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 ) (22 )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