methods, quantifying potential gains  Results and key recommendations from first round of evaluations published in Bornkamp et al, 2007

6. 6 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 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)

7. 7 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

8. 8 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

9. 9 Exposure-response in dose finding Exposure-Response model  Parallel groups – k doses: d 1 < …< d k, d 1 = placebo  Exposure represented by steady-state area under the concentration curve AUC ss,ij = d i /CL ij  CL ij is clearance of patient j in dose group i  Sigmoid-Emax model for median response μ ij E 0 is placebo response, E max is max effect, EC 50 is AUC ss giving 50% of E max, h is Hill coefficient

10. 10 Exposure-response in dose finding Exposure-Response model (cont.)  Conditional on μ ij, response y ij has log-normal distr. σ y ≈ coeff. of variation (CV) – intrinsic PD variability  Clearance assumed log-normally distributed σ CL – intrinsic PK variability  In practice, CL ij measured with error: observed value σ U – measurement error variability

11. 11 Exposure-response in dose finding ER models: E 0 =20, E max =100, σ y =10%

12. 12 Exposure-response in dose finding PK and measurement variability on CL  Impact of σ CL  Impact of σ U ( σ CL =50%)

13. 13 Exposure-response in dose finding PD and measurement variability on response  σ y =10%

14. 14 Exposure-response in dose finding Dose-Response model  Dose derived from exposure as d i = CL ij AUC ss,ij  Sigmoid-Emax ER model for median response μ ij can be re-expressed as a mixed-effects DR model E 0, E max, and h defined as in ER model and ED 50,ij = CL ij EC 50 is the (subject-specific) dose at which 50% of the max effect is attained  From distributional assumptions of ER model

15. 15 Exposure-response in dose finding Dose-Response model (cont.)  Typical value of ED 50 : TVED 50 = TVCL×EC 50  DR model accommodates intrinsic inter-subject (PK) variation by allowing ED 50 to vary with patient  Not estimable (under frequentist approach) unless multiple observations per patient available  In practice, model is fitted assuming ED 50 is fixed median response depends on dose only, not varying with subject

16. 16 Exposure-response in dose finding DR models: E 0 =20, E max =100, σ y =10%

17. 17 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 observed CL as realizations from (marginal) lognormal distr. with pars. log(TVCL) and - note that σ CL and σ U are confounded  Model with fixed ED 50 used for direct DR estimation  Indirect DR estimation can be obtained from fitted ER model, using TVED 50 = TVCL×EC 50 to estimate ED 50 – 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)

18. 18 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 σ CL  Alternative target dose: EDx – dose producing x% of maximum (median) effect with at least 100p% prob.

19. 19 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 E 0 =20 and E max =100:  intrinsic PK variability (3): σ CL = 30%, 50%, and 70%  PK measurement error var. (5): σ U = 0%, 20%, 40%, 60%, and 80%  PD variability (2): σ y = 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

20. 20 Exposure-response in dose finding Simulation ER models: E 0 =20, E max =100, σ y =10%

21. 21 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 σ CL  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) σ CL Model30%50%70% 1333640 2626976 3667482 4728089

22. 22 Exposure-response in dose finding MED estimation – Model 1

23. 23 Exposure-response in dose finding 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 σ Y, but not much  Model 2: estimation features magnified: ER performance worsens more dramatically with  U, DR deterioration with σ CL also more severe. ER only competitive with DR  U ≤ 20%

24. 24 Exposure-response in dose finding MED estimation – Model 2

25. 25 Exposure-response in dose finding MED estimation – Model 3

26. 26 Exposure-response in dose finding ER vs. DR MED Performance – model 3  DR underestimates MED; ER overestimates it with increased σ U (as in the previous two models). Bias gets worse with increase in σ CL. Because of the high bias associated with DR, ER estimation is competitive up to 40% values of σ U.  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 σ U = 0%.  Poor choice of dose/exposure range (not allowing proper estimation of Emax parameter) partly explains bad performance.

27. 27 Exposure-response in dose finding Evaluating estimation of DR profile  Performance metric: average relative prediction error (ARPE) where denotes the median response for dose d i and its estimate  Relative errors calculated at doses used in trial (k = 5)

28. 28 Exposure-response in dose finding ARPE – Model 1

29. 29 Exposure-response in dose finding ARPE – Model 2

30. 30 Exposure-response in dose finding ARPE – Model 3

31. 31 Exposure-response in dose finding DR profile estimation – highlights  Model 1: DR prediction performance parallels that for MED estimation : - ER performance deteriorates as σ U increases - DR modeling gets worse with increase in σ CL - PD variability has a modest impact on the overall performance.  ER better than DR for σ U ≤ 60%, and up to 80% when σ CL = 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 σ U.  DR modeling quite competitive with ER modeling for σ CL = 30% and moderately competitive for σ CL = 50%.

32. 32 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 σ U or σ CL  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

33. 33 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 σ CL from σ U  combined estimate obtained, overestimating intrinsic PK variability; gets worse as σ U increases

34. 34 Exposure-response in dose finding Conclusions (cont.)  Likewise, if σ CL is high, dose is poor predictor of response and ER methods have greater potential to produce gains  Performance driver of ER modeling (σ U ) can be improved via better technology (e.g., PK models, bioassays), while σ CL, 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.

35. 35 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.