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Adaptive Designs for Dose Ranging Trials:
ADRS WG Simulation study
Vlad Dragalin Quintiles Innovation
RTP, NC, U.S.A.
KOL Lecture Series on Adaptive Designs July 9th 2010
V. Dragalin | Adaptive Designs for Dose Ranging Trials
Outline
–Dose-ranging studies
–Adaptive model-based designs
–Statistical Operational Characteristics
–Conclusion
2
Simulation Study: Complete Summary
3
V. Dragalin | Adaptive Designs for Dose Ranging Trials
To appear in: Statistics in Biopharmaceutical Research, 2010
Dose-Ranging Studies
– The overall goal of dose-ranging studies is to establish the existence, nature and extent of dose effect: • Detecting DR: evaluate if there is evidence of activity associated with the
drug, represented by a change in clinical response resulting from a change in dose (PoC);
• Identifying clinical relevance: if PoC is established, determine if a pre-defined clinically relevant response (compared to the placebo response) can be obtained within the observed dose range;
• Selecting a target dose: when the previous goal is met, select the dose to be brought into the confirmatory phase, the so-called target dose;
• Estimating the dose response: finally, estimate the dose-response profile within the observed dose range.
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V. Dragalin | Adaptive Designs for Dose Ranging Trials
New Adaptive Designs
– AMCP-Mod – Adaptive MCP-Mod approach combining multiple comparisons
and modeling (Bornkamp, Bretz, Pinheiro)
– DcoD – D-optimal followed by a c-optimal design based on sigmoid Emax
model (Dragalin, Padmanabhan)
– IntR – Bayesian design minimizing average variance of all LS-estimates for
“interesting part” of dose-response curve (Miller)
– MultObj – Multi-objective optimal design incorporating 2nd order moments and
based on inverse quadratic model (Smith)
– T-Stat – Dose-adaptive design based on t-statistics (Patel, Perevozskaya)
5
V. Dragalin | Adaptive Designs for Dose Ranging Trials
AMCP-Mod Design
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V. Dragalin | Adaptive Designs for Dose Ranging Trials
Adaptive MCP-Mod Design
– Extension to a response-adaptive version of the MCP-Mod methodology using • optimal design theory to allocate new cohorts of patients
• posterior model probabilities and posterior parameter estimates to update initial guesses
– AMCP-Mod Before Trial Start
1. Select the candidate models (two logistic and one beta models)
2. Select “best guesses” for , m = 1, . . . ,M
3. Choose prior model probabilities p(Mm)
4. Choose prior for
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V. Dragalin | Adaptive Designs for Dose Ranging Trials
Adaptive MCP-Mod Design at IA
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V. Dragalin | Adaptive Designs for Dose Ranging Trials
Adaptive MCP-Mod Design at Trial End
1. Calculate optimal contrasts and critical value using MCP
2. Select one of the significant models for dose-response
and MED estimation
3. Fit dose-response model and estimate MED
– Bayesian model is only used for updating the design;
the classical MCP-Mod procedure is wrapped around this.
9
V. Dragalin | Adaptive Designs for Dose Ranging Trials
DcoD: Adaptive Dc-optimal Design
– Working Model Sigmoid Emax model (4 parameter logistic)
dose
Mea
n R
espo
nse
0 2 4 6 8
-1.5
-1.0
-0.5
0.0
0 2 4 6 8
-1.5
-1.0
-0.5
0.0
t4=1t4=2t4=4t4=10
Dragalin et al
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V. Dragalin | Adaptive Designs for Dose Ranging Trials
V. Dragalin | To adapt or to confirm: what is the question?|
St. Petersburg, Russia
Sigmoid Emax Fit
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V. Dragalin | Adaptive Designs for Dose Ranging Trials
D- and c-optimal Designs
A design is locally D-optimal (LDoD) if and only if
A design is locally c-optimal (LcoD) if it minimizes
is the Fisher information matrix at dose x
is the normalized information
matrix for design
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V. Dragalin | Adaptive Designs for Dose Ranging Trials
D- and c-Optimal Designs
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V. Dragalin | Adaptive Designs for Dose Ranging Trials
Dc-Optimal Designs
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V. Dragalin | Adaptive Designs for Dose Ranging Trials
Adaptive Dc-optimal Design
–For 2 adaptations:
• 1/3rd of the subjects allocated according to a fixed 5-
dose design
• Parameters are estimated –> next 1/3rd allocated
according to augmented LDoD
• Parameters are re-estimated –> final 1/3rd allocated
according to augmented LcoD
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V. Dragalin | Adaptive Designs for Dose Ranging Trials
IntR Design
– Estimation of the interesting part of the
dose-response curve
– Working model: sigmoid Emax
– Inference based on LS estimates from
this sigmoid Emax model
– Minimize average variance of all LS-
estimates for
f(x) - f(0) with xδ<x<8.
xδ is dose with effect 1 compared to
placebo
– “Detecting Dose-Response”:
trend test used to test null hypothesis
of flat dose-response
xδ
16
V. Dragalin | Adaptive Designs for Dose Ranging Trials
IntR Design
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V. Dragalin | Adaptive Designs for Dose Ranging Trials
MULTOBJ Design
– Primary focus within MULTOBJ criterion is MED estimation
– Lower weighted components also included related to POC and EDp
(for a range of p’s)
– Weights chosen to reflect importance of component criteria
– MULTOBJ criterion is essentially an extended form of S-optimality
but incorporating 2nd order moments and with MSE in place of
variances
– Working Model: Non-Monotonic 4 parameter Inverse Quadratic
model
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V. Dragalin | Adaptive Designs for Dose Ranging Trials
T-statistic design
– Non-parametric design adaptive approach
– Concentrates dose allocations around the dose with target (pbo-adjusted) response level
– Patients are randomized sequentially in cohorts of fixed size; all assigned to the same dose or pbo (e.g. 3:1)
– Dose selection is adaptive and driven by the value of t-statistic at the last dose studied (Ti):
• Escalate to xi+1 if Ti ≥∆ • Stay at xi if -∆<Ti≤∆ • De-escalate to xi-1 if Ti ≤-∆ • Ti is standardized pbo-adjusted mean response at dose xi • ∆ is a design parameter
Ivanova A., Bolognese JA, Perevozskaya I. Adaptive dose-finding based on t-statistic in dose-response trial. Stat in Medicine, 2008; 27:1581-1592 19
V. Dragalin | Adaptive Designs for Dose Ranging Trials
Simulation Study: Assumptions
– Doses:
• 9 doses: {0,1,2,3,4,5,6,7,8}
• 5 doses: {0,2,4,6,8}
– Endpoint: change from baseline in VAS score
– Clinically meaningful difference: –1.3
– Variance: 4.5
– Sample Size: 250
– Number of adaptations: 0,1,2,4,9
– Total of 56 combinations
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V. Dragalin | Adaptive Designs for Dose Ranging Trials
Simulation Scenarios
1. Linear: y = -(1.65/8) d + ε
2. Umbrella: y = -(1.65/3)d + (1.65/36)d2 + ε
3. Sigmoid Emax: y = -1.70 d5/(45 + d5) + ε
4. Emax: y = -1.81 d/(0.79 + d) + ε
5. Emax low: y = -1.14 d/(0.79 + d) + ε
6. Explicit: y = {0, -1.29, -1.35, -1.42, -1.5, -1.6, -1.63, -1.65, -1.65} + ε
7. Flat: y = ε.
21
V. Dragalin | Adaptive Designs for Dose Ranging Trials
Simulation Scenarios
22
V. Dragalin | Adaptive Designs for Dose Ranging Trials
Performance metrics
– Statistical significance level
– Probability of detecting dose response: Pr(DR)
– Probability of identifying clinically relevant dose: Pr(dose)
– Target Dose selection • Distribution of selected doses
• Summary statistics (mean and standard deviation) for percentage difference from target
• pDiff = 100( d - dtarg)/dtarg
– Dose Response estimation: • summary statistics for absolute prediction error
– Subject Allocation pattern
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V. Dragalin | Adaptive Designs for Dose Ranging Trials
ANOVA
aMCPMod
DcoD
IntR
t-test
MULTOB
0 1 2 3 4 5 6
0 IAs5 doses
1 IAs5 doses
0 1 2 3 4 5 6
2 IAs5 doses
4 IAs5 doses
0 1 2 3 4 5 6
9 IAs5 doses
ANOVA
aMCPMod
DcoD
IntR
t-test
MULTOB
0 IAs9 doses
0 1 2 3 4 5 6
1 IAs9 doses
2 IAs9 doses
0 1 2 3 4 5 6
4 IAs9 doses
9 IAs9 doses
Significance level
Detecting Dose-Response: type I error
24
V. Dragalin | Adaptive Designs for Dose Ranging Trials
ANOVA
aMCPMod
DcoD
IntR
t-test
MULTOB
95 96 97 98 99 100
explicit
94 96 98 100
umbrella
85 90 95 100
linear
ANOVA
aMCPMod
DcoD
IntR
t-test
MULTOB
94 95 96 97 98 99 100
Emax
90 92 94 96 98 100
Sig Emax
65 70 75 80 85 90
Emax low
Pr(DR) (%)
9 doses0 IAs 1 IAs 2 IAs 4 IAs 9 IAs
Detecting D-R: power for 9 doses
25
V. Dragalin | Adaptive Designs for Dose Ranging Trials
ANOVA
aMCPMod
DcoD
IntR
t-test
MULTOB
0.1 0.3
0 IAs5 doses
0.1 0.3
1 IAs5 doses
0.2 0.4
2 IAs5 doses
0.1 0.3
4 IAs5 doses
0.1 0.3
9 IAs5 doses
ANOVA
aMCPMod
DcoD
IntR
t-test
MULTOB
0 1 2 3 4
0 IAs9 doses
0 1 2 3 4
1 IAs9 doses
0 1 2 3 4
2 IAs9 doses
0 1 2 3 4
4 IAs9 doses
0 1 2 3 4
9 IAs9 doses
Pr(dose | flat DR) (%)
Identifying clinically-relevant dose: flat D-R
26
V. Dragalin | Adaptive Designs for Dose Ranging Trials
ANOVA
aMCPMod
DcoD
IntR
t-test
MULTOB
84 86 88 90 92 94
explicit
80 85 90
umbrella
75 80 85 90
linear
ANOVA
aMCPMod
DcoD
IntR
t-test
MULTOB
86 88 90 92 94
Emax
88 90 92 94 96 98
Sig Emax
30 40 50 60
Emax low
Pr(dose) (%)
9 doses0 IAs 1 IAs 2 IAs 4 IAs 9 IAs
Identifying clinically-relevant dose
27
V. Dragalin | Adaptive Designs for Dose Ranging Trials
Selecting Target Dose: 9 doses
ANOVA
aMCPMod
DcoD
IntR
t-test
MULTOB
65 70 75 80
explicit
30 35 40 45 50
umbrella
30 35 40 45
linear
ANOVA
aMCPMod
DcoD
IntR
t-test
MULTOB
35 40 45 50
Emax
50 55 60 65 70
Sig Emax
Correct target interval probability (%)
0 IAs1 IAs2 IAs4 IAs9 IAs
28
V. Dragalin | Adaptive Designs for Dose Ranging Trials
0
10
20
30
40
2 4 6 8
ANOVA0 IAs
aMCPMod0 IAs
2 4 6 8
DcoD0 IAs
IntR0 IAs
2 4 6 8
t-test0 IAs
MULTOB0 IAs
ANOVA1 IAs
aMCPMod1 IAs
DcoD1 IAs
IntR1 IAs
t-test1 IAs
0
10
20
30
40
MULTOB1 IAs
0
10
20
30
40
ANOVA2 IAs
aMCPMod2 IAs
DcoD2 IAs
IntR2 IAs
t-test2 IAs
MULTOB2 IAs
ANOVA4 IAs
aMCPMod4 IAs
DcoD4 IAs
IntR4 IAs
t-test4 IAs
0
10
20
30
40
MULTOB4 IAs
0
10
20
30
40
ANOVA9 IAs
2 4 6 8
aMCPMod9 IAs
DcoD9 IAs
2 4 6 8
IntR9 IAs
t-test9 IAs
2 4 6 8
MULTOB9 IAs
Dose selected
% T
rials
Sig Emax, 9 dosesSelecting a target dose: distribution
29
V. Dragalin | Adaptive Designs for Dose Ranging Trials
-2.0
-1.5
-1.0
-0.5
0.0
0.5
0 2 4 6 8
ANOVA aMCPMod
0 2 4 6 8
DcoD
IntR
0 2 4 6 8
t-test
-2.0
-1.5
-1.0
-0.5
0.0
0.5
MULTOB
Dose
Ave
rage
pre
dict
ion
erro
r
Sig Emax, nIA = 9, 9 doses
5%, 95% 25%, 75% 50%
Estimating D-R curve
30
V. Dragalin | Adaptive Designs for Dose Ranging Trials
Summary and Conclusions
–Detecting DR is considerably easier than estimating it
–Current sample sizes used for D-R studies are inadequate for dose selection and D-R estimation
–Adaptive methods lead to gain in power to detect DR + precision of target dose selection + DR estimation compared to traditional ANOVA design
31
V. Dragalin | Adaptive Designs for Dose Ranging Trials
Summary and Conclusions
– None of the designs was uniformly superior to the others • All 5 designs performed well with respect to achieving specific
objective they were designed for:
– IntR, did well for DR estimation
– AMCPMod, t-test: did well for dose selection
– MULTOB and DcoD: did well for both objectives
– The appeal of a particular design will depend on • the specific goal of the trial
• and the set of plausible DR scenarios, because the latter affects relative performance of the designs
32
V. Dragalin | Adaptive Designs for Dose Ranging Trials
Summary and Conclusions
– Due to complexity of the designs, operating characteristics can be assessed only via simulations during the DR trial planning stage
– Need software which is sufficiently flexible, comprehensive and extensible to allow in-depth exploration of various methods to determine design most appropriate for the study
– We investigated impact of only one component of AD: allocation rule and adaptation based on efficacy endpoint only
– The approach can be extended to examine other sources of “adaptivity”: • sampling rule,
• early stopping for futility/efficacy,
• information-driven SS determination,
• using early data through longitudinal modeling
• incorporating safety endpoint 33
V. Dragalin | Adaptive Designs for Dose Ranging Trials