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PK-PD model of multiple follicular development during controlled ovarian stimulation

Explore a PK-PD model for controlled ovarian stimulation using Markovian elements. Understand diagnosis, treatment, and clinical trial results for managing subfertility. Learn about ultrasound scan measurements and modeling follicular growth. Discover implementation of Markovian features in simulation. <br>

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PK-PD model of multiple follicular development during controlled ovarian stimulation

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  1. PK-PD model of multiple follicular development during controlled ovarian stimulation application of Markovian elements

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

  3. 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 PAGE Meeting – Stuck in modelling

  4. Ultrasound scan measurements • Count data • Categorical ordinal • Repeated measurements • Dependent measurements • Follicles not individually tracked Table. Total follicle count (left and right ovary) of a representative subject. PAGE Meeting – Stuck in modelling

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

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

  7. Multinomial model P ≤1mm P 16mm P 15mm P 17+mm P 14mm P 2mm P 3mm P 13mm P =P≤1mm+P 2mm+…+P16mm+P17mm+P out =1 n =50 P 4mm P 12mm P 5mm P 11mm P 10mm P 6mm P 9mm P 7mm P 8mm PAGE Meeting – Stuck in modelling

  8. Multinomial model P ≤1mm P 16mm P 15mm P 17+mm P 14mm P 2mm likelihood P (n11-14mm= k1 , n15-16 mm= k2 , n17+ mm= k3) = P 3mm P 13mm P 4mm P11-14 mmk1 *P15-16 mmk2 *P17+ mmk3 *Pother(50- k1-k2-k3) * P 12mm 50! k1!* k2!* k3!*(50- k1-k2-k3)! P 5mm P 11mm P 10mm P 6mm P 9mm P 7mm P 8mm PAGE Meeting – Stuck in modelling

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

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

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

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

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

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

  15. 100 80 observed model predicted 60 Relative frequency (%) Day 3 40 20 0 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 Follicles 17+ mm PAGE Meeting – Stuck in modelling

  16. 100 80 observed model predicted 60 Relative frequency (%) Day 5 40 20 0 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 Follicles 17+ mm PAGE Meeting – Stuck in modelling

  17. 100 80 observed model predicted 60 Relative frequency (%) Day 8 40 20 0 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 Follicles 17+ mm PAGE Meeting – Stuck in modelling

  18. 18 P75 16 14 P50 12 10 P25 Number of follicles 11-14 mm 8 6 4 2 0 0 1 2 3 4 5 6 7 Time (days) Follicles 11-14 mm (representative subject) Observed and predicted follicle counts. PAGE Meeting – Stuck in modelling

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

  20. 18 16 14 12 10 Number of follicles 11-14 mm 8 6 4 2 0 0 1 2 3 4 5 6 7 Time (days) Physiologically plausible profile PAGE Meeting – Stuck in modelling

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

  22. 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 PAGE Meeting – Stuck in modelling

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

  24. Conclusion • A transit compartment multinomial Markovmodel 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. PAGE Meeting – Stuck in modelling

  25. 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? PAGE Meeting – Stuck in modelling

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