Background
Standard 3+3
CRM
Dose finding methodology
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
John O’Quigley
Laboratoire de Statistique Théorique et Appliquée
Université Paris VI
2-stage
designs
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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Model for cytotoxics (3 patients)
Background
Standard 3+3
Pr(Tox)
1.00
CRM
One/two
parameter
models
Flawed case
studies
0.75
0.50
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
0.25
0.00
d1
d2
d3
d4
d5
d6
d7
Dose
More complex
problems
Finding MSD
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Dose finding methodology
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Model for cytotoxics (3 patients)
Background
Standard 3+3
Pr(Tox)
1.00
CRM
One/two
parameter
models
Flawed case
studies
0.75
0.50
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
0.25
0.00
d1
d2
d3
d4
d5
d6
d7
Dose
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
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Model for cytotoxics (3 patients)
Background
Standard 3+3
Pr(Tox)
1.00
CRM
One/two
parameter
models
Flawed case
studies
0.75
0.50
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
0.25
0.00
d1
d2
d3
d4
d5
d6
d7
Dose
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
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Empirical distribution for 3 patients
Background
Standard 3+3
Pr(Tox)
1
CRM
One/two
parameter
models
2/3
Flawed case
studies
Equivalent
designs
1/3
Optimal
design
2-stage
designs
0
Using grades
d1
d2
d3
d4
d5
d6
d7
Dose
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
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Model for cytotoxics (population)
Background
Standard 3+3
Pr(Tox)
1
CRM
One/two
parameter
models
2/3
Flawed case
studies
Equivalent
designs
1/3
Optimal
design
2-stage
designs
0
Using grades
d1
d2
d3
d4
d5
d6
d7
Dose
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
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Model for cytotoxics (population)
Background
Pr(tox.)
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Target
1
0.75
0.5
Equivalent
designs
Optimal
design
2-stage
designs
0.25
0
d1
d2
d3
d4
d5
d6
d7
dose
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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Ethical considerations for a Phase I trial
Background
Standard 3+3
1
We must do the best for the treated patient. We cannot
knowingly undertreat leaving no chance for therapeutic
benefit. (Smith et al (1998) J. Clin. Oncology). We can
not knowingly overtreat.
2
There is no “treatment versus experimentation
dilemma” (Azriel et al 2011) .
3
There is no “future benefit”, “current patient benefit”
conflict.
4
We must abide by Helsinki Declaration
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
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Ethical considerations for a Phase I trial
Background
Standard 3+3
1
We must do the best for the treated patient. We cannot
knowingly undertreat leaving no chance for therapeutic
benefit. (Smith et al (1998) J. Clin. Oncology). We can
not knowingly overtreat.
2
There is no “treatment versus experimentation
dilemma” (Azriel et al 2011) .
3
There is no “future benefit”, “current patient benefit”
conflict.
4
We must abide by Helsinki Declaration
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
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Ethical considerations for a Phase I trial
Background
Standard 3+3
1
We must do the best for the treated patient. We cannot
knowingly undertreat leaving no chance for therapeutic
benefit. (Smith et al (1998) J. Clin. Oncology). We can
not knowingly overtreat.
2
There is no “treatment versus experimentation
dilemma” (Azriel et al 2011) .
3
There is no “future benefit”, “current patient benefit”
conflict.
4
We must abide by Helsinki Declaration
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
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Ethical considerations for a Phase I trial
Background
Standard 3+3
1
We must do the best for the treated patient. We cannot
knowingly undertreat leaving no chance for therapeutic
benefit. (Smith et al (1998) J. Clin. Oncology). We can
not knowingly overtreat.
2
There is no “treatment versus experimentation
dilemma” (Azriel et al 2011) .
3
There is no “future benefit”, “current patient benefit”
conflict.
4
We must abide by Helsinki Declaration
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
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Ethical considerations for a Phase I trial
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
1
We do not want to “undertreat”
2
We do not want to “overtreat”, i.e. too much toxicity.
3
Use as few patients as possible (efficiency).
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
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Ethical considerations for a Phase I trial
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
1
We do not want to “undertreat”
2
We do not want to “overtreat”, i.e. too much toxicity.
3
Use as few patients as possible (efficiency).
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
7 / 58
Ethical considerations for a Phase I trial
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
1
We do not want to “undertreat”
2
We do not want to “overtreat”, i.e. too much toxicity.
3
Use as few patients as possible (efficiency).
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
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Up and Down Designs (Storer Biometrics
(1989, 1993)
Background
Standard 3+3
1
Random walk (no memory)
2
Decision rule uses only part of data.
3
Standard design is 3+3 design + stopping rule.
4
Fails all 3 ethical criteria;
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
1
More patients under-treated than necessary.
2
More patients over-treated than necessary.
3
Poor (inefficient) estimate of MTD.
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
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Up and Down Designs (Storer Biometrics
(1989, 1993)
Background
Standard 3+3
1
Random walk (no memory)
2
Decision rule uses only part of data.
3
Standard design is 3+3 design + stopping rule.
4
Fails all 3 ethical criteria;
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
1
More patients under-treated than necessary.
2
More patients over-treated than necessary.
3
Poor (inefficient) estimate of MTD.
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
8 / 58
Up and Down Designs (Storer Biometrics
(1989, 1993)
Background
Standard 3+3
1
Random walk (no memory)
2
Decision rule uses only part of data.
3
Standard design is 3+3 design + stopping rule.
4
Fails all 3 ethical criteria;
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
1
More patients under-treated than necessary.
2
More patients over-treated than necessary.
3
Poor (inefficient) estimate of MTD.
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
8 / 58
Up and Down Designs (Storer Biometrics
(1989, 1993)
Background
Standard 3+3
1
Random walk (no memory)
2
Decision rule uses only part of data.
3
Standard design is 3+3 design + stopping rule.
4
Fails all 3 ethical criteria;
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
1
More patients under-treated than necessary.
2
More patients over-treated than necessary.
3
Poor (inefficient) estimate of MTD.
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
8 / 58
Continual Reassessment Method
Background
Gasparini and Eisele (A curve-free method for Phase I
clinical trials. Biometrics 2000) described CRM as:
Standard 3+3
CRM
1
An allocation rule to assign sequentially the incoming
patients to one of the possible doses, with the intent of
assigning doses ever closer to, and eventually
recommending, the MTD.
2
A statistical procedure that updates the information on
the probabilities of toxicity in light of the results
obtained for the patients already observed
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
Same idea for MCRM (Faries 1994), GCRM (Goodman
1995, Heyd and Carlin 1998), RCRM, ECRM (Moller 1995).
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
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Continual Reassessment Method
Background
1
Select target θ
(usually 1/4, 1/5 or 1/3).
2
Pr(Yi = 1|dj ) = ψ(dj , a) = αj
3
Calculate
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
exp(a)
log L(a) =
Equivalent
designs
X
yi log ψ(xi , a) +
1
X
(1 − yi ) log[1 − ψ(xi , a)]
0
Optimal
design
2-stage
designs
4
Allocate to dose xi ∈ {d1 , ..., dk } where;
Using grades
More complex
problems
|ψ(xi , â) − θ| ≤ |ψ(dj , â) − θ| ∀dj
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
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Continual Reassessment Method
Background
1
Select target θ
(usually 1/4, 1/5 or 1/3).
2
Pr(Yi = 1|dj ) = ψ(dj , a) = αj
3
Calculate
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
exp(a)
log L(a) =
Equivalent
designs
X
yi log ψ(xi , a) +
1
X
(1 − yi ) log[1 − ψ(xi , a)]
0
Optimal
design
2-stage
designs
4
Allocate to dose xi ∈ {d1 , ..., dk } where;
Using grades
More complex
problems
|ψ(xi , â) − θ| ≤ |ψ(dj , â) − θ| ∀dj
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
10 / 58
Continual Reassessment Method
Background
1
Select target θ
(usually 1/4, 1/5 or 1/3).
2
Pr(Yi = 1|dj ) = ψ(dj , a) = αj
3
Calculate
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
exp(a)
log L(a) =
Equivalent
designs
X
yi log ψ(xi , a) +
1
X
(1 − yi ) log[1 − ψ(xi , a)]
0
Optimal
design
2-stage
designs
4
Allocate to dose xi ∈ {d1 , ..., dk } where;
Using grades
More complex
problems
|ψ(xi , â) − θ| ≤ |ψ(dj , â) − θ| ∀dj
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
10 / 58
Continual Reassessment Method
Background
1
Select target θ
(usually 1/4, 1/5 or 1/3).
2
Pr(Yi = 1|dj ) = ψ(dj , a) = αj
3
Calculate
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
exp(a)
log L(a) =
Equivalent
designs
X
yi log ψ(xi , a) +
1
X
(1 − yi ) log[1 − ψ(xi , a)]
0
Optimal
design
2-stage
designs
4
Allocate to dose xi ∈ {d1 , ..., dk } where;
Using grades
More complex
problems
|ψ(xi , â) − θ| ≤ |ψ(dj , â) − θ| ∀dj
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
10 / 58
Continual Reassessment Method
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
11 / 58
Bayesian and likelihood estimation
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
-0.69
-0.27
-0.03
0.23
0.40
0.61
0.08
0.17
0.25
0.35
0.42
0.50
0.26
0.32
0.37
0.42
0.47
John O’Quigley (Université Paris VI)
d1
d2
d3
d3
d4
d4
d3
d3
d4
d4
d4
d4
d4
d4
d4
d4
d4
0.2
0.13
0.21
0.13
0.21
0.14
0.18
0.15
0.26
0.23
0.20
0.18
0.26
0.23
0.22
0.20
0.19
0
0
0
0
0
1
0
0
0
0
0
1
0
0
0
0
Dose finding methodology
–
–
–
–
–
0.34
0.52
0.64
0.74
0.87
0.58
0.65
0.35
0.42
0.47
0.52
0.56
d1
d2
d3
d4
d5
d4
d4
d4
d5
d5
d4
d4
d4
d4
d4
d4
d4
–
–
–
–
–
0.23
0.17
0.14
0.29
0.24
0.15
0.13
0.23
0.20
0.19
0.17
0.16
London, U.K.. 20.11.2012
0
0
0
0
1
0
0
0
0
1
0
1
0
0
0
0
12 / 58
Behaviour of SM (no stopping rule) and CRM
Background
Ri
Standard 3+3
unknown probabilities at level i
.04 .11 .23 .34 .42 .61
CRM
One/two
parameter
models
Optimal
design
2-stage
designs
6
5
5
4
4
dose
Equivalent
designs
6
dose
Flawed case
studies
3
3
2
2
1
1
Using grades
1
4
7
10
13
16
19
22
25
28
31
nb of patients
34
37
40
1
4
7
10
13
16
19
22
25
28
31
nb of patients
34
37
40
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
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CRM examples, no stopping rule
Background
MTD = level 3
Standard 3+3
MTD = level 1
CRM
Equivalent
designs
Optimal
design
2-stage
designs
6
5
5
4
4
DOSES
Flawed case
studies
6
DOSES
One/two
parameter
models
3
3
2
2
1
1
1
5
10
Using grades
15
20
25
PATIENT NUMBER
30
35
40
1
5
10
15
PATIENT NUMBER
20
25
30
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
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Potential sample paths
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
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15 / 58
Model and inference (likelihood)
Background
Using likelihood and letting
Standard 3+3
Pr(Yi = 1|Xi = dj ) = (αj )a
CRM
One/two
parameter
models
then the models
αi
αi
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
.85
.03
.89
.09
.92
.16
.95
.35
.98
.59
.10
.10
.20
.20
.30
.30
.50
.40
.70
.50
behave identically,
whereas the models
αi
αi
Using grades
More complex
problems
Finding MSD
.81
.01
.05
.05
behave differently.
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Dose finding methodology
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Model and inference (Bayes)
Background
For distance measure use;
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
1
O’Quigley, Pepe, Fisher (1990) suggest E ψ(dj , a)
2
O’Quigley, Pepe, Fisher (1990) suggest ψ(dj , E(a))
3
Chu, Lin, Shih (2009) suggest
4
Shih (1999) suggest γ = 0.5 corresponding to median.
5
Babb, Rogatko, Zacks (1998) suggest γ = 0.75
This is known as EWOC.
ψ1−γ (dj , a)
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
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1-parameter versus 2-parameter models
O’Quigley, Pepe and Fisher (1990) show that;
Background
1
Standard 3+3
2
2-parameter logistic model more noisy
Final recommendations less accurate
CRM
One/two
parameter
models
Table: 2-param logistic (O’Quigley, Pepe, Fisher 1990)
Flawed case
studies
Equivalent
designs
R(di )
1
.06
2
.08
Dose
3
4
.12 .18
5
.40
6
.71
1-CRM
2-CRM
.00
.01
.04
.11
.23
.16
.15
.19
.00
.05
Optimal
design
2-stage
designs
Using grades
More complex
problems
.57
.48
Finding MSD
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Dose finding methodology
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Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Proba. of Tox.
One parameter CRM models
1
*
*
0.5
Equivalent
designs
Optimal
design
2-stage
designs
*
θ
*
*
0
Using grades
*
d1
d2
d3
More complex
problems
d4
d5
d6
Dose level
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
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Two parameter CRM (ADEPT, BLR)
Background
Standard 3+3
Two parameter CRM has weaker theoretical foundation
CRM
One/two
parameter
models
Flawed case
studies
2CRM can be erratic, eg., first patient treated at level 1,
suffers DLT, the recommendation is treat at level 6 (Shu
2008).
Equivalent
designs
ADEPT is 2CRM, using patient benefit as metric.
Optimal
design
BLR (Neuenschwander et al 2007) is also 2CRM
2-stage
designs
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
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Two versus one parameter CRM models
Background
Standard 3+3
CRM
1
R̂j = ψ(dj , â) may be too inflexible to work well for all j.
One/two
parameter
models
2
R̂j ≈
3
R̂j → Rj and is fully efficient (Shen & O’Quigley,
Biometrika 96 )
4
Rj = ψ(dj , a, b) is over-parameterized, cannot identify a
and b.
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
P
Yij /nj at recommended level.
P
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
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Simulations: Gerke and Siedentop (2008)
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
Table: Percentage of found MTD for the 3 scenarios from Gerke
and Siedentop using fixed sample size. 3 scenarios, n=23, 18, 17.
1
4.85
1.05
0.10
0.00
0.00
0.00
2
9.90
12.30
0.20
0.00
0.00
0.00
3
34.95
39.50
1.90
1.45
0.00
0.00
Dose
4
38.65
38.35
8.50
11.65
0.20
0.05
5
11.05
8.60
38.25
42.90
0.40
0.70
6
0.60
0.20
46.75
37.10
5.65
12.30
7
0.00
0.00
4.20
6.85
44.35
43.45
8
0.00
0.00
0.10
0.05
47.65
35.55
9
0.00
0.00
0.00
0.00
1.75
7.80
10
0.00
0.00
0.00
0.00
0.00
0.15
2-stage
designs
Using grades
More complex
problems
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Background
Standard 3+3
Table: The toxicity rate of six simulated scenarios
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
Scenario
1
2
3
4
5
6
1
0.35
0.25
0.15
0.10
0.05
0.02
2
0.45
0.35
0.25
0.15
0.10
0.05
Dose
3
4
0.55 0.70
0.45 0.55
0.35 0.45
0.25 0.35
0.15 0.25
0.10 0.15
5
0.80
0.70
0.55
0.45
0.35
0.25
6
0.95
0.80
0.70
0.55
0.45
0.35
More complex
problems
Finding MSD
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One/two parameter CRM models: first patients
Background
First 4 patients
5
3.0
First 8 patients
Standard 3+3
1−parameter CRM
1−parameter CRM
2−parameter CRM (ADEPT)
2−parameter CRM (ADEPT)
2.5
CRM
0.5
1
2-stage
designs
1.0
Optimal
design
1.5
3
Number of toxicities
Equivalent
designs
2
Flawed case
studies
Number of toxicities
2.0
4
One/two
parameter
models
0
0.0
Using grades
More complex
problems
1
2
3
4
5
6
Scenarios
1
2
3
4
5
6
Scenarios
Finding MSD
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Novartis case study (Neuenschwander et al,
Bailey and Neuenschwander 2008)
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
doses
# pats
1.0
3
2.5
4
5
5
10
4
15
0
20
0
25
2
30
-
40
-
50
-
# DLTs
0
0
0
0
-
-
2
-
-
-
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
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Logical errors in Novartis case study
doses
E(prior)
1.0
.07
2.5
.08
5
.09
10
.11
15
.12
20
.14
25
.16
30
.24
40
.33
50
.46
E(post)
.02
.05
.09
.13
.18
.23
.28
.34
.41
.47
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
CRM recommends decrease in 3 levels and not an
increase.
Optimal
design
CRM is coherent (Cheung 2003).
2-stage
designs
Bayesian methods require care.
Using grades
More complex
problems
Finding MSD
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Impact of skeleton/prior when using Bayes
doses
BackgroundE(prior)
1.0
.07
2.5
.08
5
.09
10
.11
15
.12
20
.14
25
.16
30
.24
40
.33
50
.46
Standard 3+3
E(post)
.02
.05
.09
.13
.18
.23
.28
.34
.41
.47
doses
E(prior)
1.0
.00
2.5
.00
5
.00
10
.02
15
.12
20
.30
25
.50
30
.68
40
.80
50
.88
E(post)
.00
.00
.01
.05
.18
.38
.57
.73
.84
.90
doses
E(prior)
Using grades
1.0
.00
2.5
.02
5
.12
10
.30
15
.50
20
.68
25
.80
30
.88
40
.93
50
.96
E(post)
.00
.00
.01
.08
.23
.44
.62
.76
.86
.92
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
More complex
problems
Finding MSD
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Curve free designs (Gasparini, Eisele 2000)
1
θ1 = 1 − R(d1 ) ,
Background
θi =
Standard 3+3
CRM
One/two
parameter
models
2
Flawed case
studies
For each θi , (i = 1, . . . , k ),
f (θi ) = B −1 (ai , bi )θiai −1 (1 − θi )bi −1
Equivalent
designs
Optimal
design
for parameters ai and bi and where B(a, b) is the beta
function. with parameters a and b.
2-stage
designs
Using grades
More complex
problems
1 − R(di )
, i = 2, . . . , k .
1 − R(di−1 )
3
R(di ) = 1 − θ1 θ2 ...θi
4
O’Quigley (Biometrics 2005) shows Curve free ≡ CRM.
Finding MSD
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Dose finding methodology
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EWOC designs (Babb, Rogatko, Zacks 1998)
Background
Standard 3+3
1
Iterative updating same as CRM
2
Allocate to dose level dj such that posterior probability
of toxicity being greater than θ is α. BRZ choose
α = 0.25
3
Chu, Lin and Shih (2009) show that, when α = 0.5,
then EWOC ≡ CRM.
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
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Simple take home message
Background
Standard 3+3
CRM
One/two
parameter
models
CRM, BLR, ADEPT EWOC, Curve-free
Flawed case
studies
Equivalent
designs
are all essentially equivalent.
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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How good can any design be?
Background
Super-optimal designs:
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
1
Include zero patients in study: recommend level 2.
2
Include 5 patients at level 3. Recommend according to
table:
Equivalent
designs
Optimal
design
2-stage
designs
Outcome
Recommendation
0/5
5
1/5
4
2/5
3
3/5
2
4/5
1
5/5
1
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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Super optimality
Background
Super-optimality is common in the statistical literature, in
particular for Bayesian designs.
Standard 3+3
CRM
One/two
parameter
models
Example for combinations, using partial orderings;
1
Yin and Yuan (2009) Appl. Statist, 211 - 224, show for
4×4 combinations, copula design finds MTD 52%.
2
PO-CRM (Wages et al, Biometrics 2011 ) finds MTD in
45%.
3
When ordering is known, CRM finds MTD 48%.
4
When ordering is known Optimal Design finds MTD
49%.
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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Optimal design benchmark
Background
Subject h experiences a toxicity at d5 .
Subject j a non-toxicity at level d3 .
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
Doses
Observed Yhk
Unobserved Yhk
Observed Yjk
Unobserved Yjk
d1
X
0
0
0
d2
X
0
0
0
d3
X
1
0
0
d4
X
1
X
0
d5
1
1
X
0
d6
1
1
X
1
Consider;
2-stage
designs
Using grades
More complex
problems
Dose
Rk = Pr (Yk = 1)
d1
0.05
d2
0.11
d3
0.22
d4
0.35
d5
0.45
d6
0.60
Finding MSD
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Dose finding methodology
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Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
Subject
vj
j
1
.53
2
.08
.29
3
.41
4
5
.79
6
.04
.87
7
8
.15
9
.63
10
.56
11
.32
.72
12
13
.20
.97
14
15
.52
16
.24
Frequencies
More complex
problems
sj
6
2
4
5
1
3
6
4
3
6
4
R̂k
Rk
1
0
0
0
0
0
1
0
0
0
0
0
0
0
0
0
0
0.06
0.05
Toxicity at dose level
2
3
4
5
0
0
0
0
1
1
1
1
0
0
1
1
0
0
0
1
0
0
0
0
1
1
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0
0
0
0
0
1
1
1
0
0
0
0
0
0
0
0
0
0
1
1
0.13 0.25 0.44 0.50
0.11 0.22 0.35 0.45
6
1
1
1
1
0
1
0
1
0
1
1
0
1
0
1
1
0.69
0.60
Finding MSD
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Summarizing results
Relative performance by levels;
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
dk
Rk
pk (16)
qk (16)
1
0.05
0.05
0.04
2
0.11
0.26
0.27
3
0.22
0.42
0.48
4
0.35
0.21
0.17
5
0.45
0.06
0.04
6
0.60
0.0
0.0
Relative performance by cumulative errors; Let α = 0.1 be
% simulations where Pr (Y = 1) ∈ (0.10, 0.30). This is 0.69
for CRM and 0.74 for optimal.
2-stage
designs
Using grades
More complex
problems
α
pα
qα
0.02
0.42
0.48
0.05
0.42
0.48
0.10
0.69
0.74
0.15
0.94
0.96
0.20
1.0
1.0
Finding MSD
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Graph of cumulative errors
1
CRM
optimal
Background
Standard 3+3
0.8
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
Cumulative frequency
CRM
0.6
0.4
0.2
2-stage
designs
Using grades
0
0
More complex
problems
0.05
0.1
0.15
0.2
differences
0.25
0.3
0.35
0.4
Finding MSD
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Optimal .... , CRM1 .... , CRM2 ....
1
Background
0.9
Standard 3+3
0.8
CRM
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
FrØquence CumulØe
0.7
One/two
parameter
models
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.025 0.05 0.075
0.1
0.125 0.15 0.175
More complex
problems
0.2 0.225 0.25 0.275
ecarts
0.3
Finding MSD
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Optimal .... , CRM .... , 3+3 ....
1
Background
Standard 3+3
0.8
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
Cumulative Frequency
CRM
0.6
0.4
0.2
2-stage
designs
Using grades
0
0
0.05
0.1
0.15
More complex
problems
0.2
0.25
differences
0.3
0.35
Finding MSD
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Two stage designs (likelihood)
Background
Standard 3+3
1
Likelihood is monotone unbounded until first observed
toxicity.
2
First stage is largely arbitrary.
3
Different first stage algorithms lead to different
operating characteristics.
Optimal
design
4
First stage can incorporate information on grades.
2-stage
designs
5
Two stage designs accommodate many/open number
of levels.
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Using grades
More complex
problems
Finding MSD
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Two stage designs (likelihood)
Background
Standard 3+3
1
Likelihood is monotone unbounded until first observed
toxicity.
2
First stage is largely arbitrary.
3
Different first stage algorithms lead to different
operating characteristics.
Optimal
design
4
First stage can incorporate information on grades.
2-stage
designs
5
Two stage designs accommodate many/open number
of levels.
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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Two stage designs (likelihood)
Background
Standard 3+3
1
Likelihood is monotone unbounded until first observed
toxicity.
2
First stage is largely arbitrary.
3
Different first stage algorithms lead to different
operating characteristics.
Optimal
design
4
First stage can incorporate information on grades.
2-stage
designs
5
Two stage designs accommodate many/open number
of levels.
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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Two stage designs (likelihood)
Background
Standard 3+3
1
Likelihood is monotone unbounded until first observed
toxicity.
2
First stage is largely arbitrary.
3
Different first stage algorithms lead to different
operating characteristics.
Optimal
design
4
First stage can incorporate information on grades.
2-stage
designs
5
Two stage designs accommodate many/open number
of levels.
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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39 / 58
Two stage designs (likelihood)
Background
Standard 3+3
1
Likelihood is monotone unbounded until first observed
toxicity.
2
First stage is largely arbitrary.
3
Different first stage algorithms lead to different
operating characteristics.
Optimal
design
4
First stage can incorporate information on grades.
2-stage
designs
5
Two stage designs accommodate many/open number
of levels.
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Using grades
More complex
problems
Finding MSD
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Design modifications
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
1
Patients can be included in groups, eg 3 at a time.
2
Grouping can be by design.
3
Overdose control.
4
Underdose control.
5
Joint underdose/overdose control.
2-stage
designs
Using grades
More complex
problems
Finding MSD
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Design modifications
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
1
Patients can be included in groups, eg 3 at a time.
2
Grouping can be by design.
3
Overdose control.
4
Underdose control.
5
Joint underdose/overdose control.
2-stage
designs
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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Design modifications
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
1
Patients can be included in groups, eg 3 at a time.
2
Grouping can be by design.
3
Overdose control.
4
Underdose control.
5
Joint underdose/overdose control.
2-stage
designs
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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Design modifications
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
1
Patients can be included in groups, eg 3 at a time.
2
Grouping can be by design.
3
Overdose control.
4
Underdose control.
5
Joint underdose/overdose control.
2-stage
designs
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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Design modifications
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
1
Patients can be included in groups, eg 3 at a time.
2
Grouping can be by design.
3
Overdose control.
4
Underdose control.
5
Joint underdose/overdose control.
2-stage
designs
Using grades
More complex
problems
Finding MSD
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Some initial escalation schemes
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
# pats
3+3
CRM(2S)
CRM(G)
1
d1
d1
d1
2
d1
d2
d2
3
d1
d2
d3
4
d2
d3
d3
5
d2
d3
d4
6
d2
d3
d4
7
d3
d4
d5
8
d3
d4
d5
9
d3
d4
d5
etc.
etc.
etc.
etc.
Optimal
design
2-stage
designs
Table: Example of initial escalation stage using acceleration.
Using grades
More complex
problems
Finding MSD
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Rapid early escalation using grades
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Severity
0
1
2
3
4
Table: Toxicity “grades” (severities) for trial.
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
Degree of Toxicity
No toxicity
Mild toxicity (non dose-limiting)
Non-mild toxicity (non dose-limiting)
Severe toxicity (non dose-limiting)
Dose limiting toxicity
The rule is to escalate providing S(i) is less than 2.
Furthermore, once we have included 3 patients at some
level then escalation to higher levels only occurs if each
cohort of 3 patients does not experience dose limiting
toxicity.
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Rapid escalation based on grades
Trial History
Background
9
Standard 3+3
CRM
8
One/two
parameter
models
7
Dose Level
Flawed case
studies
6
5
4
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
3
2
1
1
4
7
10
13
16
Patient No
19
22
More complex
problems
Finding MSD
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More complex problems
Background
Standard 3+3
CRM
One/two
parameter
models
Two group problem (patient heterogeneity)
Bridging studies
Within patient escalation
Flawed case
studies
Recording errors and non-drug related DLTs
Equivalent
designs
Multi-drug problem, partial ordering
Optimal
design
Graded toxicities
2-stage
designs
Using grades
More complex
problems
Finding MSD
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More complex problems
Background
Standard 3+3
CRM
One/two
parameter
models
Two group problem (patient heterogeneity)
Bridging studies
Within patient escalation
Flawed case
studies
Recording errors and non-drug related DLTs
Equivalent
designs
Multi-drug problem, partial ordering
Optimal
design
Graded toxicities
2-stage
designs
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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More complex problems
Background
Standard 3+3
CRM
One/two
parameter
models
Two group problem (patient heterogeneity)
Bridging studies
Within patient escalation
Flawed case
studies
Recording errors and non-drug related DLTs
Equivalent
designs
Multi-drug problem, partial ordering
Optimal
design
Graded toxicities
2-stage
designs
Using grades
More complex
problems
Finding MSD
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More complex problems
Background
Standard 3+3
CRM
One/two
parameter
models
Two group problem (patient heterogeneity)
Bridging studies
Within patient escalation
Flawed case
studies
Recording errors and non-drug related DLTs
Equivalent
designs
Multi-drug problem, partial ordering
Optimal
design
Graded toxicities
2-stage
designs
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
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More complex problems
Background
Standard 3+3
CRM
One/two
parameter
models
Two group problem (patient heterogeneity)
Bridging studies
Within patient escalation
Flawed case
studies
Recording errors and non-drug related DLTs
Equivalent
designs
Multi-drug problem, partial ordering
Optimal
design
Graded toxicities
2-stage
designs
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
London, U.K.. 20.11.2012
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More complex problems
Background
Standard 3+3
CRM
One/two
parameter
models
Two group problem (patient heterogeneity)
Bridging studies
Within patient escalation
Flawed case
studies
Recording errors and non-drug related DLTs
Equivalent
designs
Multi-drug problem, partial ordering
Optimal
design
Graded toxicities
2-stage
designs
Using grades
More complex
problems
Finding MSD
John O’Quigley (Université Paris VI)
Dose finding methodology
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Two groups in a single trial
R1
R2
Background
.02
.03
.19
.05
Standard 3+3
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
.45
.21
.51
.39
.63
.50
Trial History
Dose level
CRM
.31
.11
: toxicity
d6
: non toxicity
d5
G2
d4
G1 G2 G1 G2
d3
G1
d2
G1
G1
G1
d1
1
5
10
15
20
25
30
Patient number
Finding MSD
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Dose finding methodology
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Modification of algorithm
Background
1
Standard 3+3
2
Choose level dj closest to target.
Choose level dj according to some probability
mechanism.
CRM
One/two
parameter
models
Trial History
Flawed case
studies
6
Equivalent
designs
8
Optimal
design
6
5
dose level
7
Dose Level
2-stage
designs
Trial History
9
5
4
3
Using grades
More complex
problems
Finding MSD
4
3
2
2
1
1
1
4
John O’Quigley (Université Paris VI)
7
10
13
16
Patient No
19
22
Dose finding methodology
1
3
5
7
9
11
13
15
17
Patient no
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19
21
23
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Within patient escalation
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
Patient
1
2
3
4
5
6
level 1
0
level 2
1
0
level 3
1
1
2
level 4
level 5
2
1
?
3
4 (DLT)
Table: Acceleration information from graded toxicities. Entries are
the grades.
More complex
problems
Finding MSD
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Dose finding methodology
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Phase I study of a combination
Background
Standard 3+3
Table: Drug combinations used in Phase 1 trial of Samarium
Lexidronam and Bortezomib DLT defined by as a grade 3+
neutropenia (Berenson et al. 2009)
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Agent
Sm (mCi/kg)
Bortezomib (mg/m2 )
d1
0.25
1.0
Drug Combination
d2
d3
d4
d5
0.5 1.0 0.25 0.5
1.0 1.0 1.3 1.3
d6
1.0
1.3
We index the models by M where M takes value Mh
under the hth possible ordering
Using grades
More complex
problems
M1 : d1 → d2 → d3 → d4 → d5 → d6
M2 : d1 → d2 → d4 → d3 → d5 → d6
Finding MSD
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Dose finding methodology
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Set of possible orders of toxicity probabilities
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
M
M1
M2
M3
M4
M5
R(d1 )
R(d1 )
R(d1 )
R(d1 )
R(d1 )
≤
≤
≤
≤
≤
R(d2 )
R(d2 )
R(d2 )
R(d4 )
R(d4 )
≤
≤
≤
≤
≤
Simple Order
R(d3 ) ≤ R(d4 )
R(d4 ) ≤ R(d3 )
R(d4 ) ≤ R(d5 )
R(d2 ) ≤ R(d3 )
R(d2 ) ≤ R(d5 )
≤
≤
≤
≤
≤
R(d5 )
R(d5 )
R(d3 )
R(d5 )
R(d3 )
2-stage
designs
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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Model choice
Likelihood Lmj (a) for model m after j patients is
(proportional);
Background
Standard 3+3
j
X
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
y` log ψm (x` , a) +
`=1
j
X
(1 − y` ) log(1 − ψm (x` , a))
`=1
Obtain âmj
Estimate probability of toxicity di via:
R̂(di ) = ψm (di , âmj ) , (i = 1, . . . , k ).
Given m, the dose to be given to the (j + 1) th patient,
xj+1 is determined.
Given Ωj , posterior model probabilities are:
R∞
π(m) −∞ exp{Lmj (u)}g(u) du
π(m|Ωj ) = PM
R∞
m=1 π(m) −∞ exp{Lmj (u)}g(u) du
In some cases the π(m|Ωj ) are only of very indirect interest,
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Dose finding methodology
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Illustration
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
R = (0.04, 0.07, 0.20, 0.35, 0.55, 0.70).
Target toxicity rate θ = 0.20.
The trial will treat n = 24 patients.
For each ordering, we used the power model,
a
ψm (di , a) = αmi
;
m = 1, . . . , 5 ;
i = 1, . . . , 6
2-stage
designs
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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Working Models
Background
Standard 3+3
Table: Working model for five simple orders
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
M
m=1
m=2
m=3
m=4
m=5
1-2-3-4-5-6
1-2-4-3-5-6
1-2-4-5-3-6
1-4-2-3-5-6
1-4-2-5-3-6
1
0.01
0.01
0.01
0.01
0.01
2
0.07
0.07
0.07
0.20
0.20
Combinations
3
4
0.20 0.38
0.38 0.20
0.56 0.20
0.38 0.07
0.56 0.07
5
0.56
0.56
0.38
0.56
0.38
6
0.71
0.71
0.71
0.71
0.71
More complex
problems
Finding MSD
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Dose finding methodology
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Simulation results
Background
Standard 3+3
Dose
R(di )
Conaway et al.
POCRM
CRM
d1
0.26
0.35
0.29
0.27
d2
0.33
0.52
0.50
0.49
d3
0.51
0.11
0.16
0.23
d4
0.62
0.02
0.04
0.01
d5
0.78
0.00
0.01
0.00
d6
0.86
0.00
0.00
0.00
n
21.3
22.0
22.0
tox
8.5
8.4
7.9
R(di )
Conaway et al.
POCRM
CRM
0.12
0.07
0.02
0.01
0.21
0.29
0.23
0.18
0.34
0.42
0.55
0.63
0.50
0.21
0.11
0.17
0.66
0.01
0.10
0.01
0.79
0.00
0.00
0.00
25.6
26.0
25.0
9.0
10.0
7.5
R(di )
Conaway et al.
POCRM
CRM
0.04
0.00
0.00
0.00
0.07
0.02
0.00
0.01
0.20
0.38
0.26
0.19
0.33
0.51
0.50
0.67
0.55
0.08
0.23
0.13
0.70
0.02
0.01
0.00
28.5
29.0
28.0
8.8
10.8
8.0
R(di )
Conaway et al.
POCRM
CRM
0.01
0.00
0.00
0.00
0.04
0.00
0.00
0.00
0.05
0.06
0.01
0.00
0.17
0.25
0.29
0.18
0.33
0.64
0.61
0.76
0.67
0.05
0.09
0.06
29.0
29.0
28.0
7.8
9.4
6.3
R(di )
Conaway et al.
POCRM
CRM
0.01
0.00
0.00
0.00
0.02
0.00
0.00
0.00
0.05
0.01
0.00
0.00
0.15
0.04
0.20
0.05
0.20
0.37
0.12
0.26
0.33
0.59
0.68
0.69
26.2
27.0
27.0
5.8
6.4
4.3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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Most successful dose (MSD)
Example in HIV;
Background
1
Treatment over long period.
Standard 3+3
2
Toxicity is inability to take treatment.
3
Observation window for efficacy comparable to toxicity.
4
Lack of efficacy as bad, possibly worse, than toxicity.
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Introduce the following definitions;
1
R(xj ) = Pr(Yj = 1|Xj = xj )
2
Q(xj ) = Pr(Vj = 1|Xj = xj , Yj = 0)
3
P(di ) = Q(di ){1 − R(di )}.
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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Models
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Let; R(xj ) = E(Yj |xj ) = ψ(xj , a) ;
Q(xj ) = E(Vj |xj , Yj = 0) = φ(xj , b)
P(xj ) = φ(xj , b){1 − ψ(xj , a)} and Q(x) = H{R(x)}
Q(x)
Q(x)
Equivalent
designs
Optimal
design
2-stage
designs
R(x)
R(x)
Using grades
More complex
problems
Figure: Possible relationships for Q(x) = H{R(x)}
Finding MSD
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Dose finding methodology
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Compromise structure
Background
Standard 3+3
CRM
O’Quigley, Hughes and Fenton (Biometrics 57, 1018-29)
suggest;
One/two
parameter
models
1
Choose, say, θ = 0.1
Flawed case
studies
2
Use SPRT to test H0 : P ∈ (0, 0.7) versus
H1 : P ∈ (0.7, 1.0)
3
If SPRT chooses H0 at di then remove levels d1 , ..., di ,
and, modify θ to θ + ∆.
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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Some simulated situations
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
Using grades
More complex
problems
Rk
Qk
Pk
Rk
Qk
Pk
Rk
Qk
Pk
Rk
Qk
Pk
d1
0.06
0.21
0.20
0.15
0.82
0.70
0.00
0.10
0.10
0.00
0.20
0.20
d2
0.15
0.82
0.70
0.30
0.71
0.50
0.05
0.32
0.30
0.00
0.30
0.30
d3
0.25
0.80
0.60
0.40
0.83
0.50
0.15
0.82
0.70
0.10
0.56
0.50
d4
0.30
0.71
0.50
0.50
0.80
0.40
0.30
0.71
0.50
0.15
0.82
0.70
Scheme 1
Scheme 2
Scheme 3
Scheme 4
Finding MSD
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Dose finding methodology
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Some simulated situations
Background
Standard 3+3
CRM
One/two
parameter
models
Flawed case
studies
Equivalent
designs
Optimal
design
2-stage
designs
% rec
% alloc
% rec
% alloc
% rec
% alloc
% rec
% alloc
d1
0.00
0.23
0.96
0.76
0.00
0.06
0.00
0.00
d2
0.97
0.75
0.04
0.24
0.01
0.44
0.00
0.37
d3
0.03
0.02
0.00
0.00
0.93
0.44
0.12
0.32
d4
0.00
0.00
0.00
0.00
0.06
0.06
0.87
0.31
Scheme 1
= 24.9
n
Scheme 2
= 21.7
n
Scheme 3
= 37.6
n
Scheme 4
= 48.5
n
Table: Recommendation and in-trial allocation for the 4 schemes
Using grades
More complex
problems
Finding MSD
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Dose finding methodology
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