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

1. Adaptive Dose Finding Using
the “Maximizing Procedure”:
Case Study and Mi i D t
C 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 Size
Goal Design N/ Total
arm N
Better 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 270 810
Control
X-over 3
X 3-period
i d 46 138
+ Dose finding among 5 Parallel 7 arm 270 1890
doses
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 Design
3-Period, 6-Sequence C
3 P i d 6 S Crossover
Sequence Peri d 1 WO Peri d 2 WO Peri d 3
Period Period Period
1 MK Pbo AC
2 Pbo AC MK
3 AC MK Pbo
4 MK AC Pbo
5 Pbo MK AC
6 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. AN
1
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 washout
Wk: 0 2 4 6 8 10 12 14 16 18 20 22 …
16

17. AN
1
8 Example of Patient
2
10
3 8 Enrollment Chart
10
4
5 10 with Maximizing Procedure
6 8 Implementation
7 10
8 8
9 10
10 8
11 8
12 10
13 10
8
MK
14
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….
AN
1
8 Example of Patient
2
10
3 8 Enrollment Chart
10
4
5 10 with Maximizing Procedure
6 12 Implementation
7 10
8 12
9 10
10 8
11 12
12 10
13 10
8
MK
14
15 10
16 12 Placebo
17
18
10
Active Control
19
20
21
22 12
23
24
10
25
26
27
…
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 −
10
Δd=Efficacy: MK – Active Control
δd=Tolerability composite of (Events of Clinical Interest,
Drug Rel Discon, Drug Rel SAE):
MK - placebo
d ∈ 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
+ +
o
N 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
50
N 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
0.2
Power 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 6
Effic
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. References
Anastasia 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