Transcript Study started August, 1987

DOSE SPACING IN EARLY DOSE
RESPONSE CLINICAL TRIAL DESIGNS
Naitee Ting, Ph. D.
Associate Director
Pfizer Global Research & Development
STUDY 1 - WHAT’S NEXT?
25
20
15
Series1
10
5
0
Placebo
20 mg
30 mg
40 mg
STUDY 2
25
20
15
Series1
10
5
0
Placebo
5 mg
10 mg
20 mg
Questions in Designing the First
Dose Response Study
• How many doses to be tested?
• What are the high and low doses?
• What are the spaces between the test doses
(what is the dose spacing)?
• How frequent should subjects be dosed?
• How many subjects for the study?
Dose Response Study Design
•
•
•
•
Selection of control
Selection of endpoints
Fixed dose vs titration dose
Two-stage designs vs Two designs
Dose Response Study Design
• In early Phase II, drug first tested in patients
• Assume maximum tolerable dose (MTD)
known, assume monotonicity
• Efficacy response, toxicity response
• Range and spacing of doses
Limited Number of Fixed Doses
•
•
•
•
Concerns in interpreting titration dose
Multiple center designs
Formulation considerations
Placebo and maximum tolerable dose
(MTD)
• Incorporate active control?
Considerations in Dose
Allocation
• Selecting a wide range of doses
• Find doses to capture the steepest increasing
portion of efficacy dose response curve
• Use of some low doses to help identify the
minimum effective dose (MinED)
• Not very high to be too close to MTD
Binary Dose Spacing
• For 2 active doses, one above 1/2, one
below
• Continue with this fashion to the lower end
• Any cut for 1/p, where p  2
• Non-parametric, model independent
• Applies to titration design, sequential
design, active control, early or late Phase
Compare to Optimal Designs
• For a given model, optimal design allocate
doses according to D-optimality
• The most frequently used model is logistic
E ( yi )  1 /[1  exp( 1   2 xi )]
• Another model is normal cdf (with
parameters m and s)
Criteria for Comparison
• Provide a steeper slope from placebo
• Identify a minimum effective dose (MinED)
Simulation Procedure
• Ten and fifty obs. generated from each dose
• Each obs. is normal with mean from model
and standard deviation of 0.1 & 0.025
• Slopes from placebo to each dose
• Assuming minimum effect is 0.2, MinED is
obtained from lower 95% confidence limit
Table 1. Treatment Group Means, Slopes From Placebo To Each Dose,
And 95% Confidence Limits From Simulated Data Under Different Sample
Sizes And Standard Deviations
Simulation based on Model: with 1 =1.565 and 2 =4.174
E ( yi ) 
1
1  exp(1   2 xi )
BDS doses:
Low = 0.125, Medium = 0.375, High = 0.750
Optimal doses: Low = 0.082, Medium = 0.375, High = 0.668
Mean (Pcbo)
n/group = 10
std. dev. =0.1
std. dev. =0.25
BDS
Opt.
BDS Opt.
n/group = 50
std. dev. =0.1
std. dev. =0.25
BDS
Opt.
BDS
Opt.
0.1804 0.1516
0.1508 0.1747
0.1626
0.2724
0.0833
0.5133
0.3261
0.8170
0.6292
0.2799 0.1382
0.0253 -0.1420
0.4834 0.4883
0.2230 0.2173
0.7871 0.8005
0.5164 0.5266
0.1813 0.1926
Mean (Low) 0.2468 0.2315 0.3351 0.2153
Lower L
-0.0153 -0.0133 -0.1039 -0.2009
Mean (Med) 0.5223 0.5533 0.4792 0.4787
Lower L
0.2588 0.2958 -0.0451 0.0652
Mean (High) 1.8610 0.7624 0.8148 0.8436
Lower L
0.6068 0.5111 0.3679 0.4890
0.2439
0.0311
0.4995
0.2829
0.7544
0.5350
0.1802
Table 2. Simulation Results with 3 Active Doses Using a Logistic Model to
Compare D-optimal Dose Spacing and Binary Dose Spacing of ½ distance
1
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
4
4
4
4
4
4
4
2
Low
Medium
4
6
8
10
12
14
16
18
6
8
10
12
14
16
18
6
8
10
12
14
16
18
B
B
B
B
B
B
B
B
O
O
O
O
B
B
B
O
O
O
O
O
O
O
O
O
B
B
O
O
O
O
O
B
B
B
B
O
O
O
O
O
B
B
B
B
High
B
O
O
O
O
O
O
O
B
O
O
O
O
O
O
O
O
O
O
O
O
O
Overall
B
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
O
MinED
BD2
OP2
OP2
BD1
BD1
BD1
OP2
OP2
BD2
OP2
OP2
OP2
OP2
OP1
BD1
OP1
OP1
OP1
OP1
OP1
OP1
OP1
Table 3. Simulation Results with 4 Active Doses Using a Normal Model to
Compare D-optimal Dose Spacing and Binary Dose Spacing of ½ distance
1
2
0.1
0.2
0.2
0.3
0.3
0.3
0.4
0.4
0.4
0.4
0.5
0.5
0.5
0.5
0.5
0.6
0.6
0.6
0.6
0.1
0.1
0.2
0.1
0.2
0.3
0.1
0.2
0.3
0.4
0.1
0.2
0.3
0.4
0.5
0.1
0.2
0.3
0.4
Low
B
O
B
O
O
B
O
O
B
O
O
O
O
O
B
O
O
B
B
Low Med.
B
B
B
O
O
B
O
O
O
O
O
O
O
O
B
O
O
O
O
Hign Med.
O
O
O
B
B
B
O
O
O
O
O
O
O
O
O
O
O
O
O
High
O
O
O
O
O
O
O
O
O
B
O
O
O
B
B
B
O
B
B
Overall
O
O
O
O
O
O
O
O
O
B
B
O
O
B
B
B
B
O
O
MinED .
BD1
OP2
OP2
OP1
BD2
BD2
OP1
OP2
OP2
OP2
OP1
OP1
BD3
BD3
OP2
OP1
OP1
BD3
BD3
Table 4. Treatment Group Means, Slopes From Placebo To Each Dose, And
95% Confidence Limits From Simulated Data When The Underlying Model Is
Mis-specified
xi
E ( yi )   (22 )1 / 2 exp[ (u  1 )2 / 2 2 ]du
2
2

True Model: 1 = .38 and 2 = .32.
Using optimal design, this model was mis-specified as 1 = .32 and 2 = .38
BDS doses:
Low = 0.125, Medium = 0.375, High = 0.750
Optimal doses (mis-specified model): Low = 0.010, Medium = 0.320, High = 0.630
(the correct doses should be Low = 0.119, Medium = 0.380, High = 0.641)
Simulation performed with n=20 per group and std. dev. = 0.25.
BDS Dose Allocation
Optimal Dose Allocation
Point
Point
Lower L estimate Upper L Lower L estimate
Upper L
Mean (Pcbo)
Mean (Low)
Mean (Med)
Mean (High)
0.0675
0.3648
0.7420
0.1123
0.1958
0.4955
0.8699
Slope Low
Slope Med
Slope High
0.540
0.973
0.989
0.668
1.022
1.010
0.796
1.071
1.031
0.0021
0.2865
0.5797
0.1976
0.2141
0.4997
0.7904
0.202
0.895
0.921
1.575
0.944
0.942
2.948
0.993
0.962
Conclusion
• Assume MTD known and monotonic
relationship
• Intuitive and with wide applications
• Model independent approach vs parametric
optimality - Not much of a comparison
• A general recommendation, not one size fits
all
Analysis of Dose Response
Studies
•
•
•
•
•
Multiple comparison adjustment
Placebo control, active control, or both
Dunnett’s method, Step down method
Linear, quadratic dose response
Minimum effective dose (MinED)
Analysis of Dose Response
Studies
•
•
•
•
Drug safety in dose response studies
Estimation vs hypothesis testing
Exploratory vs confirmatory
Analysis of the entire database