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WHY BAYES? INNOVATIONS IN CLINICAL TRIAL DESIGN & ANALYSIS Donald A. Berry dberry@mdanderson.org Conclusion These data add to the growing evidence that supports the regular use of aspirin and other NSAIDs … as effective chemopreventive agents for breast cancer. 2 Results Ever use of aspirin or other NSAIDs … was reported in 301 cases (20.9%) and 345 controls (24.3%) (odds ratio 0.80, 95% CI 0.66-0.97). 3 Bayesian analysis? Bayesian analysis of Naïve ―Results‖ is wrong Gives Bayesians a bad name Anynaïve frequentist analysis is also wrong 4 What is Bayesian analysis? Bayes' theorem: '( q| X ) (q) * f( X | q ) Assess prior (subjective, include available evidence) Construct model f for data 5 Implication: The Likelihood Principle Where X is observed data, the likelihood function LX(q) = f( X | q ) contains all the information in an experiment relevant for inferences about q 6 Shortversion of LP: Take data at face value Data: Among cases: 301/1442 Among controls: 345/1420 But ―Data‖ is deceptive These are not the full data 7 The data Methods: ―Population-based case-control study of breast cancer‖ ―Study design published previously‖ Aspirin/NSAIDs? (2.25-hr ?naire) Includes superficial data: Among cases: 301/1442 Among controls: 345/1420 Other studies (& fact published!!) 8 Silent multiplicities Are the most difficult problems in statistical inference render what we do irrelevant Can —and wrong! 9 Which city is furthest north? Portland, OR Portland, ME Milan, Italy Vladivostok, Russia 10 Beating a dead horse . . . Piattelli-Palmarini (inevitable illusions) asks: ―I have just tossed a coin 7 times.‖ Which did I get? 1: THHTHTT 2: TTTTTTT Most people say 1. But ―the probabilities are totally even‖ Most people are right; he’s totally wrong! Data: He presented us with 1 & 2! 11 THHTHTT or TTTTTTT? LR = Bayes factor of 1 over 2 = P(Wrote 1&2 | Got 1) P(Wrote 1&2 | Got 2) LR > 1 P(Got 1 | Wrote 1&2) > 1/2 Eg: LR = (1/2)/(1/42) = 21 P(Got 1 | Wrote 1&2) = 21/22 = 95% [Probs ―totally even‖ if a coin was used to generate the alternative sequence] 12 Marker/dose interaction Marker negative Marker positive 1.0 1.0 0.9 0.9 0.8 Std (96) 0.8 Hi (38) 0.7 0.7 D D F 0.6 Low (93) F 0.6 Std (41) S 0.5 Hi (95) S 0.5 0.4 0.4 Low (36) 0.3 0.3 0.2 0.2 0.1 0.1 0.0 0.0 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 Years Years 13 Proportional hazards model Variable Comp RelRisk P #PosNodes 10/1 2.7 <0.001 MenoStatus pre/post 1.5 0.05 TumorSize T2/T1 2.6 <0.001 Dose –– –– NS Marker 50/0 4.0 <0.001 MarkerxDose –– –– <0.001 This analysis is wrong! 14 Data at face value? How identified? Why am I showing you these results? What am I not showing you? What related studies show? 15 Solutions? Short answer: I don’t know! A solution: Superviseexperiment yourself Become an expert on substance Partial solution: Supervise supervisors Learn as much substance as you can Danger: You risk projecting yourself as uniquely scientific 16 A consequence Statisticians come to believe NOTHING!! 17 OUTLINE Silentmultiplicities Bayes and predictive probabilities Bayes as a frequentist tool Adaptive designs: Adaptive randomization Investigating many phase II drugs Seamless Phase II/III trial Adaptive dose-response Extraim analysis Trial design as decision analysis 18 Bayes in pharma and FDA … 19 http://www.cfsan.fda.gov/~frf/bayesdl.html http://www.prous.com/bayesian2004/ BAYES AND PREDICTIVE PROBABILITY component of Critical experimental design In monitoring trials 23 Example calculation Data: 13 A's and 4 B's Likelihood p13 (1–p)4 24 Posterior density of p for uniform prior: Beta(14,5) 13 4 p (1–p) 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 p 25 Laplace’s rule of succession P(A wins next pair | data) = EP(A wins next pair | data, p) = E(p | data) = mean of Beta(14, 5) = 14/19 26 Updating w/next observation Beta(15, 5) Beta(14, 6) prob 5/19 prob 14/19 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 p 27 Suppose 17 more observations P(A wins x of 17 | data) = EP(A wins x | data, p) =E [( ) 17 x p x(1–p)17–x | data, p] 28 Best fitting binomial vs. predictive probabilities Binomial, p=14/19 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Predictive, p ~ beta(14,5) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 29 Comparison of predictive with posterior 13 4 .15 p (1–p) .10 .05 .00 1 3 0 0 .1 2 .2 4 .35 6.47 8 9 10 11 .7 13 .8 15 .9 17 1 12 14 16 .5 .6 p 30 Example: Baxter’s DCLHb & predictive probabilities Cross-Linked Hemoglobin Diaspirin Blood substitute; emergency trauma Randomized controlled trial (1996+) Treatment: DCLHb Control: saline N = 850 (= 2x425) Endpoint: death 31 Waiver of informed consent Data Monitoring Committee First DMC meeting: DCLHb Saline Dead 21 (43%) 8 (20%) Alive 28 33 Total 49 41 P-value? No formal interim analysis 32 Predictive probability of future results (after n = 850) Probability of significant survival benefit for DCLHb after 850 patients: 0.00045 DMC paused trial: Covariates? No imbalance DMC stopped trial 33 OUTLINE Silentmultiplicities Bayes and predictive probabilities Bayes as a frequentist tool Adaptive designs: Adaptive randomization Investigating many phase II drugs Seamless Phase II/III trial Adaptive dose-response Extraim analysis Trial design as decision analysis 34 BAYES AS A FREQUENTIST TOOL Design a Bayesian trial Check operating characteristics Adjust design to get = 0.05 frequentist design That’s fine! We have 50+ such trials at MDACC 35 OUTLINE Silentmultiplicities Bayes and predictive probabilities Bayes as a frequentist tool Adaptive designs: Adaptive randomization Investigating many phase II drugs Seamless Phase II/III trial Adaptive dose-response Extraim analysis Trial design as decision analysis 36 ADAPTIVE DESIGN Look at accumulating data … without blushing Update probabilities Find predictive probabilities Modify future course of trial Give details in protocol Simulate to find operating characteristics 37 OUTLINE Silentmultiplicities Bayes and predictive probabilities Bayes as a frequentist tool Adaptive designs: Adaptive randomization Investigating many phase II drugs Seamless Phase II/III trial Adaptive dose-response Extraim analysis Trial design as decision analysis 38 Giles, et al JCO (2003) Troxacitabine(T) in acute myeloid leukemia (AML) when combined with cytarabine (A) or idarubicin (I) Adaptive randomization to: IA vs TA vs TI Max n = 75 End point: CR (time to CR < 50 days) 39 Randomization Adaptive Assign1/3 to IA (standard) throughout (unless only 2 arms) Adaptive to TA and TI based on current results Final results 40 Patient Prob IA Prob TA Prob TI Arm CR<50 1 0.33 0.33 0.33 TI not 2 0.33 0.34 0.32 IA CR 3 0.33 0.35 0.32 TI not 4 0.33 0.37 0.30 IA not 5 0.33 0.38 0.28 IA not 6 0.33 0.39 0.28 IA CR 7 0.33 0.39 0.27 IA not 8 0.33 0.44 0.23 TI not 9 0.33 0.47 0.20 TI not 10 0.33 0.43 0.24 TA CR 11 0.33 0.50 0.17 TA not 12 0.33 0.50 0.17 TA not 13 0.33 0.47 0.20 TA not 14 0.33 0.57 0.10 TI not 15 0.33 0.57 0.10 TA CR 16 0.33 0.56 0.11 IA not 17 0.33 0.56 0.11 TA CR 41 Patient Prob IA Prob TA Prob TI Arm CR<50 18 0.33 0.55 0.11 TA not 19 0.33 0.54 0.13 TA not 20 0.33 0.53 0.14 IA CR 21 0.33 0.49 0.18 IA CR 22 0.33 0.46 0.21 IA CR IA Drop 23 0.33 0.58 0.09 CR 24 0.33 0.59 0.07 IA CR TI 25 0.87 0.13 0 IA not 26 0.87 0.13 0 TA not 27 0.96 0.04 0 TA not 28 0.96 0.04 0 IA CR 29 0.96 0.04 0 IA not 30 0.96 0.04 0 IA CR 31 0.96 0.04 0 IA not 32 0.96 0.04 0 TA not 33 0.96 0.04 0 IA not 34 0.96 0.04 0 IA CR 42 Compare n = 75 Summary of results CR rates: IA: 10/18 = 56% TA: 3/11 = 27% TI: 0/5 = 0% Criticisms . . . 43 OUTLINE Silentmultiplicities Bayes and predictive probabilities Bayes as a frequentist tool Adaptive designs: Adaptive randomization Investigating many phase II drugs Seamless Phase II/III trial Adaptive dose-response Extraim analysis Trial design as decision analysis 44 Example: Adaptive allocation of therapies Design for phase II: Many drugs Advanced breast cancer (MDA); endpoint is tumor response Goals: Treat effectively Learn quickly 45 Comparison: Standard designs One drug (or dose) at a time; no drug/dose comparisons Typical comparison by null hypothesis: response rate = 20% Progress is slow! 46 Standard designs One stage, 14 patients: If 0 responses then stop If ≥ 1 response then phase III Two stages, first stage 20 patients: If≤ 4 or ≥ 9 responses then stop Else second set of 20 patients 47 An adaptive allocation When assigning next patient, find r = P(rate ≥ 20%|data) for each drug [Or, r = P(drug is best|data)] Assign drugs in proportion to r Add drugs as become available Drop drugs that have small r Drugs with large r phase III 48 Suppose 10 drugs, 200 patients 9 drugs have mix of response rates 20% & 40%, 1 (―nugget‖) has 60% Standard 2-stage design finds nugget with probability < 70% (After 110 patients on average) Adaptive design finds nugget with probability > 99% (After about 50 patients on average) Adaptive also better at finding 40% 49 Suppose 100 drugs, 2000 patients 99 drugs have mix of response rates 20% & 40%, 1 (―nugget‖) has 60% Standard 2-stage design finds nugget with probability < 70% (After 1100 patients on average) Adaptive design finds nugget with probability > 99% (After about 500 patients on average) Adaptive also better at finding 40% 50 Consequences Recall goals: (1) Treat effectively (2) Learn quickly Attractive to patients, in and out of the trial Better drugs identified faster; move through faster 51 OUTLINE Silentmultiplicities Bayes and predictive probabilities Bayes as a frequentist tool Adaptive designs: Adaptive randomization Investigating many phase II drugs Seamless Phase II/III trial Adaptive dose-response Extraim analysis Trial design as decision analysis 52 Example: Seamless phase II/III Drug vs placebo, randomized Local control (or biomarker, etc): early endpoint related to survival? May depend on treatment 53 *Inoue et al (2002 Biometrics) Conventional drug development Survival Local advantage Market control No survival advantage Not No local control Stop Phase II Phase III 6 mos 9-12 mos > 2 yrs Seamless phase II/III < 2 yrs (usually) 54 Seamless phases Phase II: Two centers; 10 pts/mo. drug vs placebo. If predictive probabilities look good, expand to Phase III: Many centers; 40+ pts/mo. (Initial centers accrue during set-up) Max sample size: 900 [Single trial: survival data from both phases combined in final analysis] 55 Early stopping Use predictive probs of stat. signif. Frequent analyses (total of 18) using predictive probabilities: To switch to Phase III To stop accrual For futility For efficacy To submit NDA 56 Comparisons Conventional Phase III designs: Conv4 & Conv18, max N = 900 (same power as adaptive design) 57 Expected N under H0 1000 884 855 800 600 431 400 200 0 Bayes Conv4 Conv18 58 Expected N under H1 1000 887 888 800 649 600 400 200 0 Bayes Conv4 Conv18 59 Benefits Durationof drug development is greatly shortened under adaptive design: Fewer patients in trial No hiatus for setting up phase III Use all patients to assess phase III endpoint and relationship between local control and survival 60 Possibility of large N N seldom near 900 When it is, it’s necessary! Thispossibility gives Bayesian design its edge [Other reason for edge is modeling local control/survival] 61 OUTLINE Silentmultiplicities Bayes and predictive probabilities Bayes as a frequentist tool Adaptive designs: Adaptive randomization Investigating many phase II drugs Seamless Phase II/III trial Adaptive dose-response Extraim analysis Trial design as decision analysis 62 * *Berry, et al. Case Studies in Bayesian Statistics 2001 Example: Stroke and adaptive dose-response Adaptive doses in Phase II setting: learn efficiently and rapidly about dose-response relationship Pfizer trial of a neutrofil inhibitory factor; results recently announced Endpoint: stroke scale at week 13 Early endpoints: weekly stroke scale 64 Standard Parallel Group Design Equal sample sizes at each of k doses. Doses 65 True dose-response curve (unknown) Response Doses 66 Observe responses (with error) at chosen doses Response Doses 67 Dose at which 95% max effect Response True ED95 Doses 68 Uncertainty about ED95 Response True ED95 Dose ? 69 Uncertainty about ED95 Response Dose ? 70 Solution: Increase number of doses Response ED95 71 Doses But, enormous sample size, and . . . wasted dose assignments—always! Response ED95 72 Doses Our adaptive approach Observe data continuously Select next dose to maximize information about ED95, given available evidence Stop dose-ranging trial when know ED95 & response at ED95 ―sufficiently well‖ 73 Our approach (cont’d) Info accrues Longitudinal Model Copenhagen Stroke Database gradually 50 40 about each 30 patient; 20 prediction 10 using 0 -10 longitudinal -20 model -30 -40 -30 -20 -10 0 10 20 30 40 50 Difference from baseline in SSS week 3 74 Our approach (cont’d) Modeldose-response (borrow strength from neighboring doses) Many doses (logistical issues) 75 Possible decisions each day: Stop trial and drug’s development Stop and set up confirmatory trial Continue dose-finding (what dose?) Size of confirmatory trial based on info from dose-ranging phase Choices by decision analysis (Human safeguard: DSMB) 76 Dose-response trial Learn efficiently and rapidly about dose-response; if + go to Phase III Assign dose to maximize info about dose-response parameters given current info Use predictive probabilities, based on early endpoints Doses in continuum, or preset grid 77 Dose-response trial (cont’d) Learn about SD on-line dose-ranging when know Halt dose sufficiently well Seamless switch from dose- ranging to confirmatory trial— 2 trials in 1! 78 Advantages over standard design Fewer patients (generally); faster & more effective learning Better at finding ED95 Tends to treat patients in trial more effectively Drops duds early —actual trial! 79 Dose-assignment simulation Assumes particular dose- response curve Assumes SD = 12 Shows weekly results, several patients at a time (green circles) 80 Prior 30 25 20 E(f) 15 10 5 0 0.0 0.5 1.0 1.5 81 DOSE DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 82 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 83 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 84 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 85 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 86 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 87 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 88 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 89 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 90 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 91 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 92 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 93 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 94 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 95 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 96 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 97 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 98 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 99 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 100 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 101 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 102 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 103 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 104 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 105 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 106 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 107 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 108 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 109 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 110 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 111 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 112 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 113 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 114 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 115 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 116 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 117 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 118 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 119 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 120 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 121 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 122 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 123 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 124 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 125 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 126 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 127 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 128 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 129 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 130 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 131 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 0 0.0 0.5 1.0 1.5 132 DOSE green=obs, blue=imputed, black=true mn DATA 30 25 20 15 Y 10 5 Estimated ED95 0 0.0 0.5 1.0 1.5 133 DOSE green=obs, blue=imputed, black=true mn Confirmatory Ao e s n sD e il s s km i d y- ge ns e b oa nt Wu o ei 1.5 1.5 1.0 0.5 0.DOSE 1.0 0.5 0.0 0 0 1 0 2 0 3 134 E E K W Estimated f unctions 20 15 d:/data/build13/run11/ 10 F 5 0 0.0 0.5 1.0 1.5 135 Z Doses assigned across all simulations 0.14 20 0.12 15 0.10 0.08 Proportion 10 0.06 0.04 5 0.02 0.0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 136 ASSIGNED DOSES Black: median; Red: upper & lower quartiles; Green: Nominal Estimated f unctions (no dose effect) 20 15 d:/data/build13/run12/ 10 F 5 0 0.0 0.5 1.0 1.5 137 Z Doses assigned across all simulations 20 0.25 0.20 15 0.15 Proportion 10 0.10 5 0.05 0.0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 138 ASSIGNED DOSES Black: median; Red: upper & lower quartiles; Green: Nominal Consequences of Using Bayesian Adaptive Approach Fundamental change in the way we do medical research More rapid progress We’ll get the dose right! Better treatment of patients . . . at less cost 139 Reactions FDA: Positive. ―Makes coming to work worthwhile.‖ ―In five years all trials may be seamless.‖ Pfizer management: Enthusiastic Other companies: Cautious 140 OUTLINE Silentmultiplicities Bayes and predictive probabilities Bayes as a frequentist tool Adaptive designs: Adaptive randomization Investigating many phase II drugs Seamless Phase II/III trial Adaptive dose-response Extraim analysis Trial design as decision analysis 141 Example: Extraim analysis Endpoint: CR (detect 0.42 vs 0.32) 80% power: N = 800 Two extraim analyses, one at 800 Another after up to 300 added pts Maximum n = 1400 (only rarely) Accrual: 70/month Delay in assessing response 142 After 800 patients, have response info on 450 Find predictive probability of stat significance when full info on 800 Also when full info on 1400 Continue if . . . Stop if . . . If continue, n via predictive power Repeat at second extraim analysis 143 Table 1: p0=0.42 p1 P(succ) meanSS sdSS P(800) P(1400) P(succ1) P(succ2) 0.37 0.0001 844.6 122.0 0.8707 0.0194 0.0001 0.0001 0.42 0.0243 1011.2 247.6 0.5324 0.2360 0.0084 0.0059 0.47 0.4467 1188.5 254.5 0.2568 0.5484 0.1052 0.0914 0.52 0.9389 1049.9 248.7 0.4435 0.2693 0.4217 0.2590 0.57 0.9989 874.2 149.1 0.7849 0.0268 0.7841 0.1729 Table 2: p0=0.32 p1 P(succ) meanSS sdSS P(800) P(1400) P(succ1) P(succ2) 0.27 0.0001 836.5 111.1 0.8937 0.0152 0.0005 0.0000 0.32 0.0284 1013.1 246.3 0.5238 0.2338 0.0094 0.0083 0.37 0.4757 1186.6 252.0 0.2513 0.5339 0.1083 0.1044 0.42 0.9545 1045.5 245.9 0.4485 0.2449 0.4316 0.2505 0.47 0.9989 922.7 181.0 0.6632 0.0258 0.6632 0.2111 vs 0.80 Table 3: p0=0.22 p1 P(succ) meanSS sdSS P(800) P(1400) P(succ1) P(succ2) 0.17 0.0000 827.7 95.3 0.9163 0.0086 0.0000 0.0000 0.22 0.0288 1013.3 246.6 0.5242 0.2340 0.0090 0.0062 0.27 0.5484 1199.0 246.3 0.2313 0.5392 0.1089 0.1063 0.32 0.9749 1074.4 234.8 0.3702 0.2030 0.3577 0.2065 0.37 0.9995 1024.7 205.4 0.4121 0.0508 0.3977 0.1685 OUTLINE Silentmultiplicities Bayes and predictive probabilities Bayes as a frequentist tool Adaptive designs: Adaptive randomization Investigating many phase II drugs Seamless Phase II/III trial Adaptive dose-response Extraim analysis Trial design as decision analysis 145 Decision-analytic approach For each trial design … List possible results Calculate their predictive probabilities Evaluate their utilities Average utilities by probabilities to give utility of trial with that design Compare utilities of various designs Choose design with high utility 146 Choosing sample size* Special case of above One utility: Effective overall treatment of patients, both those after the trial in the trial Example,dichotomous endpoint: Maximize expected number of successes over all patients 147 *Cheng et al (2003 Biometrika) Compare Joffe/Weeks JNCI Dec 18, 2002 ―Many respondents viewed the main societal purpose of clinical trials as benefiting the participants rather than as creating generalizable knowledge to advance future therapy. This view, which was more prevalent among specialists such as pediatric oncologists that enrolled greater proportions of patients in trials, conflicts with established principles of research ethics.‖ 148 Maximize effective treatment overall What is ―overall‖? patients who will be treated All with therapies assessed in trial Call it N, ―patient horizon‖ Enough to know mean of N Enough to know magnitude of N: 100? 1000? 1,000,000? 149 Goal: maximize expected number of successes in N Either one- or two-armed trial Suppose n = 1000 is right for N = 1,000,000 Then for other N’s use n = 150 Optimal allocations in a two-armed trial 151 Knowledge about success rate r 152 OUTLINE Silentmultiplicities Bayes and predictive probabilities Bayes as a frequentist tool Adaptive designs: Adaptive randomization Investigating many phase II drugs Seamless Phase II/III trial Adaptive dose-response Extraim analysis Trial design as decision analysis 153

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