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University of Groningen

Translational PKPD modeling in schizophreniaPilla Reddy, Venkatesh

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Publication date:2012

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Citation for published version (APA):Pilla Reddy, V. (2012). Translational PKPD modeling in schizophrenia: linking receptor occupancy ofantipsychotics to efficacy and safety. Groningen: s.n.

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CHAP

TER4

Modelling and Simulation of the Positive and Negative Syndrome Scale (PANSS) time Course and

Dropout Hazard in Placebo Arms of Schizophrenia Clinical Trials

Venkatesh Pilla Reddy,1 Magdalena Kozielska,1 Martin johnson,1 Ahmed Abbas Suleiman,1

An Vermeulen,2 jing liu,3 Rik de Greef,4 Geny M.M. Groothuis,1 Meindert Danhof5

and johannes H. Proost.1

Clinical Pharmacokinetics 2012; 51 (4): 261-275

1Division of Pharmacokinetics, Toxicology and Targeting, University of Groningen, Groningen, the Netherlands

2Advanced PKPD Modelling and Simulation, Janssen Research & Development, a Division of Janssen

Pharmaceutica NV, Beerse, Belgium 3Clinical Pharmacology, Pfizer Global Research and

Development, Groton, CT, USA 4Clinical PKPD, Merck Research Labs, Merck Sharp &

Dohme, Oss, the Netherlands 5Division of Pharmacology, Leiden/Amsterdam Center for

Drug Research, Leiden, the Netherlands

4

AbSTRACTbackground and objectives: The likelihood of detecting a therapeutic signal of an effective drug for schizophrenia is impeded by a high placebo effect and by high dropout of patients. Several unsuccessful trials of schizophrenia, at least partly due to highly variable placebo effects, have indicated the necessity for a robust methodology to evaluate such a placebo effect and reasons for dropout. Hence, the objectives of this analysis were to (i) develop a longitudinal placebo model that accounts for dropouts and predictors of the placebo effect, using the Positive and Negative Syndrome Scale (PANSS) score; (ii) compare the performance of empirical and semi-mechanistic placebo models; and (iii) compare different time-to-event (TTE) dropout modelling approaches used to account for dropouts.

Methods: The PANSS scores from 1436 individual patients were used to develop and validate a placebo model. This pooled dataset included 16 trials (conducted between 1989 and 2009), with different study durations, in both acute and chronic schizophrenic patients. A nonlinear mixed-effects modelling approach was employed, using NONMEM VII software.

Results: Among the different tested placebo models, the Weibull model and the indirect response model adequately described the PANSS data. Covariate analysis showed that the disease condition, study duration, study year, geographic region where the trial was conducted, and route of administration were important predictors for the placebo effect. All three parametric TTE dropout models, namely the exponential, Weibull and Gompertz models, described the probability of patients dropping out from a clinical trial equally well. The study duration and trial phase were found to be predictors for high dropout rates. Results of joint modelling of the placebo effect and dropouts indicated that the probability of patients dropping out is associated with an observed high PANSS score. The indirect response model was found to be a slightly better model than the Weibull placebo model to describe the time course of the PANSS score.

Conclusions: Our modelling approach was shown to adequately simulate the longitudinal PANSS data and the dropout trends after placebo treatment. Data analyses suggest that the Weibull and indirect response models are more robust than other placebo models to describe the nonlinear trends in the PANSS score. The developed placebo models, accounting for dropouts and predictors of the placebo effect, could be a useful tool in the evaluation of new trial designs and for better quantification of antipsychotic drug effects.

74

PLACEBO EFFECT AND DROPOUT MODELLING IN SCHIZOPHRENIA

4

bACKGROuND Over the past decade, several antipsychotic drug trials failed to show a positive clinical effect, because of a high placebo effect[1,2] (i.e. the percentage change in the Positive and Negative Syndrome Scale [PANSS] score from the PANSS score at baseline [BASL]) and a high patient dropout rate. In these trials, ranges of 20–70% in the placebo effect and 40–70% in the dropout rate were observed.[3-5] Therefore, current efforts in psychiatric research are focused on better understanding of the mechanisms underlying a placebo effect and identification of the contributors to a high placebo effect. The analysis of subject-level data from placebo-controlled trials, using modelling approaches such as pharmacokinetic-pharmacodynamic modelling, has been shown to be efficient in identifying the predictors of a placebo effect and can be implemented in the design of clinical trials of new drugs via simulations.[6,7]

The severity of illness and the time course of the clinical response to drugs in schizophrenia are commonly measured using the PANSS, a scoring system based on 30 items, with a total score ranging from 30 to 210.[8] Another, less common, scoring method used in earlier studies is the Brief Psychiatric Rating Scale (BPRS).[9] Welge and Keck[10] attempted to identify the contributors to the placebo effect via a statistical approach using pooled literature data on the BPRS. However, as generally only mean outcomes are reported in the literature, such an approach is not able to detect covariates that might systematically affect the placebo response. In contrast, pooled analysis of longitudinal individual data (the PANSS or BPRS scores) from patients would be more valuable in estimating the effect of covariates on the treatment-effect size.

A model for disease progression and the placebo effect can be developed separately for diseases such as Alzheimer’s disease and Parkinson’s disease.[11,12] However, in other cases, it is difficult to separate disease progression from the placebo effect, because of the episodic nature of the disease (e.g. schizophrenia and depression); in such cases, disease progression and the placebo effect can be considered as a single entity.[13] When developing models to evaluate the consequences of a placebo effect, the missing data from patients who dropped out of the trial should be considered for accurate interpretation of the outcomes in clinical trials. Missing data due to dropout events can be categorized into three types: completely random dropout (CRD), random dropout (RD) and informative dropout (ID).[14,15] CRD can be ignored during the model development and simulation process, as it is independent of the observed response. In RD, the dropout event depends on the observed response and/or covariates, and can be ignored during the model development if appropriate modelling methodology is used, but it cannot be ignored while performing clinical trial simulations. In ID, the dropout probability depends upon both observed and one or more unobserved (predicted) response variables. A special case of ID is restrictive informative dropout (RID), where missing data depend only on the unobserved

75

4

response variables and not on the observed response variables.[16] ID and RID are considered non-ignorable during model development and clinical trial simulations, as the missing data contain information on the dropout process. An adequate placebo model should therefore include not only the actual placebo effect but also the covariates and the occurrence of dropout. The information about the placebo effect and the dropout process from prior clinical trials can be used in subsequent drug-effect modelling work and in prospective clinical trial design recommendations.[6,17,18]

In the area of pharmacokinetic-pharmacodynamic modelling of antipsychotic drugs, various empirical models,[18-22] and semi-mechanistic models like the indirect response model (IRM),[23,24] have been used to describe the PANSS data following placebo treatment from that particular trial. To the best of our knowledge, no pooled analysis of subject-level data, using pharmacokinetic-pharmacodynamic modelling approaches that identify the predictors of a placebo effect in schizophrenia, including long-term trials, under varying trial conditions, has been reported.

So far, several time-to-event (TTE) dropout modelling approaches, such as the exponential, Weibull and Gompertz models, have been utilized to account for dropouts in longitudinal clinical trials; however, there is no literature available comparing the different TTE models using longitudinal data. Hence, the objectives of this analysis were to (i) develop a longitudinal placebo model that accounts for dropouts and predictors of the placebo effect, using the PANSS score; (ii) compare the performance of empirical and semi-mechanistic placebo models; and (iii) compare different TTE dropout modelling approaches used to account for dropouts.

METHODSPatients and Study DesignThe PANSS data from 1338 patients were used as an index dataset to develop and to evaluate the placebo models. The external validation dataset included 98 patients. The overview of the trial design, summary statistics of the PANSS scores and dropout rates across the studies used in the development of the placebo models are shown in table I.

A representative spaghetti plot describing individual time courses of PANSS scores after placebo treatment (study SCH-303) is shown in figure 1a. The modelling approach to describe the time course of PANSS data was implemented using NONMEM VII software.[25] Perl-speaks-NONMEM (PsN, v 3.2.4) was used to communicate with NONMEM. R (v 2.11) was used for graphical inspection of the results.

76


4

Model DevelopmentThe Placebo ModelA nonlinear mixed-effects modelling approach was used to test several models (table II) in order to describe the PANSS time course following placebo treatment. For all of the models, first-order conditional estimation (FOCE), with or without the interaction estimation method in NONMEM, was used.[25] Normal or log-normal distribution was applied to account for the interindividual variability (IIV) on the structural model parameters. An additional hierarchical level of random effects, to handle between-study heterogeneity, was tested by estimating the inter-study variability (ISV), as described by Laporte-Simitsidis et al.[26] Different residual error models were explored to explain the intra-individual variability (denoted as σ) or residual unexplained variability (RUV). During model building, differences in the objective function value (OFV; difference denoted as ΔOFV) between the models, together with the relative standard error (RSE) [<30%] of the parameters and goodness-of-fit plots, were used to guide the selection of the best base placebo model.[25,27] The best-performing base placebo models from both empirical and semi-mechanistic modelling approaches were selected to perform the covariate and dropout modelling.

Fig. 1. (a) Time course of Positive and Negative Syndrome Scale (PANSS) scores from study SCH-303 (reproduced from Pilla Reddy et al.,[13] with permission); (b) PANSS scores for placebo treatment from study SCH-303 were plotted vs visit time, grouped by the time of dropout. The numbers listed in the key indicate the numbers of patients who dropped out from the trial at each visit (on days 4, 8, 14, 21, 28 and 35) or completed the study (day 42). Completers (n=69) had the lowest PANSS score compared with those who dropped out, indicating that the dropout mechanism is not completely random.

77

4

tab

le I

. Ove

rvie

w o

f clin

ical

tria

ls in

sub

ject

s w

ith s

chiz

ophr

enia

incl

uded

in th

e de

velo

pmen

t of t

he p

lace

bo m

odel

Stu

dy n

o.St

udy

year

Tri

alp

has

eD

rug/

dos

e(m

g)A

DM

Sub

ject

s/ob

serv

atio

ns

(n)

Stu

dyd

ura

tion

(wee

ks)

Sub

ject

sra

nd

omiz

edto

pla

ceb

o (%

)Fe

mal

es :

mal

es (

%)

bA

SL [

SE]

PAN

SSsc

ore

chan

gea

Dro

pou

t(%

)D

atas

ets

use

d fo

r m

odel

dev

elop

men

t an

d e

valu

atio

n (

ind

ex d

atas

et)

SCH

-303

2004

III

Palip

erid

one

6, 9

, 12

Oral

/od

126/

814

617

48 :

5294

.1 [3

.2]

−4.1

54

SCH

-304

2004

III

Palip

erid

one

6, 1

2Or

al/o

d10

5/60

46

2022

: 78

93.6

[3.4

]−8

.066

SCH

-305

2004

III

Palip

erid

one

3, 9

, 15

Oral

/od

120/

727

624

31 :

6993

.9 [3

.5]

−2.8

62

USA-

121

2000

III

Risp

erid

one

25, 5

0, 7

5IM

/ on

ce e

very

2

wee

ks10

2/45

512

2024

: 76

82 [1

.5]

3.9

69

INT-

319

89II

IRi

sper

idon

e0.

5, 2

, 4, 6

, 8Or

al/b

id88

/369

817

16 :

8492

.6 [2

]2.

528

128-

114

1994

III

Zipr

asid

one

40, 8

0Or

al/b

id92

/487

620

32 :

6897

.3 [2

.3]

−6.4

51

128-

115

1995

III

Zipr

asid

one

20, 6

0, 1

00Or

al/b

id83

/380

630

35 :

6590

.9 [1

.8]

−0.4

67

128-

303

1995

III

Zipr

asid

one

20, 4

0, 8

0Or

al/b

id75

/335

5425

19 :

7987

.9 [2

.2]

−0.7

81

128-

307

1997

III

Zipr

asid

one

40, 6

0Or

al/o

d64

/266

5430

27 :

7386

.5 [2

.1]

+8.5

75

0410

0220

00II

Asen

apin

e0.

2, 0

.4, 0

.8SL

/bid

61/2

726

2620

: 80

93.6

[1.9

]−4

.472

0410

1320

01II

Asen

apin

e1.

6, 2

.4SL

/bid

59/2

886

2320

: 80

90.3

[2.1

]−3

.769

0410

0420

02II

Asen

apin

e5

SL/b

id60

/289

651

20 :

8092

.4 [1

.9]

−5.3

65

0410

2120

06II

IAs

enap

ine

5, 1

0SL

/bid

93/6

046

3244

: 56

94.6

[1.1

]−1

1.1

46

0410

2220

06II

IAs

enap

ine

5–10

SL/b

id88

/562

651

22 :

7885

.8 [1

.1]

−11.

745

0410

2320

06II

IAs

enap

ine

5SL

/bid

122/

808

636

48 :

5288

.9 [0

.9]

−10.

843

Ext

ern

al v

alid

atio

n d

atas

et

SCH

-200

220

09II

JNJ-3

7822

681

10, 2

0, 3

0Or

al/b

id98

/615

6N

A48

: 52

90.4

[1.0

]−4

.846

a M

ean

chan

ge in

the

PAN

SS s

core

, usi

ng th

e la

st o

bser

vatio

n ca

rrie

d fo

rwar

d.A

DM

= r

oute

of a

dmin

istr

atio

n; b

ASL

= b

asel

ine

PAN

SS s

core

; bid

= tw

ice

daily

; IM

= in

tram

uscu

lar;

NA

= n

ot a

pplic

able

; od

= o

nce

daily

; PA

NSS

= P

ositi

ve

and

Neg

ativ

e Sy

ndro

me

Scal

e; S

E =

sta

ndar

d er

ror;

SL

= su

blin

gual

.

78


4

tab

le I

I. S

umm

ary

of b

ase

plac

ebo

mod

els

expl

ored

to d

escr

ibe

the

time

cour

se o

f the

Pos

itive

and

Neg

ativ

e Sy

ndro

me

Scal

e (P

ANSS

)

Pla

ceb

o m

odel

saM

odel

str

uct

ure

bEq

uat

ion

no.

Par

amet

ers

(fix

ed +

ran

dom

)co

FVΔ

oFV

Em

pir

ical

mod

els

Base

line

mod

elEq

. 13

+ 1

45 6

63Li

near

Eq. 2

5 +

244

128

−153

5Bi

-line

arEq

. 311

+ 4

43 4

39−2

224

Pow

erEq

. 46

+ 2

43 7

65−1

898

Expo

nent

ial

Eq. 5

6 +

243

688

−197

5

Wei

bull

Eq. 6

8 +

342

624

−303

9

Wei

bull

+ lin

ear

Eq. 7

8 +

342

624

−303

9

Wei

bull

+ lin

ear

[As

prop

osed

by

Gom

eni e

t al.]

[6]

Eq. 8

7 +

143

953

−171

0

Poly

nom

ial

Eq. 9

6 +

243

995

−166

8

Inve

rse

Bate

man

func

tion

Eq. 1

08

+ 4

44 1

84−1

479

Sem

i-m

ech

anis

tic

mod

els

IRM

Eq. 1

17

+ 3

43 4

58−2

205

Tran

sit m

odel

Eq. 1

27

+ 3

43 7

20−1

943

a The

fina

l pla

cebo

bas

e m

odel

s ar

e sh

own

in b

old

italic

text

.b F

or d

etai

ls o

n th

e m

odel

str

uctu

re, p

leas

e re

fer t

o th

e re

cent

revi

ew a

rtic

le o

n pl

aceb

o m

odel

s by

Pill

a Re

ddy

et a

l.[13]

c Incl

udes

str

uctu

ral m

odel

par

amet

ers,

IIV

para

met

ers

and

RUV

para

met

ers.

bA

SL =

bas

elin

e PAN

SS sc

ore;

CEO

N =

hyp

othe

tical

pla

cebo

conc

entr

atio

n; D

REC

= am

plitu

de o

f sco

re im

prov

emen

t dur

ing

reco

very

; DR

IFt

= sl

ope p

aram

eter

; II

v =

inte

rind

ivid

ual v

aria

bilit

y; IR

M =

indi

rect

resp

onse

mod

el; k

= ra

te o

f cha

nge

in d

isea

se s

ever

ity; k

in =

rate

con

stan

t of w

orse

ning

; kon

= ra

te c

onst

ant o

f w

orse

ning

; kou

t = ra

te c

onst

ant o

f im

prov

emen

t; k

rec =

rate

con

stan

t of i

mpr

ovem

ent a

fter p

lace

bo d

osin

g; n

= n

umbe

r of t

rans

ition

s; o

FV =

obj

ectiv

e fu

nctio

n va

lue;

Δo

FV =

chan

ge in

the

OFV

from

the

base

line

mod

el; P

E =

mag

nitu

de o

f the

pla

cebo

effe

ct; P

max

= m

axim

um p

lace

bo e

ffect

; PO

W =

shap

e pa

ram

eter

; PR

E =

prec

urso

r sta

tus;

Qu

AD

= q

uadr

atic

coe

ffici

ent;

Ru

v =

resi

dual

une

xpla

ined

var

iabi

lity;

SH

IFt

= tr

ansi

tion

betw

een

two

slop

es; S

LOP

= s

lope

par

amet

er; t

=

time;

TC

= tr

ansi

t com

part

men

t; T

D =

tim

e to

reac

h 63

.2%

of t

he m

axim

um c

hang

e fr

om b

asel

ine.

79

4

table III. Overview of the covariates included in the covariate analysis (covariates of the external dataset are not shown here.

Covariatea value

Age (years; median [range]) 40 [18–76]BASL (median [range]) 91 [56–132]YEAR (median [range]) 2001 [1989–2006]Subjects randomized to placebo (%; median [range]) 24 [17–51]Females randomized to placebo (%; median [range]) 24 [16–48]Sex (n [%]) 0 = female 402 [30] 1 = male 936 [70]Race (n [%]) 1 = White, non-Hispanic 816 [61] 2 = Black, non-Hispanic 364 [27] 3 = Hispanic (White or Black) 48 [3.5] 4 = Asian or Pacific Islander 48 [3.5] 5 = other 62 [5]DIS (n [%]) 0 = acute schizophrenic patients 1009 [75] 1 = chronic/sub-chronic schizophrenic patients 329 [25]DUR (n [%]) 0 = short-term trials (6–12 weeks) 1199 [89] 1 = long-term trials (54 weeks) 139 [11]US (n [%]) 0 = study site outside the US 473 [35] 1 = study site in the US 865 [65]PHASE (n [%]) 0 = phase II trial 180 [13] 1 = phase III trial 1158 [87]ADM (n [%]) 0 = oral 753 [56] 2 = IM 102 [8] 3 = SL 483 [36]Dosing regimen (n [%]) 0 = od 439 [33] 2 = bid 797 [59.5] 3 = once every 2 weeks 102 [7.5]Washout period (n [%]) 0 = yes (4–7 days) 1199 [89] 1 = no 139 [11]

a The effect of a categorical covariate on a parameter is described as: Typical parameter = q1 * (1 + q2 * covariate). The effect of a continuous covariate on a parameter is described as: Typical parameter = q1 * (1 + q2 * (covariate − median covariate). ADM = route of administration; bASL = baseline PANSS score; bid = twice daily; DIS = disease condition; DuR=trial duration; IM = intramuscular; od = once daily; PANSS=Positive and Negative Syndrome Scale; PHASE = trial phase; SL = sublingual; uS=location of study site (in or outside the US); yEAR = study year

80


4

The Covariate ModelThe inclusion of potential covariates in the final model was based on their clinical relevance and diagnostic plots of empirical Bayes parameter estimates versus covariate values. Covariates included in this analysis are listed in table III. The clinical relevance of these covariates was discussed in detail recently.[13] To test the covariate-parameter relationship, covariates are added to structural parameters, using the stepwise covariate modelling approach (SCM), as implemented in the PsN software package.[28,29] With this technique, different covariate-parameter relationships can be tested in a forward fashion (p < 0.001 and ΔOFV of 10.8) to build up the final full model, which in turn is evaluated in the backward elimination step (p < 0.001 and ΔOFV of 10.8). When a correlation between covariates was found, one of them was omitted on the basis of the prior clinical preference, if not at random. The resulting final placebo model contains only covariates that meet the pre-defined statistical criteria and show an acceptable precision of parameter estimates (<50% RSE).

The Dropout ModelThe joint likelihood of observing both the PANSS score and a dropout event is shown in equation 1

(Eq. 1)

where P is probability; D is the dropout indicator at the time of the event; Y is the observed PANSS score; Y1 is the unobserved PANSS score; α represents placebo model parameters; X represents independent variables or covariates; β represents parameters of the dropout model; t represents time; P(Y|X,α) represents the probability distribution of the complete PANSS score data, conditioned on parameters of the placebo and covariate model; and P(D|Y1,X,β) represents the probability distribution that characterizes the dropout. The conditional probability of dropout within a time period, depending on the observed as well as the unobserved PANSS score, i.e., P(D|Y,Y1, X, β) can be modelled using a hazard function as shown in equation 2:

(Eq. 2)

where h represents hazard; T is the dropout time and Δt is the time interval. This approach is commonly known as the TTE approach.[30]

Three different parametric dropout models, namely the exponential, Weibull and Gompertz models along with different dropout mechanisms[16,31] (CRD, RD, ID & RID), were tested for their suitability to describe missing PANSS data due to dropout. A summary of the different TTE model structures is shown in table IV. The exponential

81

4

tab

le I

V. S

umm

ary

of th

e tim

e-to

-eve

nt (T

TE) d

ropo

ut m

odel

s us

ed to

acc

ount

for d

ropo

utsa

Dro

pou

t p

atte

rnE

xpon

enti

al h

azar

d m

odel

Wei

bu

ll h

azar

d m

odel

Gom

per

tz h

azar

d m

odel

CRD

RD RID

ID a Th

e pr

obab

ility

of a

pat

ient

dro

ppin

g ou

t can

be

pred

icte

d by

des

crib

ing

the

haza

rd fo

r the

eve

nt. H

azar

d is

the

inst

anta

neou

s rat

e of

the

even

t: h(

t).

Cum

ulat

ive

haza

rd (C

HZ)

pre

dict

s the

risk

of a

pat

ient

dro

ppin

g ou

t fro

m th

e st

udy

over

the

time

inte

rval

, whi

ch is

obt

aine

d by

inte

grat

ing

the

haza

rd

with

resp

ect t

o tim

e:

. The

pro

babi

lity

of s

urvi

val (

not d

ropp

ing

out)

can

be

pred

icte

d fr

om th

e cu

mul

ativ

e ha

zard

: exp

(−CH

Z).

γ =

base

line

haza

rd o

f pat

ient

dro

pout

from

the

stud

y (B

HAZ

); β

1 a

nd β

2 =

par

amet

ers

rela

ting

haza

rd to

the

PAN

SS s

core

(BET

A); λ

and

φ =

sha

pe

para

met

er in

the

Wei

bull

and

Gom

pert

z ha

zard

mod

els,

resp

ectiv

ely;

CR

D =

com

plet

ely

rand

om d

ropo

ut; I

D =

info

rmat

ive

drop

out;

ob

s =

obse

rved

; PA

NSS

= P

ositi

ve a

nd N

egat

ive

Synd

rom

e Sc

ale;

Pre

d =

pre

dict

ed; R

D =

rand

om d

ropo

ut; R

ID =

rest

rict

ive

info

rmat

ive

drop

out;

t = ti

me

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4

TTE model assumes that the baseline hazard of patient dropout from the study (BHAZ) is independent of time. In contrast, a time factor is considered in the Weibull and the Gompertz model. The TTE model estimates the BHAZ and BETA. BETA is a parameter that describes the probability of a patient dropping out on the basis of predictors such as the predicted or observed PANSS score. In addition, the covariate-dropout model parameter relationship was tested in a linear or nonlinear manner, as described in the Covariate Model subsection of the Methods. The TTE model parameters were estimated using the Laplace approximation method with or without the interaction option within NONMEM. Each of the dropout models with different dropout mechanisms was first combined with only the base placebo model to ascertain the influence of the dropout model on the placebo model parameter estimates and to determine the mechanism of the dropout process. Afterwards, the dropout model was combined with covariates of the placebo effect and dropouts to obtain the final placebo model. A simultaneous approach was used in the case of ID and RID dropout processes, where a placebo model, a covariate model and a dropout model were fitted simultaneously to all of the data. For the CRD and RD dropout processes, the sequential approach was used.[32,33]

Model Evaluation and External ValidationBootstrap analysis[34-36] with 1000 bootstrap datasets was performed without stratification on the final placebo model, to obtain median values and nonparametric 95% confidence intervals for the model parameters. The case deletion diagnostics (CDD) tool was used to identify influential studies that may affect parameter estimates and model fitting conclusions. A detailed description of the CDD tool in modelling is illustrated by Lindbom et al.[29] Simulations were performed after the final model was identified. In brief, 1000 datasets, identical in structure and covariate values to the original dataset, were simulated, using the parameter estimates and inter- and intra-individual variability from the final model. Visual predictive check (VPC) plots were plotted after calculating the 2.5th, 50th and 97.5th percentiles of PANSS scores for the simulated datasets.

The final placebo model was validated using an external dataset from a recent phase II clinical trial, SCH-2002, which was not available during the time of model development and evaluation. One thousand simulations were performed on the basis of the available covariates in the external dataset to obtain model-based individual-predicted PANSS scores. These predicted PANSS scores were then plotted versus the PANSS scores that were actually observed in this external dataset. Prediction errors were also computed as described by Sheiner and Beal,[37] which provided a measure of bias and precision by assessing the differences between the observed and predicted PANSS scores.

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RESuLTSPlacebo Model SelectionTable II depicts the summary of placebo models that were explored. On the basis of the model selection criteria (as described in the Methods), the Weibull model and the IRM were chosen for testing the influence of covariates and dropouts.

the Weibull ModelThe Weibull model equation (see equation 6 in table II) describes the decrease of the PANSS score from baseline, which eventually reaches a plateau. Pmax is the maximum placebo effect, TD is the time to reach 63.2% of the maximum change from baseline, and POW is the shape parameter. The placebo effect was included proportionally to the BASL. In this model, IIV for the BASL and Pmax parameters was assumed to be of log-normal distribution and normal distribution, respectively. The normal distribution of the IIV for the Pmax parameter allows the placebo effect to be worsening or improving. An additive error model was found to better describe the RUV. Some patients were more variable or stable in the placebo response than others, for unknown reasons. This was accounted for by including an IIV term in the RUV.

the Indirect Response ModelThe IRM describes the time course of the change from the BASL as the net result of the rate of worsening and the rate of improvement processes (as shown in equation 11 in table II). In this model, different pharmacokinetic driving functions (table V) were used to reflect the time course of the hypothetical placebo concentration (CEON). Fixing CEON to 1 for each PANSS observation after the first dose was preferred over other approaches (see table V for details).

The assumed CEON was allowed to affect either the rate constant of improvement (kout) or the rate constant of worsening (kin) in a linear manner with a slope (SLOP) parameter. Data analysis indicated that the model with a stimulatory effect on the rate of improvement resulted in a better fit compared with the inhibitory effect on the rate of worsening. A normally distributed IIV for the SLOP parameter was included to allow the SLOP parameter to be negative or positive, such that the IRM could predict improvement or worsening in the PANSS score. The best results were obtained when a log-normal distribution IIV was introduced for the kout and BASL parameters and a normally distributed IIV was introduced for the SLOP parameter. The shrinkage values for random effects were negligible except for kout (56%), indicating that empirical Bayes estimates related to kout are not reliable for diagnostics (e.g. the plot of covariate vs empirical Bayes estimates of kout). Moreover, we believe that shrinkage does not affect the likelihood ratio testing of covariates. We did not succeed in estimating the ISV. Moreover, including ISV would not lead to an improved prediction of the placebo effect in future studies.

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tab

le V

. Diff

eren

t app

roac

hes

to e

stim

atin

g th

e hy

poth

etic

al p

lace

bo c

once

ntra

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(CEO

N) f

or th

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dire

ct re

spon

se m

odel

(IRM

)

Ap

pro

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el[3

9]

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and

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rtm

ent m

odel

Long

er N

ONM

EM ru

n tim

es

Expo

nent

ial i

nfus

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type

fu

nctio

n (k

inet

ic-

phar

mac

odyn

amic

func

tion)

[40]

Assu

mes

that

CEO

N re

ache

s st

eady

sta

te s

low

ly a

fter t

he fi

rst

plac

ebo

dose

The

corr

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betw

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k e and

kou

t was

hi

gh (>

0.98

). To

ove

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e fix

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ue fr

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35 a

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, sh

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all C

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Assu

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type

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1 a

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and

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ains

at a

ste

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1 u

nit u

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rem

ent

CL =

ass

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e = r

ate

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the

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f th

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kou

t = r

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SS =

Pos

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d N

egat

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PLA

C =

PLAC

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aceb

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ent e

ffect

with

(PL

AC (

0|1)

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g tim

e; t

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v d

= v

olum

e of

dis

trib

utio

n

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4

table VI. Final Weibull placebo model

Parametersa Mean [95% CI]b Remarks

Weibull placebo model parameters

BASL 90.9 [90.0, 91.8]TD (days) 12.6 [10.9, 14.5]Pmax 0.078 [0.064, 0.092]POW 1.21 [1.11, 1.32]

Covariates on placebo model parametersc

BASL-DIS (acute vs chronic) −0.044 [−0.067, −0.018] Chronic patients had a 4.4%

lower BASL

Pmax-DUR (short- vs long-term) −1.86 [−2.81, −1.23]

Long-term studies have shown a 186% lower placebo effect (worsening)

Pmax-YEAR 0.099 [0.06, 0.15] Increase of 9.9% in Pmax from the median study year

TD-US (US vs non-US trials) 0.35 [0.12, 0.61]

The time to reach the maximum placebo effect in non-US trials was 35% longer

σ-ADM (oral vs IM) −0.28 [−0.34, −0.20]28% lower intra-individual variability with IM administration vs oral administration

σ-ADM (oral vs SL) −0.29 [−0.41, −0.16]29% lower intra-individual variability with SL administration vs oral administration

σ-DIS (acute vs chronic) 0.51 [0.33, 0.74] 51% higher intra-individual variability for chronic patients

σ-US (US vs non-US trials) −0.28 [−0.33, −0.18] Non-US trials have shown 28% lower intra-individual variability

Exponential dropout model parameters (RD)

BHAZ (1/day) 0.00079 [0.00045, 0.0012]

BETA −0.035 [−0.041, −0.030]The risk of dropout increased with a high PANSS score on the preceding visit

Covariates on dropout model parameters

BHAZ-DUR (short- vs long-term) −0.98 [−0.99, −0.90] Long-term studies had a 98%

lower BHAZ

BETA-DUR (short- vs long-term) 0.87 [0.25, 1.82]

The relative hazard of dropout with an increasing PANSS score on the preceding visit increased more for long-term studies than for short-term studies

BETA-PHASE (phase III vs phase II) 0.12 [0.06, 0.19]

The hazard of dropout with a high PANSS score on the preceding visit increased more for phase II trials than for phase III trials

continued on next page

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table VI. Final Weibull placebo model


Random effects (IIV and RuV)d

IIV BASL [% CV] 15 [14, 16]IIV Pmax [SD] 0.18 [0.16, 0.22]IIV-σ [% CV] 43.1 [39, 46]σ [SD] 7.74 [7.16, 8.53]

a Total number of parameters: 21.b 95% CI from 1000 bootstrap samples. c The parameter-covariate relationship represents a proportional increase in the parameter value by the covariate. d Shrinkage values for random effects were less than 10%.

σ = intra-individual variability; ADM = route of administration; bASL = baseline PANSS score; bETA = parameter relating hazard to the PANSS score; bHAZ = baseline hazard of patient dropout from the study; CI = confidence interval; Cv = coefficient of variation; DIS = disease condition; DuR = study duration; IIv = interindividual variability; IM = intramuscular; PANSS = Positive and Negative Syndrome Scale; PHASE = trial phase (phase III or phase II trial); Pmax = maximum placebo effect; POW = shape parameter; RD = random dropout; Ruv = residual unexplained variability; SD = standard deviation; SL = sublingual; TD = time to reach 63.2% of the maximum change from baseline; uS = location of study site (in or outside the US); yEAR = study year.

the Covariate ModelTables VI and VII summarize the placebo and dropout model parameter-covariate relationships for the Weibull model and the IRM, respectively. Covariate modelling results showed that the disease condition, study duration, geographic region, study year and route of administration were important predictors for the variable placebo effect. The study duration and trial phase were found to be explanatory factors for high dropout rates. In the final covariate model, none of the covariates were correlated with each other, thus reflecting true covariate effects.

the Dropout ModelTo predict the mean changes in the PANSS score appropriately, it was necessary to account for the dropout rate. Figure 1b shows the time course of absolute PANSS scores and its relation to dropouts. From figure 1b, it is evident that those patients who had a higher PANSS score had a greater tendency to drop out from the study, which indicates that the dropout mechanism is not CRD but either RD, RID or ID, as the dropout contains information on disease severity. The performance of the RD, RID and ID dropout patterns was compared, considering CRD as the base model for each of the TTE dropout models. An overview of the parameter estimates with the OFV is shown in table VIII. The RD mechanism had the lowest OFV value irrespective of the TTE model used. In addition to the observed PANSS score (RD), other predictors like the predicted PANSS score

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table VII. Final indirect response model (IRM) placebo model


IRM placebo model parameters

BASL 90.4 [89.3, 91.3]kout (rate of improvement: 1/day) 0.030 [0.023, 0.036]

kin (1/day) 2.90 [2.05, 3.28] Derived from kin = BASL× kout

SLOP 0.14 [0.09, 0.17]

Covariates on placebo model parametersc

BASL-DIS (acute vs chronic) −0.044 [−0.071, −0.020] Chronic patients had a 4.4% lower BASL

kout-DUR (short -vs long-term) −0.84 [−0.95, −0.21] Long-term studies have shown an

84% lower rate of improvement

kout-DIS (acute vs chronic) −0.68 [−0.95, −0.31] Chronic patients had a 68% lower rate of improvement

SLOP-YEAR 0.13 [0.061, 0.23] Increase of 13% in SLOP from the median study year

σ-ADM (oral vs IM) −0.22 [−0.30, −0.13]22% lower intra-individual variability with IM administration vs oral administration

σ-ADM (oral vs SL) −0.41 [−0.51, −0.27]41% lower intra-individual variability with SL administration vs oral administration

σ-DIS (acute vs chronic) 0.68 [0.38, 0.94] 68% higher intra-individual variability for chronic patients

σ-US (US vs non-US trials) −0.27 [−0.35, −0.18] Non-US trials have shown 27% lower intra-individual variability

Exponential dropout model (RD)BHAZ (1/day) 0.00079 [0.00048, 0.00124]

BETA −0.035 [−0.041, −0.030]The risk of dropout increased with a high PANSS score on the preceding visit

Covariates on dropout model parametersb

BHAZ-DUR (short- vs long-term) −0.98 [−0.99, −0.90] Long-term studies had a 98%

lower BHAZ

BETA-DUR (short- vs long-term) 0.85 [0.33, 1.68]

The hazard of dropout with an increasing PANSS score on the preceding visit increased more for long-term studies than for short-term studies

BETA-PHASE (phase III vs phase II) 0.12 [0.07, 0.19]

The hazard of dropout with a high PANSS score on the preceding visit increased more for phase II trials than for phase III trials

continued on next page

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table VII. Final indirect response model (IRM) placebo model


Random effects (IIV and RuV)d

IIV BASL [% CV] 16 [15, 17]IIV SLOP [SD] 0.42 [0.34, 0.43]IIV kout [% CV] 40 [16, 60]σ [SD] 9.18 [8.5, 9.89]

a Total number of parameters: 19. b 95% CI from 1000 bootstrap samples. c The parameter-covariate relationship represents a proportional increase in the parameter value by the covariate. d Shrinkage values for random effects were less than 20%, except for IIV kout (56%).

σ = intra-individual variability; ADM = route of administration; bASL = baseline PANSS score; bETA = parameter relating hazard to the PANSS score; bHAZ = baseline hazard of patient dropout from the study; CI = confidence interval; Cv = coefficient of variation; DIS = disease condition; DuR = study duration; IIv = interindividual variability; IM = intramuscular; kin = rate constant of worsening; kon = rate constant of worsening; kout = rate constant of improvement; PANSS = Positive and Negative Syndrome Scale; PHASE = trial phase (phase III or phase II trial); RD = random dropout; Ruv = residual unexplained variability; SD = standard deviation; SL = sublingual; SLOP = slope parameter linking the placebo concentration with kout; uS = location of study site (in or outside the US); yEAR = study year.

table VIII. Comparison of time-to-event (TTE) dropout models with different dropout patterns in conjunction with the indirect response model (IRM) placebo modela,b

Model Exponential [% RSE] Weibull [% RSE] Gompertz [% RSE]

Dropout patternc CRD RD RID CRD RD RID CRD RD RID

OFV 51082 50551 50848 51051 50514 50842 51059 50550 50857

BHAZ 0.0207 [5]

0.0008 [24]

0.0011 [22]

0.0363 [18]

0.0009 [38]

0.0016 [37]

0.022 [5]

0.0008 [25]

0.0013 [23]

Shape parameter

0.84 [6]

0.96 [7]

0.93 [6]

0.99 [0.1]

0.99 [0.1]

0.99 [0.1]

BETA −0.035 [8]

−0.031 [8]

−0.034 [8]

−0.030 [9]

−0.035 [8]

−0.030 [8]

a The IRM and covariate model parameter estimates are not shown in this table.b A simultaneous approach was used for all of the models to compare the OFV.c We could not estimate both parameters of the ID dropout model (i.e. BETA1 and BETA2).

bETA = parameter relating hazard to the PANSS score; bHAZ = baseline hazard of patient dropout from the study; CRD = completely random dropout; ID = informative dropout; oFV = objective function value; PANSS = Positive and Negative Syndrome Scale; RD = random dropout; RID = restrictive informative dropout; RSE = relative standard error.

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(RID), the observed and predicted PANSS scores (ID), the change in the PANSS score from baseline, the BASL and the difference in PANSS between the last two scores also resulted in a significant drop in OFV. However, on the basis of the simulation results, the probability of a patient dropping out from a trial was best described by the RD mechanism, which is based on the observed PANSS score. The shape parameter estimate of the Weibull and the Gompertz TTE model was close to 1, indicating that both of these dropout models were not different from the exponential dropout model. The NONMEM implementation of the exponential dropout model is simpler than the Weibull and Gompertz dropout models, and this model has one parameter less. Therefore, the exponential dropout model was chosen for further model validation analysis. Stepwise covariate analysis using the exponential dropout model with the RD mechanism, i.e. covariates on BHAZ and BETA parameters, identified the trial duration (DUR) and the trial phase as important contributors to dropout, in addition to the high observed PANSS score.

Fig. 2. Visual predictive check (VPC) plots of total Positive and Negative Syndrome Scale (PANSS) scores including the prediction intervals for the final placebo model. The light blue shaded areas represents the 95% confidence intervals of the corresponding 2.5th, 50th and 97.5th percentiles of the simulated data. The red dashed lines represents the 2.5th, 50th and 97.5th percentiles of the observed data. Graphs (a) to (d) show the VPC results for (a) the Weibull base model; (b) the Weibull model + dropout model + covariates; (c) the external validation dataset: Weibull base model; (d) the Weibull model + dropout model + covariates. Graphs (e) to (h) show the VPC results for (e) the indirect response model (IRM) base model; (f) the IRM + dropout model + covariates; (g) the external validation dataset: IRM base model; (h) the IRM + dropout model + covariates. The marked improvements in the accuracy of predictions in the final models were mainly due to inclusion of a dropout model.

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The NONMEM code for the indirect response model for simulation of the PANSS score and dropout events is shown in Appendix A.

the Final Placebo ModelModel Evaluation and Predictive Performance of Final ModelsBoth placebo models minimized successfully without any numerical difficulties. Condition numbers for the final Weibull and IRM placebo models were 356 and 371, respectively. The uncertainty of the final Weibull model parameter estimates (table VI) was less than 30%, except for one-covariate model parameters, namely Pmax-DUR (41% RSE). The uncertainty of the final IRM parameter estimates (table VII) was also less than 30% except for two-covariate model parameters, namely SLOP-YEAR (34% RSE) and BETA-DUR (39% RSE).

The Weibull model and the IRM estimated parameters and their non-parametric 95% confidence intervals obtained from 1000 bootstrap samples are shown in tables VI and VII. Most of the bootstrap parameter estimates were normally distributed and the median bootstrap parameter values were close to the estimated parameters.

CDDs of the final model showed that both the Weibull and IRM parameters were robust and precise towards the deletion of any one study. Placebo and dropout model-related parameter estimates were consistent upon removal of one study at a time (data not shown).

VPC plots of 1000 simulated datasets for short-term studies are shown in figure 2. In the first scenario, simulations were performed only with the base model using the index dataset (Weibull base model: figure 2a; IRM base model: figure 2e) and the external dataset (Weibull base model: figure 2c; IRM base model: figure 2g). For the second scenario, simulations were performed along with the combined PANSS + dropout model + covariates, in which the observed PANSS scores were replaced with the simulated PANSS scores from the placebo-effect model accounting for dropouts via the dropout model (Weibull final model: figure 2b and 2d; IRM final model: figure 2f and 2h). Simulations using the index dataset and the external dataset indicated that both the Weibull model and the IRM described the placebo data adequately. On the basis of the VPC plots, the IRM base model was found to be more sensitive to the addition of the dropout model and covariates compared with the base Weibull model. The VPC plots were also plotted separately for the different studies and trial designs. Both models could predict the time course of the PANSS score reasonably well when conditioned on study and trial design factors. Representative VPC plots for the IRM are shown in Appendix B. The prediction errors (% bias and % precision) for both models were less than 10%, indicating acceptable predictability of both models.

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DISCuSSIONWe recently reviewed various placebo models that have potential to quantify the placebo response in neuropsychiatric trials.[13] In the present analysis, we have applied these placebo models with the aim of identifying a robust placebo model that can be a useful tool for evaluating the time course of the PANSS score and detecting drug effects in schizophrenia. To achieve this goal, a better understanding of contributors to the placebo effect, patterns of dropouts and factors leading to dropouts across the studies is crucial. Therefore, we applied a nonlinear mixed-effects modelling approach to obtain a more precise estimate of the placebo effect on the basis of the individual level PANSS scores from 1436 patients obtained from studies that included a wide range of patient populations, different dosage regimens and trial designs.

We included long-term studies in our analysis, for two reasons. First, more complex placebo models, such as IRMs or the inverse Bateman function, can estimate parameters related to the rate of improvement and the rate of worsening. Usually, short-term studies carry the information on the rate of improvement,

Fig. 3. Goodness-of-fit plots for the final placebo models corresponding to the index dataset: (a) the indirect response model (IRM) base model in short-term studies; (b) the IRM base model in long-term studies; (c) the Weibull placebo base model in short-term studies; (d) the Weibull placebo base model in long-term studies. PANSS= Positive and Negative Syndrome Scale.

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while long-term studies also carry information on the rate of worsening. The lack of data on worsening might lead to correlations between the structural parameters that eventually inflate the type I and II errors when evaluating the drug effect. Second, inclusion of long-term studies helps to improve our understanding of the trajectory of the placebo response over a longer period of time.

The base placebo model development results showed that both the Weibull and the IRM base models appeared to be adequate to characterize the PANSS data from an entire pooled dataset and from short-term trials only. However, when we modelled the PANSS data from long-term trials separately, parameter estimates of the IRM of the long-term trials were more precise and the corresponding goodness-of-fit plots (figure 3a and 3b) were better than those in the Weibull model (figure 3c and 3d).

In a separate analysis excluding the long-term studies, the covariate analysis detected similar covariate-parameter relationships. Moreover, no differences in model parameter estimates were observed in the placebo model with and without long-term studies, i.e. when covariates related to long-term studies were omitted. Therefore, in this paper, we only present the results of the complete dataset, including long-term studies.

The clinical significance of the covariates that were included in the final placebo model is discussed below.

Study Duration: A considerable part of the ISV in the placebo effect and dropouts was explained by the study duration. The early, pronounced placebo effect in short-term trials could reflect the immediate stabilizing effects of hospitalization. Our findings of a high placebo effect in short-term studies were consistent with the findings of Welge and Keck.[10] Trials of a longer duration have shown weakening of the placebo effect. The lowest dropout in placebo treatment occurred in trials of short duration, which indicates that there is lower risk of dropout in a short-term trial. The higher dropout rate with an increase in the study duration period, as observed in our analysis, is in line with the previous results reported by Wahlbeck et al.[5]

Disease Condition: Data analysis indicated that chronic patients had a lower rate of improvement compared with acute patients. It is possible that a flat placebo effect in chronic patients (as seen in our data analysis) could be responsible for a negative correlation between the BASL and the change in the PANSS score.

Clinical Trial Phase: Results showed a higher dropout rate for phase II trials. Higher dropout rates can be anticipated for phase II trials because of stringent patient inclusion criteria and trial design factors.

Geographical Region: High variability in the placebo effect was observed in studies conducted in the US compared with studies conducted outside the US. It is unclear why this difference exists between the different geographical regions.

Route of Administration: Poor compliance with oral antipsychotic medications was reported for patients with schizophrenia and is probably a reason why oral dosing is associated with high variability in the placebo effect.

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Study Year: A significant correlation between the mean improvement in the PANSS score and the year of the trial was shown.[3,40] This association may be caused by the patient characteristics or trial design features.

Other covariates such as the percentage randomized to placebo, the percentage of females assigned to the placebo arm and the washout period had no or minimal effect on the placebo response. Mallinckrodt et al.[41] reported that the percentage of patients randomized to the placebo arm may be associated with a higher placebo response. However, our results using individual-level data revealed that it had minimal consequences for the placebo effect. Hospitalization information was not available for all of the studies and hence the influence of hospitalization was not investigated. However, Friberg et al.[18] have shown that hospitalization can be an important contributor to the variable response. In our covariate analysis, we did not include ‘study’ as a potential covariate of the placebo effect, because it likely has little clinical relevance for future trial predictions via simulations.

A longitudinal placebo model and the ID model were developed together to study the influence of the dropout model on the placebo structural model parameters. However, joint modelling revealed that the dropout model had a minimal effect on the placebo-covariate model parameter estimates. All three TTE dropout models performed comparatively similarly after accounting for the covariates. The most important factor increasing the dropout rate was a high observed PANSS score, i.e. an RD mechanism. Study duration and the clinical trial phase were contributory factors to dropout on top of the high PANSS score. Our simulations (VPCs) indicated that the accuracy of model predictions was more dependent on the dropout model than on the covariate model. When dropout was ignored, the simulations showed a high PANSS score at the end of the study, while the actual observed PANSS score was much lower. When dropout was included in the simulations, the simulated and observed PANSS scores were similar, reflecting the fact that most patients with the highest PANSS score had dropped out by the end of the study.

The empirical models demonstrated their potential to predict the clinical trials results via a simulation-based approach.[18] However, empirical models usually do not consider physiological mechanisms of the disease. In contrast, the parameter estimates of semi-mechanistic modelling will be more clinically meaningful, as they consider the physiological mechanisms. Post et al.[42] and de Winter et al.[43] have shown the advantages of the mechanistic models over the empirical models in diabetes. The development of mechanism-based models may be challenging for psychiatric disorders where the mechanism of drug action is not fully understood. However, in schizophrenia, dopamine D2 receptor occupancy is assumed to play an important role in the drug effect. Hence, we emphasize more the IRM, as mechanistic components can be integrated within the IRM structure. The IRM for placebo treatment is still rather empirical in nature, with a hypothetical placebo concentration, but it may be considered as a semi-mechanistic model when the

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mechanism of the placebo effect is known[44] or when a drug component is included in the model. In this paper, we focused on the development of robust models for the placebo effect and the dropout rate, including the identification of covariates. The clinical utility (quantification of the true treatment effect for all antipsychotic drugs, as listed in table I) of the developed placebo models integrated with a drug-effect model will be reported elsewhere (Pilla Reddy et al.; in preparation).

CONCLuSIONSOur data analysis using pooled individual PANSS data showed the usefulness of the nonlinear mixed-modelling approach to quantify the time course of the placebo effect and dropout. Our modelling results suggest that the Weibull model and the IRM are more suitable than other placebo models to describe the nonlinear trends in the PANSS score following placebo treatment in schizophrenia trials. The developed placebo models, accounting for dropouts and predictors of the placebo effect, could be a useful tool for evaluation of future trial designs and better quantification of antipsychotic drug effects.

ACKNOWLEDGEMENTSThis research article was prepared within the framework of project no. D2-104 of the Dutch Top Institute Pharma (Leiden, the Netherlands; www.tipharma.com). The authors thank Dr Gijs Santen, Mr Klas Petersson, Dr Lena Friberg, Ms Nisha Kuzhuppilly Ramakrishnan and Dr Teun Post for their suggestions.

An Vermeulen is an employee of Janssen Research & Development (Beerse, Belgium). Jing Liu is an employee of Pfizer Global Research and Development (Groton, CT, USA). Rik de Greef is an employee of Merck Sharp & Dohme (Oss, the Netherlands). None of the other authors have any conflicts of interest that are directly relevant to the content of this study.

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APPENDIX ANoNMEM Code for the Indirect Response Model for Simulation of the PANSS Score and Dropout

$PROBLEM IRM code for simulation of the PANSS score and dropout of placebo effect$INPUT ID ; Patient numberTIID ; Study numberDAY ; Scheduled Day of PANSS measurementTIME ; Actual Day of PANSS or dropout eventDV ; PANSS or dropout EventFLG ; FLG=0 PANSS; FLG=3 dropout; FLG=4 completer; DOSE ; Dose (Zero)STAR ; STAR=1; to indicate that PANSS was measured BASE ; Baseline PANSSCMT ; CMT=1 Dosing; CMT=2 PANSS; CMT=3 Dropout DIS ; Disease typeADM ; Route of AdministrationUS ; Study Centre (US vs. NON USA)YEAR ; Study YearDUR ; Study Duration (short-term vs. long-term)PHAS ; Trial Phase $DATA Data.csv IGNORE=@ $SUBROUTINE ADVAN6 TOL=6$MODEL NCOMP=3 COMP (DOS,DEFDOSE) COMP (EFFECT) COMP (HAZ)

$PK; ------------Dropout Model Covariates-------------------------------------------------------------------IF (PHAS.EQ.1) BEPHAS = 1 ; Most common IF (PHAS.EQ.0) BEPHAS = ( 1 + THETA(16))

IF (DUR.EQ.0) BHDUR = 1 ; Most commonIF (DUR.EQ.1) BHDUR = ( 1 + THETA(15))BHCOV=BHDUR

IF (DUR.EQ.0) BEDUR = 1 ; Most commonIF (DUR.EQ.1) BEDUR = ( 1 + THETA(14))BECOV=BEDUR*BEPHAS

; ---------------Placebo effect covariates------------------------------------------------------------------SLYEA =(1+THETA(17)*(YEAR-2000.5))SLCOV=SLYEA

IF (US.EQ.1) WUS = 1 ; Most commonIF (US.EQ.0) WUS = ( 1 + THETA(11))

IF (DIS.EQ.0) WDIS = 1 ; Most commonIF (DIS.EQ.1) WDIS = ( 1 + THETA(10))

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IF (ADM.EQ.0) WADM = 1 ; Most commonIF (ADM.EQ.3) WADM = ( 1 + THETA(8))IF (ADM.EQ.2) WADM = ( 1 + THETA(9))WCOV=WADM*WDIS*WUS

IF (DUR.EQ.0) KODUR = 1 ; Most commonIF (DUR.EQ.1) KODUR = ( 1 + THETA(7))

IF (DIS.EQ.0) KODIS = 1 ; Most commonIF (DIS.EQ.1) KODIS = ( 1 + THETA(6))KOCOV=KODIS*KODUR

IF (DIS.EQ.0) BLDIS = 1 ; Most commonIF (DIS.EQ.1) BLDIS = ( 1 + THETA(5))BLCOV=BLDIS

;---------------- Baseline PANSS ---------------------------------------------------------------- TVBL = BLCOV*(THETA(1)) ; BL=TVBL*EXP(ETA(1))

;---------------- Placebo Effect Parameters --------------------------------------------------- TVKO = KOCOV*(THETA(2)) ; KO= TVKO*EXP(ETA(3)) KIN= BL*KO TVSL= SLCOV *(THETA(3)) SL=TVSL+ETA(2) TVW = WCOV*(THETA(4)) ; W=TVW;------ Driving function for hypothetical placebo conc.-----------------------------------------------ACTI=0IF(STAR.EQ.1) ACTI=1CEON=ACTIEFF=CEON*SL; --------- Initialize the CMT2 at baseline PANSS------------------------------------------------------- A_0(2) = BL; ------------- Dropout Model Parameters---------------------------------------------------------------- TVBH = BHCOV*(THETA(12)) ; Baseline Hazard BH=TVBH TVBE = BECOV*(THETA(13)) ; Parameter relating dropout hazard to PANSS score BE=TVBE $DES

IF (DAY.LE.7) PTIM=0 IF (DAY.LE.7) LOCF=BLIF (T.LE.TIME) LOCF=KIN-KO*(1+EFF)*A(2)

DADT(1) = 0 ; Dose CMTDADT(2)= LOCF ; Simulate the PANSS score and carry forward as LOCFDADT(3)= BH*EXP(-LOCF*BE)IF(ISFINL.EQ.1) PTIM=TIME

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$ERROR;------------------- PANSS simulation-----------------------------------------------------------------------IPAN=KIN-KO*(1+EFF)*A(2) SCOR=A(2)IF(FLG.LT.2) THEN F_FLAG=0 ;If continuous type data (PANSS data)IPRED=A(2)+ERR(1)*WIRES= DV-IPREDIWRES= IRES/WOPAN=IPRED; ------------------HAZARD PREDCITION -----------------------------------------------------------------IF (NEWIND.NE.2) LOC=0 ; Set LOCF value to 0 for new ID at time 0 IF (NEWIND.NE.2) TIM1=0 ; Set time value to 0 for new ID at time 0 IF (NEWIND.NE.2) CHZ1=0 ; Set CHZ value to 0 for new ID at time 0 CHZ2=BH*EXP(-BE*LOC) ; Calculate cumulative hazard for each timeTOCH=CHZ1+CHZ2*(TIME-TIM1) ; Total cumulative hazard over timeCHZ1=TOCH ; Redefine previous CHZ to currentTIM1=TIMELOC = OPAN ; Redefine previous PANSS to the currently simulated SUR= EXP(-TOCH) ; SurvivalIF (FLG.EQ.3) IPRED = SUR*BH*EXP(-BE*LOC) ; Hazard of Dropout from a trialIF (FLG.EQ.4) IPRED = SUR ; No dropout event CompletersIF (FLG.GT.2) THENF_FLAG= 1 ; For categorical data (dropout event)Y = IPRED ; Y is probability for TTE dataENDIF;------------Simulation code for dropout event based on PANSS Score-----------------------------IF (NEWIND.NE.2) FLAG1=0 ; Set FLAG1=0 for every new IDREP=IREP ; IREP The number of the current replication IF(ICALL.EQ.4)THEN ; During Simulation when it’s a categorical event IF(NEWIND.NE.2) THEN CALL RANDOM (2,R) ; Call a random number TMP=R ; Store the random number ENDIF IF(FLG.GT.2)THEN DV=0 FLG=-1 ; Set all categorical DV’s to 0 ENDIF ; for different study designs different conditions, one such example is given hereIF (TIID.EQ.384.AND.TMP.GT.SUR.AND.TIME.LT.52.AND.FLAG1.EQ.0) THEN DV=1 FLG=3 ; Dropout event ENDIF

; Once patient drops out no more event happens in this patient IF (FLG.EQ.3) FLAG1=1 IF (TIID.EQ.384.AND.FLAG1.EQ.1.AND.TIME.GT.52.AND.FLG.EQ.-1)THEN DV=0 FLG=5 ; Once patient drops out no more event happens in this patient ENDIF

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; If ID had no event until time 52 then censor last observation and FLG to 4 IF (TIID.EQ.384.AND.FLAG1.EQ.0.AND.TIME.GT.52.AND.FLG.EQ.-1)THEN DV=0 FLG=4 ; Completed the study ENDIF ENDIF;-----------------------------------------------------------------------------------------------------------------$THETA .......$OMEGA .......$SIGMA .......$SIMULATION (578988566) (1234 UNIFORM) ONLYSIM SUB=1000

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APPENDIX b

Figure B-1. Visual predictive checks for the final indirect response model (IRM) conditioned on different studies.

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