Bayesian Adaptive Designs for Precision Medicine: Promise, Progress, and Challenge. J. Jack Lee, Ph.D. Professor, Department of Biostatistics

Transcription

1 Bayesian Adaptive Designs for Precision Medicine: Promise, Progress, and Challenge J. Jack Lee, Ph.D. Professor, Department of Biostatistics

2 Nothing to disclose. Disclosure

3 How Do We Bring Theory to Practice and Make An Impact on Advancing Cancer Research and Patient Care? Education Innovation Implementation

4 Take Home Message Bayesian adaptive designs provide an ideal platform for learning. Bayesian adaptive designs enhance the efficiency of clinical trial designs to benefit patients, both in the trials and beyond the trials. Software programs are available for implementation.

5 Outline Statistical Inference Frequentist vs. Bayesian Paradigms Bayesian Update via Shiny Why Bayesian? Bayesian Adaptive Designs Adaptive Dose Finding Adaptive Randomization Predictive Probability Adaptive Randomization + Predictive Probability Multi-arm, Multi-stage, Biomarker-based Designs Master Protocols: Umbrella Trials; Basket Trials Multi-Arm Platform designs Past, Present, and Future of Clinical Trials

6 Statistical Inference Frequentist Approach Assume data is random and parameter q is fixed Make inference based on the data likelihood L (data q ) Bayesian Approach Assume data is fixed and parameter q is random Make inference based on P(q data) Bayesian is simply: Prior + Data Posterior New Prior + New Data New Posterior We learn as we go! Frequent and Bayesian methods are complementary to each other.

7 Video 1: Frequentist and Bayesian Inference # Response (data) ~ Binomial Distrib.(N=30, Response Rate (theta))

8 Video 2: Estimate the Response Rate

9 Estimate the Response Rate Bayesian Which method gives you more information? Frequentist

10 80+Programs Freely Available!

11

12 Bayesian Update via Shiny Use HTML and CSS to make webpages. HTML (Hypertext Markup Language) is the markup language to tell browsers how to display a web page (e.g., headings, lists, tables, etc.). CSS (Cascading Style Sheets) is the stylesheet language to style and beautify the page (e.g., telling browsers to change the color, font, layout, and more). A great tool for learning statistics and trial designs. Only need a browser. No software to install.

13

14

15 Sensitivity = 0.95, Specificity = 0.90, PPV=? Prevalence = 0.3 Positive Predictive Value = 0.803

16 Diagnostic Test Sensitivity=0.95, Specificity=0.90 Prior Prevalence Posterior Positive Predictive Value Negative Predictive Value Note: Prevalence is Prior Probability of disease PPV is Posterior Probability of disease Without Prior, even when sensitivity and specificity of a test are specified, there is no way to calculate Posterior

17 Bayesian Paradigm A Superior Way for Making Inference Advantages of Bayesian Method Models unknown parameters with statistical distributions. Properly addresses various levels of uncertainty. Use all available information prior, current, (future); within and outside of the trial. Allows more frequent monitoring and decision making. Be aware Are data and model compatible? Check model fitting. Prior specification. Perform sensitivity analysis by varying priors. Spiegelhalter, Abrams, Myles, Bayesian Approaches to Clinical Trials and Health-Care Evaluation. Wiley, D. A. Berry, Bayesian clinical trials, Nature Reviews Drug Discovery, vol. 5, pp , Biswas S, Liu DD, Lee JJ, Berry DA. Bayesian clinical trials at the University of Texas MD Anderson Cancer Center. Clin Trials 6(3):205-16, 6/2009. Lee JJ. Demystify statistical significance time to move on from the P value to Bayesian analysis. JNCI, Lee and Chu, Bayesian Clinical Trials in Action. Statistics in Medicine 31: , 2012 Berry S, Carlin B, Lee JJ, Mueller P. Bayesian Adaptive Methods for Clinical Trials, CRC Press

18

19 What Are Adaptive Designs? Trials that use interim data to guide the study conduct Adaptive dose finding and estimation Bayesian Optimal Interval (BOIN) Design in Phase I trials Adaptive patient assignment to treatment Adaptive randomization in Phase II or Phase III trials Adaptive decision making Predictive probability in Phase II or Phase III trials Drop bad treatments; add new treatments Adaptive Multi-Arm, Multi-Stage (MAMS) Design Seamless phase I/II, II/III designs, platform designs and basket designs Adaptive learning Build a comprehensive knowledge database (e.g. EHR); assign best treatment to each patient; continuous update covariates and outcomes; test and validate hypotheses

20 Why Adaptive? Clinical trial is a learning process. It makes sense to adjust the study conduct based on real-time learning during the trial. Use Bayesian paradigm for flexible and efficient designs and adaptive learning Adaptive design provides an ideal platform for learning We learn as we go. Validation is the key! For both drugs and markers: Many are Called, But Few Are Chosen Bayesian paradigm is particularly suitable for adaptive designs, but not all adaptive designs are Bayesian. Calibrate Bayesian adaptive designs to have desirable frequentist properties. Berry DA. Adaptive clinical trials in oncology. Nature Reviews Clinical Oncology, 2012.

21 Ƹ Bayesian Optimal Interval (BOIN) Design With the target probability of toxicity φ, an interval design makes decision of dose escalation, stay, or de-escalation by comparing the estimated probability of toxicity p j at dose j with a pre-specified toxicity interval. The interval boundaries 1j and 2j are selected to minimize the decision error of dosing. Liu S, Yuan Y. Bayesian optimal interval designs for phase I clinical trials. Appl. Statist. (2015) 64,

22 Optimal Interval Boundaries Assume the prior probability of the 3 decisions are equal A simple, yet, powerful result:

23 BOIN Design with φ= 0.2 The operating characteristics is much better than the 3+3 design and comparable to the continual reassessment method (CRM) design

24 Software for the BOIN Design The R package "BOIN" is available at CRAN. Standalone GUI based software is also available from MD Anderson Biostatistics software download website. /SingleSoftware.aspx?Software_Id=99 Statistical tutorial and protocol templates are provided at

25 Adaptive Randomization Traditional designs randomize patients equally to treatments via equal randomization (ER) Simple: 1:1 for two-arm trials; 1:1:1 for three-arm trials Consistent to the clinically equipoise principle. Maximize statistical power (collective ethics) Outcome adaptive randomization (AR) Assigning more patients to the better arm based on the observed data; Treat patients better in the trial (individual ethics) Imbalance causes loss of statistical power Study accrual may be faster Lee, Chen, Yin. Worth adaptive? CCR, 2012; Du, Wang, Lee. Contem. Clin Trials, 2015.

26 Video 3: q 1 =0.2, q 2 =0.4

27 AR versus ER AR enhances individual ethics; whereas ER emphasizes collective ethics. AR requires a larger N than ER in general. AR yields a higher overall success ( response rate or survival) than ER at the cost of increasing N. The differences between AR and ER are less pronounced with early stopping for efficacy and/or futility. AR has substantial benefit over ER when the efficacy difference between treatments is large Outside trial population is small, e.g., rare disease, and there is an effective treatment The choice of AR or ER depends on the focus of the trial and the utility function of the clinical trialists. Lee, Chen, and Yin, Worth adaptive? (CCR, 2012)

28 Bayesian Predictive Probability Design For testing H 0 : q q 0 vs. H 1 : q q 1 Predictive Probability (PP): The probability of a positive conclusion at the end of study should the current trend continue. At any given time of the trial, try to predict whether the drug is likely to work or not Continuous monitoring for timely action If PP is very low, then, stop the trial for futility Otherwise, continue to the end of study No early stopping for efficacy PP = i Prob( Y=i x) [Prob(q > q 0 x,y=i ) > q T ] If PP < q L, stop the trial and reject H 1, otherwise, continue to the next stage until max(n) Lee JJ, Liu D. Clin Trials 2008; 5:

29 Stopping Boundaries for q 0 =0.2, q 1 =0.4, = = 0.1 n Simon s Optimal Rej Region PET(q 0) Rej Region PP PET(q 0 ) prior for p = beta(0.2,0.8) q L =0.001, q T =0.900 = = E(N q 0 ) = PET(q 0 ) = 0.86 Simon s MiniMax: = = E(N q 0 ) = PET(q 0 ) = 0.46 Simon s Optimal: = = E(N q 0 ) = PET(q 0 ) = 0.55

30 Rejection Region in Number of Responses Stopping Boundaries Simon's MiniMax Simon's Optimal PP Data Number of Patients

31 Bayesian AR with Predictive Probability In a two-arm trial, start with ER for initial learning Switch to AR to assign more patients to the better treatment Test treatment efficacy by computing the predictive probability While the trial is still ongoing, compute the probability of a positive finding at the end of the study should the current trend continues (Predictive Probability) If PP is very large, stop the trial for efficacy If PP is very small, stop the trial for futility Continue until reaching early stopping criteria or N max Make a final decision on treatment efficacy Yin, Chen, and Lee. Phase II trial design with Bayesian adaptive randomization and predictive probability. Applied Statistics (JRSS-C), 2012 Yin, Chen, and Lee. Bayesian Adaptive Randomization and Trial Monitoring with Predictive Probability for Time-to-event Endpoint. Statistics in Biosciences, 2017.

32 Video 4:Adaptive Randomization /w Predictive Probability

33 Multi-marker, Multi-Arm, Multi-Stage Bayesian Adaptive Randomization Design Biopsy required Biomarker guided Adaptive randomization Interim monitoring Early stopping due to futility Early stopping due to efficacy Dropping losers Adding new treatments Examples BATTLE trials I-SPY2 trial (

34 Video 5: Bayesian Toxicity Monitoring

35

36

37

38

39

40

41 Master Protocol Trials Umbrella In a single type of cancer test different drugs on different mutations in BATTLE I-SPY2 GBM-Agile Lung MAP Focus 4 ALCHEMIST Basket In a variety of cancer types test a drug(s) on a single mutation(s) Imatinib Basket BRAF+ NCI MATCH 41

42 BATTLE (Biomarker-based Approaches of Targeted Therapy for Lung Cancer Elimination) Patient Population: Stage IV recurrent non-small cell lung cancer (NSCLC) Primary Endpoint: 8-week disease control rate (DCR) 4 Targeted treatments, 11 Biomarkers 200 evaluable patients Goal: Test treatment efficacy Test biomarker effect and their predictive roles to treatment Treat patients better in the trial based on their biomarkers 1. Zhou X, Liu S, Kim ES, Lee JJ. Bayesian adaptive design for targeted therapy development in lung cancer - A step toward personalized medicine (Clin Trials, 2008). 2. Kim ES, Herbst RS, Wistuba II, Lee JJ, et al, Hong WK. The BATTLE Trial: Personalizing Therapy for Lung Cancer. (Cancer Discovery, 2011)

43 BATTLE Schema Umbrella Protocol Core Biopsy EGFR KRAS/BRAF VEGF RXR/CyclinD1 Biomarker Profile Randomization: Equal Adaptive Erlotinib Vandetanib Erlotinib + Bexarotene Sorafenib Primary end point: 8 week Disease Control (DC)

44 Video 6:Adaptive Randomization in BATTLE Trial

45 Multiple-Arm Platform Design Biological knowledge advances in a lightning speed Many new agents and many more combination therapies are needed to be evaluated Only a small fraction of the drugs are tested in clinical trials Success rate for cancer drug development is very low How can we do better? Screen multiple agents simultaneously Include a control arm in a randomized study Early stopping for futility Control type I error with multiple testings Hobbs, Chen, Lee. Stat Methods Med Res. 2016

46 Sequential vs. Platform Designs Each shape depicts a study arm. The horizontal axis represents calendar time. Increases in the direction of the vertical axes represent increasing enrollment. The randomized two-arm approach necessitates that the standard of care therapy is repeated five times. The platform design enables consolidation of the control arms as well as seamless incorporation of novel investigational agents and as they emerge. This reduces redundancy and enhances efficiency. White Space

47 Sequential vs. Platform Designs Each shape depicts a study arm. The horizontal axis represents calendar time. Increases in the direction of the vertical axes represent increasing enrollment. The randomized two-arm approach necessitates that the standard of care therapy is repeated five times. The platform design enables consolidation of the control arms as well as seamless incorporation of novel investigational agents and as they emerge. This reduces redundancy and enhances efficiency. White Space

48 Conceptual Schema of the Platform Design Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 Year 7 Control Exp 1 Exp 2 Control Exp 1 Exp 2 Control Exp 2 Exp 3 Control Exp 2 Exp 3 Control Exp 4 Control Exp 4 Exp 5 Exp 3 Exp 4 Exp 6 Drop Bad Drug Exp 1 Exp 3 Graduate Good Drug Exp 2

49 Platform Design - Summary Start with one control and multiple new experimental treatments Enroll patients and apply equal randomization Calculate the predictive probability of a high response rate of each one of the new treatments Sufficiently low: drop the treatment Add additional new treatments Potential expansion Graduate the effective treatment early Start with equal randomization but switch to outcome adaptive randomization (AR) at a certain point Add covariates A perpetual, drug screening platform

50 Bayesian Basket Design Trippa and Alexander, Bayesian Baskets: A Novel Design for Biomarker-Based Clinical Trials, JCO 2017

51 Bayesian Basket Design Trippa and Alexander, Bayesian Baskets: A Novel Design for Biomarker-Based Clinical Trials, JCO 2017

52 Past, Present, and Future of Clinical Trials Past: One trial, one drug, one patient population at a time expensive, high failure rate Disjoint process, non-targeted agents, no patient selection Fixed design, infrequent interim analyses Rush into Phase III too early Present: biomarker integrated Biomarker-based patient selection and drug matching All comers, master protocol trials; basket trials Future: smart trials More adaptive designs in Phases I, II and III trials Smaller, more focused Phase III trials Bayesian platform, basket, multi-arm, multi-stage trials Speed up drug development Step towards precision medicine

53 Team Work!