PK-PD model of multiple follicular development during controlled ovarian stimulation
description
Transcript of PK-PD model of multiple follicular development during controlled ovarian stimulation
PAGE meeting 2008
Anthe Zandvliet, Anton de Haan, Pieta IJzerman-Boon, Rik de Greef, Thomas Kerbusch
PK-PD model of multiple follicular development during controlled ovarian stimulation
application of Markovian elements
20-Jun-2008PAGE Meeting – Stuck in modelling 2
Controlled ovarian stimulation
AuthorFunctionDate
12-Mar-2008 |M&S corifollitropin alfa - ACoP | 2
Controlled ovarian stimulation
Diagnosis:
• Subfertility – reduced chance of conception– Tubal factor, pelvic pathology, endometriosis, unknown
– Male factor
Treatment:
• Gonadotropins (e.g. recFSH) to induce multifollicular growth for– In vitro fertilization (IVF)
– Intra-cytoplasmic sperm injection (ICSI)
hCGrecFSH
Multifollicular growth Oocyte retrieval
IVF/ICSI
Embryo transfer
Diagnosis • Subfertility – reduced chance of conception
Treatment• Gonadotropins to induce multiple follicular development
– Recombinant FSH– Corifollitropin alfa
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Controlled ovarian stimulation
AuthorFunctionDate
12-Mar-2008 |M&S corifollitropin alfa - ACoP | 2
Controlled ovarian stimulation
Diagnosis:
• Subfertility – reduced chance of conception– Tubal factor, pelvic pathology, endometriosis, unknown
– Male factor
Treatment:
• Gonadotropins (e.g. recFSH) to induce multifollicular growth for– In vitro fertilization (IVF)
– Intra-cytoplasmic sperm injection (ICSI)
hCGrecFSH
Multifollicular growth Oocyte retrieval
IVF/ICSI
Embryo transfer
Clinical trials corifollitropin alfa
• Phase I, II, III• n = 495
Pharmacokinetics
• 3 compartment model• Empirical Bayes estimates used in PK-PD model
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Ultrasound scan measurements
2-4 mm 5-7 mm 8-10 mm 11-14 mm 15-16 mm 17+ mm
Day 1 0 3 2 0 0 0
Day 3 - - - 1 0 0
Day 5 - - - 6 1 0
Day 6 - - - 5 2 0
Day 7 - - - 1 4 3
• Count data• Categorical ordinal• Repeated measurements• Dependent measurements• Follicles not individually tracked
Table. Total follicle count (left and right ovary) of a representative subject.
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Transit compartment model
≤1 mm
2 mm
3 mm
4 mm
5 mm
6 mm
7 mm 8 mm9 mm
10 mm
11 mm
12 mm
13 mm
14 mm
15 mm16 mm
17+ mm
k out: follicular decline
k tr: follicular growthCorifollitropin alfa concentration
k tr (follicular growth)
Corifollitropin alfa concentration
k out (follicular decline)
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Poisson model
2mm
3mm
4mm
5mm
6mm
7mm
8mm
9mm
10mm
11mm
12mm
13mm
14mm
15mm
16mm
17+mm
≤1mm
= 1.3
1 2 3 4 5 6 7
P
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Multinomial model
P2mm
P3mm
P4mm
P5mm
P6mm P
7mmP
8mm
P9mm
P10mm
P11mm
P12mm
P13mm
P14mm
P15mm
P16mm
P17+mm
P≤1mm
P =P ≤1mm +P 2mm +…+P 16mm +P 17mm +P out =1
n =50
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Multinomial model
P2mm
P3mm
P4mm
P5mm
P6mm P
7mmP
8mm
P9mm
P10mm
P11mm
P12mm
P13mm
P14mm
P15mm
P16mm
P17+mm
P≤1mm
likelihood
P (n11-14mm = k1 , n15-16 mm = k2 , n17+ mm = k3) =
50! k1!* k2!* k3!*(50- k1-k2-k3)!
P11-14 mmk1 *P15-16 mm
k2 *P17+ mmk3 *Pother
(50- k1-k2-k3) *
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Follicles 11-14 mm
0
20
40
60
80
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Number of follicles 11-14 mm
Rel
ativ
e fr
equ
ency
(%
) observed
model predicted
Day 3
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0
20
40
60
80
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Number of follicles 11-14 mm
Rel
ativ
e fr
equ
ency
(%
) observed
model predicted
Day 5
Follicles 11-14 mm
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0
20
40
60
80
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Number of follicles 11-14 mm
Rel
ativ
e fr
equ
ency
(%
) observed
model predicted
Day 8
Follicles 11-14 mm
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Follicles 15-16 mm
0
20
40
60
80
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Number of follicles 15-16 mm
Rel
ativ
e fr
equ
ency
(%
) observed
model predicted
Day 3
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0
20
40
60
80
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Number of follicles 15-16 mm
Rel
ativ
e fr
equ
ency
(%
) observed
model predicted
Day 5
Follicles 15-16 mm
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0
20
40
60
80
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Number of follicles 15-16 mm
Rel
ativ
e fr
equ
ency
(%
) observed
model predicted
Day 8
Follicles 15-16 mm
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Follicles 17+ mm
0
20
40
60
80
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Number of follicles 17+ mm
Rel
ativ
e fr
equ
ency
(%
) observed
model predicted
Day 3
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0
20
40
60
80
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Number of follicles 17+ mm
Rel
ativ
e fr
equ
ency
(%
) observed
model predicted
Day 5
Follicles 17+ mm
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0
20
40
60
80
100
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Number of follicles 17+ mm
Rel
ativ
e fr
equ
ency
(%
) observed
model predicted
Day 8
Follicles 17+ mm
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Follicles 11-14 mm (representative subject)
P25
P75
P50
0
2
4
6
8
10
12
14
16
18
0 1 2 3 4 5 6 7Time (days)
Nu
mb
er o
f fo
llic
les
11-1
4 m
m Observed and predicted follicle counts.
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02468
1012141618
0 1 2 3 4 5 6 7
Time (days)
Num
ber
of f
ollic
les
11-1
4 m
m
- Independent measurements.- Simulated values highly variable.- Simulated profile physiologically not plausible.
Simulation without Markovian features
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Physiologically plausible profile
0
2
4
6
8
10
12
14
16
18
0 1 2 3 4 5 6 7Time (days)
Nu
mb
er o
f fo
llic
les
11-1
4 m
m
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Markovian features
• Model should ‘remember’ the size of follicles at previous time point.
• Attempts to implement Markovian elements in NONMEM: unsuccessful.
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Markovian features: implementation in SAS
• Empirical Bayes estimation of PK-PD parameters in NONMEM
• Calculation of transition rates for each 0.1-hour interval:
– Pdecline = 1- exp(-0.1*kout)
– Pgrow = 1- exp(-0.1*ktr)
– Punchanged = 1 – Pdecline – Pgrow
• Markov simulation for individual follicles in SAS
– 50 growth courses of individual follicles are simulated for each subject
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0
5
10
15
20
0 1 2 3 4 5 6 7
Time (days)
Num
ber
of f
ollic
les
11-1
4 m
m
0
5
10
15
20
0 1 2 3 4 5 6 7
Time (days)
Num
ber
of f
ollic
les
11-1
4 m
m
0
5
10
15
20
0 1 2 3 4 5 6 7
Time (days)
Num
ber
of f
ollic
les
11-1
4 m
m
Simulation with Markovian features
3 examples of simulated profiles in SAS
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Conclusion
• A transit compartment multinomial Markov model seems suitable
to describe follicular growth during treatment with corifollitropin alfa.
• The transit compartment multinomial model required ordinary differential equation calculation in NONMEM.
• Markovian features were implemented for simulation purposes in SAS.
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Discussion
• How to apply Markovian elements in NONMEM?– Poisson model – multinomial model
• Models for count data with less dispersion?
• Is the work-around acceptable?– Estimation in NONMEM (empirical Bayes estimates of PK and PD parameters)– Simulation in SAS (Markov simulation of 50 follicles for each subject)
• Other examples of repeated dependent categorical count data?
• Diagnostic plots? Diagnostic methods?