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Bayesian Adaptive Dose Finding Studies: Smaller, Stronger, Faster

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Dose Finding Trial. Generic example. All details hidden, but flavor is the same ' ... Combine multiple efficacy safety in the dose finding decision ... – PowerPoint PPT presentation

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Title: Bayesian Adaptive Dose Finding Studies: Smaller, Stronger, Faster


1
Bayesian Adaptive Dose Finding Studies Smaller,
Stronger, Faster
Scott M. Berry scott_at_berryconsultants.com
2
Dose Finding Trial
  • Generic example. All details hidden, but flavor
    is the same
  • Delayed Dichotomous Response
  • Combine multiple efficacy safety in the dose
    finding decision
  • Use utility approach for combining various goals
  • Multiple statistical goals
  • Adaptive stopping rules

3
Statistical Model
  • The statistical model captures the uncertainty in
    the process.
  • Capture data, quantities of interest, and
    forecast future data
  • Be flexible, (non-monotone?) but capture prior
    information on model behavior.
  • Invisible in the process

4
Empirical Data
  • Observe Yij for subject i, outcome j
  • Yij 1 if event, 0 otherwise
  • j 1 is type 1 efficacy response ()
  • j 2 is type 2 efficacy response (FDA)
  • j 3 is minor safety event

5
Efficacy Endpoints
  • Let d be the dose
  • Pj(d) probability of event j1,2

?j(d) N(?, ??2)
G(1,1)
N(1,1)
N(2,1)
IG(2,2)
6
Safety Endpoint
  • Let d be the dose
  • Pj(d) probability of safety j3

N(-2,1)
G(1,1)
N(1,1)
7
Utility Function
  • Multiple Factors
  • Monetary Profile (value on market)
  • FDA Success
  • Safety Factors
  • Utility is critical Defines ED?

8
Utility Function
Monetary
FDA Approval
P2(0) is prob Efficacy 2 success for d0
9
Monetary Utility (Fake)
10
(No Transcript)
11
(No Transcript)
12
(No Transcript)
13
U3 FDA Success
Statistical Significance
This is a posterior predictive calculation. The
probability of trial success, averaged over the
current posterior distribution
14
Statistical Utility Output
  • EU(d)
  • E?j(d), V?j(d)
  • EPj(d), VPj(d)
  • Prdj max U
  • PrP2(d) gt P0
  • Pr d gtgt 0 250/per arm) each d

15
Allocator
  • Goals of Phase II study?
  • Find best dose?
  • Learn about best dose?
  • Learn about whole curve?
  • Learn the minimum effective dose?
  • Allocator and decisions need to reflect this (if
    not through the utility function)
  • Calculation can be an important issue!

16
Allocator
Best Dose
2nd Best Dose
  • Find best dose?
  • Learn about best dose?

d is the max utility dose, d second best
Find the ?V for each dose gt allocation probs
17
Allocator
?V(d?0)
?V(d0)
18
Allocator
  • Drop any rdlt0.05
  • Renormalize

19
Decisions
Pr(d d) gt C1
  • Find best dose?
  • Learn about best dose?
  • Shut down allocator wj if stop!!!!
  • Stop trial when both happen
  • If Pr(P2(d) gtgt P0) lt 0.10 stop for futility

If found, stop
Pr(P2(d) gtgt P0)gtC2
If found, stop
20
More Decisions?
  • Ultimate EU(dosing) gt EU(stopping)?
  • Wait until significance?
  • Goal of this study?
  • Roll in to phase III set up to do this, though
    goal becomes w2 and w3
  • Utility and why? are critical and should be
    done--easy to ignore and say it is too hard.

21
Simulations
  • Subject level simulation
  • Simulate 2/day first 70 days, then 4/day
  • Delayed observation
  • exponential mean 10 days
  • Allocate Decision every week
  • First 140 subjects 20/arm

22
Scenario 1
Dose P1 P2 P3 P4 UTIL
0 0.05 0.06 0.05 0 0
0.25 0.05 0.10 0.06 0 0
0.5 0.08 0.13 0.07 0 0.063
1 0.12 0.17 0.08 0 0.323
2.5 0.15 0.20 0.09 0 0.457
5 0.18 0.23 0.10 0 0.532
10 0.25 0.30 0.11 0 0.656
MAX
Stopping Rules C1 0.80, C2 0.90
23
18 2 2 0 2
15 0 5 3 5
18 1 1 0 2
20 0 2 1 0
19 0 5 3 1
17 4 4 2 3
18 3 5 2 2
Nin 1 2 3 Nout
24
Dose Probabilities
0 .25 .5 1 2.5 5 10
P(gtgtPbo) .18 .33 .27 .29 .67 .67
P(max) .01 .04 .06 .04 .33 .52
P(2nd) .03 .06 .10 .13 .35 .32
Alloc .06 .01 .02 .04 .06 .35 .46
25
18 2 2 0 2
19 1 5 4 1
Nin 1 2 3 Nout
20 1 1 0 3
20 0 2 1 0
19 0 5 3 3
25 8 7 2 7
24 5 7 2 7
26
Dose Probabilities
0 .25 .5 1 2.5 5 10
P(gtgtPbo) .12 .38 .36 .38 .92 .91
P(max) .00 .00 .02 .04 .41 .53
P(2nd) .00 .03 .06 .07 .47 .37
Alloc .00 .00 .02 .04 .09 .34 .51
27
19 2 3 0 1
20 1 5 4 0
Nin 1 2 3 Nout
21 1 2 0 2
20 0 2 1 0
21 0 5 3 4
29 9 7 2 11
31 6 11 3 17
28
Dose Probabilities
0 .25 .5 1 2.5 5 10
P(gtgtPbo) .13 .39 .38 .26 .97 .85
P(max) .00 .02 .03 .01 .39 .55
P(2nd) .00 .03 .10 .05 .46 .35
Alloc .11 .00 .03 .10 .05 .46 .35
29
20 2 4 0 0
21 1 5 4 4
Nin 1 2 3 Nout
23 1 2 0 4
20 0 2 1 0
25 1 5 4 0
36 10 7 3 10
45 10 12 3 16
30
Dose Probabilities
0 .25 .5 1 2.5 5 10
P(gtgtPbo) .16 .41 .38 .48 .93 .93
P(max) .00 .02 .03 .04 .26 .65
P(2nd) .00 .05 .07 .10 .49 .29
Alloc .00 .00 .08 .11 .18 .35 .28
31
20 2 4 0 0
25 1 5 4 6
Nin 1 2 3 Nout
26 1 2 0 1
20 0 2 1 0
26 2 6 4 5
44 13 7 3 12
52 10 13 4 15
32
Dose Probabilities
0 .25 .5 1 2.5 5 10
P(gtgtPbo) .16 .40 .31 .41 .98 .89
P(max) .00 .02 .03 .06 .27 .63
P(2nd) .00 .06 .06 .12 .48 .28
Alloc .16 .00 .10 .04 .13 .26 .30
33
21 2 4 0 3
26 1 6 4 5
Nin 1 2 3 Nout
26 1 2 0 6
20 0 2 1 0
33 3 7 4 5
52 13 8 4 10
61 15 18 4 12
34
Dose Probabilities
0 .25 .5 1 2.5 5 10
P(gtgtPbo) .13 .36 .32 .65 .96 .96
P(max) .00 .01 .01 .09 .08 .81
P(2nd) .00 .05 .05 .23 .52 .15
Alloc
35
Trial Ends
  • P(10-Dose max Util dose) 0.907
  • P(10-Dose gtgt Pbo 250/arm) 0.949
  • 280 subjects
  • 32, 20, 24, 31, 38, 62, 73 per arm

36
Operating Characteristics
Pbo 0.25 0.5 1 2.5 5 10
SS 39 21 25 37 63 89 110
Pmax --- 0.00 0.00 0.00 0.00 0.04 0.96
SS 66 66 66 66 66 66 66
Pmax --- 0.00 0.00 0.00 0.01 0.06 0.93
37
Operating Characteristics
Adaptive Constant Constant/ No Model
P(Sufficient) 0.936 0.810 0.700
P(Cap) 0.064 0.190 0.300
P(Futility) 0.000 0.000 0.000
P(10mg Best) 0.96 0.93 0.88
Mean SS 384 459 517
SD SS 186 224 235
Mean TDose 1754 1263 1420
Max TDose 4818 2370 2341
38
Scenario 2
Dose P1 P2 P3 P4 UTIL
0 0.06 0.05 0.05 0 0
0.25 0.10 0.05 0.06 0 0
0.5 0.13 0.08 0.07 0 0.063
1 0.17 0.12 0.08 0 0.323
2.5 0.20 0.15 0.10 0 0.452
5 0.23 0.18 0.15 0 0.502
10 0.25 0.20 0.40 0 0.302
Stopping Rules C1 0.80, C2 0.90
39
Operating Characteristics
Pbo 0.25 0.5 1 2.5 5 10
SS 71 27 41 81 137 172 164
Pmax --- 0.00 0.00 0.03 0.22 0.60 0.16
SS 100 100 100 100 100 100 100
Pmax --- 0.00 0.00 0.03 0.20 0.44 0.33
40
Operating Characteristics
Adaptive Constant Constant/ No Model
P(Sufficient) 0.314 0.266 0.286
P(Cap) 0.686 0.734 0.708
P(Futility) 0.000 0.000 0.006
P(5mg Best) 0.60 0.44 0.58
Mean SS 694 702 704
SD SS 193 190 182
Mean TDose 2954 1933 1937
Max TDose 4489 2455.25 2436
41
Simulation 3
Dose P1 P2 P3 P4 UTIL
0 0.06 0.05 0.05 0 0
0.1 0.10 0.05 0.06 0 0
0.5 0.13 0.08 0.07 0 0.063
1 0.30 0.25 0.11 0 0.656
2.5 0.17 0.12 0.08 0 0.323
5 0.20 0.15 0.09 0 0.457
10 0.23 0.18 0.10 0 0.532
Stopping Rules C1 0.80, C2 0.90
42
Operating Characteristics
Pbo 0.25 0.5 1 2.5 5 10
SS 53 23 28 119 52 76 102
Pmax --- 0.00 0.00 0.92 0.00 0.01 0.07
SS 87 87 87 87 87 87 87
Pmax --- 0.00 0.00 0.83 0.00 0.02 0.15
43
Operating Characteristics
Adaptive Constant Constant/ No Model
P(Sufficient) 0.906 0.596 0.708
P(Cap) 0.092 0.404 0.290
P(Futility) 0.002 0.000 0.002
P(1mg Best) 0.92 0.83 0.87
Mean SS 453 606 542
SD SS 187 205 225
Mean TDose 1663 1662 1491
Max TDose 3771 2384.25 2414.25
44
Scenario 4
Dose P1 P2 P3 P4 UTIL
0 0.06 0.05 0.05 0 0
0.1 0.07 0.06 0.06 0 0
0.5 0.08 0.07 0.07 0 0
1 0.09 0.08 0.08 0 0
2.5 0.09 0.08 0.09 0 0
5 0.09 0.08 0.10 0 0
10 0.09 0.08 0.11 0 0
Stopping Rules C1 0.80, C2 0.90
45
Operating Characteristics
Pbo 0.25 0.5 1 2.5 5 10
SS 92 91 75 66 76 83 90
Pmax --- 0.45 0.04 0.07 0.10 0.13 0.21
SS 84 84 84 84 84 84 84
Pmax --- 0.44 0.04 0.08 0.12 0.15 0.17
46
Operating Characteristics
Adaptive Constant Constant/ No Model
P(Sufficient) 0.004 0.006 0.030
P(Cap) 0.484 0.544 0.752
P(Futility) 0.512 0.450 0.218
Mean SS 574 589 699
SD SS 250 258 196
Mean TDose 1637 1615 1922
Max TDose 3223.5 2523.75 2467.75
47
Scenario 5
Dose P1 P2 P3 P4 UTIL
0 0.06 0.05 0.05 0 0
0.1 0.06 0.05 0.05 0 0
0.5 0.06 0.05 0.05 0 0
1 0.06 0.05 0.05 0 0
2.5 0.06 0.05 0.05 0 0
5 0.06 0.05 0.05 0 0
Stopping Rules C1 0.80, C2 0.90
48
Operating Characteristics
Pbo 0.25 0.5 1 2.5 5 10
SS 66 77 51 34 38 41 43
Pmax --- 0.90 0.01 0.02 0.02 0.02 0.03
SS 56 56 56 56 56 56 56
Pmax --- 0.86 0.01 0.02 0.03 0.03 0.05
49
Operating Characteristics
Adaptive Constant Constant/ No Model
P(Sufficient) 0.000 0.000 0.002
P(Cap) 0.122 0.190 0.362
P(Futility) 0.878 0.810 0.636
Mean SS 350 395 542
SD SS 215 241 241
Mean TDose 811 1086 1491
Max TDose 2404 2428.75 2455.5
50
Bells Whistles
  • Interest in Quantiles
  • Minimum Effective Dose
  • Significance, control type I error
  • Seamless phase II --gt III
  • Partial Interim Information
  • Biomarkers of endpoint
  • Continuous, Poisson, Survival, Mixed
  • Continuum of doses (IV)--little additional n!!!

51
Conclusions
  • Approach, not answers or details!
  • Shorter, smaller, stronger!
  • Better for Sponsor, Regulatory, PATIENTS (in and
    out), Science
  • Why study?--adaptive can help multiple needs.
  • Adaptive Stopping Bid Step!
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