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

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45021

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025

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026

15026

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083

15083

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085

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30085

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087

0 10 20 30 40

15087

20087

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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)

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0.0

0.05

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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