University of Groningen

Translational PKPD modeling in schizophreniaPilla Reddy, Venkatesh

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CHAP

TER9

Pharmacokinetic-Pharmacodynamic Modelling of Severity levels of

Extrapyramidal Side Effects with Markov Elements

Venkatesh Pilla Reddy,1* Klas j. Petersson,2* Ahmed Abbas Suleiman,2 An Vermeulen,3 johannes H. Proost,1 and lena E. Friberg2.

Submitted

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

2 Department of Pharmaceutical Biosciences, Uppsala University, Uppsala, Sweden

3Advanced PKPD Modelling and Simulation, Janssen Research & Development, a Division of Janssen

Pharmaceutica NV, Beerse, Belgium

* The first and second authors contributed equally to the paper

AbSTRACTA major problem in the treatment of schizophrenic patients with current antipsychotic drugs, mainly acting as dopamine-2 receptor antagonists, is the occurrence of side effects such as Extra-Pyramidal-Symptoms (EPS). Meta-analyses of summary data of EPS occurrence, and receptor occupancies inferred from mean plasma concentrations, have shown the incidence of EPS to rise when receptor occupancy is above approximately 80%. In this analysis, individual longitudinal EPS data from 2630 patients participating in one of seven different trials and treated with haloperidol, paliperidone, ziprasidone, olanzapine, JNJ-37822681, or placebo, was analyzed using a compartment-based probability model with Markov elements. The developed pharmacokinetic-pharmacodynamic model describes the longitudinal changes of spontaneously reported EPS-related adverse events and their severity levels rated by clinicians. Individual steady-state concentrations and occupancy levels were found to be predictors for EPS. The results confirm 80 % occupancy as a level of increased EPS occurrence rates, also at the individual level.

9

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PKPD MODELLING OF EPS SIDE EFFECTS

INTRODuCTIONSchizophrenia is a chronic psychiatric condition that includes positive symptoms (e.g. delusions, hallucinations), negative symptoms (e.g. lack of motivation, social withdrawal), and cognitive symptoms (e.g. lack of attention, loss of memory). These symptoms can severely affect the social, educational, occupational and health related functioning of the individual.[1] It has been hypothesized that schizophrenia is associated with excessive dopamine activity in the mesolimbic dopaminergic neurons (causing positive psychotic symptoms) and reduced dopamine activity in the mesocortical dopaminergic neurons (causing negative and cognitive symptoms).[2]

Antagonism at the dopamine D2 receptor is the common mechanism of action for currently available treatment of schizophrenia.[3] However, D2 receptor occupancy (D2RO) higher than 80% in other regions than the mesolimbic and mesocortical dopaminergic pathways, e.g., nigrostriatal pathway in the brain increases the risk of adverse effects (AEs) such as extrapyramidal symptoms (EPS).[4]

Extrapyramidal side effects of antipsychotic drugs (APs) include acute movement disorders such as Parkinsonism, akathisia, dystonia and chronic movement disorders such as tardive dyskinesia and tardive dystonia. In addition to being uncomfortable to patients, these side effects could behave as confounding factors and may lead to an underestimation of efficacy of the APs.[5] In drug development EPS symptoms are often accessed using rating scales [e.g. Simpson–Angus Scale (SAS) and Extrapyramidal Symptom Rating Scale (ESRS)] or by occurrences spontaneously reported by patients, the severity of which are graded by clinicians at the time of planned visits.

Atypical antipsychotics (ATAPs) were introduced to the clinic in an attempt to lower the EPS incidence compared to the typical antipsychotics (e.g. haloperidol) and to improve the negative and cognitive symptoms of schizophrenia. One of the claims while marketing ATAPs is “the absence of EPS side effects”.[6,7] Recently, a meta-analysis of ATAPs vs. haloperidol using a central-tendency statistical approach to evaluate such a claim was performed and it demonstrated that at least some ATAPs do produce EPS and that there are differences between drugs in their tendency to produce EPS.[7] Previously described assessments of EPS either looked at mean differences in either Simpson-Angus Scale or EPS-incidence on a study level[8] or indirect measurements such as the prescription of anti-EPS treatment. Until now, no papers have been published linking individual data of EPS to predictors such as plasma concentrations or receptor occupancy using pharmacokinetic-pharmacodynamic (PKPD) models developed describing the longitudinal aspect of EPS events following antipsychotic treatment. However, de Ridder and Vermeulen[9] modeled the time to the first treatment-emergent EPS-related event using hazard models, without considering the severity of the EPS events and presented the results in a book chapter.[9]

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203

The discrete nature of observations of events or discrete type scales as the ones used for EPS assessments calls for likelihood type models. In the field of PKPD models, one of the approaches that could be used is the proportional odds model. However, this model does not assume dependency between observations and the profiles generated from simulations can be physiologically implausible with individuals moving more frequently between the EPS severity levels than observed. Markov elements would be needed to handle that property of the data. Another approach would be to assess the time-to-EPS of a certain severity grade using survival models but these would not take into account that patients stay in one state for several observations nor that the probability of states are correlated. A compartmental Markov type of model is capable of estimating parameters considering time factor and hence eliminating the need of having frequent observations at equal spaces of time needed in ordinary Markov models or ordered categorical models.[10] In addition, we can scale time (e.g. compute probability for one day and scale to X days). Markov type of model allows predicting the probability of observing a patient at any of the EPS severity grades depending on what severity grade he or she had at the last observation and the time elapsed since the last observation. Thus, Markov modelling approach can help to quantify and compare the potency of different APs to induce EPS AEs over a time.

In this analysis, the aim was to develop a compartmental, population-based mixed-effects Markov model to describe the probability of EPS incidence and EPS severity as a function of dose, individual steady-state drug exposure (Css) or predicted dopamine D2RO of APs. All available ordered categorical EPS data after the administration of placebo, four ATAPs (paliperidone extended release, ziprasidone, and JNJ-37822681, olanzapine) and haloperidol from seven clinical studies were used.

METHODSStudies, Patients and EPS scores EPS modelling was performed using individual-level data obtained from six randomized, placebo-controlled, clinical trials, and one open-label study conducted in schizophrenic patients. The study durations ranged from 4 to 12 weeks, following oral administration of one of five APs, namely, haloperidol, olanzapine, paliperidone extended release, ziprasidone, and JNJ-37822681.

EPS-related AEs included side effects that were reported spontaneously by patients over the study period. The important AEs documented were akathisia, hyperkinesia, dystonia, Parkinsonism, dyskinesia, tardive dyskinesia, hypokinesia, and tremor. Since the total number of events was too low for some AEs to draw conclusions about the exposure-response relationship, and since not all trials reported on all types of EPS-related AEs, the model was developed without discriminating between the different types of EPS-related AE.

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PKPD MODELLING OF EPS SIDE EFFECTS

According to the design of the studies, the clinicians consulted patients at least once a week during the total study duration. Some studies included two visits during the first week of the trial. Patients were directed to record the incidence of EPS, the duration of the EPS episode and resolution of any EPS, the severity of which was graded by clinicians on a scale from 0 to 3 (0: no EPS, 1: mild EPS, 2: moderate EPS and 3: severe EPS). Transitions were thus possible on any day and not only on visit days. If the patient dropped out before the end of the study, all available EPS scores until the day of dropout were included in the analysis. If several manifestations of EPS were experienced simultaneously, but differing in grade, the grade was set to the highest grade. In all trials, patients were hospitalized for the first 2-3 weeks of the study period.

Data were analyzed by non-linear mixed-effects modelling using the LAPLACE method in NONMEM 7, level 1.2,[11] with front-end interface PsN 3.4.2.[12] R version 2.11 and higher versions were used for data management purposes and generating graphic outputs.[13]

PharmacokineticsA patient-specific steady-state concentration (Css) was calculated using post-hoc Bayesian estimates of clearance obtained from previously developed PK models.[14-17] The typical apparent clearance (CL/F) estimates were 88 l/h for haloperidol, 14 l/h for paliperidone, 20 l/h for olanzapine, 54 l/h for ziprasidone, and 25 l/h for JNJ-37822681. The calculated individual Css was then linked to the time-course of EPS incidence. Css was set at 0 for subjects receiving placebo.

EPS model structureA first-order Markov chain–type model was used. Figure 1 shows the model structure and corresponding differential equations used to model the EPS incidence rates. EPS events were categorized on an ordered categorical scale based on the intensity of EPS-related AEs. Because there were few observations on severe EPS, the moderate and severe EPS states were combined and consequently a three-state scale was used. A Markov transition model with three compartments (Figure 1) was used and the rate constants of the change in probability over time of an observation being in the different states were estimated. Each compartment represented the probabilities of a different state (no EPS, mild EPS, and moderate/severe EPS). The probability at t=0 was set to 1 for the observed EPS state. The probabilities were allowed to distribute between the compartments and the first-order rate constants between the compartments were estimated. After an observation, all compartments were reset to zero and the compartment corresponding to the observed EPS state of the patient was initialized with a 100 % probability.

Effects of time, drug exposure, receptor occupancy, and covariates on transition probabilities were evaluated in the Markov model as a proportional relation on the transition rate parameters. Drug and covariate effects were tested on each transition parameter separately, and in combination.

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tab

le 1

. 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 E

PS m

odel

Stu

dy

Des

ign

Stu

dyD

ura

tion

Rou

te o

f A

dm

inis

trat

ion

Dru

g/D

ose

#Su

bje

cts

% E

PS

rate

*

SCH

-303

Phas

e-II

I, do

uble

-blin

d, p

aral

lel,

plac

ebo

cont

rolle

d, ra

ndom

ized

6

wee

ksOr

al/o

nce

daily

Palip

erid

one

ER 6

,9,1

2 m

g33

519

Olan

zapi

ne 1

0 m

g12

27

Plac

ebo

116

8

SCH

-304

Phas

e-II

I, do

uble

-blin

d, p

aral

lel,

plac

ebo

cont

rolle

d, ra

ndom

ized

6 w

eeks

Oral

/onc

e da

ilyPa

liper

idon

e ER

6,1

2 m

g19

916

Olan

zapi

ne 1

0 m

g10

18

Plac

ebo

976

SCH

-305

Phas

e-II

I, do

uble

-blin

d, p

aral

lel,

plac

ebo

cont

rolle

d, ra

ndom

ized

6 w

eeks

Oral

/onc

e da

ilyPa

liper

idon

e ER

3,9

,15

mg

333

21Ol

anza

pine

10

mg,

121

7Pl

aceb

o10

77

128-

114

Phas

e-II

I, do

uble

-blin

d, p

aral

lel,

plac

ebo

cont

rolle

d, ra

ndom

ized

6 w

eeks

Oral

/tw

ice

daily

Zipr

asid

one

40, 8

0 m

g13

126

Plac

ebo

9220

128-

115

Phas

e-II

I, do

uble

-blin

d, p

aral

lel,

plac

ebo

cont

rolle

d, ra

ndom

ized

6 w

eeks

Oral

/tw

ice

daily

Zipr

asid

one

20,6

0,10

0 m

g15

429

Hal

oper

idol

10

mg

8559

Plac

ebo

8220

SCH

-200

2Ph

ase-

II, d

oubl

e-bl

ind,

par

alle

l, pl

aceb

o co

ntro

lled,

rand

omiz

ed 6

-12

Wee

ksOr

al/t

wic

e da

ilyJN

J-378

2268

130

124

Olan

zapi

ne 1

5 m

g (Q

D)

9315

Plac

ebo

103

6LM

UOp

en-la

bel s

tudy

4

wee

ksOr

al/o

nce

daily

Hal

oper

idol

2.5

-40

mg

5895

Dem

ogra

phic

s inc

lude

d in

this

ana

lysi

s: G

ende

r: m

ales

(55

%) a

nd fe

mal

es (4

5 %

); R

ace:

Cau

casi

ans (

67 %

), Bl

acks

(18

%),

Asia

ns (7

%) a

nd o

ther

s (6

%);

Geo

grap

hica

l reg

ion:

Uni

ted

Stat

es o

f Am

eric

a (~

41

%),

East

ern

Euro

pe (~

35

%),

Asia

(~10

%) a

nd o

ther

regi

ons (

~13

%) a

nd c

onco

mita

nt

med

icat

ions

for

trea

ting

EPS:

ant

i-cho

liner

gic

drug

s (1

2 %

), be

ta-b

lock

ers

(1.8

%) a

nd b

enzo

diaz

epin

es (1

%).

*EPS

rate

: [nu

mbe

r of

sub

ject

s w

ith

trea

tmen

t-em

erge

nt E

PS-r

elat

ed A

Es (i

rres

pect

ive

of s

ever

ity)/

tota

l num

ber o

f sub

ject

s ra

ndom

ized

in a

tria

l or t

reat

men

t arm

]

9

206

PKPD MODELLING OF EPS SIDE EFFECTS

Fig. 1. EPS compartmental model structure with possible transitions (no EPS, mild EPS and pooled moderate/severe, defined as compartment 1, 2, and 3, respectively). The forward rate transitions constants KF12 and KF23 were allowed to be influenced by drug exposure or D2RO.

Placebo effect and drug effect Various functions such as constant, linear, exponential and Weibull functions were explored for describing a change over time in the transition probability rate constants. The contribution of drug effect to the transition probabilities were modeled after the placebo model was built. The antipsychotic drug exposure was related to the EPS incidence with increasing complexity using linear, Emax and sigmoid Emax models and tested on top of parameters estimated for the placebo group. To characterize the relationship between EPS incidence and dopamine D2RO levels, the following relationship was used to calculate D2RO for each patient:

Where, ROmax is the maximum receptor occupancy, Kd is the plasma level of antipsychotic drug associated with 50 % of ROmax. The values of Kd for D2 receptor binding were obtained from literature, where Emax models were used to fit D2RO and plasma drug concentrations data obtained from PET studies. The Kd values for D2 receptor binding (assuming ROmax 100%) were 0.56 ng/ml for haloperidol, 12 ng/ml for olanzapine, 4.9 ng/ml for paliperidone, 33 ng/ml for ziprasidone,[18] and 15 ng/ml for JNJ-37822681.[19]

Covariate modelInfluences of patient and study specific covariates were evaluated as possible explanatory variables for the individual variability in the model parameters (Table 1). The potential effect of concomitant medications for treating EPS was tested using the data from paliperidone trial where exact time of start and stop of these medications were known.

Covariates were included in the model using different functional forms like linear, piece-wise linear, power and exponential functions.[12] Only non-missing, clinically relevant, and uncorrelated covariates that met the pre-defined statistical criteria (p <0.05) were included in the EPS model.

Final model selection and model evaluation During initial model building, differences in the objective function value (OFV; difference denoted as ΔOFV: 3.84 as a cut-off value) between the models together with % RSE (from NONMEM covariance step) of the parameters were used to

9

207

guide the selection of the model. A bootstrap analysis (1000 samples) was carried out, for both the drug exposure-EPS and the receptor occupancy-EPS models, to check the precision of the estimates and to construct a 95 % confidence interval for each of the parameter estimates. The adequacy of the model was investigated with simulation-based visual predictive checks (VPC). Briefly, lower and upper prediction intervals of the proportions of patients at each EPS state at each planned observation as well as transitions between the different EPS states were constructed using 100 simulated replicates of the initial dataset and compared with the corresponding observed proportions or transitions.

RESuLTS EPS dataThe EPS dataset consisted of 16,598 observations (rated as no EPS, mild, moderate or severe) collected from 2,630 subjects with acute schizophrenic condition. Of these subjects, 594 subjects received placebo; 867 subjects paliperidone (3-15 mg/day); 437 subjects olanzapine (10 or 15 mg/day); 143 subjects haloperidol (2.5-40 mg/day); 285 subjects ziprasidone (40-200 mg/day) and 301 received JNJ-37822681[20] treatment (10-30 mg/day). Table 1 summarizes the trial designs and the observed EPS incidence rates of APs that were used in this study. The calculated individual-level Css and the predicted D2RO range (min-max) were as follows; for haloperidol (1-4 ng/ml; 55-98 %); olanzapine (9-76 ng/ml; 44-86 %); paliperidone (0.5-115 ng/ml; 9-95 %); ziprasidone (24-282 ng/ml; 38-89 %); JNJ-37822681 (8-178 ng/ml; 35-92%).

Structural model for EPS incidenceTo be able to calculate the probabilities of observing each EPS severity grade at any time point, the probabilities were determined by a Markov model with a compartmental structure using differential equations (Figure 1). To model the EPS occurrence, a placebo model was first developed based on the placebo data alone. Thereafter the combined placebo and drug effects model was built by estimating placebo and drug effect parameters. Following the start of the study, the decrease of the transition rates as a function of time over the study period was best described by the exponential model (Eqs. 1 and 2). A linear model described the relationship between the drug exposure (Eq 3) and the effect of APs on the transition rate constants reasonably well. Modelling the drug effect, using dose or Css, as proportional to the placebo effect resulted in a better model fit and lower relative standard errors of the parameter estimates, compared to additive drug effects. Emax model was the best to link D2RO and EPS events (Eq 4).

9

208

PKPD MODELLING OF EPS SIDE EFFECTS

(Eq. 1)

(Eq. 2)

(Eq. 3)

(Eq. 4)

Differential equations used to model the probability of observing EPS event

dA(1)/dt=KB21×A(2) - KF12×A(1)

dA(2)/dt=KF12×A(1) + KB32×A(3)- KB21×A(2) - KF23×A(2)

dA(3)/dt =KF23×A(2) - KB32×A(3)

KF12=Base12×exp (-k12×time) × (Drug Effect)

KB21= Base21×exp (-k21*time)

KF23=Base23×exp (-k23*time) × (Drug Effect)

KB32= Base32×exp (-k32*time)

KFxy is the forward transition probability rate constant at a given time and treatment; KBxy is the backward transition probability rate constant at time t. Basexy the transition probability rate constant at the start of the study; x: present EPS state; y: future EPS state; t(1/2)= ln2⁄kxy ; t1/2: half-life describing the change in KFxy or KBxy with time; Drug effect is the effect of antipsychotic drug on KFxy; EFF is the drug dependent slope parameter in relation to drug exposure; Emax represents the maximum drug effect on the transition rate from state x to state y; RO50 is the model parameter that corresponds to compound independent D2RO required for 50% of Emax effect; A(1), A(2), A(3) represents the compartments for EPS probabilities.

Inclusion of inter-individual variability (IIV) as an exponential function (log-normal distribution) to describe differences between patients’ sensitivity to treatment effects resulted in an improved model fit by objective function, however the model was numerically unstable and parameters were estimated with less precision and simulation properties worsened, probably due to non-normal distributions of random effects that frequently arise for categorical type models. Allowing for semi-parametric distributions[21] did not improve simulation properties. Therefore, the model was built without IIV in the typical parameters. Visit 4, scheduled to be between day 14 and day 21 (except LMU

9

209

study), corresponds to the point in the study at which subjects were allowed to enter into an outpatient status. The improvement in the model fit and in visual predictive checks showed that it was important to allow some parameters to have different values before and after visit 4 (approximately day 16).

The effect of predictors was only significant to estimate on the forward transition rate constants [i.e. transitions from no EPS to mild (KF12) and from mild to moderate/severe EPS (KF23)]. Based on the NONMEM OFV value, Css was better than dose (decrease of ~45 OFV units) in describing the drug-EPS relationships. The final EPS model structure (based on all drugs simultaneously) was able to describe the observed EPS occurrence adequately with acceptable low relative standard errors.

To further characterize the relationship between D2RO by different APs and the emergence of EPS, predicted D2RO levels associated with Css were linked to the transition rate constants by either using a linear function (Eq 3) or sigmoidal function (Eq 4) with Q transformation of the D2RO: Q=D2RO/(100-D2RO). The advantage of this transformation is that it allows Q to have a value from zero to infinity for D2RO from 0 to 100% and allowing the Drug Effect to reach its maximum effect (Emax ) for D2RO approaching 100% (Eq. 4). This parameterization resulted in statistically better and numerically more stable estimation than directly linking the absolute D2RO levels to the transition rate constants.

The parameter estimates of the EPS model when using Css and D2RO as predictors are shown in Table 2. The dopamine D2RO needed for half of the maximum effect of APs on the transition rate was found to be 86.5 %. The post-hoc forward transition rate constants for each individual vs. predicted individual D2RO (based on Css and Kd) for different antipsychotic drugs are depicted in Figure 2. It is evident that haloperidol exhibited higher EPS occurrence rates when compared to ATAPs despite the same level of D2RO.

Olanzapine was found to be less associated with EPS events than placebo treatment, causing difficulties in estimating the effect of olanzapine on EPS transitions. The EPS incidence was higher (15 %) for the olanzapine arm compared to the placebo treatment in one of the studies (SCH-2002), but individual plasma olanzapine profiles were not available from this study, which may have contributed to difficulties in estimating the effect of olanzapine exposure effect on the probability of EPS.

Covariate modelCovariates were included in the model based on their statistical significance and clinical effect. The final EPS model included only one covariate (regional difference: Eastern Europe vs. other) which was added as a proportional linear term to the corresponding transition probability. Residing in Eastern Europe increased the chances of improvement of the EPS side effects since it increased backward movement probability rate constants (KB21 and KB32) by ~100 % (Table 2). Not all covariate information was available for all trials to test the influence

9

210

PKPD MODELLING OF EPS SIDE EFFECTS

of covariates on the probability of EPS. Only paliperidone trials had important covariate information such as co-medication and complete demographic details. Based on only the paliperidone data, administration of anti-cholinergic drug for the treatment of EPS was found to be an influential covariate, decreasing the transition probability rate constant for movement from a mild EPS state to moderate/severe EPS states by ~80 %.

Model evaluationThe final models (Table 2) were evaluated using a bootstrap analysis with 1000 samples. 95% confidence intervals were constructed for each of the parameters and none of these overlapped zeros. The population estimates of the final model are in close agreement with the median values of the 952 successful bootstrap replicates. Visual predictive checks (VPCs) using 100 simulated data sets were

Fig. 2. Increase in forward rate constants for all individuals by the final model vs. predictions of drug occupancy based on individual Css. All doses for ATAPs and only lower doses of haloperidol (<10 mg/day) were used.

9

211

tab

le 2

: Par

amet

er e

stim

ates

(95%

CI f

rom

boo

tstr

ap a

naly

sis)

of t

he fi

nal E

PS m

odel

s us

ing

C ss a

nd D

2-rec

epto

r occ

upan

cy a

s pr

edic

tors

of E

PS.

Pre

dic

tor

Stea

dy-S

tate

Exp

osu

re(l

inea

r M

odel

)D

2 R

ecep

tor

Occ

up

ancy

(Em

ax M

odel

)

Par

amet

ers

<=

Day

16

> D

ay 1

6<

=D

ay 1

6>

Day

16

Base

12 (d

ay-1

)0.

0178

(0.0

14-0

.022

)0.

0186

(0.0

15-0

.022

)Ba

se21

(day

-1)

0.13

5 (0

.104

-0.1

7)#

0.07

03 (0

.051

-0.0

96)#

0.13

4 (0

.107

-0.1

68)#

0.07

8 (0

.06-

0.10

)#

Base

23 (d

ay-1

)0.

263

(0.1

83-0

.310

)0.

0703

(0.0

51-0

.096

)#0.

369

(0.2

52-0

.522

)0.

078

(0.0

6-0.

10)#

Base

32 (d

ay-1

)0.

135

(0.1

04-0

.17)

#0.

134

(0.1

07-0

.168

)#

t ½ fo

r KF 12

(day

s)8.

8 (7

.2-1

0.6)

#8.

9 (7

.5-1

0.0)

#

t ½ fo

r KF 23

(day

s)2.

9 (2

.1-3

.7)

8.8

(7.2

-10.

6)#

2.7

(2.2

-3.3

)#8.

9 (7

.5-1

0.0)

#

t ½ fo

r KB 21

and

KB32

(day

s)22

(14.

8-33

.2)

20 (1

4.7-

27)

EFF:

Hal

oper

idol

2.

4 (1

.43-

2.84

)-

EFF:

Pal

iper

idon

e 0.

0198

(0.0

11-0

.032

)-

EFF:

Zip

rasi

done

0

.008

9 (0

.004

5-0.

0142

)-

EFF:

JNJ-3

7822

681

0.01

94 (0

.011

2-0.

029)

-Ef

fect

of r

esid

ence

in E

aste

rn E

urop

e on

KB 21

and

KB 32

0.79

(0.2

7-1.

55)¥

1.08

(0.5

8-1.

73)

Emax

-1.

73*

(0.9

7-3.

0)RO

50 (%

)-

86.5

* (7

5.9-

95.3

)γ

(sha

pe p

aram

eter

)-

1.3*

(0.7

8-4.

8)Φ

OFV

7740

(713

0-82

81)

7963

(742

6-84

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made to evaluate the predictive ability of the model. The model was capable of satisfactorily predicting the proportions of the patients experiencing each of the EPS states across time (Figure 3). The number of transitions simulated from the model was found to be reasonably consistent with the observed number of transitions as shown for the paliperidone data (supplementary file figure 1).

DISCuSSION This work describes a PKPD modelling approach that successfully characterized the temporal course of the proportions of patients experiencing different grades of EPS following exposure to one of 5 different antipsychotic drugs or placebo. The dependency of a future EPS event on the current state was accounted for by using a compartmental structure, defined by differential equations, for the probabilities of observing each severity grade at any time point (Fig. 1).[10,22] The probabilities were thereby continuous with respect to time, and coupled to the observed scores through a probabilistic model. Markov elements can also be incorporated in a proportional odds model,[23] however, that type of model is discrete in time and the sampling times and frequencies can greatly influence the parameter estimates.[24] The analyzed studies included self-reported EPS events, and consequently the EPS observations were not equally spaced in time. Therefore, the compartmental Markov modelling approach was chosen and was shown to handle the dependency between successive observations of ordered adverse events well.

The simultaneous fit of the model to all data resulted in one set of parameter estimates that to an adequate degree could simulate the proportions of patients experiencing EPS after treatment with one of four different compounds studied in seven different trials (Figure 3). The simulations of the transitions between different states show that the model cannot recreate exactly every transition seen in the data, but in relation to the huge differences between the occurrence of the different transition types, from 0.1 % to above 90%, we conclude that the overall pattern of transitions can be described by the model (supplementary file; Figure 1). A linear model with respect to steady-state concentrations was better than using the predicted D2-receptor occupancy as a direct link to EPS. Looking at figure 2, this finding concurs with what de Greef et al.[5] found on the meta-data level, where the incidence rate increases at occupancy >80%.

A 100% increase in forward rate constants corresponds to a 50% decrease of the half-time to having an event, compared to placebo. The model dependent on the D2-receptor occupancy can however be used to predict EPS for a new D2-receptor antagonist using the drug Kd and information on the typical PK profile. The model can also simulate the longitudinal correlations seen in EPS AE data.

It has been suggested that ATAPs induce EPS[5] at a lower rate than typical antipsychotics. A model-based approach can help to investigate and quantify

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these hypotheses and to compare the potency of different APs to induce EPS by using the same model structure. The EPS occurrence rate was approximately 16 times higher for haloperidol than for ATAPs. Haloperidol exhibited higher EPS occurrence rate even at the lower doses of ≤10 mg/day (Figure 2).

Regional differences in the EPS incidence might be an important factor explaining the differences between studies and need to be taken into consideration. Study region was found to be an important covariate where patients studied in Eastern Europe had a lower incidence and shorter average event lengths of EPS than other countries. The reason for this is not clear but regional differences in study results are not uncommon, different attitudes towards reporting adverse events could be one reason.

The present EPS model did not consider the dropouts, as in dropout modelling; a standard assumption is that within a subject the risk of dropout is independent of the risk for the EPS event or whatever the effect modeled. If this is not the case, the parameter estimates of the effect model could be slightly biased.[25] However, EPS was not the major reason for discontinuation of treatment, but primarily discontinuation was due to lack of efficacy and subject’s choice.

It is an important task to ascertain a dose and dosing regimen that would provide adequate exposure maintaining target D2RO of 60-80 % with a low risk of AEs such as EPS. Overall, this data analysis indicated that olanzapine was well tolerated in patients with schizophrenia as it was not possible to estimate a slope parameter for the effect (EFF in Eq 3). However, the proportions of patients with EPS at a given time point, and therefore the absolute numbers of events were relatively low for both placebo and olanzapine in this study and hence the parameter estimates were uncertain. It may be that olanzapine has a favorable EPS profile[26] due to binding to receptors such as 5-HT2A, but that olanzapine would truly have lower incidence rates than placebo seems unlikely.

In conclusion, a model was successfully developed that can characterize the temporal course of the proportions of patients experiencing different grades of EPS using a compartmental model structure incorporating Markov elements. To our knowledge, this approach has not been used for characterizing side-effect data in general and no population models have been developed for EPS side effects. The approach could be used for any adverse event with severity grading and a reported duration. The model quantifies the relationship between the occurrence of EPS and movement to higher EPS states and the different predictors of exposure (dose, Css), as well as receptor occupancy of the different APs.

ACKNOWLEDGEMENTSKlas J. Petersson was supported by a grant from Janssen Research & Development (Beerse, Belgium). Venkatesh Pilla Reddy was supported financially by the Dutch Top Institute Pharma (Leiden, The Netherlands; www.tipharma.com) within the framework of project no. D2-104 (Mechanism-based PK-PD modelling platform).

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We thank Dr. Jing Liu (Pfizer Global Research and Development, Groton, USA) for her contribution to this article via Top Institute Pharma. We also thank Professor Dan Rujescu (Department of Psychiatry, Ludwig Maximilians University, Munich, Germany) for sharing the haloperidol data. We thank Professor Geny M.M. Groothuis, Professor Meindert Danhof, and Dr. Magdalena Kozielska for their scientific inputs.

SuPPlEMENtARy FIlE:

Fig. 1. Visual predictive check of Markov model transitions for paliperidone treatment. The dashed black lines represent the 10th and 90th percentiles of the simulated number of transitions. Green and red solid line indicates the median observed and simulated transitions, respectively.

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