Evaluating benefit of exposure-response modeling for dose finding and José Pinheiro 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
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 finding 2
What is the problem? Response Selected doses Dose • True DR model unknown • Current practice: − Few doses Large uncertainty about the DR − Pairwise comparisons curve and the final dose estimate “dose vs. placebo“ − Sample size based on power to detect DR Exposure-response in dose finding 3
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 4
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 h E AUC μ max , SS ij = + , E 0 ij h h + EC AUC 50 , SS 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 Exposure-response in dose finding 5
Exposure-Response model (cont.) � Conditional on μ ij , response y ij has log-normal distr. 2 μ μ σ log N log y ( ) | ~ ( ( ), ) y ij ij ij σ y ≈ coeff. of variation (CV) – intrinsic PD variability � Clearance assumed log-normally distributed ( ) 2 ⎛ ⎞ σ CL ( ), log N log TVCL ⎜ ⎟ ~ CL ⎝ ⎠ ij σ CL – intrinsic PK variability � In practice, CL ij measured with error: observed value ( ) ⎛ ⎞ * 2 σ U ( ), log ⎜ ⎟ N log CL CL | ~ CL ⎜ ⎟ ij ij ⎝ ⎠ ij σ U – measurement error variability Exposure-response in dose finding 6
PK and measurement variability on CL � Impact of σ CL � Impact of σ U ( σ CL =50%) Exposure-response in dose finding 7
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 h E d μ max i = + , E 0 ij h h + ED d 50 , ij i 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 � In practice, model is fitted assuming ED 50 is fixed h E d μ max i = + , E 0 i h h + ED d 50 i Exposure-response in dose finding 8
DR models: E 0 =20, E max =100, σ y =10% Exposure-response in dose finding 9
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% = μ − μ ≥ Δ ≥ arg min Pr( ( ) ( 0 ) | ) MED data p d d � 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. Exposure-response in dose finding 10
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 Exposure-response in dose finding 11
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 σ CL Model 30% 50% 70% 1 33 36 40 2 62 69 76 3 66 74 82 4 72 80 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 12
MED estimation – Model 1 Exposure-response in dose finding 13
MED estimation – Model 2 Exposure-response in dose finding 14
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 σ U increases: up to 20%, still superior to DR, but same, or worse for σ U = 40%; DR better than ER for σ U > 40%. � Performance of DR worsens with increase in σ CL - dose decreases its predictive power for the response. � Bias of ER MED estimate decreases with σ 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 σ U , DR deterioration with σ CL also more severe. ER only competitive with DR σ U ≤ 20% Exposure-response in dose finding 15
Evaluating estimation of DR profile � Performance metric: average relative prediction error (ARPE) 100 k ) ∑ = μ − μ μ ( ) ( ) / ( ) ARPE d d d i i i k = 1 i ) μ μ where denotes the median response for dose d i and ( ) ( ) d d i i its estimate � Relative errors calculated at doses used in trial (k = 5) Exposure-response in dose finding 16
ARPE – Model 1 Exposure-response in dose finding 17
ARPE – Model 2 Exposure-response in dose finding 18
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%. Exposure-response in dose finding 19
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 Exposure-response in dose finding 20
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. Exposure-response in dose finding 21
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