phase ii selection design with adaptive randomization in a limited-resource environment
DESCRIPTION
Phase II Selection Design with Adaptive Randomization in a Limited-Resource Environment. Hyung Woo Kim, Ph.D. Takeda Global R & D Center, Inc. Donald A. Berry, Ph.D. M.D. Anderson Cancer Center. Overview. Phase 2a designs in oncology - PowerPoint PPT PresentationTRANSCRIPT
Phase II Selection Design with Adaptive Randomization in a
Limited-Resource Environment
Hyung Woo Kim, Ph.D.Takeda Global R & D Center, Inc.
Donald A. Berry, Ph.D.M.D. Anderson Cancer Center
Overview
• Phase 2a designs in oncology
• Phase 2 selection design (P2S) with
adaptive randomization
• Simulation Results
• Summary
• Discussions
Phase 2a Designs in Oncology
• Identify promising drugs for
further evaluation
• Screen out inefficacious
drugs
Phase 2a Designs in Oncology vs.
• Multi-stage (Schultz et al., 1973)
– Boundaries: &
– Stop & fail to reject Ho
– Stop & reject Ho
– Continue
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0: Ho ppH
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• Simon’s Optimal 2-Stage
– Find (n1 , a1) & (n2 , a2) that
– Minimizes E(N|H0) or N
subject to constraints on type I and
type II errors
• Fleming’s 2-stage design
Phase 2a Designs in Oncology
Example:
• Hypothesis to be tested
– H0: p = 0.2 vs. H1: p = 0.4
• Ten treatments of interest with
– p = 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.4, 0.4, 0.4, 0.6
• Only 200 subjects available
• Run one study at a time? – sample size?
• Initiate all ten studies at the same time?
(Based on R=1000 runs)
#Trt n rej FP TP #resp -------------------------------------------2-stg 7.8 200 3.2 7% 70% 58.8
1-stg 10 200 3.8 9% 81% 60.1
Example (cont’d):
Compare two approaches:
• Two-stage study with N = 40, = .1, = .10
• Single-stage study with N = 20, = .1, = .25
Pr(finding the best treatment) = ?
(Based on R=1000 runs)
#Trt n rej FP TP #resp nug?-------------------------------------------2-stg 7.8 200 3.2 7% 70% 58.8 75%
1-stg 10 200 3.8 9% 81% 60.1 99%
Example (cont’d):
Compare two approaches:
• Two-stage study with N = 40, = .1, = .10
• Single-stage study with N = 20, = .1, = .25
Pr(finding the best treatment) = ?
0 50 100 150 200
0
20
40
60
80
100
Number of Patients
Bes
t T
reat
men
t F
ound
(%
)Time to find the best treatment?
75%
2-stage
0 50 100 150 200
0
20
40
60
80
100
Number of Patients
Bes
t T
reat
men
t F
ound
(%
)Time to find the best treatment?
75%
99%
2-stage
1-stage
We need a method that
• finds the best/better treatment
FASTER
• While maintaining comparable (or
better) operating characteristics, such
as type I and type II errors
P2S with Adaptive Randomization
• Many Treatments
• Limited number of patients
• We want to
– Treat patients effectively, Learn quickly
– Identify better drugs faster
• Assign/Treat more patients in the
better result group
P2S with Adaptive Randomization
• When assigning next patient, compute
ri = Pr(…|datai) for each drug i
• Assign treatments in proportion to ri’s
• Drop inefficacious drugs
• Efficacious drugs phase IIb/III
P2S with Adaptive Randomization
Example:
• Hypothesis to be tested
– H0: p = 0.2 vs. H1: p = 0.4
• Ten treatments of interest with
– p = 0.2, 0.2, 0.2, 0.2, 0.2, 0.2, 0.4, 0.4, 0.4, 0.6
• Only 200 subjects available
P2S with Adaptive Randomization
• Beta-binomial with prior p~Beta(1,1) =u(0,1)
• Initial assignment = equally = 1/10
• Randomization probability
r = Pr(p > .3 | data)
• Update “r” when new outcome is observed
• stop in favor of H1 if Pr(p > .2 | data) > 0.995
• stop in favor of H0 if Pr(p < .4 | data) > 0.99
• At trial end, reject H0 if Pr(p > .2 | data) > 0.995
Beta-Binomial
Prior
Data
Post
Beta(1, 1)
Beta(2, 1)
S
Beta-Binomial
Prior
Data
Post
Beta(1, 1)
Beta(3, 1)
SS
Beta-Binomial
Prior
Data
Post
Beta(1, 1)
Beta(4, 1)
SSS
Beta-Binomial
Prior
Data
Post
Beta(1, 1)
Beta(4, 1)
FSSS
Beta-Binomial
Prior
Data
Post
Beta(1, 1)
Beta(4, 2)
FSSS
Beta-Binomial
Prior
Data
Post
Beta(1, 1)
Beta(4, 3)
FSS FS
Beta-Binomial
Prior
Data
Post
Beta(1, 1)
Beta(4, 4)
F F FSSS
r = Pr(p > .3 | data)
0.70
0.91 0.49
0.97 0.78 0.78 0.34
0.99 0.24
with Beta (1,1)
r.ratio (normalized)
1.00
1.30 0.70
1.39 1.12 1.12 0.49
1.42 0.34
F\S 0 1 2 3 4 5 6 7 8 9012345678910111213141516171819
When to stop?Pr(p > .2 | data) > 0.995
Pr(p < .4 | data) > 0.99
(Based on R=1000 runs)
#Rx n rej FP TP #resp nug?-------------------------------------------1-stg 10 200 3.8 9% 81% 60.1 99%
Example (cont’d):
Compare two approaches:
• Single-stage study with N = 20, = .1, = .25
• P2S with adaptive randomization
------------------------------------------- P2S 10 196 3.5 5% 81% 54.7 99%
Reason for smaller # of response?
1-stg
p Avg(n) # success # failure Pr(p< H1) Pr(p> H0) Pr(rej H0) stop.trial
0.2 20.0 4.0 16.0 8.7%
0.4 20.0 8.0 12.0 75.0%
0.6 20.0 12.0 8.0 99.1%
P2S
p Avg(n) # success # failure Pr(p< H1) Pr(p> H0) Pr(rej H0) stop.trial
0.2 21.0 4.2 16.8 0.928 0.492 5.1% 46.9%0.4 20.3 8.1 12.3 0.404 0.944 74.8% 77.0%0.6 8.6 5.1 3.5 0.116 0.995 99.1% 99.1%
Time to find the best treatment?
0 50 100 150 200
0
20
40
60
80
100
Number of Patients
Bes
t T
reat
men
t F
ound
(%
)Time to find the best treatment?
99%
1-stage
P2S
Can r be more/less flexible?
r = Pr(p > .3 | data)c c
0 50 100 150 200
0
20
40
60
80
100
Number of Patients
Bes
t T
reat
men
t F
ound
(%
)Can r be more/less flexible?
99%
c = 1/2c = 2
c = 3
F\S 0 1 2 3 4 5 6 7 8 9012345678910111213141516171819
Pr(p > .2 | data) > 0.995
Pr(p < .4 | data) > 0.99
What if min(n) = 10 is required?
What if min(n) = 10 is required?P2S
p Avg(n) # success # failure Pr(p< H1) Pr(p> H0) Pr(rej H0) stop.trial
0.2 21.0 4.2 16.8 0.928 0.492 5.1% 46.9%
0.4 20.3 8.1 12.3 0.404 0.944 74.8% 77.0%
0.6 8.6 5.1 3.5 0.116 0.995 99.1% 99.1%
P2S, min(n ) = 10
p Avg(n) # success # failure Pr(p< H1) Pr(p> H0) Pr(rej H0) stop.trial
0.2 20.2 4.0 16.2 0.939 0.491 3.2% 37.2%0.4 21.6 8.6 13.0 0.435 0.936 71.0% 73.0%0.6 11.7 7.1 4.6 0.111 0.996 98.8% 98.8%
0 50 100 150 200
0
20
40
60
80
100
Number of Patients
Bes
t T
reat
men
t F
ound
(%
)What if min(n) = 10 is required?
99%
1-stage
P2S
In practice,
• Outcomes may not be observed right away
• Lag time between the first dose of treatment
and the observation of outcome
• e.g., Outcomes from 1st subject is observed
when the 30th subject is enrolled
• May cause inefficiency in operating
characteristics
• Simulate!
1-stg
p Avg(n) # success # failure Pr(p< H1) Pr(p> H0) Pr(rej H0) stop.trial
0.2 20.0 4.0 16.0 8.7%
0.4 20.0 8.0 12.0 75.0%
0.6 20.0 12.0 8.0 99.1%
P2S(1) with delayed response
p Avg(n) # success # failure Pr(p< H1) Pr(p> H0) Pr(rej H0) stop.trial
0.2 18.8 3.8 15.0 0.932 0.510 4.4% 23.9%0.4 24.2 9.6 14.5 0.470 0.928 64.5% 56.2%0.6 14.8 8.9 5.9 0.084 0.997 98.6% 97.6%
P2S(2) with delayed response
p Avg(n) # success # failure Pr(p< H1) Pr(p> H0) Pr(rej H0) stop.trial
0.2 19.8 4.0 15.8 0.930 0.507 9.4% 30.8%0.4 22.7 9.1 13.6 0.451 0.932 73.5% 65.1%0.6 12.9 7.8 5.1 0.088 0.997 99.3% 99.1%
Note: Reject H0 if Pr(p > .2 | data) > 0.99
Comparisons
Note: Reject H0 if Pr(p > .2 | data) > 0.995
0 50 100 150 200
0
20
40
60
80
100
Number of Patients
Bes
t T
reat
men
t F
ound
(%
)Delayed response by n = 30?
1-stage
P2S(1)
P2S(2)
Summary
• When we have many treatments with
limited resources (e.g., budget, patients)
• Look at accumulating data
• Update probabilities
• Modify future course of trial using adaptive
randiomization
• Gain efficiency
In practice,
• Should give details in protocol
• Simulate to find operating characteristics
• Could be used in the early phase of
development process (non-registrational)
• Require more time to prepare
• Require additional tools: EDC, IVRS
• Require response to be measured quickly
Thank you!
• Discussion
Backup
Q: unlimited patients resources?
• Hypothesis to be tested– H0: p = 0.3 vs. H1: p = 0.5
• Three treatment arms of interest:– Standard Trt + Dose A– Standard Trt + Dose B– Standard Trt + Dose C
Arm
1
2
3
Case 1
0.3
0.3
0.3
Case 2
0.4
0.5
0.6
Case 3
0.2
0.2
0.5
can beDrug ADrug BDrug C
H0: P 0.3 vs. H1: P 0.5
• Two Stage Design (N = 120)
At n = 20; a1 6; r1 12
At n = 40; a2 16; r2 17
• P2S with adaptive randomization (N = 120)
Prior p~Beta(1,1)
r = Pr(p>.4|Data)
Stop in favor of H0 if Pr(p < .5 | data) > 0.99
Stop in favor of H1 if Pr(p > .3 | data) > 0.995
At trial end, reject H0 if Pr(p > .3 | data) > 0.995
Method Arm p Favor H0 Favor H1Average # of pts
# of
Response
2-stg
1
2
3
0.3
0.3
0.3
0.94
0.94
0.94
0.06
0.06
0.06
28
28
28
8.3
8.3
8.3
P2S
1
2
3
0.3
0.3
0.3
0.95
0.96
0.95
0.05
0.04
0.05
28
28
28
8.3
8.4
8.3
Operating Characteristics
Case 1
Method Arm p Favor H0 Favor H1Average # of pts
# of
Response
2-stg
1
2
3
0.4
0.5
0.6
0.58
0.15
0.01
0.42
0.85
0.99
34
34
28
13.6
17.0
16.8
P2S
1
2
3
0.4
0.5
0.6
0.61
0.15
0.02
0.39
0.85
0.98
42
28
16
16.2
14.1
9.6
Operating Characteristics
Case 2
Method Arm p Favor H0 Favor H1Average # of pts
# of
Response
2-stg
1
2
3
0.5
0.2
0.2
0.16
1.00
1.00
0.84
0.00
0.00
34
22
22
16.8
4.2
4.2
P2S
1
2
3
0.5
0.2
0.2
0.10
1.00
1.00
0.90
0.00
0.00
30
15
15
14.7
3.1
3.0
Operating Characteristics
Case 3
0 20 40 60 80 100 120
020
4060
8010
0
83.5%
90.5%
Adaptive(c=1)
Adaptive(c=2)
Two-stage
p=(0.2, 0.2, 0.5)
Number of Patients
Bes
t T
reat
men
t F
ound
(%
)
Time to find the best treatment?
0 20 40 60 80 100 120
020
4060
8010
0
99.9%98.1%
p=(0.4, 0.5, 0.6)
Number of Patients
Bes
t T
reat
men
t F
ound
(%
)
Time to find the best treatment?
Adaptive (c=1)
Adaptive (c=2)
Two-stage
Apply to Phase 2b Design?
• Control arm: assign a fixed randomization ratio (e.g, x % of patients are always assigned to the control)
• Treatment arms are compared against– Control arm– Other treatments arms
• Drop inferior arms
• Keep control arms to the end