1. Anthe Zandvliet, Anton de Haan, Pieta IJzerman-Boon, Rik de Greef, Thomas Kerbusch PAGE meeting 2008 PK-PD model of multiple follicular development during controlled ovarian stimulation application of Markovian elements

2. 220-Jun-2008PAGE Meeting – Stuck in modelling Controlled ovarian stimulation Diagnosis Subfertility – reduced chance of conception Treatment Gonadotropins to induce multiple follicular development –Recombinant FSH –Corifollitropin alfa

3. 320-Jun-2008PAGE Meeting – Stuck in modelling Controlled ovarian stimulation Clinical trials corifollitropin alfa Phase I, II, III n = 495 Pharmacokinetics 3 compartment model Empirical Bayes estimates used in PK-PD model

4. 420-Jun-2008PAGE Meeting – Stuck in modelling Ultrasound scan measurements 2-4 mm5-7 mm8-10 mm11-14 mm15-16 mm17+ mm Day 1 032000 Day 3 ---100 Day 5 ---610 Day 6 ---520 Day 7 ---143 Count data Categorical ordinal Repeated measurements Dependent measurements Follicles not individually tracked Table. Total follicle count (left and right ovary) of a representative subject.

5. 520-Jun-2008PAGE Meeting – Stuck in modelling Transit compartment model ≤1 mm 2 mm 3 mm 4 mm 5 mm 6 mm 7 mm 8 mm 9 mm 10 mm 11 mm 12 mm 13 mm 14 mm 15 mm 16 mm 17+ mm k out: follicular decline k tr: follicular growth

6. 620-Jun-2008PAGE Meeting – Stuck in modelling Poisson model 2mm 3mm 4mm 5mm 6mm 7mm 8mm 9mm 10mm 11mm 12mm 13mm 14mm 15mm 16mm 17+mm ≤1mm = 1.3

7. 720-Jun-2008PAGE Meeting – Stuck in modelling Multinomial model P 2mm P 3mm P 4mm P 5mm P 6mm P 7mm P 8mm P 9mm P 10mm P 11mm P 12mm P 13mm P 14mm P 15mm P 16mm P 17+mm P ≤1mm  P =P ≤1mm +P 2mm +…+P 16mm +P  17mm +P out =1 n =50

8. 820-Jun-2008PAGE Meeting – Stuck in modelling Multinomial model P 2mm P 3mm P 4mm P 5mm P 6mm P 7mm P 8mm P 9mm P 10mm P 11mm P 12mm P 13mm P 14mm P 15mm P 16mm P 17+mm P ≤1mm likelihood P (n 11-14mm = k 1, n 15-16 mm = k 2, n 17+ mm = k 3 ) = 50! k 1 !* k 2 !* k 3 !*(50- k 1 -k 2 -k 3 )! P 11-14 mm k1 *P 15-16 mm k2 *P 17+ mm k3 *P other (50- k1-k2-k3) *

9. 920-Jun-2008PAGE Meeting – Stuck in modelling Follicles 11-14 mm 0 20 40 60 80 100 01234567891011121314151617181920 Number of follicles 11-14 mm Relative frequency (%) observed model predicted Day 3

10. 1020-Jun-2008PAGE Meeting – Stuck in modelling 0 20 40 60 80 100 01234567891011121314151617181920 Number of follicles 11-14 mm Relative frequency (%) observed model predicted Day 5 Follicles 11-14 mm

11. 1120-Jun-2008PAGE Meeting – Stuck in modelling 0 20 40 60 80 100 01234567891011121314151617181920 Number of follicles 11-14 mm Relative frequency (%) observed model predicted Day 8 Follicles 11-14 mm

12. 1220-Jun-2008PAGE Meeting – Stuck in modelling Follicles 15-16 mm 0 20 40 60 80 100 01234567891011121314151617181920 Number of follicles 15-16 mm Relative frequency (%) observed model predicted Day 3

13. 1320-Jun-2008PAGE Meeting – Stuck in modelling 0 20 40 60 80 100 01234567891011121314151617181920 Number of follicles 15-16 mm Relative frequency (%) observed model predicted Day 5 Follicles 15-16 mm

14. 1420-Jun-2008PAGE Meeting – Stuck in modelling 0 20 40 60 80 100 01234567891011121314151617181920 Number of follicles 15-16 mm Relative frequency (%) observed model predicted Day 8 Follicles 15-16 mm

15. 1520-Jun-2008PAGE Meeting – Stuck in modelling Follicles 17+ mm 0 20 40 60 80 100 01234567891011121314151617181920 Number of follicles 17+ mm Relative frequency (%) observed model predicted Day 3

16. 1620-Jun-2008PAGE Meeting – Stuck in modelling 0 20 40 60 80 100 01234567891011121314151617181920 Number of follicles 17+ mm Relative frequency (%) observed model predicted Day 5 Follicles 17+ mm

17. 1720-Jun-2008PAGE Meeting – Stuck in modelling 0 20 40 60 80 100 01234567891011121314151617181920 Number of follicles 17+ mm Relative frequency (%) observed model predicted Day 8 Follicles 17+ mm

18. 1820-Jun-2008PAGE Meeting – Stuck in modelling Follicles 11-14 mm (representative subject) P25 P75 P50 0 2 4 6 8 10 12 14 16 18 01234567 Time (days) Number of follicles 11-14 mm Observed and predicted follicle counts.

19. 1920-Jun-2008PAGE Meeting – Stuck in modelling - Independent measurements. - Simulated values highly variable. - Simulated profile physiologically not plausible. Simulation without Markovian features

20. 2020-Jun-2008PAGE Meeting – Stuck in modelling Physiologically plausible profile 0 2 4 6 8 10 12 14 16 18 01234567 Time (days) Number of follicles 11-14 mm

21. 2120-Jun-2008PAGE Meeting – Stuck in modelling Markovian features Model should ‘remember’ the size of follicles at previous time point. Attempts to implement Markovian elements in NONMEM: unsuccessful.

22. 2220-Jun-2008PAGE Meeting – Stuck in modelling Markovian features: implementation in SAS Empirical Bayes estimation of PK-PD parameters in NONMEM Calculation of transition rates for each 0.1-hour interval: –P decline = 1- exp(-0.1*k out ) –P grow = 1- exp(-0.1*k tr ) –P unchanged = 1 – P decline – P grow Markov simulation for individual follicles in SAS –50 growth courses of individual follicles are simulated for each subject

23. 2320-Jun-2008PAGE Meeting – Stuck in modelling Simulation with Markovian features 3 examples of simulated profiles in SAS

24. 2420-Jun-2008PAGE Meeting – Stuck in modelling 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.

25. 2520-Jun-2008PAGE Meeting – Stuck in modelling 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?