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![Page 1: Bayesian Adaptive Dose Finding Studies: Smaller, Stronger, Faster Scott M. Berry scott@berryconsultants.com Scott M. Berry scott@berryconsultants.com.](https://reader036.fdocuments.us/reader036/viewer/2022062619/5514bcb0550346b0478b4578/html5/thumbnails/1.jpg)
Bayesian Adaptive Dose Finding Studies: Smaller, Stronger, FasterBayesian Adaptive Dose Finding
Studies: Smaller, Stronger, Faster
Scott M. [email protected]
Scott M. [email protected]
BERRY
STATISTICAL INNOVATION
CONSULTANTS
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Dose Finding TrialDose 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
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
![Page 3: Bayesian Adaptive Dose Finding Studies: Smaller, Stronger, Faster Scott M. Berry scott@berryconsultants.com Scott M. Berry scott@berryconsultants.com.](https://reader036.fdocuments.us/reader036/viewer/2022062619/5514bcb0550346b0478b4578/html5/thumbnails/3.jpg)
Statistical ModelStatistical 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
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
![Page 4: Bayesian Adaptive Dose Finding Studies: Smaller, Stronger, Faster Scott M. Berry scott@berryconsultants.com Scott M. Berry scott@berryconsultants.com.](https://reader036.fdocuments.us/reader036/viewer/2022062619/5514bcb0550346b0478b4578/html5/thumbnails/4.jpg)
Empirical DataEmpirical Data
Observe Yij for subject i, outcome j
Yij = 1 if event, 0 otherwise
j = 1 is type #1 efficacy response ($$)j = 2 is type #2 efficacy response (FDA) j = 3 is minor safety event
Observe Yij for subject i, outcome j
Yij = 1 if event, 0 otherwise
j = 1 is type #1 efficacy response ($$)j = 2 is type #2 efficacy response (FDA) j = 3 is minor safety event
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Efficacy EndpointsEfficacy EndpointsLet d be the dosePj(d) probability of event j=1,2;
Let d be the dosePj(d) probability of event j=1,2;
j(d) ~ N(, 2)
IG(2,2)N(–2,1) N(1,1)
G(1,1)
j d logPj d
1 Pj d
j d j j
d
d j
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Safety EndpointSafety EndpointLet d be the dosePj(d) probability of safety j=3;
Let d be the dosePj(d) probability of safety j=3;
N(-2,1)N(1,1)
G(1,1)
j d logPj d
1 Pj d
j j
d
d j
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Utility FunctionUtility Function
Multiple Factors:Monetary Profile (value on market)
FDA SuccessSafety Factors
Utility is critical: Defines ED?
Multiple Factors:Monetary Profile (value on market)
FDA SuccessSafety Factors
Utility is critical: Defines ED?
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Utility FunctionUtility Function
MonetaryFDA Approval
P2(0) is prob Efficacy #2 success for d=0
U d U1 P1 d U2 P3 d U3 P2 0 ,P2 d
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Monetary Utility (“Fake”)Monetary Utility (“Fake”)
U1 P1 P1 0.1
0.4
U2 P3 1 2 P3 1.5
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U3: FDA SuccessU3: FDA Success
U3 P2 0 ,P2 d Pr d 0 250/arm trial
StatisticalSignificance
This is a posterior predictive calculation. The probabilityof trial success, averaged over the current posteriordistribution
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Statistical + Utility OutputStatistical + Utility OutputE[U(d)]E[j(d)], V[j(d)]
E[Pj(d)], V[Pj(d)]
Pr[dj max U]
Pr[P2(d) > P0]Pr[ d >> 0 | 250/per arm) each
d
E[U(d)]E[j(d)], V[j(d)]
E[Pj(d)], V[Pj(d)]
Pr[dj max U]
Pr[P2(d) > P0]Pr[ d >> 0 | 250/per arm) each
d
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AllocatorAllocator 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!
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!
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AllocatorAllocator Find best dose?
Learn about best dose?
Find best dose?
Learn about best dose?
Find the V* for each dose ==> allocation probs
V P1 d* P1 d
** V P2 d
* P0
V* w1V P1 d* P1 d
** w2V P2 d* P0
d* is the max utility dose, d** second best
Best Dose
2nd Best Dose
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AllocatorAllocator
V*(d≠0) = V P1 d nd 1
w1 Pr d d* w2 Pr d d**
V P2 d nd 1
w2 Pr d d*
V*(d=0) = V P2 0 n0 1
w2
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AllocatorAllocator
“Drop” any rd<0.05
Renormalize
“Drop” any rd<0.05
Renormalize
rd V * d V * d
d0
k
for all d
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DecisionsDecisionsFind best dose? Learn about best dose?
Shut down allocator wj if stop!!!!
Stop trial when both happen
If Pr(P2(d*) >> P0) < 0.10 stop for futility
Find best dose? Learn about best dose?
Shut down allocator wj if stop!!!!
Stop trial when both happen
If Pr(P2(d*) >> P0) < 0.10 stop for futility
If found, stop:
If found, stop:
Pr(d = d*) > C1
Pr(P2(d*) >> P0)>C2
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More Decisions?More Decisions?
Ultimate: EU(dosing) > 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.
Ultimate: EU(dosing) > 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.
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SimulationsSimulations
Subject level simulationSimulate 2/day first 70 days, then
4/dayDelayed observation
exponential mean 10 daysAllocate + Decision every weekFirst 140 subjects 20/arm
Subject level simulationSimulate 2/day first 70 days, then
4/dayDelayed observation
exponential mean 10 daysAllocate + Decision every weekFirst 140 subjects 20/arm
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Scenario #1Dose 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
Stopping Rules: C1 = 0.80, C2 = 0.90
MAX
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181102
200210
182202
150535
190531
174423
183522
Nin
#1#2#3Nout
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Dose ProbabilitiesDose Probabilities
0 .25 .5 1 2.5 5 10
P(>>Pbo) .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
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201103
200210
182202
191541
190533
258727
245727
Nin
#1#2#3Nout
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Dose ProbabilitiesDose Probabilities
0 .25 .5 1 2.5 5 10
P(>>Pbo) .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
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211202
200210
192301
201540
210534
29972
11
316
113
17
Nin
#1#2#3Nout
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Dose ProbabilitiesDose Probabilities
0 .25 .5 1 2.5 5 10
P(>>Pbo) .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
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231204
200210
202400
211544
251540
361073
10
4510123
16
Nin
#1#2#3Nout
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Dose ProbabilitiesDose Probabilities
0 .25 .5 1 2.5 5 10
P(>>Pbo) .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
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261201
200210
202400
251546
262645
441373
12
5210134
15
Nin
#1#2#3Nout
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Dose ProbabilitiesDose Probabilities
0 .25 .5 1 2.5 5 10
P(>>Pbo) .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
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261206
200210
212403
261645
333745
521384
10
6115184
12
Nin
#1#2#3Nout
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Dose ProbabilitiesDose Probabilities
0 .25 .5 1 2.5 5 10
P(>>Pbo) .13 .36 .32 .65 .96 .96
P(max) .00 .01 .01 .09 .08 .81
P(2nd) .00 .05 .05 .23 .52 .15
Alloc
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Trial EndsTrial Ends
P(10-Dose max Util dose) = 0.907
P(10-Dose >> Pbo 250/arm) = 0.949
280 subjects: 32, 20, 24, 31, 38, 62, 73 per
arm
P(10-Dose max Util dose) = 0.907
P(10-Dose >> Pbo 250/arm) = 0.949
280 subjects: 32, 20, 24, 31, 38, 62, 73 per
arm
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Operating CharacteristicsOperating 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
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Operating CharacteristicsOperating Characteristics
Adaptive ConstantConstant/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
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Scenario #2Scenario #2Dose 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
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Operating CharacteristicsOperating 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
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Operating CharacteristicsOperating Characteristics
Adaptive ConstantConstant/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
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Simulation #3Simulation #3Dose 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
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Operating CharacteristicsOperating 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
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Operating CharacteristicsOperating Characteristics
Adaptive ConstantConstant/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
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Scenario #4Scenario #4Dose 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
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Operating CharacteristicsOperating 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
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Operating CharacteristicsOperating Characteristics
Adaptive ConstantConstant/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
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Scenario #5Scenario #5Dose 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
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Operating CharacteristicsOperating 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
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Operating CharacteristicsOperating Characteristics
Adaptive ConstantConstant/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
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Bells & WhistlesBells & Whistles Interest in QuantilesMinimum Effective Dose“Significance,” control type I errorSeamless phase II --> IIIPartial Interim Information“Biomarkers” of endpointContinuous, Poisson, Survival,
MixedContinuum of doses (IV)--little
additional n!!!
Interest in QuantilesMinimum Effective Dose“Significance,” control type I errorSeamless phase II --> IIIPartial Interim Information“Biomarkers” of endpointContinuous, Poisson, Survival,
MixedContinuum of doses (IV)--little
additional n!!!
![Page 51: Bayesian Adaptive Dose Finding Studies: Smaller, Stronger, Faster Scott M. Berry scott@berryconsultants.com Scott M. Berry scott@berryconsultants.com.](https://reader036.fdocuments.us/reader036/viewer/2022062619/5514bcb0550346b0478b4578/html5/thumbnails/51.jpg)
ConclusionsConclusions
Approach, not answers or details!Shorter, smaller, stronger!Better for: Sponsor, Regulatory,
PATIENTS (in and out), ScienceWhy study?--adaptive can help
multiple needs.Adaptive Stopping Bid Step!
Approach, not answers or details!Shorter, smaller, stronger!Better for: Sponsor, Regulatory,
PATIENTS (in and out), ScienceWhy study?--adaptive can help
multiple needs.Adaptive Stopping Bid Step!