Download An introduction to Phase 1 dual

An introduction to Phase I dual-agent dose
escalation trials
Michael Sweeting
MRC Biostatistics Unit, Cambridge
13th March 2013
Outline
Introduction to phase I trials
I
I
Aims, objectives and key elements.
The CRM method.
Dual-agent phase I trials
I
I
I
Escalation strategies.
Patient vs. Population gain.
Toxicity vs. Efficacy trade-off.
Introduction to Phase I trials
Aims
I
I
Phase I studies involve the first experimentation of a new drug /
clinical procedure in human subjects.
To seek the highest possible dose subject to toxicity constraints:I
I
This is known as the maximum tolerated dose (MTD).
Based on a monotonicity assumption that the benefit (efficacy) of
treatment increases with dose.
Sample size
I
I
Typically small: 20-50 patients.
Due to ethical considerations patients are added sequentially
after side-effects from previous patients have been assessed.
Subjects
I
I
Healthy volunteers for relatively non-toxic agents (e.g. molecular
entities for CNS disorders).
Patients when drugs are highly toxic (e.g. in oncology).
Introduction to Phase I trials
Aims
I
I
Phase I studies involve the first experimentation of a new drug /
clinical procedure in human subjects.
To seek the highest possible dose subject to toxicity constraints:I
I
This is known as the maximum tolerated dose (MTD).
Based on a monotonicity assumption that the benefit (efficacy) of
treatment increases with dose.
Sample size
I
I
Typically small: 20-50 patients.
Due to ethical considerations patients are added sequentially
after side-effects from previous patients have been assessed.
Subjects
I
I
Healthy volunteers for relatively non-toxic agents (e.g. molecular
entities for CNS disorders).
Patients when drugs are highly toxic (e.g. in oncology).
Introduction to Phase I trials
Aims
I
I
Phase I studies involve the first experimentation of a new drug /
clinical procedure in human subjects.
To seek the highest possible dose subject to toxicity constraints:I
I
This is known as the maximum tolerated dose (MTD).
Based on a monotonicity assumption that the benefit (efficacy) of
treatment increases with dose.
Sample size
I
I
Typically small: 20-50 patients.
Due to ethical considerations patients are added sequentially
after side-effects from previous patients have been assessed.
Subjects
I
I
Healthy volunteers for relatively non-toxic agents (e.g. molecular
entities for CNS disorders).
Patients when drugs are highly toxic (e.g. in oncology).
Key elements
1. A starting dose that will be given to the first patient:I
I
In psychiatric trials: no observable effect level (NOEL) in animals.
1
In oncology trials: 10
LD10 in mice (one tenth of the lethal dose in
10% of mice).
2. Potential doses for experimentation.
3. Dose regime (single dose or multiple doses per individual).
4. Outcomes:I
I
Safety (Toxicity) outcomes: often binary (e.g. occurrence of a
dose-limiting toxicity (DLT) is used in cancer trials).
PD measures of efficacy: often biomarker based.
5. A target level (TL) or therapeutic index:I
The desired target level that corresponds to the MTD (e.g. cancer
trials often propose 30% prevalence of DLT at the MTD).
6. A dose-escalation design:I
I
I
Rule or model based.
Cohort size:- Number individuals treated at each dose level.
Sample size / stopping rules.
Key elements
1. A starting dose that will be given to the first patient:I
I
In psychiatric trials: no observable effect level (NOEL) in animals.
1
In oncology trials: 10
LD10 in mice (one tenth of the lethal dose in
10% of mice).
2. Potential doses for experimentation.
3. Dose regime (single dose or multiple doses per individual).
4. Outcomes:I
I
Safety (Toxicity) outcomes: often binary (e.g. occurrence of a
dose-limiting toxicity (DLT) is used in cancer trials).
PD measures of efficacy: often biomarker based.
5. A target level (TL) or therapeutic index:I
The desired target level that corresponds to the MTD (e.g. cancer
trials often propose 30% prevalence of DLT at the MTD).
6. A dose-escalation design:I
I
I
Rule or model based.
Cohort size:- Number individuals treated at each dose level.
Sample size / stopping rules.
Key elements
1. A starting dose that will be given to the first patient:I
I
In psychiatric trials: no observable effect level (NOEL) in animals.
1
In oncology trials: 10
LD10 in mice (one tenth of the lethal dose in
10% of mice).
2. Potential doses for experimentation.
3. Dose regime (single dose or multiple doses per individual).
4. Outcomes:I
I
Safety (Toxicity) outcomes: often binary (e.g. occurrence of a
dose-limiting toxicity (DLT) is used in cancer trials).
PD measures of efficacy: often biomarker based.
5. A target level (TL) or therapeutic index:I
The desired target level that corresponds to the MTD (e.g. cancer
trials often propose 30% prevalence of DLT at the MTD).
6. A dose-escalation design:I
I
I
Rule or model based.
Cohort size:- Number individuals treated at each dose level.
Sample size / stopping rules.
Key elements
1. A starting dose that will be given to the first patient:I
I
In psychiatric trials: no observable effect level (NOEL) in animals.
1
In oncology trials: 10
LD10 in mice (one tenth of the lethal dose in
10% of mice).
2. Potential doses for experimentation.
3. Dose regime (single dose or multiple doses per individual).
4. Outcomes:I
I
Safety (Toxicity) outcomes: often binary (e.g. occurrence of a
dose-limiting toxicity (DLT) is used in cancer trials).
PD measures of efficacy: often biomarker based.
5. A target level (TL) or therapeutic index:I
The desired target level that corresponds to the MTD (e.g. cancer
trials often propose 30% prevalence of DLT at the MTD).
6. A dose-escalation design:I
I
I
Rule or model based.
Cohort size:- Number individuals treated at each dose level.
Sample size / stopping rules.
Key elements
1. A starting dose that will be given to the first patient:I
I
In psychiatric trials: no observable effect level (NOEL) in animals.
1
In oncology trials: 10
LD10 in mice (one tenth of the lethal dose in
10% of mice).
2. Potential doses for experimentation.
3. Dose regime (single dose or multiple doses per individual).
4. Outcomes:I
I
Safety (Toxicity) outcomes: often binary (e.g. occurrence of a
dose-limiting toxicity (DLT) is used in cancer trials).
PD measures of efficacy: often biomarker based.
5. A target level (TL) or therapeutic index:I
The desired target level that corresponds to the MTD (e.g. cancer
trials often propose 30% prevalence of DLT at the MTD).
6. A dose-escalation design:I
I
I
Rule or model based.
Cohort size:- Number individuals treated at each dose level.
Sample size / stopping rules.
Key elements
1. A starting dose that will be given to the first patient:I
I
In psychiatric trials: no observable effect level (NOEL) in animals.
1
In oncology trials: 10
LD10 in mice (one tenth of the lethal dose in
10% of mice).
2. Potential doses for experimentation.
3. Dose regime (single dose or multiple doses per individual).
4. Outcomes:I
I
Safety (Toxicity) outcomes: often binary (e.g. occurrence of a
dose-limiting toxicity (DLT) is used in cancer trials).
PD measures of efficacy: often biomarker based.
5. A target level (TL) or therapeutic index:I
The desired target level that corresponds to the MTD (e.g. cancer
trials often propose 30% prevalence of DLT at the MTD).
6. A dose-escalation design:I
I
I
Rule or model based.
Cohort size:- Number individuals treated at each dose level.
Sample size / stopping rules.
Response
A dose-response curve
θ
1
θ = Target level
2
3MTD 4
Dose level
5
6
The Continual Reassessment Method (CRM)
I
I
The CRM is an adaptive design that adjusts the dose for the next
cohort based on all information accrued to date.
The aim is to choose the dose that is ‘closest’ to the target level.
I
d(i): dose administered to patient i.
I
π(d; α): probability of a DLT at dose d with parameter α.
I
f (α): prior distribution for α.
I
Posterior distribution for α:
f (α|y n ) = R ∞
0
I
f (α)L(α; y n )
.
f (u)L(u; y n ) du
The dose whose posterior probability of DLT closest to the TTL, θ , is
chosen, that is:
d(n + 1) = arg min E [π(ξ ; α)] − θ ξ ∈{1,...,k}
The Continual Reassessment Method (CRM)
I
I
The CRM is an adaptive design that adjusts the dose for the next
cohort based on all information accrued to date.
The aim is to choose the dose that is ‘closest’ to the target level.
I
d(i): dose administered to patient i.
I
π(d; α): probability of a DLT at dose d with parameter α.
I
f (α): prior distribution for α.
I
Posterior distribution for α:
f (α|y n ) = R ∞
0
I
f (α)L(α; y n )
.
f (u)L(u; y n ) du
The dose whose posterior probability of DLT closest to the TTL, θ , is
chosen, that is:
d(n + 1) = arg min E [π(ξ ; α)] − θ ξ ∈{1,...,k}
The Continual Reassessment Method (CRM)
I
I
The CRM is an adaptive design that adjusts the dose for the next
cohort based on all information accrued to date.
The aim is to choose the dose that is ‘closest’ to the target level.
I
d(i): dose administered to patient i.
I
π(d; α): probability of a DLT at dose d with parameter α.
I
f (α): prior distribution for α.
I
Posterior distribution for α:
f (α|y n ) = R ∞
0
I
f (α)L(α; y n )
.
f (u)L(u; y n ) du
The dose whose posterior probability of DLT closest to the TTL, θ , is
chosen, that is:
d(n + 1) = arg min E [π(ξ ; α)] − θ ξ ∈{1,...,k}
Example escalation scheme
Cohort 0
1.00
Probability of DLT
0.75
0.50
0.25
0.00
1
2
3
Dose level
Previous slide
Next slide
4
5
Example escalation scheme
Cohort 1
1.00
Probability of DLT
0.75
0.50
0.25
0.00
●
1
2
3
Dose level
Previous slide
Next slide
4
5
Example escalation scheme
Cohort 2
1.00
Probability of DLT
0.75
0.50
0.25
●
0.00
1
2
3
Dose level
Previous slide
Next slide
4
5
Example escalation scheme
Cohort 3
1.00
Probability of DLT
0.75
0.50
0.25
●
0.00
1
2
3
Dose level
Previous slide
Next slide
4
5
Example escalation scheme
Cohort 4
1.00
Probability of DLT
0.75
0.50
0.25
●
0.00
1
2
3
Dose level
Previous slide
Next slide
4
5
Example escalation scheme
Cohort 5
1.00
Probability of DLT
0.75
0.50
●
0.25
0.00
1
2
3
Dose level
Previous slide
Next slide
4
5
Example escalation scheme
Cohort 6
1.00
Probability of DLT
0.75
0.50
●
0.25
0.00
1
2
3
Dose level
Previous slide
Next slide
4
5
Example escalation scheme
Cohort 7
1.00
Probability of DLT
0.75
0.50
●
0.25
0.00
1
2
3
Dose level
Previous slide
Next slide
4
5
Example escalation scheme
Cohort 8
1.00
Probability of DLT
0.75
0.50
●
0.25
0.00
1
2
3
Dose level
Previous slide
Next slide
4
5
Example escalation scheme
Cohort 9
1.00
Probability of DLT
0.75
0.50
●
0.25
0.00
1
2
3
Dose level
Previous slide
Next slide
4
5
Example escalation scheme
Cohort 10
1.00
Probability of DLT
0.75
0.50
●
0.25
0.00
1
2
3
Dose level
Previous slide
Next slide
4
5
Extending to dual-agent phase I trials
Antagonism
Probability DLT
0.0
0.1
Drug B
0.2
0.3
0.4
0.5
0.6
0.7
0.8
Synergy
Drug A
Comparison of single and dual-agent phase I trials
Aim
Single-agent To identify a single maximum tolerated dose (MTD).
Dual-agent To identify numerous MTD combinations.
Escalation
Single-agent Quick and safe escalation to the target level (TL).
Dual-agent Quick and safe escalation to the TL, with varied
experimentation of doses at the TL.
Prior information
Single-agent Pre-clinical, Learning from similar compounds.
Dual-agent Pre-clinical, Learning from similar compounds and
combinations, Results from single-agent Phase I-III
studies.
Comparison of single and dual-agent phase I trials
Aim
Single-agent To identify a single maximum tolerated dose (MTD).
Dual-agent To identify numerous MTD combinations.
Escalation
Single-agent Quick and safe escalation to the target level (TL).
Dual-agent Quick and safe escalation to the TL, with varied
experimentation of doses at the TL.
Prior information
Single-agent Pre-clinical, Learning from similar compounds.
Dual-agent Pre-clinical, Learning from similar compounds and
combinations, Results from single-agent Phase I-III
studies.
Comparison of single and dual-agent phase I trials
Aim
Single-agent To identify a single maximum tolerated dose (MTD).
Dual-agent To identify numerous MTD combinations.
Escalation
Single-agent Quick and safe escalation to the target level (TL).
Dual-agent Quick and safe escalation to the TL, with varied
experimentation of doses at the TL.
Prior information
Single-agent Pre-clinical, Learning from similar compounds.
Dual-agent Pre-clinical, Learning from similar compounds and
combinations, Results from single-agent Phase I-III
studies.
Series of 1-agent CRMs
I
I
Fix one drug at a single dose, escalate the other, in a series of
‘sub-trials’.
Identified MTD from one ‘sub-trial’ can be used to limit dose
range for next ‘sub-trial’. 1
6
Drug B
5
4
3
2
1
1
1 Yuan,
2
3
4
Drug A
5
6
Y. and Yin, G. Statistics in Medicine 2008; 27: 5664-78.
Series of 1-agent CRMs
I
I
Fix one drug at a single dose, escalate the other, in a series of
‘sub-trials’.
Identified MTD from one ‘sub-trial’ can be used to limit dose
range for next ‘sub-trial’. 1
6
Drug B
5
4
3
2
1
1
1 Yuan,
2
3
4
Drug A
5
6
Y. and Yin, G. Statistics in Medicine 2008; 27: 5664-78.
Series of 1-agent CRMs
I
I
Fix one drug at a single dose, escalate the other, in a series of
‘sub-trials’.
Identified MTD from one ‘sub-trial’ can be used to limit dose
range for next ‘sub-trial’. 1
6
Drug B
5
4
3
2
1
1
1 Yuan,
2
3
4
Drug A
5
6
Y. and Yin, G. Statistics in Medicine 2008; 27: 5664-78.
Series of 1-agent CRMs
I
I
Fix one drug at a single dose, escalate the other, in a series of
‘sub-trials’.
Identified MTD from one ‘sub-trial’ can be used to limit dose
range for next ‘sub-trial’. 1
6
Drug B
5
4
3
2
1
1
1 Yuan,
2
3
4
Drug A
5
6
Y. and Yin, G. Statistics in Medicine 2008; 27: 5664-78.
Series of 1-agent CRMs
I
I
Fix one drug at a single dose, escalate the other, in a series of
‘sub-trials’.
Identified MTD from one ‘sub-trial’ can be used to limit dose
range for next ‘sub-trial’. 1
6
Drug B
5
4
3
2
1
1
1 Yuan,
2
3
4
Drug A
5
6
Y. and Yin, G. Statistics in Medicine 2008; 27: 5664-78.
Series of 1-agent CRMs
I
I
Fix one drug at a single dose, escalate the other, in a series of
‘sub-trials’.
Identified MTD from one ‘sub-trial’ can be used to limit dose
range for next ‘sub-trial’. 1
6
Drug B
5
4
3
2
1
1
1 Yuan,
2
3
4
Drug A
5
6
Y. and Yin, G. Statistics in Medicine 2008; 27: 5664-78.
Series of 1-agent CRMs
I
I
Fix one drug at a single dose, escalate the other, in a series of
‘sub-trials’.
Identified MTD from one ‘sub-trial’ can be used to limit dose
range for next ‘sub-trial’. 1
6
Drug B
5
4
3
2
1
1
1 Yuan,
2
3
4
Drug A
5
6
Y. and Yin, G. Statistics in Medicine 2008; 27: 5664-78.
Using 1-dimensional CRM with partial ordering
I
I
Drug B
I
If a prior ordering of the dose combinations can be assumed
then a 1-dimensional CRM can be applied. 2
Alternatively, the likelihood of each possible ordering can be
assessed after each patient is recruited. 3
Can become problematic if many dose levels are used (many
possible orderings).
2
1
1
2 Kramar,
3 Wages,
2
Drug A
3
A. et al. Statistics in Medicine 1999; 18: 1849-64.
N. A. et al. Clinical Trials 2011; 8: 380-89.
Using 1-dimensional CRM with partial ordering
I
I
Drug B
I
If a prior ordering of the dose combinations can be assumed
then a 1-dimensional CRM can be applied. 2
Alternatively, the likelihood of each possible ordering can be
assessed after each patient is recruited. 3
Can become problematic if many dose levels are used (many
possible orderings).
2
1
1
2 Kramar,
3 Wages,
2
Drug A
3
A. et al. Statistics in Medicine 1999; 18: 1849-64.
N. A. et al. Clinical Trials 2011; 8: 380-89.
Using 1-dimensional CRM with partial ordering
I
I
Drug B
I
If a prior ordering of the dose combinations can be assumed
then a 1-dimensional CRM can be applied. 2
Alternatively, the likelihood of each possible ordering can be
assessed after each patient is recruited. 3
Can become problematic if many dose levels are used (many
possible orderings).
2
1
1
2 Kramar,
3 Wages,
2
Drug A
3
A. et al. Statistics in Medicine 1999; 18: 1849-64.
N. A. et al. Clinical Trials 2011; 8: 380-89.
Using 1-dimensional CRM with partial ordering
I
I
Drug B
I
If a prior ordering of the dose combinations can be assumed
then a 1-dimensional CRM can be applied. 2
Alternatively, the likelihood of each possible ordering can be
assessed after each patient is recruited. 3
Can become problematic if many dose levels are used (many
possible orderings).
2
1
1
2 Kramar,
3 Wages,
2
Drug A
3
A. et al. Statistics in Medicine 1999; 18: 1849-64.
N. A. et al. Clinical Trials 2011; 8: 380-89.
Escalation strategies for 2-dimensional models:
Admissible next doses4
Diagonal (or ‘Fast’)
escalation.
I
6
5
5
4
4
3
3
2
2
1
1
1
I
Non-diagonal (or ‘Slow’)
escalation.
6
Drug B
Drug B
I
2
3
4
Drug A
5
6
1
2
3
4
Drug A
5
A third strategy: Allow any previously experimented dose
combination to be admissible.
4 Sweeting,
MJ. and Mander, AP. Pharm. Stats. 2012;11(3):258-266.
6
Escalation strategies: Decision rules
Patient gain
I
I
The next cohort is treated at our best estimate of the MTD.
Patient gain used in most CRM methodology.
Variance (population) gain
I
I
The next cohort is treated at the dose that will provide the most
information regarding the dose-toxicity surface.
This dose is the one that will provide most benefit to the
population (by giving more precise estimates at the end of the
trial).
Hybrid patient/variance gain
I
I
In dual-agent trials, we want doses close to the TL, but also allow
experimentation across the dose-toxicity surface.
Hence this requires a trade-off between Patient and Population
Gain.
Escalation strategies: Decision rules
Patient gain
I
I
The next cohort is treated at our best estimate of the MTD.
Patient gain used in most CRM methodology.
Variance (population) gain
I
I
The next cohort is treated at the dose that will provide the most
information regarding the dose-toxicity surface.
This dose is the one that will provide most benefit to the
population (by giving more precise estimates at the end of the
trial).
Hybrid patient/variance gain
I
I
In dual-agent trials, we want doses close to the TL, but also allow
experimentation across the dose-toxicity surface.
Hence this requires a trade-off between Patient and Population
Gain.
Escalation strategies: Decision rules
Patient gain
I
I
The next cohort is treated at our best estimate of the MTD.
Patient gain used in most CRM methodology.
Variance (population) gain
I
I
The next cohort is treated at the dose that will provide the most
information regarding the dose-toxicity surface.
This dose is the one that will provide most benefit to the
population (by giving more precise estimates at the end of the
trial).
Hybrid patient/variance gain
I
I
In dual-agent trials, we want doses close to the TL, but also allow
experimentation across the dose-toxicity surface.
Hence this requires a trade-off between Patient and Population
Gain.
Escalation strategies: Decision rules
Patient gain
I
I
The next cohort is treated at our best estimate of the MTD.
Patient gain used in most CRM methodology.
Variance (population) gain
I
I
The next cohort is treated at the dose that will provide the most
information regarding the dose-toxicity surface.
This dose is the one that will provide most benefit to the
population (by giving more precise estimates at the end of the
trial).
Hybrid patient/variance gain
I
I
In dual-agent trials, we want doses close to the TL, but also allow
experimentation across the dose-toxicity surface.
Hence this requires a trade-off between Patient and Population
Gain.
An example trial in practice: using non-diagonal
escalation
n=0
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
0.0
0.2
0.4
Drug A
Previous slide
Next slide
0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n=1
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
0.0
0.2
0.4
Drug A
Previous slide
Next slide
0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n=2
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
0.0
0.2
0.4
Drug A
Previous slide
Next slide
0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n=3
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
0.0
0.2
0.4
Drug A
Previous slide
Next slide
0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n=4
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
0.0
0.2
0.4
Drug A
Previous slide
Next slide
0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n=5
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
0.0
0.2
0.4
Drug A
Previous slide
Next slide
0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n=6
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
0.0
0.2
0.4
Drug A
Previous slide
Next slide
0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n=7
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
0.0
0.2
0.4
Drug A
Previous slide
Next slide
0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n=8
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
0.0
0.2
0.4
Drug A
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0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n=9
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
0.0
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Drug A
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0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n = 10
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
0.0
0.2
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Drug A
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0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n = 11
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
0.0
0.2
0.4
Drug A
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0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n = 12
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
0.0
0.2
0.4
Drug A
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0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n = 13
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
0.0
0.2
0.4
Drug A
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0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n = 14
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
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0.8
0.2
0.0
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Drug A
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0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n = 15
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
0.0
0.2
0.4
Drug A
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0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n = 20
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
0.0
0.2
0.4
Drug A
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0.6
0.8
1.0
An example trial in practice: using non-diagonal
escalation
n = 30
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
0.4
0.5
0.4
0.6
0.7
0.8
0.2
0.0
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Drug A
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An example trial in practice: diagonal escalation with
population gain function
n = 30
1.0
0.8
Probability DLT
0.0
0.1
0.6
Drug B
0.2
0.3
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Drug A
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1.0
Incorporating measures of efficacy
I
A trade-off must be made between efficacy and toxicity.
Response
I
There is increasing interest in developing dose finding methods
that incorporate both toxicity and efficacy endpoints.
Considered as a ‘phase I-II’ trial.
I
Toxicity
Efficacy
MED
MTD Dose
Incorporating measures of efficacy
I
A trade-off must be made between efficacy and toxicity.
Response
I
There is increasing interest in developing dose finding methods
that incorporate both toxicity and efficacy endpoints.
Considered as a ‘phase I-II’ trial.
I
Toxicity
Efficacy
MED
MTD Dose
Incorporating measures of efficacy
I
A trade-off must be made between efficacy and toxicity.
Response
I
There is increasing interest in developing dose finding methods
that incorporate both toxicity and efficacy endpoints.
Considered as a ‘phase I-II’ trial.
I
Toxicity
Efficacy
MED
MTD Dose
Incorporating measures of efficacy
I
A trade-off must be made between efficacy and toxicity.
Response
I
There is increasing interest in developing dose finding methods
that incorporate both toxicity and efficacy endpoints.
Considered as a ‘phase I-II’ trial.
I
Toxicity
Efficacy
MED
MTD Dose
EffTox contours of desirability5
Dose-Finding Based on Efficacy–Toxicity Trade-Offs
1.0
0.8
q
π*2
C
Prob(TOXICITY)
0.6
p
0.4
L(q)
π*3
0.2
π*1
0.0
0.0
0.2
0.4
0.6
0.8
1.0
Prob(EFFICACY)
5 Thall,
Figure 1. Efficacy–toxicity trade-off contours for the
Pentostatin trial. The target contour C is given by the solid
PF. and Cook,
JD.theBiometrics
60: 684-693.
line, and
three elicited2004;
target points
that determine C are
This may be used to construct a
that partition Π, with the points
desirable. Given any p ∈ C and z >
hz (p) = q if q ∈ L(p) and ρ(p)/ρ
hz (p) = (1 − (1 − pE )/z, pT /z). W
not be a subset of Π for some z, sin
contours inside Π we define Cz = {
contour in Π obtained by shifting e
point q in Π such that ρ(p)/ρ(q) =
ordered by their desirabilities and
contours is a partition of Π, the co
on Π.
We require f (π E ) to be strictly
given (πE , πT ) ∈ C and " > 0, prov
Π, it must be the case that (π E + "
C and hence is more desirable than
(π E , π T + ") ∈ Π must be on a con
desirable than (π E , π T ). In partic
binary outcome case, the rectang
line segments from (π E , π̄T ) to (π
¯
¯
(1, π̄T ) does not satisfy this admis
the convenient form π T = f (π E )
the applications described here, fit
pairs subject to the constraint th
π E such that {πE , f (πE )} ∈ C. O
elliptical contour, should work as w
4.2 The Trade-Off-Based Algorithm
Initially, the physician must provid
dose for the first cohort, N , c, a
used in the acceptability criteria
∗
∗
∗
Summary
I
I
I
Escalation strategies more complex in two-agent trials.
Generally require twice as many patients as single-agent trials.
May wish for varied experimentation around MTD contour:I
I
I
I
Non-diagonal escalation rarely behave in a step-like manner, and
may get ‘stuck’ in regions where one drug is given at a low dose.
Need to consider carefully trade-off between:I
I
I
I
Allows more drug combinations to be recommended for phase II
experimentation.
Such an objective requires sequential learning about MTD contour
to choose next optimal dose.
Patient and Population gain.
Toxicity and Efficacy.
In summary, more consideration needs to be given to these
design aspects in order to gain optimal information from the
available patients.
Most of these designs are disappointingly under used in practice.
Summary
I
I
I
Escalation strategies more complex in two-agent trials.
Generally require twice as many patients as single-agent trials.
May wish for varied experimentation around MTD contour:I
I
I
I
Non-diagonal escalation rarely behave in a step-like manner, and
may get ‘stuck’ in regions where one drug is given at a low dose.
Need to consider carefully trade-off between:I
I
I
I
Allows more drug combinations to be recommended for phase II
experimentation.
Such an objective requires sequential learning about MTD contour
to choose next optimal dose.
Patient and Population gain.
Toxicity and Efficacy.
In summary, more consideration needs to be given to these
design aspects in order to gain optimal information from the
available patients.
Most of these designs are disappointingly under used in practice.
Summary
I
I
I
Escalation strategies more complex in two-agent trials.
Generally require twice as many patients as single-agent trials.
May wish for varied experimentation around MTD contour:I
I
I
I
Non-diagonal escalation rarely behave in a step-like manner, and
may get ‘stuck’ in regions where one drug is given at a low dose.
Need to consider carefully trade-off between:I
I
I
I
Allows more drug combinations to be recommended for phase II
experimentation.
Such an objective requires sequential learning about MTD contour
to choose next optimal dose.
Patient and Population gain.
Toxicity and Efficacy.
In summary, more consideration needs to be given to these
design aspects in order to gain optimal information from the
available patients.
Most of these designs are disappointingly under used in practice.
Summary
I
I
I
Escalation strategies more complex in two-agent trials.
Generally require twice as many patients as single-agent trials.
May wish for varied experimentation around MTD contour:I
I
I
I
Non-diagonal escalation rarely behave in a step-like manner, and
may get ‘stuck’ in regions where one drug is given at a low dose.
Need to consider carefully trade-off between:I
I
I
I
Allows more drug combinations to be recommended for phase II
experimentation.
Such an objective requires sequential learning about MTD contour
to choose next optimal dose.
Patient and Population gain.
Toxicity and Efficacy.
In summary, more consideration needs to be given to these
design aspects in order to gain optimal information from the
available patients.
Most of these designs are disappointingly under used in practice.
Summary
I
I
I
Escalation strategies more complex in two-agent trials.
Generally require twice as many patients as single-agent trials.
May wish for varied experimentation around MTD contour:I
I
I
I
Non-diagonal escalation rarely behave in a step-like manner, and
may get ‘stuck’ in regions where one drug is given at a low dose.
Need to consider carefully trade-off between:I
I
I
I
Allows more drug combinations to be recommended for phase II
experimentation.
Such an objective requires sequential learning about MTD contour
to choose next optimal dose.
Patient and Population gain.
Toxicity and Efficacy.
In summary, more consideration needs to be given to these
design aspects in order to gain optimal information from the
available patients.
Most of these designs are disappointingly under used in practice.
Summary
I
I
I
Escalation strategies more complex in two-agent trials.
Generally require twice as many patients as single-agent trials.
May wish for varied experimentation around MTD contour:I
I
I
I
Non-diagonal escalation rarely behave in a step-like manner, and
may get ‘stuck’ in regions where one drug is given at a low dose.
Need to consider carefully trade-off between:I
I
I
I
Allows more drug combinations to be recommended for phase II
experimentation.
Such an objective requires sequential learning about MTD contour
to choose next optimal dose.
Patient and Population gain.
Toxicity and Efficacy.
In summary, more consideration needs to be given to these
design aspects in order to gain optimal information from the
available patients.
Most of these designs are disappointingly under used in practice.
Summary
I
I
I
Escalation strategies more complex in two-agent trials.
Generally require twice as many patients as single-agent trials.
May wish for varied experimentation around MTD contour:I
I
I
I
Non-diagonal escalation rarely behave in a step-like manner, and
may get ‘stuck’ in regions where one drug is given at a low dose.
Need to consider carefully trade-off between:I
I
I
I
Allows more drug combinations to be recommended for phase II
experimentation.
Such an objective requires sequential learning about MTD contour
to choose next optimal dose.
Patient and Population gain.
Toxicity and Efficacy.
In summary, more consideration needs to be given to these
design aspects in order to gain optimal information from the
available patients.
Most of these designs are disappointingly under used in practice.
Summary
I
I
I
Escalation strategies more complex in two-agent trials.
Generally require twice as many patients as single-agent trials.
May wish for varied experimentation around MTD contour:I
I
I
I
Non-diagonal escalation rarely behave in a step-like manner, and
may get ‘stuck’ in regions where one drug is given at a low dose.
Need to consider carefully trade-off between:I
I
I
I
Allows more drug combinations to be recommended for phase II
experimentation.
Such an objective requires sequential learning about MTD contour
to choose next optimal dose.
Patient and Population gain.
Toxicity and Efficacy.
In summary, more consideration needs to be given to these
design aspects in order to gain optimal information from the
available patients.
Most of these designs are disappointingly under used in practice.