DOSE SPACING IN EARLY DOSE RESPONSE CLINICAL TRIAL DESIGNS

Naitee Ting, Ph. D.

Associate Director

Pfizer Global Research & Development

STUDY 1 - WHAT’S NEXT?

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Placebo 20 mg 30 mg 40 mg

Series1

STUDY 2

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Placebo 5 mg 10 mg 20 mg

Series1

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

• Another model is normal cdf (with parameters and )

)]exp(1/[1)( 21 ii xyE

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 

BDS doses: Low = 0.125, Medium = 0.375, High = 0.750Optimal doses: Low = 0.082, Medium = 0.375, High = 0.668  

n/group = 10 n/group = 50std. dev. =0.1 std. dev. =0.25 std. dev. =0.1 std. dev. =0.25 BDS Opt. BDS Opt. BDS Opt. BDS Opt.

 Mean (Pcbo) 0.1804 0.1516 0.1813 0.1926 0.1508 0.1747 0.1626 0.1802 Mean (Low) 0.2468 0.2315 0.3351 0.2153 0.2724 0.2439 0.2799 0.1382 Lower L -0.0153 -0.0133 -0.1039 -0.2009 0.0833 0.0311 0.0253 -0.1420Mean (Med) 0.5223 0.5533 0.4792 0.4787 0.5133 0.4995 0.4834 0.4883 Lower L 0.2588 0.2958 -0.0451 0.0652 0.3261 0.2829 0.2230 0.2173Mean (High) 1.8610 0.7624 0.8148 0.8436 0.8170 0.7544 0.7871 0.8005 Lower L 0.6068 0.5111 0.3679 0.4890 0.6292 0.5350 0.5164 0.5266

)exp(1

1)(

21 ii xyE

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 Low Medium High Overall MinED

2 4 B O B B BD2 2 6 B O O O OP2 2 8 B B O O OP2 2 10 B B O O BD1 2 12 B O O O BD1 2 14 B O O O BD1 2 16 B O O O OP2 2 18 B O O O OP2 3 6 O O B O BD2 3 8 O B O O OP2 3 10 O B O O OP2 3 12 O B O O OP2 3 14 B B O O OP2 3 16 B O O O OP1 3 18 B O O O BD1 4 6 O O O O OP1 4 8 O O O O OP1 4 10 O O O O OP1 4 12 O B O O OP1 4 14 O B O O OP1 4 16 O B O O OP1 4 18 O B O O 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 Low Low Med. Hign Med. High Overall MinED .

0.1 0.1 B B O O O BD1 0.2 0.1 O B O O O OP2 0.2 0.2 B B O O O OP2 0.3 0.1 O O B O O OP1 0.3 0.2 O O B O O BD2 0.3 0.3 B B B O O BD2 0.4 0.1 O O O O O OP1 0.4 0.2 O O O O O OP2 0.4 0.3 B O O O O OP2 0.4 0.4 O O O B B OP2 0.5 0.1 O O O O B OP1 0.5 0.2 O O O O O OP1 0.5 0.3 O O O O O BD3 0.5 0.4 O O O B B BD3 0.5 0.5 B B O B B OP2 0.6 0.1 O O O B B OP1 0.6 0.2 O O O O B OP1 0.6 0.3 B O O B O BD3 0.6 0.4 B O O B O 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  

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 = 0.750Optimal 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) 0.1123 0.1976Mean (Low) 0.0675 0.1958 0.0021 0.2141Mean (Med) 0.3648 0.4955 0.2865 0.4997Mean (High) 0.7420 0.8699 0.5797 0.7904 Slope Low 0.540 0.668 0.796 0.202 1.575 2.948Slope Med 0.973 1.022 1.071 0.895 0.944 0.993Slope High 0.989 1.010 1.031 0.921 0.942 0.962

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i duuyE ]2/)(exp[)2()( 22

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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