1. Handling Missing Not at Random Data for Safety Endpoint in the Multiple Dose Titration Clinical Pharmacology Trial
Li Fan*, Tian Zhao, Patrick Larson
Merck Research Laboratories
Joint Statistical Meetings
Vancouver, CA
Aug 1, 2018

2. Outline:
Introduction
Analyses methods
Simulation
Conclusions

3. Introduction
Study endpoint and design in a multiple-dose titration trial
Objective: To determine the treatment effect on a safety endpoint at the last visit
Endpoint: change from the baseline in the safety endpoint, like heart rate.
Rational for the titration: Due to potential safety/tolerability issues, like GI and heart rate increasing, use of titration regimen can mitigate the Symptoms of AE.
Design:
Treatment
Week1
Week2
Week3
Week4
Week5
Panel A
Active
Dose 1
Dose 3
Dose 5
Dose 7
Dose 9
Placebo
Panel B
Dose 2
Dose 4
Dose 6
Dose 8
Dose 10

4. Introduction Missing not at random (MNAR)
The probability of a missing value depends on the variable which is missing
Example: In a multiple-dose titration trial, Missing pattern has a possible link to treatment intolerability, a down dosing (change subsequent patient dosing) may be required due to drug-related heart rate increase, etc.

5. Introduction
For handling missing data, the agency’s recommendation is to input as the one in the placebo group.
This is more appropriate for endpoints with respect to efficacy, but not for the safety endpoint, like heart rate.
Motivation:
To see the impact of the missing not at random on the treatment related effects for the safety endpoint;
To compare among 3 competing analysis methods

6. Three Competing Analysis Methods
Method M1: Mixed Effect Model without Imputation
Method M2: Completers Analyses (Only subjects that have complete information)
Method M3: Multiple Imputation (Imputation first)
Proc Mixed data=data_long;
Model cfb = base group time group*time/ddfm=kr;
Random subjid;
Estimate 'active - pbo at last visit' group 1 -1 group*time
Based on the completers, use the above mixed effect model.
Proc MI data=data_short nimpute=20;
VAR time1 time2 time3 time4 time5;
MONTONE reg(time2 time3 time4) regpmm (time5=time1 time2 time3 time4);

7. Study Design for Simulated Data
Multiple rising dose titration scheme in parallel study design
Study Week
Panel
Active
(nsubj_a)
Placebo
(nsubj_p)
Week 1
Dose 1
Pbo
Week 2
Dose 2
Week 3
Dose 3
Week 4
Dose 4
Week 5
Dose 5

8. Simulation Procedure Step 1 : Generate complete dataset:
6 time points (t0, t1, …, t5) including baseline
True heart rate mean for two arms
Assume heart rate from both arms follow multivariate normal distribution with mean given above and variance matrix, where
μ_active
μ_placebo
Δμ (Active – Placebo)
Under H0
(73, 73, 73, 73, 73, 73)
(0, 0, 0, 0, 0, 0)
Under H1
(73, 75, 78, 79, 80, 80)
(0, 2, 5, 6, 7, 7)

9. Simulation Setup Step 2: Generate missing not at random
At 5 postdose time points (t1, t2, t3, t4 , t5) with drop-out rate (%) of R2 at t2, R3 at t3, R4 at t4 and R5 at t5 in active arm
No dropouts across all postdose time points in placebo arm
Monotone Dropout Pattern R2 R3 R4 R5
SC1 5%
10%
20%
SC2 7%
30%
SC3
50%

10. Simulation Setup
Step 3: Run under different models with different sample size enrolled for the active and placebo arms
Model
Description M1
Mixed effect model with all available including missing not at random (without any imputation) M2
Mixed effect model with all completers (i.e. removing subjects with incompleted values) M3
Apply multiple imputation first, then use mixed effect model

11. Simulation
Step 4: Evaluate the model performance based on the criteria below Absolute bias = average of absolute difference between estimation and true value Variability = average of standard error for the treatment effect at the last time point Coverage% = percentage of 90% CI covering the true treatment effect at the last time point Type 1 error = percentage of reject H0, under H0 Power = percentage of reject H0, under H1

12. Simulation Results (1) -- Under H1 with sample size 30:10
True mean difference
N_a:N_p
Drop out rate
Model
Summary at the last visit
C1:
Absolute Bias
C2:
SE for mean difference
C3:
Coverage %
C4:
Power
(0, 2, 5, 6, 7, 7)
30:10
SC1
(0%, 5%, 10%,10%, 20%) M1
1.3
1.58
88.5
98.5 M2
1.4
1.59
87.7
97.8 M3
94.0
98.0
SC2
(0%,7%,20%,20%,30%)
1.60
88.0
97.9
1.5
1.62
85.2
95.7
1.61
92.6
96.4
SC3
(0%,10%,30%,30%,50%)
1.7
1.68
81.1
92.5
2.2
1.69
66.6
81.9
76.8
84.7

13. Simulation Results (2) -- Under H1 with sample size 20:10
True mean difference
N_a:N_p
Drop out rate
Model
Summary at the last visit
C1:
Absolute Bias
C2:
SE for mean difference
C3:
Coverage %
C4:
Power
(0, 2, 5, 6, 7, 7)
20:10
SC1
(0%, 5%, 10%,10%, 20%) M1
1.4
1.69
88.6
97.0 M2
1.5
1.71
87.4
95.2 M3
1.70
93.3
95.7
SC2
(0%,7%,20%,20%,30%)
1.7
1.78
84.2
90.7
2.1
1.83
75.1
79.5
1.74
82.2
82.6
SC3
(0%,10%,30%,30%,50%)
1.8
1.82
87.6
2.4
1.86
69.9
71.9
1.75
74.9

14. Simulation Results (3) -- Under H0 with sample size 30:10
True mean difference
N_a:N_p
Drop out rate
Model
Summary at the last visit
C1:
Absolute Bias
C2:
SE for mean difference
C3:
Coverage %
C4:
Reject H0 %
(0, 0, 0, 0, 0, 0)
30:10
SC1
(0%, 5%, 10%,10%, 20%) M1
1.3
1.58
88.5
5.9 M2
1.4
1.59
87.7
6.9 M3
94.0
6.0
SC2
(0%,7%,20%,20%,30%)
1.60
88.0
6.4
1.5
1.62
85.2
8.5
1.61
92.6
7.4
SC3
(0%,10%,30%,30%,50%)
1.7
1.66
81.1
11.7
2.2
1.69
66.6
23.0
76.8
23.2

15. Simulation Results (4) -- Under H0 with sample size 20:10
True mean difference
N_a:N_p
Drop out rate
Model
Summary at the last visit
C1:
Absolute Bias
C2:
SE for mean difference
C3:
Coverage %
C4:
Reject H0 %
(0, 0, 0, 0, 0, 0)
20:10
SC1
(0%, 5%, 10%,10%, 20%) M1
1.4
1.69
88.6
6.2 M2
1.5
1.71
87.4
6.7 M3
1.70
93.3
SC2
(0%,7%,20%,20%,30%)
1.7
1.78
84.2
9.1
2.1
1.83
75.1
15.8
1.74
82.2
17.8
SC3
(0%,10%,30%,30%,50%)
1.8
1.82
10.8
2.4
1.88
69.9
20.1
1.75
25.0

16. Summary
Under H1, with the sample size decreases and drop out rate increases, M2 and M3 produce the poor coverage and less power.
Under H0, with the sample size decreases and drop out rate increases, M2 and M3 produce the poor coverage and inflate the type 1 error.
Under both H0 and H1, with the sample size decreases and drop out rate increases, M1 performs well.

17. Conclusion
Proposed Mixed effect model can handle missing not at random data scenario under difference drop-out rate & can provide reasonable results even if overall missing data rate is up to 50% and relatively modest sample sizes.
When the missing data rate increases or sample size decreases, the analysis methods only using completers or multiple imputation missing data first produces the poor coverage and less power/inflated type 1 error. Therefore, in these types of situations these two analyses are not recommended.