modeling dropout from longitudinal adverse event data · 2018. 6. 7. · modeling dropout from...
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Modeling Dropout from Longitudinal Adverse Event DataSelecting Optimal Titration RegimensBojan Lalovic, Matthew M Hutmacher, Bill Frame, Kaori Ito, Raymond Miller PGRD Ann Arbor Laboratories, Pfizer Inc, Ann Arbor, MI 48105
INTRODUCTION• Pregabalin offers a new approach in the treatment of
Generalized Anxiety Disorder (GAD)1.• Adverse events (AEs) are the predominant component of
study withdrawal (dropout) contributing with at least 60% to total dropout incidence for this indication, considerably more than other dropout components/categories2-6(Figure 1).
• Pregabalin AE incidence is dose dependent; as AEs have been modeled, we postulate a dropout model that incorporates severity of adverse effects.
• Dose was titrated based on clinical judgment; modeling approach will allow titration schedule optimization.
• Dropout analysis represents analysis of competing risk, we present a component specific approach, as if dropout arises from a specific risk of interest (AEs), the dose-dependent source of risk.
OBJECTIVE• Model the dropout across the various titration schemes and
evaluate the daily AE scores, a time-dependent covariate, as a predictor in the model.
REFERENCES[1] Frampton JE, Foster RH. Pregabalin in the Treatment of Generalized Anxiety Disorder. CNS Drugs 2006; 20 (8): 685-693. [2] Feltner DE, Crockatt JG, Dubovsky SJ, et al. A randomized, double-blind, placebo-controlled, fixed-dose, multicenter study of pregabalin in patients with generalized anxiety disorder. J Clin Psychopharmacol 2003 Jun; 23 (3): 240-9.[3] Pohl RB, Feltner DE, Fieve RR, et al. Efficacy of pregabalin in the treatment of generalized anxiety disorder: double-blind, placebo-controlled comparison of BID versus TID dosing. J ClinPsychopharmacol 2005; 25: 151-8.[4] Rickels K, Pollack MH, Feltner DE, et al. Pregabalin for treatment of generalized anxiety disorder: a 4-week, multicenter, double-blind, placebo-controlled trial of pregabalin and alprazolam. Arch Gen Psychiatry 2005; 62: 1022-30.[5] Montgomery SA, Tobias K, Zornberg GL, et al. Efficacy and safety of pregabalin in the treatment of generalized anxiety disorder: a 6-week, multicenter, randomized, double-blind,placebo-controlled comparison of pregabalin and venlafaxine. J Clin Psychiatry 2006; 67: 771-82.[6] Pande AC, Crockatt JG, Feltner DE, et al. Pregabalin in generalized anxiety disorder: a placebo-controlled trial. Am J Psychiatry 2003 Mar; 160 (3): 533-40.[7] Sheiner LB, Beal SL, Dunn A. Analysis of Nonrandomly Censored Ordered Categorical Longitudinal Data from Analgesic Trials. J Am Stat Assoc 1997 Dec; 92(440) 1235-44.[8] Mandema JW, Stanski DR. Population pharmacodynamics model for ketorolac analgesia. ClinPharmacol Ther 1996 Dec; 60 (6) 619-35. [9] Kowalski KG, McFadyen L, Hutmacher MM, Frame B and Miller R. J PharmacokinetPharmacodynam. 2003 Oct;30(5):315-36
Fig 1. Generalized Anxiety Disorder (GAD) Dropout Incidence (ITT)
Pregabalin Dataset-GAD Phase II studies2-6
•Five comparator trials with benzodiazepines or SSRI (3 alprazolam, lorazepam and venflaxamine) and a schedule optimization study (TID vs. BID) informed the model.•1630 predominantly female, 18 to 64 years old subjects receiving placebo or pregabalin all reported daily subjective AE scores [no (0), mild (1), moderate (2) and severe (3)] across the 4 or 6 week trials. •Studies employed varying dose within the first week of the protocols (Fig. 2)
Adverse Events Incidence Self-Reporting
0100200300400500600
0 10 20 30 40
021
15021
0 10 20 30 40
20021
30021
0 10 20 30 40
40021
45021
0 10 20 30 40
60021
025
15025
20025
30025
40025
45025
0100200300400500600
60025
0100200300400500600
026
15026
20026
30026
40026
45026
60026
083
15083
20083
30083
40083
45083
0100200300400500600
60083
0100200300400500600
085
15085
20085
30085
40085
45085
60085
087
0 10 20 30 40
15087
20087
0 10 20 30 40
30087
40087
0 10 20 30 40
45087
0100200300400500600
60087
Time (days)
Titra
ted
Dos
e (m
g)
Randomized Dose
Fig 2. Titrated Doses Across Study Arms (Randomized Doses)
Lack of Efficacy(3.4%)
Dropout
AEs (11.3%)
Pregab
Compliance(1.7%)
Loss to Follow-up(2.9%)
Admin. LossConsent Loss (5.9%)
METHODS Discrete Survival and Conditional (Hazard) Probabilities
• Time to subject dropout (T) is modeled as discrete survival variable. S(t) is the probability that an individual survives in the study (does not drop out) beyond time tj, where j indexes study day. )t(T Pr S(t) j>=
• Survival probability is related to hazard h(tj), the probability of the event (dropout) occurring in the time interval j, provided it has not occurred prior to j, among those “at-risk” (in study, during interval j). S(t) is also the product of conditional survival probabilities, i.e., sequential survival across each individual period tj.
• Assuming that the probability of dropout (likelihood) is only dependent on the covariate (AE score) in a particular time interval, it is:
Conditional Probability Cumulative Hazard Model• A discrete-time survival model was fit to GAD dropout time,
assuming that the hazard depends on the current self-reported AE score and time since first study day.
• T is the time of dropout, AEMAXj the maximum AE score for the patient at time tj and g(tj, AEMAXj=m) the hazard probabilities conditioned on the last observed AEMAX score (a parsimonious severity covariate).
• Nonparametric examination of risk (see Figure 3) guided the selection of the (parametric) hazard model
)dt)mAEMAXj,t(g(MAXj,jjj
tj
tjj
expm)AEtTt(T Pr ) h(t=∫−
−−==≥== 11
• Linear (exponential) and several time-dependent hazard probability models including the Weibull, loglogistic, linear-exponential and Gompertz were considered.
• Gompertz model (exponentially decreasing hazard with time) where λ is a hazard intercept and γ the slope with time, was selected based on visual inspection of the fitted vs. observed hazard plots, NONMEM OFV, predictive check model simulations and bootstrap confidence intervals. (Figures 4 and 5)
• The LAPLACIAN method as implemented in NONMEM V (Icon Corp., Ellicott City, MD) provided the maximum likelihood (-2LL)) parameter estimates for the hazard parameters7-8.
)tγλ(MAXjj
mmexp)mAE,t(g ⋅+==
RESULTS • Exponentially decreasing dropout risk (hazard) probability
model (Gompertz) adequately described the dropout across GAD studies.
• Hazard was highest with high severity of either dizziness and somnolence (AEMAX) decreasing with time for individuals with moderate or severe AEs; subjects reporting severe dizziness or somnolence on day 1 exhibit a 21% per day chance of dropout, which decreases to 9% and 1% per day on days 10 and 30 respectively.
• Patients reporting mild or no adverse events were estimated to exhibit a constant but low dropout risk, <1% per day at all times.
• Prospective studies can be planned/optimized in respect to AE and dropout across other indications.
Fig 3. Nonparametric Estimates of the Dropout Risk- Regression of Hazard Probabilities vs. Time Given Dizziness and Somnolence, Time-Dependent AE Covariates
j
jmaxAE
nd)t(h =
∧
number of observed subjects withdrawn within tj
number of subjects “at risk” (remaining in study)
Fig 4. Fitted Hazard Probability Distribution Models to the Observed Conditional Probabilities
Time
Surv
ival
0 10 20 30 40
0.0
0.2
0.4
0.6
0.8
1.0
No AEsMildModerateSevere
Days
Surv
ival
Pro
babi
lity
0 5 10 15 20 25 30 35 40 45
0.5
0.6
0.7
0.8
0.9
1.0
484 467 439 422 401 383 155 151 139484 467 439 422 401 383 155 151 139
0 mg Study 21-25-26-83-85-87
Days
Surv
ival
Pro
babi
lity
0 5 10 15 20 25 30 35 40 45
0.5
0.6
0.7
0.8
0.9
1.0
178 172 163 159 157 147 71 68 65
450 mg Study 83-85
178 172 163 159 157 147 71 68 65
Days
Surv
ival
Pro
babi
lity
0 5 10 15 20 25 30 35 40 45
0.5
0.6
0.7
0.8
0.9
1.0
207 192 170 160 156 149
600 mg Study 21-25-26
207 192 170 160 156 149
600 mg Study 21-25-26
Days
Surv
ival
Pro
babi
lity
0 5 10 15 20 25 30 35 40 45
0.5
0.6
0.7
0.8
0.9
1.0
89 82 81 78 73 70
600 mg Study 83
89 82 81 78 73 70
Days
Surv
ival
Pro
babi
lity
0 5 10 15 20 25 30 35 40 45
0.5
0.6
0.7
0.8
0.9
1.0
109 101 95 92 91 91 91 90 82
600 mg Study 87
109 101 95 92 91 91 91 90 82
Time (DAYS)
Sur
viva
l Pro
babi
lity
2 4 6 8 10
0.85
0.90
0.95
1.00
150, 150, 150, 150,150,150,150,600,600,600
150, 150, 150, 150,150,150,150,300,300, 450
150, 150, 300, 300,300,300,450,450,450,450
600, 600, 600, 600,600,600,600,600,600,600
PLACEBO
Fig 5. Simulation of Dropout (Gompertz Hazard Model) using Observed MaxAEs- Predictive Check (200 Simulations) with KM Nonparametric Survival Estimates (thick lines)
Fig 6. Dropout from Simulated AEs (3 Part Model) for Placebo, 450-600 mg Dose Groups/Titration Schemes. Blue line depicts the observed Kaplan-Meier dropout estimates.
Fig 7. Mean Dropout from Prospective 7-day Titration Schemes (300 Simulations) using the 3-Part AE-Dropout Model
Time (days)
Estim
ated
Haz
ard
(^h)
0 10 20 30 40
0.0
0.02
0.06
0.10 AE1-0 (No Dizziness)
Time (days)
Estim
ated
Haz
ard
(^h)
0 10 20 30 40
0.0
0.02
0.06
0.10 AE1-1 (Mild Dizzines
Time (days)
Estim
ated
Haz
ard
(^h)
0 10 20 30 40
0.0
0.05
0.10
0.15
0.20 AE1-2 (Moderate Dizziness)
Time (days)
Estim
ated
Haz
ard
(^h)
0 10 20 30 40
0.0
0.05
0.10
0.15
0.20 AE1-3 (Severe Dizzines
Time (days)
Estim
ated
Haz
ard
(^h)
0 10 20 30 40
0.0
0.02
0.06
0.10 AE2-0 (No Somnolence)
Time (days)
Estim
ated
Haz
ard
(^h)
0 10 20 30 40
0.0
0.02
0.06
0.10 AE2-1 (Mild Somnolenc
Time (days)
Estim
ated
Haz
ard
(^h)
0 10 20 30 40
0.0
0.05
0.10
0.15
0.20 AE2-2 (Moderate Somnolence)
Time (days)
Estim
ated
Haz
ard
(^h)
0 10 20 30 40
0.0
0.1
0.2
0.3
0.4
0.5
AE2-3 (Severe Somnolen
Time (days)
Estim
ated
Haz
ard
(^h)
0 10 20 30 40
0.0
0.00
40.
008
0.01
2 MAXAE0- NO AEs
Hazard DistributionsExponential
GompertzTime (days)
Estim
ated
Haz
ard
(^h)
0 10 20 30 40
0.0
0.00
50.
015
MAXAE1- Mild AEs
Time (days)
Estim
ated
Haz
ard
(^h)
0 10 20 30 40
0.0
0.01
0.02
0.03
0.04
MAXAE2- Moderate AEs
Time (days)
Estim
ated
Haz
ard
(^h)
0 10 20 30 40
0.0
0.05
0.10
0.15
MAXAE3- Severe AEs
Prospective Simulations•To generate prospective titration schemes AE data were simulated according to a 2-part incidence and severity AE model9. Simulated AEs and resulting dropouts are depicted below.
Study
))t(h()t(h)tTPr(j
i
t
ijj ∏−
=
−==1
1
1
Placebo 150 mg/day 600 mg/dayDizziness (%) 6-8 10-23 29-39
Somnolence (%) 11 15-29 36-50Others* (%) <20 <20
*Headache, Dry Mouth, Lack of Coordination, Nausea and Vomiting
p
∫−
−
−−=−=≥=
=≥==t
jt111
1
t)dt)(g(
j
j
j
jjjj e
)S(t)S(t
)tTPr()tTPr()tTt(T Pr ) h(t