Transcript Document

Dose-adaptive study designs offer benefits for
proof-of-concept / Phase IIa clinical trials,
as well as raise issues for continued research
OUTLINE: Dose-Adaptive Designs & Examples
 Definition & Introduction (Jim)
 Frequentist Designs, including Random Walk Designs (Jim)




3+3 Design for cancer
Up&Down Design
Biased Coin Designs
Simulations of Up&Down Design for Dental Pain Clinical Trial




Continual Reassessment Method (CRM)
Bayesian D-optimal Design
Other related approaches
Bayesian 4-parameter logistic
 Bayesian-type Designs (Inna)
 Case Study (adaptive cross-over design)
 CytelSim Software demo
 Summary & Recommendations (Inna)
 References
Jim Bolognese & Inna Perevozskaya, Sept. 12, 20081
Continual Reassessment Method
(CRM)
 Most known Bayesian method for Phase I trials
 Underlying dose-response relationship is described by a 1parameter function family
 For a predefined set of doses to be studied and a binary
response, estimates dose level (MTD) that yields a particular
proportion (P) of responses
 CRM uses Bayes theorem with accruing data to update the
distribution of MTD based on previous responses
 After each patient’s response, posterior distribution of model
parameter is updated; predicted probabilities of a toxic response
at each dose level are updated
 The dose level for next patient is selected as the one with
predicted probability closest to the target level of response
 Procedure stops after N patients enrolled
 Final estimate of MTD: dose with posterior probability closest to
P after N patients
Innovative Clinical Drug
01/25/2006
Development Conference
2
 The method is designed
to converge to MTD
Continual Reassessment Method (cont.)
Choose
initial estimate
of response
distribution
& choose
initial dose
Stop.
EDxx = Dose w/
Prob. (Resp.)
Closest to
Target level
Obtain next
Patient’s
Observation
Next Pt. Dose
= Dose w/
Prob. (Resp.)
Closest to
Target level
Update Dose
Response Model
& estimate
Prob. (Resp.)
@ each dose
no
Max N
Reached?
yes
3
Escalation With Overdose Control
(EWOC) Bayesian Design
 Assigns doses similarly to CRM, except for overdose control
 predicted probability of next assignment exceeding MTD is controlled (Bayesian feasible
design)
 this distinction is particularly important in oncology
 Assumes a model for the dose-response curve in terms of two parameters:
 MTD
 probability of response at dose D1
 EWOC updates posterior distribution of MTD based on this two-parameter model
 Free software available here:
 http://sisyphus.emory.edu/software_ewoc.php
 Reference:
 Z.Xu, M. Tighiouart, A. Rogatko
EWOC 2.0: Interactive Software for Dose Escalation in Cancer Phase I Clinical Trials
Drug Information Journal 2007 : 41(02)
Babb, et al., 1998
4
Decision Theoretic Approaches
 Similar to CRM
 Incorporates elements of Bayesian Decision Theory
 Designed to study a particular set of dose levels D1, . . ., Dk
 Two-parameter model for dose response with prior distributions on
the parameters
 Loss function minimizes asymptotic variance of dose which yields a
particular proportion of responses
 Posterior distribution estimates of the 2 parameters used to derive
next dose, i.e., that estimated to have desired response level
Whitehead, et al., 1995
5
Bayesian D-Optimal
Sequential Design
 Based on formal theory of optimal design (Atkinson and Donev, 1992)
 Similar to EWOC, a constraint is added to address the ethical dilemma of
avoiding extremely high doses
 Uses a two parameter logistic model for dose response curve
 Slope & location
 Binary endpoint
 Minimum response rate fixed at 0%, maximum at 100%
 Sequential procedure assigns dose at each stage which minimizes variance
of posterior distribution of model parameters
Haines, et al., 2003
6
Simulated Bayesian
D-Optimal Design for ED50
(http://haggis.umbc.edu/cgi-bin/dinteractive/inna1.html)
 Efficacy: Percent of patients with “Response”
assumed underlying distribution
Dose: 1
2
3 4
5
6
7
%Response: 30 40 55 65 75
75 75
 Prior estimates: ED25 between doses 1 and 2
ED50 between doses 2 and 3
 6 patients in Stage 1 for seeding purposes
D-Optimal Design: 3 pts at dose 1, 2 at dose 3, 1 at dose 4
# responses:
1
1
1
 24 subsequent patients (total 30 patients) entered sequentially at
doses yielding minimum variance of model for ED50 estimate
 Response / non-response assigned to approximate targeted %G/E
distribution above
7
Simulated Bayesian D-Optimal Design
for ED50 – Results
(http://haggis.umbc.edu/cgi-bin/dinteractive/inna1.html)
Sequence of Doses assigned together with outcome
(1=good/excellent response, 0=not)
Pt.No.,Dose(resp)
Pt.No.,Dose(resp)
Pt.No.,Dose(resp)
07, dose 3 (1)
15, dose 1 (0)
23, dose 1 (0)
08, dose 1 (0)
16, dose 5 (1)
24, dose 5 (0)
09, dose 3 (0)
17, dose 1 (0)
25, dose 1 (1)
10, dose 1 (1)
18, dose 5 (0)
26, dose 5 (1)
11, dose 5 (1)
19, dose 1 (1)
27, dose 1 (0)
12, dose 5 (0)
20, dose 5 (1)
28, dose 5 (0)
13, dsoe 5 (1)
21, dose 1 (0)
29, dose 1 (0)
14, dose 5 (1)
22, dose 5 (1)
30, dose 5 (1)
8
Simulated Bayesian D-Optimal Design
for ED50 – Summary
 Results from a single implementation
Dose: 1
2
3
4
5
assumed %Response: 30 40 55 65 75
#Responses: 4
2
1
8
#patients: 13 0
4
1 12
observed %Response: 31 50 100 67
6
75
0
-
7
75
0
-
 Bayesian estimated ED50 = dose 2.3
 However, few observations at other than 2 doses due to optimal
design for particular dose-response model
 Dose-Response curve between those two doses could be
interpolated by the underlying fitted model
Should not extrapolate from model outside observed range
2-parameter model (slope, location) forced through 0% and
100%
9
Bayesian Design for the 4-parameter
Logistic model
 Underlying model: Yij  f (di , )  ij , ij ~ N (0,  2 )
f ( d , (  ,  ,  , )   

(1  e( d ) / )
Available doses: d1 ,, d k
Yij is (continuous) response of the j-th subject on the i-th dose, di
 is the vector of parameters of the distribution f
 Patients are randomized in cohorts
 Within each cohort, fixed fraction (e.g. 25%) is allocated to placebo,
 For the remaining patients within cohort, dose is picked adaptively
out of d1 ,, d k
 Doses are picked so that QWV (Quantile Weighted Variance) utility
function is minimized
QWV  q 1 wq Var  f d q  min
Q
Developed by S. Berry for
CytelSim (~2006)
10
Bivariate Models:
Penalized Adaptive D-optimal Designs
 Addresses safety and efficacy simultaneously
 Design is characterized by two dependent binary outcomes (efficacy
and toxicity)
 Similar to univariate model: involves dose-escalation and early stopping
rules
 Similar to Bayesian Sequential D-Optimal Design:
Model-based approach with formal optimality criteria:
“maximize the expected increment of information at each dose”
Instead of Bayesian posterior update, Maximum Likelihood
Estimates of current trial data used for next dose selection
 “Penalized” design: Introduces various constraints that can be
flexible to reflect ethical concerns, cost, sample size, etc.
Dragalin, 2005
11
Bayesian-type Designs
Pros (+) & Cons (-)
+ Minimize observations at doses of little interest (too small or large)
+ CRM assigns doses which migrate & cluster around EDxx
- little info on dose-response away from targeted dose (e.g., ED50)
+ can compensate by targeting 2 or 3 response levels
+ Bayesian D-optimal design efficiently estimates model-based doseresponse curve (& targeted EDxx)
- yields most observations at 2 dose levels to optimally fit model
- model restrictive
- forced through 0% and 100% response levels
- should not extrapolate response levels beyond observed doses
12
Bayesian-type Designs
Pros (+) & Cons (-)
- Subjective nature of assignment of prior (starting) distribution
- could take many observations to overcome an incorrect prior
- Models underlying current methods not general enough for efficacy
endpoints
- 4-parameter model needed to estimate min & max response levels
- Co-factors not included; could confound estimates
+ execute designs within important co-factor levels
- Computations complex; little software available
- Difficult to explain to clients
- Not yet proven substantially better than up-and-down or t-statistic s
designs when aim is estimation of dose-response curve
13
Logistics for Conduct of a
Dose-Adaptive Designed Trial
 Response observable reasonably quickly
 Increased statistical computations / simulations to justify doseadaptive scheme in protocol
 Need on-call person to assess previous response data and generate
dose for next subject
For model-based dose-adaptive designs, need on-call unblinded
statistician for associated analyses
OR, this could be automated via web-based interface (increases
cost)
Rapid transfer of needed data
 Need special packaging or unblinded pharmacist at site to package
selected dose for each patient
14
Remarks (2)
 Logistics of implementation more complicated than usual
parallel group design
Frequent data calls / brief simple analyses
Close contact with sites re: dose assignments
Special packaging (IVRS??)
Drug Supply – needed sufficiently for many possibilities
 Tolerability rule(s) can be added for downward doseassignment if pre-specified AE criteria are encountered
This has been studied in context of Bayesian dose-adaptive
designs, but not in context of up&down designs
 Number of placebo patients maintained as designed for
intended precision vs. that group; could be down-sized, though
15
Dose-Adaptive Design
Summary
 Allocation of dose for next subject based on response(s) of previous
subject(s)
 Random Walk designs: only last subject’s response
 T-statistic (frequentist) designs: all previous subjects’ responses
 Bayesian-type designs: all previous subjects’ responses
 High potential to limit subject allocation to doses of little interest
(too high / too low)
 Maximize information gathered from fixed N
 Ethical advantage over fixed randomization
 More attractive to patients / subjects
 Inference conditional on doses assigned by design, but not overly
important in early development
 Requires more statistical up-front work (simulation)
 No pre-specified allocation schedule; requires ongoing
communication with site regarding allocation
16
Dose-Adaptive Design
Summary
 Bayesian-type designs preferable to estimate doseresponse curve; can also estimate a dose-response quantile
of interest (e.g., EDxx) or (part of?) region of increasing
dose-response
 Complex; heavy computations
 Random Walk & T-statistic Designs focus on quantile(s) of
interest
 Easy to understand & program
 Consider as starting point for implementing dose-adaptive
design
 Let other design features guide towards other adaptive
techniques based on particular experimental situation
 Ongoing incomplete simulations have yet to identify major
advantage of Bayesian-type designs over RW & T, unless
prior information is important to consider.
 Study, comparison, & refinement of these dose-adaptive
designs continues
17
Dose-adaptive study designs offer benefits for
proof-of-concept / Phase IIa clinical trials,
as well as raise issues for continued research
OUTLINE: Dose-Adaptive Designs & Examples
 Definition & Introduction (Jim)
 Frequentist Designs, including Random Walk Designs (Jim)
 3+3 Design for cancer
 Up&Down Design
 Biased Coin Designs
 Simulations of Up&Down Design for Dental Pain Clinical Trial
 Bayesian-type Designs (Inna)
 Continual Reassessment Method (CRM)
 Bayesian D-optimal Design
 Other related approaches
 Bayesian 4-parameter logistic
 Case Study (Bayesian and Adaptive cross-over designs)
 CytelSim Software demo
 Summary & Recommendations (Inna)
 References
Jim Bolognese & Inna Perevozskaya, Sept. 12, 2008
18
Case Study Example
Adaptive Dose-Ranging POC study
By I. Perevozskaya and Y. Tymofyeyev
19
Study Background
 Development phase: Ib
 Strategic objective: generate preliminary D-R info to optimize dose
selection for Phase IIb study
 Caveats:
 Phase Ib will be run using surrogate endpoint
 Future Phase IIb will be driven by clinical endpoint (chronic
symptoms)
 There is no formally established relationship between surrogate and
clinical endpoints dose-response curves, but…
 Dose selected as “sub-maximal” using surrogate endpoint D-R curve is
believed to be “sub-therapeutic” for the clinical endpoint.
20
Study objectives
 (Broad) to demonstrate that a single
administration of drug, compared with
placebo, provides response that varies by
dose
 (Specific)
1. Find “sub-maximal” dose (e.g. ED75 defined as the
dose yielding 75% of the placebo-adjusted maximal
response )
2. Meaningfully describe dose-response relationship
3. Demonstrate that at least one dose is significantly
different from placebo
21
Study Design challenges and Adaptive
design opportunity
 Easy to miss informative dose range with traditional design
 Dose-response (D-R) can be relatively steep in the sloping part of the
D-R curve
 Dose-range & shape of curve = Unknown (and “unknowable” using
PK)
 Dose range to explore is very wide (6 active doses potentially
considered)
 Logistics:
 Primary endpoint captured electronically within 1 day
 The expected subject enrolment rate is not too high
 Endpoint suitable for cross-over design
 Following single-dose administration, 3-7 day washout is sufficient
 3-period (or even 4-period) cross-over could be reasonable
22
Bayesian Adaptive Design Description
 6 active doses and placebo available
 Design uses frequent looks at the data and adaptations
(dose selections) are made after each IA
Patients are randomized in cohorts
Cohort is a small group of patients randomized between IAs
Within each cohort, fixed fraction (e.g. 25%) is allocated to
placebo
For the remaining patients within cohort, dose is picked
adaptively out of D1, ….D6.
Once endpoints for the whole cohort become available,
decision is made about next cohort allocation using Bayesian
algorithm (QWV utility function)
23
Bayesian Adaptive Design
Description (cont.)
The algorithm will try to cluster dose
assignments around the “interesting” part of
dose-response curve (e.g. ED75)
but there will be some spread around it (i.e. not all
patients within cohort will go to the same dose).
The “target” will be moving for each cohort to be
randomized
will depend on the trial information accumulated to the
moment:
• previous cohort’s dose allocations and responses.
24
Bayesian Adaptive Design for the 4Parameter Logistic Model: Details
 Underlying model: Yij  f (di , )  ij , ij ~ N (0,  2 )
f ( d , (  ,  ,  , )   

(1  e( d ) / )
Available doses: d1 ,, d k
Yij is (continuous) response of the j-th subject on the i-th dose, di
 is the vector of parameters of the distribution f
 Patients are randomized in cohorts
 Within each cohort, fixed fraction (e.g. 25%) is allocated to placebo,
 For the remaining patients within cohort, dose is picked adaptively
out of d1 ,, d k
 Doses are picked so that QWV (Quantile Weighted Variance) utility
function is minimized
QWV  q 1 wq Var  f d q  min
Q
Developed by S. Berry for
CytelSim (~2006)
25
Implementation details of
Bayesian Algorithm
 Developed by Scott Berry
 Implemented in Cytel Simulation Bench software developed by
Cytel in collaboration with Merck
 Core idea: algorithm utilizes Bayesian updates of model parameters
after each cohort
 Components of ( , , ,) in 4-param. logistic model are treated as
random with prior distribution (usually flat) placed upon them
 After each cohort’s response, the (posterior) parameter distribution is
updated and model D-R is re-estimated
 The algorithm utilizes Minimum Weighted Variance utility function for
decision making during adaptations
In our example, that translates into next cohort’s dose assignments
are picked so that the variance of the response at the current
estimate of ED75 is as small as possible
26
Flexible Modeling of Dose-Response
With 4-Parameter Logistic Model
Dose Response curves
24
ID1
ID2
ID3
22
Mean Response
ID4
20
ID5
18

5
5
5
5
-4
16
14
12
10
8

15
15
15
25
35

3
3
1
5
4

0.5
0.1
2
1
4
6
0
1
2
3
Doses
4
5
6
27
Bayesian Adaptive Design
Allocation Example
Distribution ofSubjects
Sample size
modeled: N=120
Different dose
allocations of
12 patients in each
cohort are
represented by
different colors (dark
blue is Pbo=D0,
D1 is blue, ….,
brown is D6).
Dose
Dose
Dose
Dose
Dose
10
Number of Subjects
10 cohorts of 12
patients in parallel
design setting
12
Dose 5
Dose 6
8
6
4
2
0
0
1
2
3
4
1
2
3
4
5 6 7
Cohort ID
8
9
10
28
Bayesian Adaptive Design
Example (Cont.)
D-R curve captured "Dose
3" as correct start of
plateau.
Most patients were close to
“Dose 3”
Few patients were on
plateau
30
Mean Response
Assume the "true" max.
effect dose (i.e., the dose to
be "discovered" by the study)
is "midpoint between Dose 2
and Dose 3
Subject Response Plot
40
20
10
0
-10
-20
Subjects
Dose-response curve and
Patient allocations to
each dose at the end of
this example trial
50
40
30
20
10
0
1
30
2
3
26
26
1
5
13
6
0
4
2
3
4
6
10
9
5
6
29
Bayesian Algorithm Allocation rule
 The algorithm clusters
dose assignments
around the “interesting”
part of dose-response
curve
 With some “spread”
around it (i.e. not all
patients within cohort will
go to the same dose).
 The “target” is datadependent and may
change after each IA
30
Performance of Bayesian AD
Under Various Dose-Response scenarios
 8 different dose-response
scenarios were studied,
varying in:
ID1
ID2
ID3
ID4
ID5
ID6
ID7
ID8
18
16
14
12
Mean Response
Magnitude of maximum
treatment effect
Location of the sloping part
of the DR curve
Steepness of the sloping
part of the DR curve
Dose Response curves
10
8
6
4
2
0
 Allowing "true" ED75 to
vary over the dose-range
0
1
2
3
Doses
4
5
6
31
Performance of Bayesian AD Under Various
Dose-Response scenarios (cont.)
 Performance evaluated via simulations (using
CytelSim Software)
 Key criteria for evaluation included
1.
2.
3.
4.
Subject allocation pattern
Precision of picking “right dose” correctly
Power and Type I error for detecting dose-response
Precision of overall D-R estimation across all doses
(measured by MSE)
32
Subject Allocation Pattern:
ED75 centered within the dose range (Curve ID 3)
Dose Response curves
ID1
ID2
ID3
ID4
ID5
ID6
ID7
ID8
18
50
16
45
14
35
12
30
Mean Response
Number of subjects
40
25
20
15
10
5
10
8
6
0
% Allocation
30
4
25
20
15
7.2
10
10
13
17
13
2
0
0
0
1
2
3
Doses
4
5
6
0
1
2
3
Doses
4
5
6
33
Subject Allocation Pattern:
ED75 shifted to the left of dose range (Curve ID 5)
Dose Response curves
ID1
ID2
ID3
ID4
ID5
ID6
ID7
ID8
18
50
16
45
14
35
12
30
Mean Response
Number of subjects
40
25
20
15
10
5
10
8
6
0
% Allocation
30
4
25
23
20
2
15
9.9
10
9.7
8.1
9.5
0
0
0
1
2
3
Doses
4
5
6
0
1
2
3
Doses
4
5
6
34
Subject Allocation Pattern:
ED75 shifted to the right of dose range (Curve ID 4)
Dose Response curves
ID1
ID2
ID3
ID4
ID5
ID6
ID7
ID8
18
45
16
40
14
30
12
25
Mean Response
Number of subjects
35
20
15
10
5
10
8
6
0
% Allocation
30
4
25
19
20
22
2
13
10
0
0
5.9
6.5
1
2
8.4
0
3
Doses
4
5
6
0
1
2
3
Doses
4
5
6
35
Subject Allocation Pattern:
Completely flat dose-response (Curve ID 8)
Dose Response curves
16
60
50
14
40
12
Mean Response
Number of subjects
ID1
ID2
ID3
ID4
ID5
ID6
ID7
ID8
18
Distribution of Subjects
30
20
10
10
8
6
0
% Allocation
40
30
36
25
4
2
20
10
0
0
7.2
6.8
7.4
8.1
9.4
1
2
3
Doses
4
5
0
6
0
1
2
3
Doses
4
5
6
36
Power and Type I Error for Detecting DoseResponse
D-R Curve ID
1*
2
3
4
5
6
7
8
“best dose” vs. pbo
5.0
92.5
89.5
93.5
100.0
92.0
95.5
99.5
Test of slope (dose-resp.)
4.0
98.0
98.5
97.5
100.0
90.0
100.0
100.0
*Power for D-R curve ID 1 is Type I error
37
Precision of D-R estimation: Mean
Squared Errors
Doses
D-R
Scenarios
1
d_0
d_1
d_2
d_3
d_4
d_5
d_6
4.5
2.7
2.4
2.4
2.5
2.9
4.2
2
4.4
3.7
5.0
7.0
6.4
4.6
4.7
3
3.9
5.4
7.3
6.6
3.9
3.2
3.1
4
3.1
2.9
3.1
3.9
5.7
5.1
4.1
5
4.2
6.7
5.9
3.7
3.1
3.4
4.1
6
2.6
2.5
2.5
2.7
3.2
5.0
4.9
7
3.9
3.7
4.6
7.1
6.2
3.3
4.6
8
5.5
9.5
6.5
4.1
3.1
4.0
5.8
38
MSE Efficiency Plots
Curve ID 3 (centered)
Target dose is D3
Curve ID 5 (left-shifted)
dose is between D2&D3
MSE Ratio Plot
Target
MSE Ratio Plot
3.2
3.5
3
2.8
3
MSE Efficiency
MSE Efficiency
2.6
2.4
2.2
2
2.5
2
1.8
1.6
1.5
1.4
0
1
2
3
Doses
4
5
6
1
0
1
2
3
Doses
4
5
6
39
MSE Efficiency Plots (cont.)
Curve ID is 4 (right-shifted)
target dose is D5
Curve ID is 8 (flat)
target dose- NA
MSE Ratio Plot
MSE Ratio Plot
3.4
3.5
3.2
3
3
2.8
MSE Efficiency
MSE Efficiency
2.5
2.6
2.4
2.2
2
1.5
2
1.8
1
1.6
1.4
0
1
2
3
Doses
4
5
6
0.5
0
1
2
3
Doses
4
5
6
40
Summary of Bayesian Design
Simulations
 In all 7 non-flat D-R scenarios, the design maximized allocations
around the “true” ED75.
 In case of flat D-R, most patients were allocated to max dose and
placebo with very little in between
 Type I error was preserved
 Power to detect a dose-response is at least 90%
 Power to detect a significant difference between the best dose and
placebo is at least 89.5%
 For all scenarios, AD design was uniformly more efficient than fixed
design of the same sample size (measured by MSE ratio across
doses )
41
Further Steps
Simulations have shown that Bayesian AD design
may adequately address the Ib study objectives:
A definitive single dose for Phase III was NOT needed
General idea about D-R needed: upper/lower plateau,
sloping part
Due to absence of readily available software for
crossover design, these computer simulations
used N=120 in a parallel design setting
It was anticipated that similar results for power and
Type 1 error could be obtained using N=30 subjects
each contributing 4 measurements
42
Further Steps (cont.)
 Crossover-like framework preferable to parallel design framework
 between/within subject variability => sample size considerations ( 30 vs.
120)
 short drug half-life -> short washout period
 Option 1: modify Bayesian design so that each subject can
contribute multiple measurements
 incorporate repeated-measures in modeling and simulations
 Required involvement of external vendor and extra time to complete
both simulator and randomizer
 Option 2: consider true crossover design but change doses
adaptively
 Non-Bayesian approach
 Could be accomplished in-house within approximately the same
timeframe due to lower computational complexity
 Can be reduced to “standard” crossover if no dose adjustment takes
place
43
Adaptive Crossover Design
Highlights
 Doses explored: {D1, …, D6} of Merck-X + pbo
 Based on:
4 period crossover
Pbo + active doses A,B,C
Values of A, B, C are subset of {D1, …, D6} and change
dynamically after each interim look (~twice weekly)
Time-to-endpoint + washout is 1 week
 Decision rule: pick a subset of doses {A, B, C} from
{D1, …, D6} based on (non-Bayesian) utility function
 Utility function: cumulative score describing proximity of
each dose to target ED75 according to current estimate
of D-R
 D-R estimation: based on isotonic regression model
44
Adaptive X-over Algorithm details:
50
30
0 10
Score, S(q)
70
Score function
0.0
0.2
0.4
0.6
0.8
1.0
Quantile, q
For each 3 dose combination, say {A,B,C}, the score is
S(qA)+S(qB)+S(qC).
45
Adaptive X-over Algorithm details:
Selection of 3-dose combination
Combin.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Dose A
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
4
4
4
5
Dose B
3
3
3
3
4
4
4
5
5
6
4
4
4
5
5
6
5
5
6
6
Dose C
4
5
6
7
5
6
7
6
7
7
5
6
7
6
7
7
6
7
7
7
Score
144 135 135 135 135 135 135 126 126 126 207 207 207 198 198 198 198 198 198 189
Randomly select one of these 3 combinations and use until next
adaptation.
46
Adaptive X-over Algorithm details:
10
Interim D-R estimation at using isotonic
regression
6
*
4
*
3 best dose
combinations (based
on proximity to
ED75):
1. {3, 4, 5}
2. {3, 4, 6}
3. {3, 4, 7}
*
-2
0
2
*
*
-4
Response
8
*
*
1
2
3
4
5
6
7
Algorithm randomly
choose one
combination out of
the 3 best
combinations
Dose
47
Adaptive Cross-Over Design Performance
Characteristics via Simulations
 Several D-R scenarios were explored
 Allocation pattern:
similar to Bayesian design, the algorithm allocates subjects
to the neighborhood of the effective and the highest sub-effective
dose levels
 N=60 patients adequate to achieve ~80% or better
power for “best dose” vs. placebo comparison
Type I error is preserved
 Caveat:
effect sizes were smaller than those explored for Bayesian AD
This contributed to sample size increase from N=30 (30 patients*4
obs.=120obs) for Bayesian AD to N=60 (60 patients*4 obs. =240
obs.) for the adaptive crossover design
48
Simulated dose-response
scenarios
1
2
3
4
5
6
7
Scenario 1
Scenario 2
Scenario 3
Scenario 4
Scenario 5
Scenario 6
8
6
4
2
0
8
6
Response
4
2
0
Scenario 7
Scenario 8
Scenario 9
Scenario 10
Scenario 11
Scenario 12
8
6
4
2
0
8
6
4
2
0
1
2
3
4
5
6
7
1
Dose
2
3
4
5
6
7
49
Power for testing superiority
of a dose level versus placebo
Sc
.
Dose 1 Dose 2 Dose 3 Dose 4 Dose 5 Dose 6
1
0.02
0.02
0.02
0.02
0.02
0.02
2
0.02
0.02
0.02
0.02
0.02
0.91
3
0.02
0.02
0.02
0.02
0.84
0.91
4
0.02
0.02
0.02
0.876
0.84
0.87
5
0.02
0.02
0.728
0.87
0.81
0.85
6
0.02
0.548
0.763
0.84
0.76
0.79
7
0.74
0.612
0.56
0.85
0.50
0.79
8
0.26
0.206
0.23
0.308
0.26
0.80
9
0.25
0.221
0.23
0.314
0.72
0.83
10
0.25
0.21
0.23
0.85
0.74
0.80
11
0.23
0.20
0.69
0.85
0.72
0.79
12
0.22
0.62
0.70
0.84
0.69
0.75
50
Case Study Summary
 After careful examination of many options (3 adaptive+ 3 fixed), doseadaptive crossover design was selected
 Efficiency of crossover AD over “standard” design:
 A “default” 4 period cross-over design will require 44 subjects to detect the
same effect sizes w/ similar power (44*4 = 176 observations)
 But it would explore only 3 doses and placebo
 Adaptive crossover design uses 240=60*4 observations to explore 6 doses
+ pbo
 It is 240 vs. 176 (i.e. 36% more) observations than the standard 4 period
cross-over (as a cost of exploring additional 3 doses)
 However, if 6 doses were explored with standard cross-over design
 prohibitive study duration (7 periods)
 would have 42*7=294 observations
 True efficiency of AD: 294/240=1.23 (23% more efficient)
 Protocol is approved and study is underway.
51
Dose-adaptive study designs offer benefits for
proof-of-concept / Phase IIa clinical trials,
as well as raise issues for continued research
OUTLINE: Dose-Adaptive Designs & Examples
 Definition & Introduction (Jim)
 Frequentist Designs, including Random Walk Designs (Jim)
 3+3 Design for cancer
 Up&Down Design
 Biased Coin Designs
 Simulations of Up&Down Design for Dental Pain Clinical Trial
 Bayesian-type Designs (Inna)
 Continual Reassessment Method (CRM)
 Bayesian D-optimal Design
 Other related approaches
 Bayesian 4-parameter logistic
 Case Study (Bayesian and Adaptive cross-over designs)
 CytelSim Software demo
 Summary & Recommendations (Inna)
 References
Jim Bolognese & Inna Perevozskaya, Sept. 12, 2008
52
Cytel Simulation Bench (CytelSim) Software
for adaptive designs:
Background and History
 Developed by Cytel Statistical Software in collaboration with Merck
Team
 Currently exists as an in-house tool
 Production version planned for near future
 Merck (BARDS) development team:
 Jim Bolognese
 Inna Perevozskaya
 Yevgen Tymofyeyev
 Jason Clark
53
Cytel Simulation Bench (CytelSim) Software
for adaptive designs:
Background and History (cont.)
 Focus: model – based designs for early stage adaptive doseranging studies with multiple IAs
 Development started shortly after 1st BARDS AD grand rounds in
July 2005
 Rationale for development: surging interest in innovative design
methodologies for dose-ranging studies
 Simulations are crucial step for implementation of such designs
 Original goal: to compare performances of a Bayesian design and upand-down (Frequentist) design on the same platform
 Other methods and more sophisticated interface added later as project
needs grew
 This project is still work–in-progress
54
CytelSim Underlying Methodology Overview
 Applicable to early stage adaptive dose-ranging studies
 Provides simulations for model-based design and analysis for such
studies
 General set-up:
 Doses d1 ,  , dk of the drug and d 0 of the placebo are available
for administration
 Subjects are enrolled and treated in groups, known as cohorts.
 The size and composition of each cohort can be user-specified and may
include a fixed number of subjects assigned to placebo
 Active control arm may be included as well
55
CytelSim Methodology Overview (cont.)
 Study Endpoints:
Binary
Continuous
 Bayesian Methods:
4-parameter logistic model
CRM
Reviewed
through
examples and
demo
 Frequentist Methods:
Up & Down Design
Two Up & Down Sequence Design
T-test based Up & Down Design
Design for Umbrella-shaped D-R curve
Note: All methods are available for both endpoints except for CRM
(available for binary endpoint only)
56
T-statistic methodology highlights
 Frequentist method designed to cluster allocations around target
dose of interest
 Can be ran for 1 or 2 targets
 Target is defined as difference from placebo in response or an
absolute value of response variable
 After each IA, T-test Based Up&Down Design assigns all subjects in
a next cohort to a single dose
 Dose chosen by comparing a t-statistic (based on all previous
responses at a dose) to a set of user-defined dose escalation rules:
 -2, -1, 0, +1, and +2 doses
 More details in Example 1.
Note: differences from Bayesian design are highlighted
57
Bayesian Methodology highlights
 Bayesian parametric model-based method designed to cluster
allocations around multiple targets of interest
 Can be ran for virtually any number of targets
 Target is defined as a percentage of maximal response or
difference from placebo or an absolute value of a response variable
 Priority of targets can be reflected through placing weights on them
 After each IA, Bayesian Design assigns all subjects in a next cohort
to multiple doses
 Doses and allocation proportions are chosen by computing
Quantile Weighted Variance (QWV) function (based on all previous
responses at all doses)
 Doses that give the best value of QWV (  smallest variance of
response estimate) are given preference in allocation
Note: differences from T-stat design are highlighted
58
CytelSim Interface Overview
User Interface
(GUI)
Input and store
simulation
parameters
Computational
Algorithm
Graphic
summaries
Output file in
tabular format
Export to Excel
Workbook
60
CytelSim Interface Overview:
Input and store Simulation Parameters
61
CytelSim Interface Overview:
Output file in tabular format
62
CytelSim Interface Overview:
Graphic Summaries
63
CytelSim Software Demo:
Simulating Bayesian Design
Cytel Simulation Bench
64
References
Rosenberger WF, Haines LM. Competing designs for phase I clinical trials: a review. Statistics in
Medicine. 2002; 21:2757-2770
Haines LM, Perevozskaya I, Rosenberger WF. Bayesian optimal designs for phase I clinical trials.
Biometrics. 2003; 59:561-600 (Bayesian D-optimal Design)
Stylianou M and Flournoy N. Dose Finding Using the Biased Coin Up-and-Down Design and Isotonic
Regression. Biometrics. 2002; 58:171-177. (Biased Coin and Up&Down Designs)
Krams M, Lees KR, Hacke W, et al. Acute Stroke Therapy by Inhibition of Neutrophils (ASTIN), an
adaptive dose-response study of UK-279,276 in Acute Ischemic Stroke. Stroke. 2003; 34:25432548
Dougherty TB, Porche VH, Thall PF. Maximum tolerated dose of nalmefene in patients receiving
epidural fentanyl and dilute bupivacaine for postoperative analgesia. Anesthesiology, 2000;
92(4):1010-1016.
Bolognese JA. A monte carlo comparison of three up-and-down designs for dose ranging. Controlled
Clinical Trials, 1983; 4:187-196. (Up&Down Designs)
Bolognese JA, Gomez HJ, Tobert JA, Rucinska EJ. The up-and-down design for dose ranging and its
use in various clinical settings. ASCPT, Atlanta, 1984.
Ivanova, A., Bolognese, J. and Perevozskaya, I. (2008). Adaptive design based on t-statistic for
dose-response trials. Statistics in Medicine, 27, 1581-1592. (T-statistic Design)
He W, Liu J, Bincowitz B, Quan, H. A model-based approach in the estimation of maximum tolerated
dose in phase I cancer clinical trials. MRL Technical report #102, June 2004. (3+3 Design)
65
References (cont.)
Geller NL. Design of phase I and II clinical trials in cancer: a statistician’s view. Cancer Investigations
1984; 2:483–491. (3+3 design in cancer)
Durham SD, Flournoy N. Random walks for quantile estimation. In Statistical Decision Theory and
Related Topics, Gupta SS, Berger JO (eds). Springer: New York, 1994; 467–476. (RWR)
O’Quigley J, Pepe M, Fisher L. Continual reassessment method: a practical design for phase I clinical
trials in cancer. Biometrics 1990; 46:33–48. (CRM)
Babb J, Rogatko A, Zacks S. Cancer phase I clinical trials: efficient dose escalation with overdose
control. Statistics in Medicine 1998; 17:1103 –1120.
Whitehead J, Brunier H. Bayesian decision procedures for dose determining experiments. Statistics in
Medicine1995; 14:885–893 ( decision-theoretic approach)
Dragalin V., Fedorov V. Adaptive model-based designs for dose-finding studies. To appear in Journal
of Statistical Planning and Inference, 2005 (bivariate models)
Reiner E, Paoletti X, O’Quigley J. Operating characteristics of the standard phase I clinical trial design.
Computational Statistics and Data Analysis 1999; 30:303 –315.
Atkinson AC, Donev AN. Optimum Experimental Designs. Oxford: Clarendon, 1992.
66
Dose-adaptive study designs offer benefits for
proof-of-concept / Phase IIa clinical trials,
as well as raise issues for continued research
QUESTIONS
/ COMMENTS
/ DISCUSSION
67
Backups
Additional example of Bayesian Design:
ASTIN trial
Select Simulation results for adaptive
crossover design
68
Customized Bayesian Adaptive Design
Acute Stroke example (ASTIN Trial)
 Single IV infusion of UK-279,276 (neutrophil inhibitory factor) or
placebo within 6 hours of stroke symptom onset
 Bayesian sequential design with real-time efficacy data capture
Continuous reassessment of dose-response
 Patients randomized to
Placebo (at least 15%), or
The 1 of 15 doses which minimizes expected variance of ED95
response
Krams, et al. STROKE (2003)
69
Customized Bayesian Adaptive Design
Acute Stroke example
 Pre-defined stopping rules:
Minimum 500 pts before futility rule could be invoked
Minimum 250 pts before stopping rule for efficacy could be
invoked
Maximum sample size = 1300 pts
 If successful, designed for extension to definitive Phase III trial
 Simulations used to characterize behavior (power) of design
For flat dose-response, 661 median sample size for futility
stopping w/ 5% false positive rate
For 3-point efficacy benefit, 85% of simulations correctly
stopped with median sample size 595
(w/ 4 points, 97% power, median ss 320).
Krams, et al. STROKE (2003)
70
Customized Bayesian Adaptive Design
Acute Stroke example - results
•ΔSSS/Dose curve (diff
from pbo) w/ 95%
posterior credible
intervals
•E at 2 -> efficacy
threshold
•F at 1 -> futility
threshold
Dose of UK-279,276(mg)
71
Customized Bayesian Adaptive Design
Acute Stroke example - results
72
Adaptive crossover additional simulation
results
73
Setup to Evaluate Performance of AD Under
Various Dose-Response scenarios
 AD uses 60 * 4 =240 total observations from 60
subjects.
 12 different dose-response scenarios were studied,
varying in:
Location of the sloping part of the DR curve
Steepness of the sloping part of the DR curve
 Performance of AD was addressed by simulations
incorporation the following features
Poisson distributed subject enrollment
Response generated according to the underlying true D-R,
imposing appropriate correlation structure regarding
between- and within-subject variability.
Delay in response / washout period
Missing observations
74
Performance of Selected AD
 Key criteria for evaluation included
 Subject allocation pattern
 Power for testing superiority of a dose level versus
placebo; Type I error
 Dose selection properties ( right identification of D-R
plateau )
 Simultaneous confidence interval methodology for
isotonic regression is developed in the literature and
can be used for dose-response curve estimation
75
0.
6
Example:
Mean
subject
allocation
7
1
2
3
4
5
6
7
to dose levels and
Dose power
Level
0.10
0.20
Scenario 10, dose-resp: 0, 4, 4, 4, 8, 8, 8
Power vs PLB:0, 0.25, 0.21, 0.23, 0.85, 0.74, 0.8
Proportion
4, 4, 8, 8
0.31, 0.72, 0.83
6
7
1
2
3
4
5
6
7
Dose Level
76
Example: Selecting dose level
that is the onset of D-R plateau
0
Proportion (%)
10
20
30
40
True response at doses:
0, 4, 4, 4, 8, 8, 8
none
2
3
4
Dose
5
6
7
77
Conclusions From Simulations
 On average, the algorithm allocates subjects to the
neighborhood of the effective and the highest subeffective dose levels for the studied D-R scenarios.
Depending on the underlying dose-response
scenario, the average number of observations on the
dose with highest number of subjects ranged from 43
to 60.
 Good estimation of the D-R plateau on set
 High power to declare effective and highest subeffective dose levels superior to placebo.
Depending on the scenario, the power of the AD to
declare the dose with highest number of subjects
significantly different from placebo ranged from 75 to
78
91% with most scenarios yielding power 80% or