Bayesian Trail Design 貝式試驗設計

Transcription

1 北院區臨床試驗中心生物統計組 Biostatistics Unit Clinical Trial Center, CGMH Bayesian Trail Design 貝式試驗設計 Lan-Yan Yang, PhD ( 楊嵐燕 ) 2018/03/05 1

2 Contents 1 Motivation 2 Bayesian methods 3 Examples 4 Considerations and remarks 2

3 3 Motivation

4 Bayesian Theorem is not magic Bayes classification Bayesian Network Machine learning Bayesian Network Bayesian Network 4

5 5 Bayesian Theorem is not incomprehensible

6 Example 0 某疾病的篩檢, 結果分為正 負二種, 宣稱之檢驗可靠度 90%, 且平均每 5000 人中, 有一人患此病 Q: 基於上述資訊, 你是否願意接受此檢驗? 說明 - 若無病, 檢驗會呈負反應之機率為 0.9 (Specificity) P( 負 無病 ) =0.9, P( 正 無病 ) =0.1 - 若有病, 檢驗會呈正反應之機率亦為 0.9 (Sensitivity) P( 正 有病 ) =0.9, P( 負 有病 ) =0.1 - P( 有病 )=1/5000, P( 無病 )=4999/ 但我們想知道的, 其實是當檢驗呈正反應下, 的確有病的機率 P( 有病 正 ) 當檢驗呈負反應下, 的確無病之機率 P( 無病 負 )

7 Example 0 Bayesian Theorem P( 有病 正 ) = = P( 正 有病 )P( 有病 ) P( 正 有病 )P( 有病 ) + P( 正 無病 )P( 無病 )... P( 無病 負 ) = 難道檢驗只對呈負反應可靠? 1/ % 7

8 Example 0 檢驗有 10% 的錯誤沒病卻呈正反應 而在每 5000 人中, 有病的很少 ( 平均 1 人 ), 因此在 5000 人中, 約有 500 個正反應, 但其中才約 1 人有病 1/500 = 0.002, 與所求出的 接近 檢查沒用嗎? 本來任何 1 人有病的機率為 1/5000 = , 一旦檢驗呈正反應, 有病的機率升為 , 約為 9 倍 8

9 Example 0: Conditional Probability 固定患病比 1/5000 可靠度 90% 80% 70% 60% 50% P( 有病 正 ) 固定可靠度 90% 患病比 1/5000 1/500 1/50 1/5 1/2 P( 有病 正 ) 9/5008 9/508 9/58 9/13 9/10 請注意條件機率!! 9 Ref: 引用黃文璋教授 < 機率應用不易 >, 數學傳播, 34 卷 1 期, pp

10 Example 0: Prior and Posterior 若再做 1 次同樣的檢查, 又是正反應 真的患病的機率又為何? Posterior prob. 事後機率 - P( 有病 正 ) = Prior prob. 事前機率 P( 正 有病 )P( 有病 ) P( 正 有病 )P( 有病 ) + P( 正 無病 )P( 無病 ) - Calculate using prior prob.= Ans: update posterior prob.= Bayesian updating: 依據新的資訊 ( 數據 ) 不斷修正! 10

11 Bayesian methods in clinical trials 11

12 Bayesian Formula Source: 12

13 Difference btw. Bayesians and Non-Bayesians Frequentist Bayesian Treatment Effect θ Fixed, yet unknown Random data Random Fixed Inference Prob. (data θ) Prob. (θ data) Simpler Less computation 13 Quickly adopted into clinical trial (fixed sample design) Adaptive methods in clinical trial

14 14 Bayesian adaptive Trial

15 Bayesian adaptive design Adaptive Designs - A study that includes a prospectively planned opportunity for modification of one or more specified aspects of the study design and hypotheses based on analysis of data (interim data) from subjects in the study Bayesian Designs - In the Bayesian paradigm, the parameter measuring treatment effect is regarded as a random variable - Bayesian inference is based on the posterior distribution (Bayes Rule updated based on observed data) - Outcome adaptive Fixed sample designs 15

16 Some Bayesian Adaptive Strategies Frequent interim analyses Longitudinal modeling of the relationship btw. proximate endpoints and the primary endpoint Response-adaptive randomization to efficiently address one or more trial goals Explicit decision rules based on predictive probabilities at each interim analysis Dose-response modeling Enrichment designs Extensive simulations of trial performance 16 Bayesian-Adaptive-Clinical-Trial-Design.pdf

17 Literature review of Bayesian trials Lee et al. (2012). Bayesian clinical trial in action - Ovid Medline and Ovid Embase - Published until Sep Bayes or Bayesian clinical trial 122 studies - Bayesian design and analysis (N=21) - Frequentist design with a Bayesian analysis (N=83) - Bayesian reanalysis studies (N=18) 17

18 Current status in clinicaltrial.gov In clinicaltrial.gov - Bayesian : 40 studies - Bayesian, Taiwan : 2 studies Bayesian logistic regression model Phase Ib, Open-label, Multi-center Study to Characterize the Safety, Tolerability and Pharmacodynamics (PD) of PDR001 in Combination With LCL161, Everolimus (RAD001) or Panobinostat(LBH589) Phase I, Open Label, Multicenter, Dose-escalation Study of HDM201 in Adult Patients With Advanced Solid and Hematological Tumors Characterized by Wild-type TP53 18

19 Most commonly use in clinical trials Dose finding Efficacy monitoring Toxicity monitoring Diagnosis/decision making studying PK/PD. 19

20 Bayesian approaches in clinical trials Incorporate information form previous studies - By prior distribution and historical controls - Maybe can reduce the required N to achieve objectives Useful for incorporating decision criterial into adaptive designed trial - Response-adaptive randomization - Stooping rules Useful for trial monitoring purposes - predictive probability to forecast future trial outcome(s) Can make probability statements about trial results - p-values are not probabilities of trial hypotheses 20

21 Example 1 Eicosanoids in NSCLC Eicosanoid Modulation in Advanced Lung Cancer: Cyclooxygenase-2 Expression Is a Positive Predictive Factor for Celecoxib +Chemotherapy Cancer and Leukemia Group B Trial (Edelman et al., 2008, JCO) Design - Parallel randomized phase II - Primary objective: Efficacy of 3 regimens (separately) - Primary endpoint: 9-months failure-free survival rate 21

22 Example 1 Eicosanoids in NSCLC Sample size determination (frequentist) - :. vs. :. - One-sample proportion test N39 (Type I error.and power.) Evaluation of endpoints - For arm C, responders - frequentist estimate: " $ 24.4% % &' 95% C.I.: 12% to 37% - Bayesian estimate: " * $ Under uniform prior % % &, 95% C.I.: 13% to 38% 22

23 Bayesian and Non-Bayesian estimate Bayesian " * 25.5% Traditional " 24.4% 23

24 Example 2 -- Phase II Trial of Extended-Dose Temozolomide in Melanoma (2008, JCO) 25 3 responders Bayesian Approach " * 15% Traditional Approach " 12% 24

25 Example 3- Phase II adaptive dose-finding trial 25 Consider a trial with: - 4 active dose levels plus placebo - Continuous endpoint (change from baseline to Week 2) - The primary objective is to find the best (clinically effective) dose to carry forward into Phase 3 - Clinical effectiveness is defined by difference of 3 relative to placebo subjectsare required for this trial using standard design (90% power) Adaptive Solution - Based on data observed at various interim looks, modify the randomization probabilitiesto focus allocation on better performing doses using Bayesian decision criteria

26 Example 3- Phase II adaptive dose-finding trial Bayesian decision rules given Some Results 26

27 Example 4- Bayesian adaptive trial Dose-response trial or phase II/III combined trials 27

28 Example 5: Trial monitoring Two-arm Phase III with time-to-event endpoint - Multi-national - >100 sites Monitoring Objective: Forecast accrual and events at various looks 28

29 Unique strengths of Bayesian methods Maintain validity when the study conduct deviates for the original design - The inference is conditioned on the data and not on the design Ideal for hierarchical model Incorporate prior information gathered before, during and outside of the trial More frequent monitoring and interim decision making during the trial Use learn as we go approach. - Real-time learning feature forms the basis of adaptive design 29

30 Bayesian design considerations more complex to design than the classical counterparts Homogeneity of responses/subjects between historical and current data Simulation should be used to determine trial characteristics - Sensitivity to choice of prior - Power, type-i error - Expected sample size Computational issues (posterior is not known completely) - Bayesian Central Limit Theorem - Laplace approximation - Markov Chain Monte Carlo (MCMC) 30

31 When for applying Bayesian methods When it s appropriate to use historical data/evidence In medical device trials where often there exists prior evidence for a control arm - FDA/CDRH has issued for the use of Bayesian statistics in medical device clinical trials When a Bayesian design can provide improved efficiencies in the adaptive realm When the sponsor organization wants to make internal decisions based on the results of a clinical trial 31

32 Remarks FDA recommendation for a Bayesian design: - schedule meetings to discuss experimental design and models. - discuss your prior information with FDA before the study begins. - If an investigational device exemption (IDE) is required, meet with FDA before the IDE submission. 32

33 Remarks Scientifically sound clinical trial planning and rigorous trial conduct are important regardless of whether you use a Bayesian or frequentist approach. Remain vigilant regarding randomization, concurrent controls, prospective planning, blinding, bias, precision, and all other factors 33

34 Additional infrastructure required To implement Bayesian methods in clinical trials specialized software programs to - run the study design - Simulation - Analysis Web-based applications - useful for timely data entry and analysis 34

35 References 35 Cook, J. (2006). Understanding the Exponential Tuning Parameter in Adaptively Randomized Trials. MDAndersonTechnical Report 27. see also AdaptiveRandomization documentation on MDAnderson Cancer website: Muller, P., Berry, D., Grieve, A., Krams, M. (2006). A Bayesian Decision- Theoretic Dose-Finding Trial. Decision Analysis. 3 (4) Berry, D., et al (2001). Adaptive Bayesian Designs for Dose-Ranging Drug Trials. In Case Studies in Bayesian Statistics, Vol. V. Springer-Verlag, New York. Spiegelhalter, D., Abrams, K., Myles, J. (2004). Bayesian Approaches to Clinical Trials and Health Care Evaluation. John Wiley and Sons, Chichester, UK. Gilks, W., Richardson, S., Spiegelhalter, D. (1996). Markov Chain Monte Carlo in Practice. Chapman and Hall / CRC. Gelman, A., Carlin, J., Stern, H., Rubin, D. (2004). Bayesian Data Analysis. Chapman and Hall / CRC. Lee et al. (2012) Bayesian clinical trials in actions. Stat. Med. 10; 31 (25): Jefferson. (2015) Bayesian Statistics in Clinical Trials Case Studies: Agenda. FDA. (20110) Guidance for the use of Bayesian statistics in medical device clinical trials