Scott M. Berry, PhDBerry Consultants

An Overview of Bayesian Methods in Clinical Trials

OutlineExperiences with Bayesian Clinical Trials

Ignore “Analysis” projectsExamples of Bayesian in Clinical Trials

Adaptive DesignsTherapeutic Areas

Why Bayesian?Examples:

Skip phase I (Anna), Safety DataPhase II dose findingPhase II/III cancer trialConfirmatory Trial

Experiences

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BC for 9 yearsEntirely BayesianInitially heavy on devices:Adaptive sample sizeAdaptive arm stoppingEarly success

Drugs in last several yearsAdaptive allocationPhase III predictionAdaptive dose escalation

Bayesian (AD) in Phases

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Phase I:Sample size Dose escalationCombination of armsSeamless phase I-II

Phase II:Sample sizeDose allocationIntroduce/Drop armsHistology

investigationMultiple TreatmentsMultiple endpointsPrediction of Phase IIISeamless phase II-III

Phase III:Sample sizeMultiple armsDropping armsStopping AccrualTiming

Phase IV:Sample sizeTiming

conclusionsIndicationsModeling

multiple sources

Continuous Sample Size Assessment

Therapeutic Areas/Diseases

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Oncology Migraine Lupus Sepsis Diabetes Obesity Stroke Tinnitus MS CHD

Spinal Cord Injury HIV Hepatitis C Pre-term Labor Constipation Micturition Drooling PO Ileus DVT Pain

Smoking Cessation Gastroparesis Alzheimers Atrial Fibrillation Cancer Diagnostics Disc Disease Contraceptives Valves/Stents Asthma Emphysema

PFO RA Sleep Apnea Osteoparesis Parkinsons Pain Hydrocephalus ALS Schizophrenia Crohns

“If we could first know where we are, and whither we are tending, we could then better judge what to do, and how to do it.”

--Abraham Lincoln, “House Divided” speech June 16, 1858

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What are Adaptive Designs?Adaptive Design:A design that “changes” depending on observed values in the trial

Prospective Adaptive Design:A design that has pre-specified dynamic aspects that are determined by the accruing information

Adaptive …“By Design”

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Typical Adaptive Design

Accrue Initial SubjectsCurrent

DataState

StatisticalModeling

Adaptive Decisions &

Actions

Stop

AccrueMore

• The “info” in the data is critical

• For long term results the interim values can be very informative

• Guides adaptive features, not final conclusions

Why Adaptive Designs?

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More appropriate sample size (typically smaller, sometimes bigger)

Better time issuesMore cost effectiveBetter treatment of subjects in and

out of the studyMore powerful scientific conclusionsHype?

Misconceptions

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Recipe/Table of AD“Wizard of Oz” AD“Penalty” for adaptationPost-hoc squeeze more juice from

same fruit (sometimes can!)Prior information/borrowing/face

valueFDA is negative

Role of Bayesian

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Approach of flexibilityParameter space not sample spaceParameters/Concepts that matter

Summaries of above that mean something

PredictionUnderstand uncertainty

ModelingCalculation/Software

Example of Predictive Prob

Trial, 33+ out of 100 is a SUCCESS

Look at data at n=10Predict remainder of 90 subjectsPredictive Prob accounts for uncertainty and “only” 10% of data observed

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Predictive

MLE

Possible Calculation

Simulate a from the beta(3,9)Simulate an x from binomial(90, )

Distribution of x’s is beta-binomial--the predictive distribution

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90

x

⎛⎝⎜

⎞⎠⎟∫ px 1−p( )90−x Γ 3( )Γ 9( )

Γ 12( )p2 1−p( )8 dp

Predictive, Posterior, MLE Project

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S@10Post Prob

>0.25Pred

Prob 33+MLE Proj Prob 33+

0 .042 .0096 0

1 .197 .070 6.6x10–11

2 .455 .234 .00097

3 .713 .487 .279

4 .885 .737 .948

5 .966 .900 .99991

6 .992 .973 1

7 .9988 .995 1

Interpretation

Predictive is VERY different than posterior probability

If you were using frequentist MLE to project you need to have constraints on # subjects before method “kinda works”

If there is a constraint, it should be on # for MLE not on % of the subjects

Predictive distribution handles both of these and does not need “constraints”

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Set-Up: Sanitized

Primary endpoint: Time to recovery

Cap on sample size: 250

Adaptively randomized; minimum probability assigned to placebo: 15%

Find ED90, updates weekly17

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Example 2:Seamless Phase II/III Cancer Trial

Phase II: LearnIdentify the drug worksProgression free survivalUpdate probability of Phase III success along

the wayPhase III: Confirm

Demonstrate efficacy & safety to regulatorsOverall survival

Two arm trialConventional Chemo vs.Conventional Chemo + Experimental Treatment

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Trial OutlinePhase 2:

Sample size = 40, 60, …, 160Enroll ~ 10 patients per monthInterim looks every 20 patientsCalculate Predictive Probability of Phase III

successMove to Phase 3 if high; terminate trial low

Phase 3:Sample size = 100, 150, …600Interim looks every 50 patientsEnroll ~ 20 patients per month

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Statistical ModelTime-to-progression is exponential

Time from progression to death is exponential

Priors: 1 pt of info; mean = 16 wks; median = 11 wks

Posteriors

€

θC ,TTP ~ Γ 1,16( ), θT ,TTP ~ Γ 1,16( )

€

θC ,PTD ~ Γ 1,16( ), θT ,PTD ~ Γ 1,16( )

€

θg,TTP | EVg,P ,EXPg,P ~ Γ 1+ EVg,P ,16 + EXPg,P( ) g∈ {C,T}

€

θg,PTD | EVg,D ,EXPg,D ~ Γ 1+ EVg,D ,16 + EXPg,D( ) g∈ {C,T}

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Phase II Interim AnalysisCalc Predictive Probability of Phase III Success

600-patient Phase III trial20 patient-per-month accrualTrack all patients for 6 months after last patient

inPOS pred. prob for win on overall survivalPPFS pred. prob for win on progression free survival

Adaptive decisions at n = 40,60,…,140If POS > 0.90 then move to Phase 3If POS < 0.10 then terminate trial

End of Phase IIIf PPFS > 0.70 then move to Phase 3

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Calculating Predictive Probabilities

Simulate a Phase 3 Trial … 10,000 timesDraw “true” event rates

Draw 600 patients’ values

Censor based upon enroll datePatient enroll from Day 1 to Month 30Censor from Month 6 to Month 36

Do log-rank test on ‘observed’ data: Win?

€

θg,TTP | EVg,P ,EXPg,P ~ Γ 1+ EVg,P ,16 + EXPg,P( ) g∈ {C,T}

€

ti,TTP ~ Exp λ g,TTP( ), ti,PFS ~ Exp λ g,PTD( ) i ∈ {1,...,600}€

θg,PTD | EVg,D ,EXPg,D ~ Γ 1+ EVg,D ,16 + EXPg,D( ) g∈ {C,T}

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Phase III Interim AnalysisCalc Predictive Probability of Phase III

SuccessPn,OS Assuming stop enrolling now & wait 6

months PNmax,OS Assuming enroll to max & wait 6 months 20 patient-per-month accrual

Adaptive decisions at n =100, …, 550If PNmax,OS < 0.05 then terminate trialIf Pn,OS < 0.95* then stop accruing, wait 6

months* for n ≤ 150, 0.90 when n > 150

Otherwise enroll 50 more patients & repeat

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Calculating Predictive ProbabilitiesSimulate a Completed a Phase 3 Trial

Draw “true” event rates

Draw uncensored patients’ values

Censor based upon follow-up time leftDo log-rank test on n-patient trial: Win?Also simulate for i = {n+1,…600}. Re-censor everyone’s data based on time leftDo log-rank test on 600-patient trial: Win?

€

θg,TTP | EVg,P ,EXPg,P ~ Γ 1+ EVg,P ,16 + EXPg,P( ) g∈ {C,T}

ti,TTP ~ Exp λg,TTP( ), ti,PTD ~Exp λg,PTD( ) i ∈{1,...,n}€

θg,PTD | EVg,D ,EXPg,D ~ Γ 1+ EVg,D ,16 + EXPg,D( ) g∈ {C,T}

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Operating Characteristics N Phase 2 Phase 3 Summary

Ctrl TTP PTD

Trt TTP PTD

P-2 P-3

Total Futility No Go Futility

PFS L OS L

PFS W OS L

PFS L OS W

PFS W OS W

PFS Win OS Win

10 15

10 15

112 103 215

0.424 0.328 0.222 0.016 0.002 0.005 0.003 0.005 0.008

10 15

15 15

118 278 396

0.132 0.050 0.030 0.003 0.032 0.002 0.751 0.783 0.753

10 15

15 20

103 202 305

0.068 0.042 0.001 0.009 0.014 0.038 0.828 0.842 0.866

15 20

15 20

116 112 228

0.409 0.332 0.203 0.031 0.004 0.013 0.008 0.012 0.021

15 20

25 20

116 257 372

0.125 0.021 0.000 0.000 0.009 0.000 0.845 0.854 0.845

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Phase 3 Operating Characteristics

Ctrl TTP PTD

Trt TTP PTD

Phase 2 Futility

Phase 2 No Go

Go To Phase 3

Futility Pred Win Win Early

% Win Early

Go Max Win @

Max

% Win @ Max

% Win Phase 3

10 15

10 15

0.424 0.328 0.248 0.222 0.005 0.003

0.60 0.021 0.002

0.010 0.020

10 15

15 15

0.132 0.050 0.818 0.030 0.732 0.727

0.99 0.056 0.056

1.00 0.957

10 15

15 20

0.068 0.042 0.890 0.001 0.885 0.838

0.95 0.004 0.004

1.00 0.946

15 20

15 20

0.409 0.332 0.259 0.203 0.015 0.005

0.33 0.041 0.007

0.017 0.046

15 20

25 20

0.125 0.021 0.854 0.000 0.833 0.833

1.00 0.021 0.021

1.00 1.000

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Phase II/III Conclusions

Sponsor loved the study

Trial progressing

I’m not allowed to say much more

to be continued….

ThermoCool® Catheter

2:1 randomized trial to compare to drug therapy

9-Month failure-freeComposite endpoint of AF or need

for change in drug therapy (protocol failure)

Superiority:Pr(PTC > PDRUG|Data)>0.98

Independent Beta(1,1) priors for each P

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Adaptive DesignLook when 150, 175, 200 are enrolled or go to cap of 230.

If Predictive Probability of trial success is≥0.90 then stop accrual≥0.99 then submit early for success

<0.05--for 230-- stop for futility

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Adaptive "Working" ModelModel Time to Failure:

Piecewise exponential

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HT t( ) =

θT ,1 0 < t≤12

θT ,2

12< t≤2

θT ,3 2 < t≤9

⎧

⎨

⎪⎪⎪

⎩

⎪⎪⎪

αT ~ Exp 1( ) βT ~ Exp 1( )

Time subject enters trial

9

2

0.50

Example Interim Analysis

28/4032/4543/60

Max Sample Size

Example Operating Characteristics

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Results Announced at Panel (11/08)

In July, 2007, first analysis was done for the 150-lookPredictive probability of success ≥ 0.9999

Trial accrual stoppedImmediate success claimed and PMA filed

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Final Bayesian Results…

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Final KM's

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ABLATION (N=103)

64%

AAD (N=56)

16%

FDA Approves First Ablation Catheters for the Treatment of Atrial Fibrillation (FDA Press Release)February 6, 2009 -

The U.S. Food and Drug Administration today approved the first ablation catheters for the treatment of atrial fibrillation (uncoordinated contractions of the upper heart chambers), one of the most common types of arrhythmias—or abnormal heart rhythms--affecting more than two million Americans.The devices approved today, the NaviStar ThermoCool saline irrigated radio-frequency ablation catheter and the EZ Steer ThermoCool Nav, can be used to create small, strategically placed scars in heart tissue to block irregular electrical waves that cause atrial fibrillation. … Both catheters are manufactured by BioSense Webster of Diamond Bar, Calif. 

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No mention of Bayesian or adaptive

Back to Primary Analysis:

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Pr PTC > PDRUG |data( ) ≥0.98

Viewfrom

outside

InterimAspects

Traditional

Bayesian