Transcript adaptive bayesian designs for dose

BAYESIAN
ADAPTIVE DESIGN
& INTERIM ANALYSIS
Donald A. Berry
[email protected]
Some references
Berry DA (2003). Statistical
Innovations in Cancer Research. In
Cancer Medicine e6. Ch 33. BC
Decker. (Ed: Holland J, Frei T et al.)
 Berry DA (2004). Bayesian statistics
and the efficiency and ethics of
clinical trials. Statistical Science.

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Benefits
 Adapting;
examples
 Stop
early (or late!)
 Change doses
 Add arms
 Drop arms
 Final
analysis
 Greater
precision (even full follow-up)
 Earlier conclusions
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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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OUTLINE: EXAMPLES
 Extraim
analysis
 Modeling
early endpoints
 Seamless
Phase II/III trial
 Adaptive
randomization
 Phase
II trial in AML
 Phase II drug screening process
 Phase III trial
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EXTRAIM ANALYSES*
 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
*Modeling due to Scott Berry
<[email protected]>
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 After
800 pts accrued, have
response info on 450 pts
 Find pred prob of stat sig when
full info on 800 pts available
 Also when full info on 1400
 Continue if . . .
 Stop if . . .
 If continue, n via pred prob
 Repeat at 2nd extraim analysis
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Tabl e 1: p0=0.42
p1
P(succ)
0.37 0.0001
0.42 0.0243
0.47 0.4467
0.52 0.9389
0.57 0.9989
meanSS
844.6
1011.2
1188.5
1049.9
874.2
sdSS
122.0
247.6
254.5
248.7
149.1
P(800)
0.8707
0.5324
0.2568
0.4435
0.7849
P(1400)
0.0194
0.2360
0.5484
0.2693
0.0268
P(succ1)
0.0001
0.0084
0.1052
0.4217
0.7841
P(succ2)
0.0001
0.0059
0.0914
0.2590
0.1729
Tabl e 2: p0=0.32
p1
P(succ)
0.27 0.0001
0.32 0.0284
0.37 0.4757
0.42 0.9545
0.47 0.9989
meanSS
836.5
1013.1
1186.6
1045.5
922.7
sdSS
111.1
246.3
252.0
245.9
181.0
P(800)
0.8937
0.5238
0.2513
0.4485
0.6632
P(1400)
0.0152
0.2338
0.5339
0.2449
0.0258
P(succ1)
0.0005
0.0094
0.1083
0.4316
0.6632
P(succ2)
0.0000
0.0083
0.1044
0.2505
0.2111
sdSS
95.3
246.6
246.3
234.8
205.4
P(800)
0.9163
0.5242
0.2313
0.3702
0.4121
P(1400)
0.0086
0.2340
0.5392
0.2030
0.0508
P(succ1)
0.0000
0.0090
0.1089
0.3577
0.3977
P(succ2)
0.0000
0.0062
0.1063
0.2065
0.1685
Tabl e 3: p0=0.22
p1
P(succ)
0.17 0.0000
0.22 0.0288
0.27 0.5484
0.32 0.9749
0.37 0.9995
vs 0.80
meanSS
827.7
1013.3
1199.0
1074.4
1024.7
MODELING EARLY ENDPOINTS:
LONGITUDINAL MARKERS
 Example
CA125 in ovarian cancer
 Use available data from trial (&
outside of trial) to model
relationship over time with
survival, depending on Rx
 Predictive distributions
 Use covariates
 Seamless phases II & III
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CA125 data & predictive
distributions of survival for
two of many patients* ——>
*Modeling due to Scott Berry
<[email protected]>
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Patient #1
Treatment
Days
Patient #1
Patient #2
Days
Patient #2
Methods
 Analytical
 Multiple
imputation
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SEAMLESS PHASES II/III*
 Early
endpoint (tumor response,
biomarker) may predict survival?
 May depend on treatment
 Should model the possibilities
 Primary endpoint: survival
 But observe relationships
*Inoue, et al (2002 Biometrics)
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Conventional drug development
Good
resp
No resp Stop
No survival
advantage
Not
Phase 3
Phase 2
6 mos
Survival
advantage Market
9-12 mos
> 2 yrs
Seamless phase 2/3
< 2 yrs (usually)
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Seamless phases
 Phase
2: 1 or 2 centers; 10 pts/mo,
randomize E vs C
 If pred probs “look good,” expand to
Phase 3: Many centers; 50 pts/mo
(Initial centers continue accrual)
 Max n = 900
[Single trial: survival data combined
in final analysis]
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Early stopping
 Use
pred probs of stat sig
 Frequent analyses (total of 18)
using pred probs to:
 Switch
to Phase 3
 Stop accrual for


Futility
Efficacy
 Submit
NDA
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Comparisons
Conventional Phase 3 designs:
Conv4 & Conv18, max N = 900
(same power as adaptive design)
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Expected N under H0
1000
855
884
Conv4
Conv18
800
600
431
400
200
0
Bayes
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Expected N under H1
1000
887
888
Conv4
Conv18
800
649
600
400
200
0
Bayes
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Benefits
 Duration
of drug development is
greatly shortened under adaptive
design:
 Fewer
patients in trial
 No hiatus for setting up phase 3
 All patients used for


Phase 3 endpoint
Relation between response & survival
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Possibility of large N
N
seldom near 900
 When
it is, it’s necessary!
 This
possibility gives Bayesian
design its edge
[Other reason for edge is
modeling response/survival]
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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 results
 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
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27
28
29
30
31
32
33
34
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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SCREENING PHASE II DRUGS
 Many
drugs
 Tumor response
 Goals:


Treat effectively
Learn quickly
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Standard designs
 One
drug (or dose) at a time;
no drug/dose comparisons
 Typical comparison by null
hypothesis: RR = 20%
 Progress hopelessly slow!
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Standard 2-stage design
First stage 20 patients:
 Stop if ≤ 4 or ≥ 9 responses
 Else second set of 20
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An adaptive allocation
 When
assigning next patient, find
r = P(rate ≥ 20%|data) for each drug
 Assign drugs in proportion to r
 Add drugs as become available
 Drop drugs that have small r
 Drugs with large r  phase 3
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Suppose 10 drugs, 200 patients
Identify nugget …
With probability: In average n:
110
50
Adaptive
Standard
<70%
Adaptive
>99%
Standard
9 drugs
have mix
of RRs
20% & 40%,
1 has 60%
(“nugget”)
Adaptive also better at finding “40%”, & sooner
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Suppose 100 drugs, 2000 patients
Identify nugget …
With probability: In average n:
1100
500
Adaptive
Standard
<70%
Adaptive
>99%
Standard
99 drugs
have mix
of RRs
20% & 40%,
1 has 60%
(“nugget”)
Adaptive also better at finding “40%”, & sooner
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Consequences
 Treat
pts in trial effectively
 Learn quickly
 Attractive to patients, in and
out of the trial
 Better drugs identified
sooner; move through faster
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PHASE III TRIAL
 Dichotomous
Q
endpoint
= P(pE > pS|data)
 Min
n = 150; Max n = 600
 After
n = 50, assign to arm E
with probability Q
 Except
 (Not
that 0.2 ≤ P(assign E) ≤ 0.8
“optimal,” but …)
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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
400
500
600
n
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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 1
 12/20
responses on arm 2
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Beta(9.275,
14.975)
0
.1
.2
Beta(13.275,
10.975)
.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
12
12/38
38/83
18
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
12
9 mos.
8/39
11/42
18
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
51 (34.9 ) 95 (65.1 ) 146
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
29
0.05
26
0.02
20
0.003
16
<0.001
49
FDA: Why do this?
What’s the advantage?
 Enthusiasm
of PIs
 Comparison
with
standard design . . .
50
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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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
52
OUTLINE: EXAMPLES
 Extraim
analysis
 Modeling
early endpoints
 Seamless
Phase II/III trial
 Adaptive
randomization
 Phase
II trial in AML
 Phase II drug screening process
 Phase III trial
53