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A Mechanism-Based PK/PD Model Predicts the Time-Course of Hematological responses for Epoetin beta
N. Hayashi, K. P. Zuideveld, P. Jordan & R. Gieschke
Modeling & Simulation Group & Biometrics, F. Hoffmann-La Roche AG, Basel, Switzerland
June 13th, 2003, PAGE meeting, Verona, Italy
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Objectives
to develop a Mechanism-Based PK/PD model:to describe the hematological responses in healthy volunteers’ studyto predict the hematological responses in renal anemia patients’ studies to predict not only mean values but also individual values’ distributionto predict the responses for different dose routes & different dose frequencies
Mechanism of Epoetin pharmacodynamicsOutline
PK/PD modeling with healthy volunteers’ studySimulation for renal anemia patients’ studies
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Mechanism of Epoetin pharmacodynamicsPhysiological background (1)
Erythropoietin stimulates the release of RBC (reticulocyte) from Bone Marrow
Erythropoietin is a glycoprotein produced in the kidneysRenal dysfunction patients show anemia because the endogenous EPO production is reduced
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Mechanism of Epoetin pharmacodynamicsPhysiological background (2)
1 day
EPO stimulation
Stem-cells RET Mature
RBCRET
Bone marrow Blood
Release
Death
120 days± 1 wk
> 1 dayRBC precursors RBC
Kidneys Hemoglobin↑
Endogenous EPO↓
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Mechanism of Epoetin pharmacodynamicsCharacteristics of PK/PD model
an identical life span for all RBC (zero order elimination)a homeostatic negative feed back a lag timean indirect response model for reticulocyte with a variable kout (immature reticulocyte increase)
a blood sampling effectan Emax model with a variable base line
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Mechanism of Epoetin pharmacodynamicsModel equations
)t(CEC
)t(CE)t(P)t('P
p
pmax
+
×+=
500
RET = ReticulocytesRBC = Red Blood Cell
RBC
kin
CERA Concentration
+
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Mechanism of Epoetin pharmacodynamicsModel equations
( )SPAN/)(RBCP
)t(HbSlopeexpP)t(P
00
00
=
×−×= ∆
RET = ReticulocytesRBC = Red Blood Cell
RBC
kin
CERA Concentration
+ -
Negative Feedback
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Mechanism of Epoetin pharmacodynamicsModel equations
( ))t(P)t('Pdt
)t(dP−=
τ1
RET = ReticulocytesRBC = Red Blood Cell
RBC
kin
CERA Concentration
+ -
Negative Feedback
lag-time
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Mechanism of Epoetin pharmacodynamics
RET = ReticulocytesRBC = Red Blood Cell
kzero order
( )
10001000
13
01
00
/MCV*)t(RBC)t(Ht
/MCH*)t(RBC)t(Hb
/WTVOL
)SPANt,tt(
VOLSAM*)t(RBC
dtP)t(P)(RBC)t(RBC
n
t
i
iit n
==
=<<
−−+= ∑∫=
RBC
kin
CERA Concentration
+ -
Negative Feedback
lag-time
Model equations
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Mechanism of Epoetin pharmacodynamicsModel equations
RET = ReticulocytesRBC = Red Blood Cell
kzero order
RETkout
)(RET
Pk
)t(PP
kk
k)t(RET)t(Pdt
)t(dRET
out
POW
outout
out
00
0
=
×=
×−=
RBC
kin
CERA Concentration
+ -
Negative Feedback
lag-time
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PK/PD modeling with healthy volunteers’ studyStudy design
Subjects: 46 healthy volunteers
Dosage of Epoetin beta:1) 50 IU/kg x3 / week sc2) 150 IU/kg x1 / week sc3) 300 IU/kg x1 / 2 weeks sc
Administration period: 4 weeks
Variables: RBC, Hb, Ht, reticulocyte & plasma erythropoietin concentrations
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PK/PD modeling with healthy volunteers’ studyPK analysis
The PK analysis was performed using a one compartment, first order absorption, first order elimination model including an endogenous level
The following PK/PD analysis considered the Bayes estimated PK parameters of each subject
Central comp.C0: constant
ka ke
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PK/PD modeling with healthy volunteers’ studyPK analysis with a simple model was enough for the following PK/PD analysis
Cp
[mIU
/mL]
0 10 20 30 40
020
4060
80
Cp
[mIU
/mL]
0 10 20 30 40
050
150
250
Cp
[mIU
/mL]
0 10 20 30 40
020
040
060
0
Obs
erve
d va
lues
[mIU
/mL]
0 200 400 600
020
040
060
0
Obs
erve
d va
lues
[mIU
/mL]
5 10 50 100 500
510
5050
0
days Bayes estimated values [mIU/mL]
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PK/PD modeling with healthy volunteers’ studyHematological responses for each cohort
50 IU/ kg
150 IU/ kg
300 IU/ kg
460
470
480
490
500
510
520
530
540
- 14 - 7 0 7 14 21 28 35 42 49
460
470
480
490
500
510
520
530
540
- 14 - 7 0 7 14 21 28 35 42 49
460
470
480
490
500
510
520
530
540
- 14 - 7 0 7 14 21 28 35 42 49
0
2
4
6
8
10
12
- 14 - 7 0 7 14 21 28 35 42 49
0
2
4
6
8
10
12
- 14 - 7 0 7 14 21 28 35 42 49
0
2
4
6
8
10
12
- 14 - 7 0 7 14 21 28 35 42 49
14
14.5
15
15.5
16
- 14 - 7 0 7 14 21 28 35 42 49
14
14.5
15
15.5
16
- 14 - 7 0 7 14 21 28 35 42 49
14
14.5
15
15.5
16
- 14 - 7 0 7 14 21 28 35 42 49
RBC RET HbRET HbRBC
50 IU/kg
150 IU/kg
300 IU/kg
mean±SE
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PK/PD modeling with healthy volunteers’ studyThe values of PK/PD parameters were reasonable
Theta EtaEMAX (x104/uL/day) 4.74 1.292E-06 CV(%)EC50 (mIU/mL) 25.2 101.5 CV(%)SLOPE (dL/g) 0.274 77.8 CV(%)POW 1.05 -transit time (day) 4.76 22.2 CV(%)MCH (pg) 30.1 1.077 SDMCV (uL) 88.2 2.81 SDRBC0 (x104/uL/day) 492 28.6 SDRET0 (x104/uL/day) 4.15 27.2 CV(%)
SIGMARET (x104/uL/day) 14.9 CV(%)RBC (x104/uL/day) 15.8 SDHb (g/dL) 0.458 SDHt (%) 1.46 SD
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PK/PD modeling with healthy volunteers’ studyThe values of PK/PD parameters were reasonable
Theta EtaEMAX (x104/uL/day) 4.74 1.292E-06 CV(%)EC50 (mIU/mL) 25.2 101.5 CV(%)SLOPE (dL/g) 0.274 77.8 CV(%)POW 1.05 -transit time (day) 4.76 22.2 CV(%)MCH (pg) 30.1 1.077 SDMCV (uL) 88.2 2.81 SDRBC0 (x104/uL/day) 492 28.6 SDRET0 (x104/uL/day) 4.15 27.2 CV(%)
SIGMARET (x104/uL/day) 14.9 CV(%)RBC (x104/uL/day) 15.8 SDHb (g/dL) 0.458 SDHt (%) 1.46 SD
← The theta of EC50 was similar with the one of in vitro study
← The Emax - to - P0 ratio was approximately 1.2, similar to that for mice and dogs (reserved capacity)
← The theta and eta for MCH, MCV RBC0 and RET0 was identical with the predose values
← The predose intra-individual variability (SAS proc MIXED) matches these sigma value
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PK/PD modeling with healthy volunteers’ studyBayes estimated values showed a high correlation with the observed values
Observed values
Baye
s es
timat
ed v
alue
s
0 5 10 15
05
1015
reticulocyte
Observed values
Baye
s es
timat
ed v
alue
s
400 450 500 550 600
400
450
500
550
600
RBC
Observed values
Baye
s es
timat
ed v
alue
s
12 14 16 18
1214
1618
HB
Observed values
Baye
s es
timat
ed v
alue
s
35 40 45 50 55
3540
4550
55
HT
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PK/PD modeling with healthy volunteers’ studySimulated values distribution matches the ones of observed values (PPC)
Reticulocyte RBC
DAYS
RET
0 10 20 30 40 50
-50
510
Dose: 50 ug/kg
0 10 20 30 40 50
-50
510
DAYS
RET
0 10 20 30 40 50
-50
510
Dose: 150 ug/kg
0 10 20 30 40 50
-50
510
DAYS
RET
0 10 20 30 40 50
-50
510
Dose: 300 ug/kg
0 10 20 30 40 50
-50
510
DAYS
RBC
0 10 20 30 40 50
-40
-20
020
4060
80
Dose: 50 ug/kg
0 10 20 30 40 50
-40
-20
020
4060
80
DAYS
RBC
0 10 20 30 40 50
-40
-20
020
4060
80
Dose: 150 ug/kg
0 10 20 30 40 50
-40
-20
020
4060
80
DAYS
RBC
0 10 20 30 40 50
-40
-20
020
4060
80
Dose: 300 ug/kg
0 10 20 30 40 50
-40
-20
020
4060
80
80%CI for simulation (lines) & observed values (circles)
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Simulation for renal anemia patients’ studiesSimulation method
Only RBC baseline and clearance were modified from HVThe studies for the reference were selected for
SC weeklySC dailyIV x 3 / week
Simulation was performed using Trial Simulator (n = 10000) for each cohort
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Simulation for renal anemia patients’ studiesClearance in renal anemia patients
mean±CV
1
10
100
10 100 1000
Dose (IU/kg)
CL/
F (m
L/h/
kg)
HV sc
Patients sc
Patients iv
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Simulation for renal anemia patients’ studiesStudy 1: sc weekly, Hb time course was predicted for 8 weeks
days
incr
ease
in H
b[g/
dL]
0 10 20 30 40 50
0.0
0.5
1.0
1.5
2.0
2.5
1500IU SC x 1/week
days
incr
ease
in H
b[g/
dL]
0 10 20 30 40 50
0.0
0.5
1.0
1.5
2.0
2.5
3000IU SC x 1/week
days
incr
ease
in H
b[g/
dL]
0 10 20 30 40 50
0.0
0.5
1.0
1.5
2.0
2.5
6000IU SC x 1/week
Line: median & 90%CI for simulationCircle: mean of observed valuesHb0: 7.7 g/dL
n=27-35 n=31-35 n=24-33
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Simulation for renal anemia patients’ studiesStudy 1: sc weekly, the distribution of ∆Hb was predicted
Delta Hb for 8 weeks [g/dL]
1500IU SC x 1/week
3000IU SC x 1/week
6000IU SC x 1/week
-2 -1 0 1 2 3 4
0.0
0.2
0.4
0.6
prob
abilit
y de
nsity
-2 -1 0 1 2 3 4
0.0
0.2
0.4
0.6
prob
abilit
y de
nsity
-2 -1 0 1 2 3 4
0.0
0.2
0.4
0.6
prob
abilit
y de
nsity
broken line: mean of simulated valuesreal line: mean of observed valuesred curve: distribution of simulated values
n=35
n=36
n=34
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Simulation for renal anemia patients’ studiesStudy 2: sc daily, the distribution of Ht slope was predicted
5 IU /kg sc x 7/week
10 IU /kg sc x 7/week
DHt(%)/week
20 IU /kg sc x 7/week
-1 0 1 2 3
0.0
0.4
0.8
1.2
prob
abilit
y de
nsity
-1 0 1 2 3
0.0
0.4
0.8
1.2
prob
abilit
y de
nsity
-1 0 1 2 3
0.0
0.4
0.8
1.2
prob
abilit
y de
nsity
broken line: median of simulated valuesreal line: median of observed valuesred curve: distribution of simulated values
n=33
n=32
n=33
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Simulation for renal anemia patients’ studiesStudy 3: iv x3 / week, the distribution of Ht slope was predicted
-1 0 1 2 3 4
0.0
0.4
0.8
1.2
prob
abilit
y de
nsity
-1 0 1 2 3 4
0.0
0.4
0.8
1.2
prob
abilit
y de
nsity
-1 0 1 2 3 4
0.0
0.4
0.8
1.2
prob
abilit
y de
nsity
40 IU/kg iv x 3 / week
80 IU/kg iv x 3 / week
120 IU/kg iv x 3 / week
DHt(%)/week
broken line: median of simulated valuesreal line: median of observed valuesred curve: distribution of simulated values
n=31
n=29
n=30
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Simulation for renal anemia patients’ studiesMaintenance study:
the model could also predict the distribution of maintenance dose
The observed dose distribution (from literature) for 988 hemodialysis patients (Ht was maintained 35.9 ± 3.7 %)
Red line: simulation for IV x3 / weekdose [IU/kg/week]
% fo
r tot
al p
atie
nts
0 500 1000 1500 2000
010
2030
40
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Conclusions
A mechanism-based PK/PD model was developed which is able to describe the time courses of hematological responses for Epoetin beta in healthy volunteersThis model also predicted the time courses in renal anemia patientsThe model predicts not only the mean values but also the individual values’ distributionThe model was useful for predicting responses with different dose routes, different dose frequencyThe model was useful for predicting maintenance dose
