The future of Bayesian clinical trial design

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1 Slide 1 The future of Bayesian clinical trial design Peter Müller, UT Austin slides: 2nd cycle dose (a 2 ) as function of 1st cycle outcome, toxicity (Y 1 ) & efficacy ( ), and dose 1st cycle (a 1 ); Based on toxicity and efficacy; Utility function to formalize relative preferences: Tox Eff no yes no 35 0 yes effect by cancer (col) and mutation (row) 0.45) 0.42) 0.57) 0.12) 0.41) 0.6) 0.39) 0.28) 0.4) 0.31) 0.59) 0.4) Subclone)1) Subclone)2) Subclone)3) Subclone)4) Subclone)5) Tumor heterogeneity for 5 spls adaptive allocation by cell subpopulations? Slide 5 Optimal a 2 maximizes utility in expectation; Optimization is implemented as a sequential decision with backward induction ( Q-learning ). Optimal a 1 maximizes utility in expectation, using optimal a 2. Slide 2 Some challenges for clinical trial designs 2nd cycle: Expected utility by 1st cycle outcome 2-cycle dose escalation: 2nd cycle expected utilities as a function of first cycle outcomes (ordinal response). 1. continuous information updating (adaptive designs); 2. non-randomized and diverse data sources (causal inference and borrowing strength); 3. subgroup analsis: discovery and treatment allocation; 4. multi-drug and multi-disease trials (basket and platform Y 1 = 0 Y 1 = 1 trials); 1st cycle toxicity Y 1 Y 1 = 2 5. novel efficacy endpoints (patient-centric endpoints); 6. N of 1 trials by 1st cycle efficacy (2=green; 1 = red; 0 =black); big bullets mark optimal dose Will review some of these challenges and related examples. U 2(d2, d1, y1) Slide 6 u cyc(0,0) d 2 (Y 1, ) (0, 2) (0, 1) (0, 0) U 2(d2, d1, y1) u cyc(0,0) d 2 (Y 1, ) (1, 2) (1, 1) (1, 0) U 2(d2, d1, y1) u cyc(0,0) (Y 1, ) (2, 2) (2, 1) (2, 0) d 2 Slide 3 Scenarios 1st cycle 1. Continuous information updating Ideally adjust decisions as information accrues; Big scale: standardized databases for all clinical trials; small scale: continuous within-trial and within-patient updating of information; Slide 4 U 1 (d 1 ) (1+ λ)u cyc (0,0) d Expected utilities for a 1, assuming optimal a 2 (8 different scenarios) a 2(a 1, Y 1, ) a 1 Y NT NT NT NT Optimal a 1 and a 2 (as a function of Y 1 and ). Example: Two cycle optimal dose finding Slide 7 Lee, Thall, Ji & M. (2015, J. Amer. Stat Assoc.) 2. Non-randomized data sources 1

2 Registry data, electronic medical records (EMR) and dynamic treatment regimens (DTR); Statistical post-processing to adjust for lack of randomization ( causal inference ); Combination of different sources of information. Slide 8 Density Density plot of causal effects Truth DDP GP IPTW AIPTW linear regression 6 7 N = 1000 Bandwidth = Example: Dynamic treatment regimes Estimated treatment effects under massive repeat simulation: truth (vertical line), under DDP-GP (red line), Xu, M, Thall & Wahed (2015, J. Amer. Stat. Assoc.) inverse prob weighting (green & cyan), and no adjustment (purple). A leukemia trial. Outcome = overall survival T. Frontline therapy (A), and salvage therapy (B 1, B 2 ) if needed. Slide 11 Resistance Salvage B 1 = R Induc7on A = D Z 3 = D Death = C CR Z 3 = P Progression Salvage B 2 Estimated Truth DDP GP IPTW AIPTW (a 1,b 11,b 21) (a 1,b 12,b 21) (a 1,b 12,b 22) (a 1,b 11,b 22) (a 2,b 12,b 22) (a 2,b 11,b 21) (a 2,b 11,b 22) (a 2,b 12,b 21) Slide 9 estimated expected survival by regime (over 1000 repeat sims) (yellow) = DDP-GP model; green & blue = (A)IPTW (inverse probab of treatment Counter-factual outcomes under alternative treatments: weighting). 7 transition times T R, T D, T C, T R D,..., T P D (counterfactual - can not observe all 7); Slide 12 survival regression p(t x history) for all T x history includes treatment decisions A, and B 1 or Semicompeting risks B 2 (if applicable), Z = (A, B 1, B 2 ) and earlier outcomes; Same approach for competing risks, overall survival time T = with Y. Xu (JHU), M. Daniels (UT) and D. Scharfstein (JHU) T (with sum over [will probably skip these slides] appropriate path) under alternative DTR s Z. Strategy Model-based imputation of expected E(T Z). Nonparametric Bayesian (DDP-GP) surv regression avoids dependence on parametric family Slide 10 Progression Survival Probability Treatment Control Death Survival Probability Treatment Control Estimated treatment effect Time Time 2

3 Comparison on P needs to adjust for D. Everyone dies, but not everyone progresses. Slide 16 Slide Subgroup analysis: discovery and treatment allocation Semicompeting risks: e.g., progression P and D. Comparing treatments on the basis of mean time to P requires adjustment for competing risk of D. Data: Let (P 0, D 0 ) and (P 1, D 1 ) denote (counterfactual) outcomes under treatment z = 0 (control) vs. z = 1 (experimental therapy). Estimand: odds of progression, conditional on survival under both treatments (x = baseline covariates) h(u; x) = p[p 1 < u D 0 u, D 1 Slide 17 u, x] p[p 0 < u D 0 u, D 1 u, x] =... estimate by model based inference Targeted therapies using specific enzymes, growth factor receptors, and signal transducers; challenges for clinical trial designs: need to enable discovery of optimal patient subpopulation to benefit from specific treatments; subgroups characterized by baseline markers; adaptive treatment allocation; Example: SUBA: A basket trial designs with subgroup analysis Xu, Trippa, M & Ji (2015, Stat. in Biosc.) Slide 14 round 1 Biomarker 2 Biomarker 2 S 1 L 1 Example: phase II trial, n = 222 recurrent gliomas patients; Biomarker 1 Biomarker 1 11 baseline cov s x ij (age, race, Karnofsky performance score, local vs. whole brain radiation, % tumor resection, previous use of nitrosoureas, tumor histology. Biomarker 1 Biomarker 1 Treatment is surgery (all) with (z = 1) or without (z = 0) 3.85% of carmustine. Partitioning the patient population by repeated splits w.r.t. Model: Joint p(p 0, D 0, P 1, D 1 ). biomarkers, BNP prior with different treatment allocations in each subpopulation. for p(,,, ); (essentially) only features (subdistributions) that are likelihood-identifiable are used. Slide 18 Biomarker 2 LL 12 round 3 S 1 Biomarker 2 SS 11 SL 11 LS 12 LL 12 LSL 121 LSS 121 Slide 15 Results Estimate of h(u) u ρ=0 ρ=0.3 ρ=0.5 frequency of h(u)> (a) E {h(u; x) data} (b) p {h(u; x) > 1 data} Black/red/gruen green is ρ = 0, 0.3, 0.5 (in the normal copula) u ρ=0 ρ=0.3 ρ=0.5 SUBA design: equal randomization (ER) during run-in; and subgroup-specific allocations beyond. Slide 19 3

4 Adaptive treatment allocation Scenario AR SUBA Subset / S S S S S S S S S / Under 6 scenarios, average # patients in 3 treatments in subsets defined by AR and SUBA (1,000 repeat simulations). Slide Platform and basket trials: multi-drug and multi-disease trials Select subpopoulations with largest expected utility Targeted therapies for specific biomarkers and pathways; Matching tumor molecular alterations across cancer types; Slide 24 basket trials. Massive repeat simulation under a hypothetical truth (left), and frequency (under repeat simulation) of recommending mutation-tmor pairs with treatment effect different from the overall population (right) Slide 23 Selecting the subpopulations Based on a flexible probability model; Utility function: large log hazard ratio (relative to overall population) large sub-population size plausibility (few covariates) Slide 21 Adaptive treatment allocation BRCA Colon Lung Head & Neck Cancer Ex: A basket trial design for targeted therapies Xu, M, Tsimberidou & Berry (2016, arxiv) Breast Colorectal Esophage Cervical Sarcoma Cancer Cancer al Cancer Cancer patient_allocation factor(treatment) C TT 0.0 BRAF KRAS PIK3CA PTEN TP53 BRAF KRAS PIK3CA PTEN TP53 BRAF KRAS PIK3CA PTEN TP53 factor(mutation) PI3K/AKT/ mtor pathway alterations mtor Inhibitors; Clinical Trials with PI3K/AKT/mTOR Pathway Inhibitors FGFR alterations Clinical Trials with FGFR Inhibitors ERBB2 Amplificatio n Clinical trials containing trastuzumab and/or pertuzumab BRCA1 Mutation NF1 Mutation STK11 Mutation Olaparib mtor Inhibitors mtor Inhibitors IMPACT II: patients across different cancers. Based on molecular alterations patients are eligible for certain targeted therapies. Proportion of patients allocated to targeted therapy (blue) and control (red) under subpopulations with truly differential treatment effect. Slide 22 Matching cancer types and mutations TP53 TP53 PTENTOTAL PTENTOTAL value 1.00 mutation PIK3CA mutation PIK3CA KRAS KRAS 0.25 BRAF BRAF 0.00 BRCA Lung Colon tumor_type BRCA Lung Colon tumor_type 4

5 Slide 25 Slide Novel efficacy endpoints Increased engagement of patients new (patientcentric) study endpoints; Develop trial designs (and underlying probability models) to accomodate outcome measures beyond indicators of toxicity & efficacy. DENSITY Expected utilities (a) (b) (c) G0 (CONTROL) G1 (PROGEL) UTILITY UBAR CTR PRG Slide 26 G 0 and G 1 utilities u = U. Example: Decision theoretic comparison of times to event Weighting random resolution times (left) utilities (center) = weighted average utility U (right). Xu, Thall, M & Mehran (2016 Bayesian Anal.) Bigger one wins. Times to resolution of air leaks (after pulmonary resection); Slide 29 reduction by 1 day means more for early days than later (ideally, T = 0, no air leaks); comparing means is inappropriate 6. Novel markers tumor heterogeneity Lee, M, Ji & Gulukota (2015 Ann. Appl. Stat.) Slide ) 0.12) 0.41) 0.28) 0.4) 0.31) 0.38) 0.53) 0.41) 0.6) FREQ CONTR PROGEL (a) T 0i (black) and T 1i (red shaded) DENSITY G0 (CONTROL) G1 (PROGEL) (b) G 0 (black) and G 1 (red) Left: Times to resolution under control (black) and progel (red). Right: Model for the distribution G 0 and G 1 of resolution times. 0.42) 0.57) 0.6) 0.39) 0.59) 0.4) SUBLONES Subclone)1) Subclone)2) Subclone)3) Subclone)4) Subclone)5) SAMPLES 0.36)0.58) 0.42) 0.14) 0.43) 0.55) 0.4) SUBLONES Subclone)1) Subclone)2) Subclone)3) Subclone)4) Subclone)5) Subclone)6) Subclone)7) Inference on homogeneous cell subpopulations (tumor heterogeneity); Treatment allocation by (imputed & derived) tumor heterogeneity 5

6 Slide 30 Summary Future clinical trials will be more patient-centric; exploit increasingly more complete tumor characterization (genomics, proteomics, immmune markers etc.); be adaptive to use such information; use continuous optimization of treatment selection based on learning from previous patients resemble N of 1 trials; offering a precision medicine approach to every patient with cancer. Slide 31 Lee, J., Thall, P. F., Ji, Y., and Müller, P. (2015). Bayesian dose-finding in two treatment cycles based on the joint utility of efficacy and toxicity. J. Am. Stat. Assoc. Xu, Y., Müller, P., Wahed, A. S., and Thall, P. F. (2016). Bayesian nonparametric estimation for dynamic treatment regimes with sequential transition times. J. Am. Stat. Assoc., Xu Y, Thall P, Müller P, and Mehran R, A Bayesian Nonparametric Utility-Based Design for Comparing Treatments to Resolve Air Leaks After Lung Surgery (2016), Bayesian Analysis Xu, Y., Trippa, L., Müller, P., and Ji, Y. (2016). Subgroupbased adaptive designs for multi-arm biomarker trials. Stat. Biosc. Some references of Bayesian clinical trial designs: Berry, D. (2012). Adaptive clinical trials in oncology. Nature Reviews Clinical Oncology Berry, D. (2015) The Brave New World of Clinical Cancer Research: Adaptive Biomarker-driven Trials Integrating Clinical Practice with Clinical Research, Mol Oncol. 6