Transcript adaptive bayesian designs for dose

Bayesian Trial Designs:
Drug Case Study
Donald A. Berry
[email protected]
BERRY
CONSULTANTS
STATISTICAL INNOVATION
Outline
 Some
 Why
history
Bayes?
 Adaptive
 Case
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
learning (ideal for adapting)
 Predictive
probabilities (including
modeling outcome relationships)
 Synthesis
(via hierarchical
modeling, for example)
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PREDICTIVE
PROBABILITIES
 Critical
component of
experimental design
 In
monitoring trials
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Herceptin in neoadjuvant BC
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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ADAPTIVE DESIGNS:
Approach and Methodology
 Look
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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Adaptive strategies
 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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Adaptive Randomization
 Assign
1/3 to IA (standard)
throughout (until only 2 arms)
 Adaptive
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
18
19
20
21
22
Drop 23
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TI 25
26
27
28
29
30
31
32
33
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Prob IA
Prob TA
Prob TI
Arm
CR<50
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
Compare n = 75
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Summary of results
CR < 50 days:
 IA: 10/18 = 56%
 TA: 3/11 = 27%
 TI:
0/5 = 0%
Criticisms . . .
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Consequences of Bayesian
Adaptive Approach
 Fundamental
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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CASE STUDY: PHASE III TRIAL
 Dichotomous
Q
endpoint
= P(pE > pS|data)
 Min
n = 150; Max n = 600
 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
for superiority if Q ≥ 0.99
 Stop
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
0.95
0.8
0.75
0.6
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
 12/20
responses on arm E
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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
6/20 (30%)
10/20 (50%)
Big
6/10 (60%)
2/10 (20%)
Probability of Being Assigned to
Experimental Arm for Above Example
Stratum 1
Stratum 2
Small
Big
Small
37%
24%
Big
19%
44%
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One simulation; pS = 0.30, pE = 0.45
1.0
0.9
0.8
0.7
0.6
Superiority boundary
Probability
Exp is better
178/243
= 73%
Proportion Exp
0.5
0.4
0.3
0.2
0.1
0.0
0
6
Std
Exp
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12/38
38/83
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24 Months
19/60
82/167
Final
20/65
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87/178
One simulation; pE = pS = 0.30
1.0
Probability futility
0.9
Futility boundary
0.8
0.7
87/155
= 56%
0.6
0.5
0.4
Proportion Exp
Probability
Exp is better
0.3
0.2
0.1
0.0
0
6
Std
Exp
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9 mos.
8/39
11/42
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End
15/57
32/81
24 Months
Final
18/68
22/87
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Operating characteristics
Prob
True ORR selec t
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 Prob
(mos) max n
15
<0.001
20
0.003
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0.05
26
0.02
20
0.003
16
<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
size to 0.025
 Other
null hypotheses
 We
fixed all … & willing
to modify as necessary
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The rest of the story …
 PIs
on board
 CRO
in place
 IRBs
approved
 FDA
nixed!
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Outline
 Some
 Why
history
Bayes?
 Adaptive
 Case
designs
study
36