Adaptive-Dose Finding Using the ‘Maximizing Procedure’: Case Study and Missing Data Simulation -...

Adaptive Dose Finding Using Adaptive Dose Finding Using the “Maximizing Procedure”: C St d d Mi i D t Case Study and Missing Data

SimulationEvolution Summit

Wheeling ILWheeling, IL

May 2, 2012

Kenneth Liu and Richard EntsuahMerck

1

AcknowledgementsAcknowledgements

• Anastasia IvanovaAnastasia Ivanova• Duane Snavely

Ell S d• Ellen Snyder• Joe Herring

2

Outline Part 1/3Outline Part 1/3

• Case study of adaptive trialCase study of adaptive trial– Sample size: Parallel vs X-Over vs Adaptive– Hypotheses– Hypotheses– Study design

Anastasia Ivanova’s “Maximizing Procedure” – Anastasia Ivanova s Maximizing Procedure” Stat Med (2009)Utility function– Utility function

• Simulation results

3

Outline Part 2/3Outline Part 2/3

• Study results Study results – Interim analysis 1– Interim analysis 2– Interim analysis 2– Final analysis (primary, secondary, and

exploratory endpoints)exploratory endpoints)

4

Outline Part 3/3• Missing Data Mechanisms In A Dose

Fi di Ad i T i l (Li d E h

Outline Part 3/3

Finding Adaptive Trial (Liu and Entsuah, JBS, 2012)– MCAR– MCAR– MAR– NMARNMAR– Mixture Missing Mechanism

• Simulation resultsSimulation results• Conclusion

5

Sample SizeSample SizeGoal Design N / Total

arm NBetter than placebo Parallel 2 arm 69 138

X-over 2-period 18 36X over 2 period 18 36+ at least as good as Active Control

Parallel 3 arm 270 810

X 3 i d 46 138X-over 3-period 46 138+ Dose finding among 5 doses

Parallel 7 arm 270 1890

X-over 3-period 46 690+ Constraint of N < 200 “Maximizing

Procedure” using a 3-NA 200

6

Procedure using a 3period X-over

Study Design3 P i d 6 S CSequence Peri d 1 WO Peri d 2 WO Peri d 3

3-Period, 6-Sequence CrossoverSequence Period 1 WO Period 2 WO Period 3

1 MK Pbo AC

2 Pbo AC MK

3 AC MK Pbo

4 MK AC Pbo

5 Pbo MK AC5 Pbo MK AC

6 AC Pbo MK

7

3, 5, 8, 10, or 12 mg

“Maximizing Procedure” ExampleMaximizing Procedure Example

ee

ee e

true l

eutility e

eemg 0 3 5 8 10 12

8

“Maximizing Procedure” ExampleMaximizing Procedure Example

D o

Dose response estimated using weighted quadratic

o

l

quadratic regression for efficacy and isotonic utility

oisotonic regression for tolerability

mg 0 3 5 8 10 12

9cum N 2 2 2

“Maximizing Procedure” ExampleMaximizing Procedure Example

o oo

lutility o

mg 0 3 5 8 10 12

10cum N 4 2 4 2

“Maximizing Procedure” ExampleMaximizing Procedure Example

o oo o

lutility

o

mg 0 3 5 8 10 12

11cum N 6 4 6 2

“Maximizing Procedure” ExampleMaximizing Procedure Example

o oo o

lo

utilityo

o

mg 0 3 5 8 10 12

12cum N 8 2 6 6 2

“Maximizing Procedure” ExampleMaximizing Procedure Example

oo

o o

lo

utilityo

o

mg 0 3 5 8 10 12

13cum N 10 2 8 8 2

“Maximizing Procedure” ExampleMaximizing Procedure Example

oo o

lo

utilityo

o

mg 0 3 5 8 10 12

14cum N 12 2 8 10 4

“Maximizing Procedure” ExampleMaximizing Procedure Example

o oo

l

o

o mode dose (vs Placebo)utility

o

otop 2 dose (vs Active Control)

mg 0 3 5 8 10 12

15cum N 14 2 8 12 7

8 Example of PatientEnrollment Chart

AN1

with Maximizing ProcedureImplementation

MK

PlaceboStudy begins with assignment to 8 and 10 mgdoses for MK dosing periods:

Active Control• first patient is randomized as noted above• each line represents a two-week treatment

i d d b t li tperiod and space between lines represents a one-week washout

Wk: 0 2 4 6 8 10 12 14 16 18 20 22 …

16

8 Example of PatientEnrollment Chart

108

AN123

with Maximizing ProcedureImplementation

1010

10

8

8

10

3456789

8

MK

Placebo

8

10

810

1011121314 8

Active ControlEnrollment continues over time.

When we have, say, 2 patients’ worth of y pinformation 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

8 Example of PatientEnrollment Chart

108

AN123

Adaptive Analysis: # 1 # 2 etc….

12

with Maximizing ProcedureImplementation

1010

10

8

12

10

3456789

MK

Placebo

8

10

1210

10111213141516

8

1210

Active Control16171819202122

12

10

122324252627…

10

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

18

Subsequent adaptive analyses will be conducted bi weekly if at least two new periods of information are available on the new MK doses.Dose assignment for MK periods will be assigned “just-in-time”.

Utility FunctionUtility Function

( ) δ( )10

, ddddd UU δδ −Δ=Δ=

Δd=Efficacy: MK – Active Control δd=Tolerability composite of (Events of Clinical Interest, Drug Rel Discon, Drug Rel SAE): MK - placebo

dosesMK 5∈d

19

20

N DistributionTrue Utility =xN =oEqual Allocation=+

o ox x x x x x+ +0%

Scenario 7

1 2 3 4 5 6 7

o o

x x x x x x

+ +

15% MCARScenario 7

200x x x x x x30% MCARScenario 7

o o+ +

100

150o o+ +

Dis

tribu

tion

o ox+ +0%

Scenario 6

x15% MCARScenario 6

x30% MCARScenario 6

oo

o o o+ + + + + oo

o o o+ + + + +50

o oo o o+ + + + +

N D

100

150

200 o o

x

x

x

x

x

+ +o o

x

x

x

x

x

+ +o o

x

x

x

x

x

+ +

50

100

o

oo

o o

x x

x+ + + + + oo

oo o

x x

x+ + + + + o

oo o o

x x

x+ + + + +

21Dose

1 2 3 4 5 6 7 1 2 3 4 5 6 7

Scenario 7 Scenario 7 Scenario 70%

Scenario 715% MCARScenario 7

150

200

30% MCARScenario 7

50

100

N D

istri

butio

n

200

0%Scenario 6

15% MCARScenario 6

30% MCARScenario 6

0

100

150

0

50

1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7

22Dose

1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7

Outline Part 2Outline Part 2

• Study results Study results – Interim analysis 1– Interim analysis 2– Interim analysis 2– Final analysis (primary, secondary, and

exploratory endpoints)exploratory endpoints)

23

Distribution of Patients

Treatment N Placebo 117 MK 5 mg 10 MK 8 mg 25

MK 10 46 MK 10 mg 46 MK 12 mg 38

MK (top 2 doses‡ ) 84 MK (top 2 doses ) 84 Active Control 111

24

Interim Analyses 1 and 2y

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 2) MK (top 2 doses ) vs Placebo 1 ( 1, 3) 1 ( 1, 2) 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

AE Discontinuations + Event of Cli i l IClinical Interest

MK Active Control

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 1AE Discontinuations + Event of Clinical Interest

( ) ( )

3 ( 12.0 )

8 ( 17.4 )

13 ( 34.2 )

24 ( 20.2 )

2 ( 1.8 )

1 ( 0.9 )

26

Secondary and Exploratory E d iEndpoints

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 * * * * * * MK (top 2 doses ) vs Placebo Active Control vs Placebo * ‡ This collapses MK doses of 10 and 12 mg. * p<0.05

27

Outline Part 3• Missing Data Mechanisms In A Dose

Fi di Ad i T i l (Li d E h

Outline Part 3

Finding Adaptive Trial (Liu and Entsuah, JBS, 2012)– MCAR– MCAR– MAR– NMARNMAR– Mixture Missing Mechanism

• Simulation resultsSimulation results• Conclusion

28

Missing Data Mechanismsg• MCAR

b d d t d l f – observed data are a random sample of the complete data - “flip a coin”

– analysis of completers is unbiasedanalysis of completers is unbiased• MAR

– missingness depends on observed data– missingness depends on observed data– Pr(R2=1|Y1,Y2,Y3,X) = Pr(R2=1|Y1,X)– proc mixed assumes MARproc mixed assumes MAR

• NMAR– missingness depends on datapoint itself

29

missingness depends on datapoint itself “nonignorable missingness”

Mixture Missing MechanismMixture Missing MechanismMix MixEqMix MixEq

MCAR 10% 33%MCAR 10% 33%

MAR 40% 33%

NMAR 50% 33%

30

Simulation AssumptionsSimulation Assumptions

• 3000 runs• MVN(mu sd=7) MVN(mu,sd=7) • correlation=0.5• 1 sided T-test alpha=0.025• 7 scenarios7 scenarios• missing 0%, 15%, 30%

31

N for Optimal DoseMaximizing Procedure=oEqual Allocation =+

N for Optimal Dose

o

o

MCARScenario 7

0% 15% 30%

o

MARScenario 7

o

MixScenario 7

0% 15% 30%

o

MixEqScenario 7

70

80

o

NMARScenario 7

se

o

++

o

+

o

+

o

+40

50

60o

+

N fo

r Opt

imal

Do

70

80 o

o

MCARScenario 6

o

MARScenario 6

o

MixScenario 6

o

MixEqScenario 6

o

NMARScenario 6

+ + + + 30+

30

40

50

60o

++

o

+

o

+

o

+

o

+

32% Missing

30

0% 15% 30%

+ +

0% 15% 30%

+ +

0% 15% 30%

+

Power for Optimal Dose

0% 15% 30% 0% 15% 30%

Maximizing Procedure=oEqual Allocation =+

p

MCARScenario 7

0% 15% 30%

MARScenario 7

MixScenario 7

0% 15% 30%

MixEqScenario 7

0.6

NMARScenario 7

al D

ose

o o o+ + + o o+ + o o+ + o o+ + 0 0

0.2

0.4

o o+ +

Pow

er fo

r Opt

ima

0.6

oo

o

+

+

MCARScenario 6

oo+

MARScenario 6

o+

MixScenario 6

o+

MixEqScenario 6

+

NMARScenario 6

o o o 0.0o o

0 0

0.2

0.4+ +

o+ o+ o

o

+

33% Missing

0.0

0% 15% 30% 0% 15% 30% 0% 15% 30%

Bias in Efficacy Estimation

Scenario 7

1 2 3 4 5 6 7

Scenario 7 Scenario 7

1 2 3 4 5 6 7

Scenario 7 Scenario 7

1 2 3 4 5 6 7

Scenario 7

True =xMaximizing Procedure Estimate=oEqual Allocation Estimate =+

0%Scenario 7

30% MCARScenario 7

o o o o o

o+ + + + + + +

30% MARScenario 7

o

o o o o

o+ + + + + + +

30% MixScenario 7

oo o o

o+ + + + + + +

30% MixEqScenario 7

21

22

o

o o o oo

o+ + + + + + +30% NMARScenario 7

cacy Scenario 6 Scenario 6 Scenario 6 Scenario 6 Scenario 6 Scenario 6

o o o o o o

o+ + + + + + +x x x x x x x o o o o o o

o+ + + + + + +x x x x x x xo o ox x x x x x x

o ox x x x x x xo o o ox x x x x x x

18

19

20

ox x x x x x x

Effi

c

21

22

0%Scenario 6

30% MCARScenario 6

o o o oo

+ + + + +

30% MARScenario 6

o o o o

o

+

+ + + + +

30% MixScenario 6

o oo+ + + + +

30% MixEqScenario 6

oo o o o

o

++

+ + + + +

30% NMARScenario 6

18

19

20

1 2 3 4 5 6 7

o

o

o o o oo

+

+

+ + + + +

x

x

x x x x x

o

o

o o oo

o

+

+

+ + + + +

x

x

x x x x x

1 2 3 4 5 6 7

o

oo o

+

+

x

x

x x x x xo o

o o+

+

x

x

x x x x x

1 2 3 4 5 6 7

oo

o o o o

+

+

x

x

x x x x x oo

x

x

x x x x x

34

Dose

1 2 3 4 5 6 7 1 2 3 4 5 6 7 1 2 3 4 5 6 7

ConclusionsConclusions• Introducing the “Maximizing Procedure” (Ivanova 2009)

• In our study, primary failed but secondary and exploratory endpoints succeededp y p

• Adaptive dose finding studies may yield biased estimates due todue to– adaptation, bad doses biased down good doses bias up– missing data mechanism, truncated distribution used

in NMAR and Mixture Missing Mechanism (Equal in NMAR and Mixture Missing Mechanism (Equal allocation has homogeneous bias, “Maximizing Procedure” has non-homogeneous bias)

35• Future work: burn-in, pattern mixture model

ReferencesReferencesAnastasia 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 yStatistics in Medicine, 2009, 28:2941–2951.

Kenneth Liu and Richard Entsuah “Missing Data Mechanisms In A Dose Finding Adaptive Trial” Mechanisms In A Dose Finding Adaptive Trial Journal of Biopharmaceutical Statistics, 22: 329–337, 2012. ISSN: 1054-3406 print/1520-5711 online. DOI: 10 1080/10543406 2010 536871 DOI: 10.1080/10543406.2010.536871.

Applied Longitudinal Analysis. Garrett M. Fitzmaurice , Nan M. Laird , and James H. Ware . Hoboken, NJ: Wiley 2004

36

Wiley, 2004.