# ADAPTIVE BAYESIAN DESIGNS FOR DOSE-RANGING DRUG TRIALS

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```					Bayesian Trial Designs: Drug Case Study
Donald A. Berry dberry@mdanderson.org
BERRY CONSULTANTS
STATISTICAL INNOVATION

Outline
 Some

history

 Why

Bayes?
designs

study
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2004 JHU/FDA Workshop: ―Can Bayesian Approaches to Studying New Treatments Improve Regulatory Decision-Making?‖ www.prous.com/bayesian2004
www.cfsan.fda.gov/~frf/ bayesdl.html
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Upcoming in 2005
 Special

issue of Clinical Trials

 ―Bayesian

Clinical Trials‖ Nature Reviews Drug Discovery

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Selected history of Bayesian trials
   

Medical devices (30+) 200+ at M.D. Anderson (Phase I, II, I/II) Cancer & Leukemia Group B Pharma
ASTIN (Pfizer)  Pravigard PAC (BMS)  Other




Decision analysis (go to phase III?)
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Why Bayes?
 On-line

 Predictive

probabilities (including modeling outcome relationships)

 Synthesis

(via hierarchical modeling, for example)

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PREDICTIVE PROBABILITIES
 Critical

component of experimental design monitoring trials

 In

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Endpoint: tumor response  Balanced randomized, H & C  Sample size planned: 164  Interim results after n = 34:

 

Control: 4/16 = 25% Herceptin: 12/18 = 67%

Not unexpected (prior?)  Predictive probab of stat sig: 95%  DMC stopped the trial  ASCO and JCO—reactions …

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at the accumulating data  Update probabilities  Find predictive probabilities  Use backward induction  Simulate to find false positive rate and statistical power
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 Look

 Stop

early (or late!)

 Futility  Success

 Change

doses  Add arms (e.g., combos)  Drop arms  Seamless phases
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Goals
 Learn

faster: More efficient

trials  More efficient drug/device development  Better treatment of patients in clinical trials
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ADAPTIVE RANDOMIZATION Giles, et al JCO (2003)
 Troxacitabine

(T) in acute myeloid leukemia (AML) combined with cytarabine (A) or idarubicin (I)  Adaptive randomization to: IA vs TA vs TI  Max n = 75  End point: Time to CR (< 50 days)
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 Assign

1/3 to IA (standard) throughout (until only 2 arms) to TA and TI based on current probability > IA

 Results



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Patient

Prob IA

Prob TA

Prob TI

Arm

CR<50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.33

0.33 0.34 0.35 0.37 0.38 0.39 0.39 0.44 0.47 0.43 0.50 0.50 0.47 0.57 0.57 0.56 0.56

0.33 0.32 0.32 0.30 0.28 0.28 0.27 0.23 0.20 0.24 0.17 0.17 0.20 0.10 0.10 0.11 0.11

TI IA TI IA IA IA IA TI TI TA TA TA TA TI TA IA TA

not CR not not not CR not not not CR not not not not CR not CR
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Patient

Prob IA

Prob TA

Prob TI

Arm

CR<50

18 19 20 21 22 Drop 23 24 TI 25 26 27 28 29 30 31 32 33 34

0.33 0.33 0.33 0.33 0.33 0.33 0.33 0.87 0.87 0.96 0.96 0.96 0.96 0.96 0.96 0.96 0.96

0.55 0.54 0.53 0.49 0.46 0.58 0.59 0.13 0.13 0.04 0.04 0.04 0.04 0.04 0.04 0.04 0.04

0.11 0.13 0.14 0.18 0.21 0.09 0.07 0 0 0 0 0 0 0 0 0 0

TA TA IA IA IA IA IA IA TA TA IA IA IA IA TA IA IA

not not CR CR CR CR CR not not not CR not CR not not not CR
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Compare n = 75

Summary of results
CR < 50 days:  IA: 10/18 = 56%  TA: 3/11 = 27%  TI: 0/5 = 0%

Criticisms . . .
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change in way we do medical research  More rapid progress  We’ll get the dose right!  Better treatment of patients  . . . at less cost
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 Fundamental

CASE STUDY: PHASE III TRIAL
 Dichotomous Q

endpoint

= P(pE > pS|data) n = 150; Max n = 600

 Min  1:1

randomize 1st 50, then assign to arm E with probability Q
 Except

that 0.2 ≤ P(assign E) ≤ 0.8

Small company!

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Recommendation to DSMB to
 Stop  Stop

for superiority if Q ≥ 0.99

accrual for futility if P(pE – pS < 0.10|data) > PF
 PF

depends on current n . . .

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Futility stopping boundary 1.0 0.8 0.6 0.95 0.75

PF
0.4 0.2 0.0 0 100 200 300 n 400 500 600
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Common prior density for pE & pS
 Independent
 Reasonably  Mean  SD

non-informative

= 0.30

= 0.20
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Beta(1.275, 2.975) density

0

.1

.2

.3

.4

.5 p

.6

.7

.8

.9

1
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Updating
After 20 patients on each arm


8/20 responses on arm S responses on arm E

 12/20

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Beta(9.275, 14.975)

Beta(13.275, 10.975)

Q = 0.79

0

.1

.2

.3

.4

.5 p

.6

.7

.8

.9

1
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Assumptions
 Accrual:  50-day

10/month

delay to assess response

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Need to stratify. But how?
Suppose probability assign to experimental arm is 30%, with these data . . .

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Proportions of Patients on Experimental Arm by Strata Stratum 1 Stratum 2 Small Big Small Big 6/20 (30%) 6/10 (60%) 10/20 (50%) 2/10 (20%)

Probabilit y of Being Assigned to Experimental Arm for Above Example Stratum 1 Stratum 2 Small Big Small Big 37% 19% 24% 44%
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One simulation; pS = 0.30, pE = 0.45
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0 6 12 18 24 Months
Superiority boundary

Pr obability Exp is better Pr opor tion Exp

178/243 = 73%

Std Exp

12/38 38/83

19/60 82/167

Final 20/65 29 87/178

One simulation; pE = pS = 0.30
1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

Pr obability futility

Futility boundary

87/155 = 56% Pr opor tion Exp Pr obability Exp is better

0

6

12

18

24 Months

Std Exp

9 mos. 8/39 11/42

End 15/57 32/81

Final 18/68 22/87

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Operating characteristics
Prob True ORR select Std Exp exp 0.3 0.2 <0.001 0.3 0.3 0.05 0.3 0.4 0.59 0.3 0.45 0.88 0.3 0.5 0.98 0.3 0.6 1.0 Mean # of patients (%) Std Exp Total 95 (62.1) 58 (37.9) 153 87 (43.1) 115 (56.9) 202 87 (30.4) 199 (69.6) 286 79 (30.7) 178 (69.3) 257 59 (29.5) 141 (70.5) 200 47 (30.1) 109 (69.9) 156 Mean length (mos) 15 20 29 26 20 16 Prob max n <0.001 0.003 0.05 0.02 0.003 <0.001

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FDA: Why do this? What’s the advantage?
 Enthusiasm

of patients & investigators

 Comparison

with standard design . . .
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Adaptive vs tailored balanced design w/same false-positive rate & power (Mean number patients by arm)
ORR pS = 0.20 pS = 0.30 pS = 0.40 pE = 0.35 pE = 0.45 pE = 0.55 Arm Std Exp Std Exp Std Exp Adaptive 68 168 79 178 74 180 Balanced 171 171 203 203 216 216 Savings 103 3 124 25 142 36
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FDA:
 Use

flat priors

 Error
 Other  We

size to 0.025
null hypotheses

fixed all … & willing to modify as necessary
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The rest of the story …
 PIs

on board

 CRO
 IRBs  FDA

in place
approved nixed!
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Outline
 Some

history

 Why

Bayes?
designs