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

PK-PD model of multiple follicular development during controlled ovarian stimulation. application of Markovian elements. Controlled ovarian stimulation. Diagnosis Subfertility – reduced chance of conception Treatment Gonadotropins to induce multiple follicular development Recombinant FSH

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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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