Phase II Selection Design with Adaptive Randomization in a Limited-Resource Environment

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

),,( 1 Kaa ),,( 1 Krr

g

igi as

1

,

g

igi rs

1

,

0: Ho ppH

1:1 HppH

g

igig rsa

1

,

• 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) = ?


#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):


• Two-stage study with N = 40, = .1, = .10


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

(%


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


• 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


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


• 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


#Rx n rej FP TP #resp nug?-------------------------------------------1-stg 10 200 3.8 9% 81% 60.1 99%

Example (cont’d):



• 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


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

(%


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


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


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


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


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


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


# 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


Case 2


# 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


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

(%

)


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

(%

)


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

Documents

Phase II Selection Design with Adaptive Randomization in a Limited-Resource Environment