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Adaptive-Dose Finding Using the ‘Maximizing Procedure’: Case Study and Missing Data Simulation - Kenneth Liu, Merck & Co., Inc.
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Adaptive-Dose Finding Using the ‘Maximizing Procedure’: Case Study and Missing Data Simulation - Kenneth Liu, Merck & Co., Inc.

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Kenneth Liu, Merck & Co., Inc. - Speaker at the marcus evans Evolution Summit 2012, held in Wheeling, IL, April 30-May 2, delivered his presentation entitled Adaptive-Dose Finding Using the …

Kenneth Liu, Merck & Co., Inc. - Speaker at the marcus evans Evolution Summit 2012, held in Wheeling, IL, April 30-May 2, delivered his presentation entitled Adaptive-Dose Finding Using the ‘Maximizing Procedure’: Case Study and Missing Data Simulation

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  • 1. Adaptive Dose Finding Usingthe “Maximizing Procedure”:Case Study and Mi i D tC St d d Missing Data Simulation Evolution Summit Wheeling, Wheeling IL May 2, 2012 Kenneth Liu and Richard Entsuah Merck 1
  • 2. Acknowledgements• Anastasia Ivanova• Duane Snavely• Ellen S d Ell Snyder• Joe Herring 2
  • 3. Outline Part 1/3• Case study of adaptive trial – Sample size: Parallel vs X-Over vs Adaptive – Hypotheses – Study design – Anastasia Ivanova s “Maximizing Procedure” Ivanova’s Maximizing Stat Med (2009) – Utility function• Simulation results 3
  • 4. Outline Part 2/3• Study results – Interim analysis 1 – Interim analysis 2 – Final analysis (primary, secondary, and exploratory endpoints) 4
  • 5. Outline Part 3/3• Missing Data Mechanisms In A Dose Finding Ad Fi di Adaptive T i l (Li and E i Trial (Liu d Entsuah, h JBS, 2012) – MCAR – MAR – NMAR – Mixture Missing Mechanism• Simulation results• Conclusion 5
  • 6. Sample SizeGoal Design N/ Total arm NBetter than placebo Parallel 2 arm 69 138 X over 2 period X-over 2-period 18 36+ at least as good as Active Parallel 3 arm 270 810Control X-over 3 X 3-period i d 46 138+ Dose finding among 5 Parallel 7 arm 270 1890doses X-over 3-period 46 690+ Constraint of N < 200 “Maximizing NA 200 Procedure Procedure” using a 3 3- period X-over 6
  • 7. Study Design3-Period, 6-Sequence C3 P i d 6 S CrossoverSequence Peri d 1 WO Peri d 2 WO Peri d 3 Period Period Period1 MK Pbo AC2 Pbo AC MK3 AC MK Pbo4 MK AC Pbo5 Pbo MK AC6 AC Pbo MK 3, 5, 8, 10, or 12 mg 7
  • 8. “Maximizing Procedure” Example Maximizing Procedure e e e true e utility l e e mg 0 3 5 8 10 12 8
  • 9. “Maximizing Procedure” Example Maximizing Procedure Dose response D o estimated using weighted quadratic o regression for efficacy and isotonic utility l regression for o tolerability mg 0 3 5 8 10 12 cum N 2 2 2 9
  • 10. “Maximizing Procedure” Example Maximizing Procedure o o o utility l o mg 0 3 5 8 10 12 cum N 4 2 4 2 10
  • 11. “Maximizing Procedure” Example Maximizing Procedure o o o utility l o mg 0 3 5 8 10 12 cum N 6 4 6 2 11
  • 12. “Maximizing Procedure” Example Maximizing Procedure o o o o utility l o mg 0 3 5 8 10 12 cum N 8 2 6 6 2 12
  • 13. “Maximizing Procedure” Example Maximizing Procedure o o o o utility l o mg 0 3 5 8 10 12 cum N 10 2 8 8 2 13
  • 14. “Maximizing Procedure” Example Maximizing Procedure o o o o utility l o mg 0 3 5 8 10 12 cum N 12 2 8 10 4 14
  • 15. “Maximizing Procedure” Example Maximizing Procedure o o o mode dose (vs Placebo) o utility l top 2 dose (vs Active Control) o mg 0 3 5 8 10 12 cum N 14 2 8 12 7 15
  • 16. AN1 8 Example of Patient Enrollment Chart with Maximizing Procedure Implementation Study begins with assignment to 8 and 10 mg MK doses for MK dosing periods: Placebo Active Control • first patient is randomized as noted above • each line represents a two-week treatment period and space b t i d d between li lines represents t a one-week washoutWk: 0 2 4 6 8 10 12 14 16 18 20 22 … 16
  • 17. AN1 8 Example of Patient2 103 8 Enrollment Chart 1045 10 with Maximizing Procedure6 8 Implementation7 108 89 1010 811 812 1013 10 8 MK14 Placebo Enrollment continues over time. Active Control When we have, say, 2 p y patients’ worth of information on placebo, active control and each dose of MK, we perform the first adaptive evaluation.Wk: 0 2 4 6 8 10 12 14 16 18 20 22 … 17
  • 18. Adaptive Analysis: # 1 #2 etc….AN1 8 Example of Patient2 103 8 Enrollment Chart 1045 10 with Maximizing Procedure6 12 Implementation7 108 129 1010 811 1212 1013 10 8 MK1415 1016 12 Placebo1718 10 Active Control19202122 122324 10252627…Wk: 0 2 4 6 8 10 12 14 16 18 20 22 … Subsequent adaptive analyses will be conducted bi-weekly if at least two new bi weekly periods of information are available on the new MK doses. Dose assignment for MK periods will be assigned “just-in-time”. 18
  • 19. Utility Function δd U d = U (Δ d , δ d ) = Δ d − 10Δd=Efficacy: MK – Active Controlδd=Tolerability composite of (Events of Clinical Interest, Drug Rel Discon, Drug Rel SAE): MK - placebod ∈ 5 MK doses 19
  • 20. 20
  • 21. N Distribution True Utility =x N =o Equal Allocation=+ 1 2 3 4 5 6 7 Scenario 7 Scenario 7 Scenario 7 0% 15% MCAR 30% MCAR o x + x x x x x o + x x x x x x x x x x x x 200 o + o + 150 o + o + 100 o o 50 o + + + o + + o o + + + o + + o o o o o + + + o o + + oN D istribu tio n Scenario 6 Scenario 6 Scenario 6 0% 15% MCAR 30% MCAR 200 o + x o + x x o + o + 150 x x x x x x o + o + 100 x x x x x x o o 50 o o x x o x + + + + + o + + o + + + o o o o + + + + o + o o o 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Dose 21
  • 22. Scenario 7 Scenario 7 Scenario 7 0% 15% MCAR 30% MCAR 200 150 100 50N Distribution 0 Scenario 6 Scenario 6 Scenario 6 0% 15% MCAR 30% MCAR 200 150 100 50 0 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Dose 22
  • 23. Outline Part 2• Study results – Interim analysis 1 – Interim analysis 2 – Final analysis (primary, secondary, and exploratory endpoints) 23
  • 24. Distribution of Patients Treatment N Placebo 117 MK 5 mg 10 MK 8 mg 25 MK 10 mg 46 MK 12 mg 38 MK (top 2 doses‡ ) 84 Active Control 111 24
  • 25. Interim Analyses 1 and 2 y Estimated Differences Difference in LS Means (95% CI) IA 1 IA 2 MK 5 mg vs Placebo -1 ( -6, 4) -1 ( -6, 2) MK 8 mg vs Placebo 1 ( -2, 5) 2 ( -1, 5) MK 10 mg vs Placebo 1 (-2, 4) 0 ( -2, 3) MK 12 mg vs Placebo 1 ( -2, 4) 1 ( -1, 3) MK (top 2 doses‡ ) vs Placebo 1 ( -1 3) 1, 1 ( -1 2) 1, Active Control vs Placebo 6 ( 4, 7) 4 ( 3, 6)‡ This collapses MK doses of 10 and 12 mg. No dose-response Active Control much better 25
  • 26. AE Discontinuations + Event of Clinical I Cli i l Interest MK Active Placebo Control 3mg 5mg 8mg 10mg 12mg Total N=0 N=10 N=25 N=46 N=38 N=119 N=111 N=117 n(%) n(%) n(%) n(%) n(%) n(%) n(%) n(%)AE Discontinuations + Event 3 8 13 24 2 1 of Clinical Interest ( ) ( ) ( 12.0 ) ( 17.4 ) ( 34.2 ) ( 20.2 ) ( 1.8 ) ( 0.9 ) 26
  • 27. Secondary and Exploratory Endpoints E d i Pairwised Comparison S1 S2 E1 E2 E3 E4 MK 5 mg vs Placebo MK 8 mg vs Placebo * MK 10 mg vs Placebo * * * MK 12 mg vs Placebo * * * * * MK (top 2 doses‡ ) vs Placebo * * * * * * Active Control vs Placebo *‡ This collapses MK doses of 10 and 12 mg.* p<0.05 27
  • 28. Outline Part 3• Missing Data Mechanisms In A Dose Finding Ad Fi di Adaptive T i l (Li and E i Trial (Liu d Entsuah, h JBS, 2012) – MCAR – MAR – NMAR – Mixture Missing Mechanism• Simulation results• Conclusion 28
  • 29. Missing Data Mechanisms g• MCAR – observed d t are a random sample of b d data d l f the complete data - “flip a coin” – analysis of completers is unbiased• MAR – missingness depends on observed data – Pr(R2=1|Y1,Y2,Y3,X) = Pr(R2=1|Y1,X) – proc mixed assumes MAR• NMAR – missingness depends on datapoint itself “nonignorable missingness” 29
  • 30. Mixture Missing Mechanism Mix MixEq MCAR 10% 33% MAR 40% 33% NMAR 50% 33% 30
  • 31. Simulation Assumptions• 3000 runs• MVN(mu,sd=7) MVN(mu sd=7)• correlation=0.5• 1 sided T-test alpha=0.025• 7 scenarios• missing 0%, 15%, 30% 31
  • 32. N for Optimal Dose Maximizing Procedure=o Equal Allocation =+ 0% 15% 30% 0% 15% 30% Scenario 7 Scenario 7 Scenario 7 Scenario 7 Scenario 7 MCAR MAR Mix MixEq NMAR o 80 o o o o o 70 o o o o 60 o 50 + 40 + + + + +N for Optimal Dose 30 + + + + + Scenario 6 Scenario 6 Scenario 6 Scenario 6 Scenario 6 MCAR MAR Mix MixEq NMAR 80 o o o o o 70 o o 60 o o o o 50 40 + + + + + + 30 + + + + + 0% 15% 30% 0% 15% 30% 0% 15% 30% % Missing 32
  • 33. Power for Optimal Dose p Maximizing Procedure=o Equal Allocation =+ 0% 15% 30% 0% 15% 30% Scenario 7 Scenario 7 Scenario 7 Scenario 7 Scenario 7 MCAR MAR Mix MixEq NMAR 0.6 0.4 0.2Power for Optima Dose o o o o o o o + + o + + + + + + + + o + o o al 0.0 00 Scenario 6 Scenario 6 Scenario 6 Scenario 6 Scenario 6 MCAR MAR Mix MixEq NMAR o + o o 0.6 + o + o o o + + + + o 0.4 + + o + o + 0.2 o 0.0 00 0% 15% 30% 0% 15% 30% 0% 15% 30% % Missing 33
  • 34. Bias in Efficacy Estimation True =x Maximizing Procedure Estimate=o Equal Allocation Estimate =+ 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Scenario 7 Scenario 7 Scenario 7 Scenario 7 Scenario 7 Scenario 7 0% 30% MCAR 30% MAR 30% Mix 30% MixEq 30% NMAR o o + + + + + + + 22 o o + + + + + + + o o o + + + + + + o o + o o o o 21 + + + + + + + o o o o o o o o o o o o o o o x x x x o o o x x x x o + + + + + + + + + + + + + + x x x x x x x x x x x x x x x x x x x x x x x x o o x x x x x x x x x x 20 o o o o o o o o 19 18 cacy Scenario 6 Scenario 6 Scenario 6 Scenario 6 Scenario 6 Scenario 6Effic 0% 30% MCAR 30% MAR 30% Mix 30% MixEq 30% NMAR 22 o + + + + + o + + + + + + 21 o o o + + + o o + + + + o + o o + + o o o + o o o + o o o + + + + + o o x x o x x x + + + + + o o x 20 o o x x o x x x o x x x x x o o x x x x x + x x x x o x x x x x o o o + + o o o 19 x + o x + x x + x x o o + 18 x o + x o + x x x x 1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7 Dose 34
  • 35. Conclusions• Introducing the “Maximizing Procedure” (Ivanova 2009)• In our study, primary failed but secondary and exploratory endpoints succeeded p y p• Adaptive dose finding studies may yield biased estimates due to – adaptation, bad doses biased down good doses bias up – missing data mechanism, truncated distribution used in NMAR and Mixture Missing Mechanism (Equal allocation has homogeneous bias, “Maximizing Procedure” has non-homogeneous bias)• Future work: burn-in, pattern mixture model 35
  • 36. ReferencesAnastasia Ivanova, Ken Liu, Ellen Snyder, Duane Snavely. y y " An Adaptive Design for Identifying the Dose with the Best Efficacy/Tolerability Profile with Application to a Crossover Dose-Finding Study." pp g y Statistics in Medicine, 2009, 28:2941–2951.Kenneth Liu and Richard Entsuah “Missing Data Mechanisms In A Dose Finding Adaptive Trial” Trial Journal of Biopharmaceutical Statistics, 22: 329– 337, 2012. ISSN: 1054-3406 print/1520-5711 online. DOI: 10 1080/10543406 2010 536871 10.1080/10543406.2010.536871.Applied Longitudinal Analysis. Garrett M. Fitzmaurice , Nan M. Laird , and James H. Ware . Hoboken, NJ: Wiley, 2004. Wiley 2004 36