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

Outline: Introduction Analyses methods Simulation Conclusions

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

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.

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

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 0 0 0 0 1 0 0 0 0 -1 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);

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

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)

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%

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

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

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

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

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

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

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.

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.