PK-PD model of multiple follicular development with corifollitropin alfa during controlled ovarian stimulation: application of Markovian elements.
Anthe Zandvliet, Anton de Haan, Pieta IJzerman-Boon, Rik de Greef, Thomas Kerbusch.
Organon, part of Schering-Plough Corporation.
Background: Corifollitropin alfa is a novel gonadotropin that has different pharmacokinetic properties than follicle stimulating hormone (FSH) but similar pharmacodynamic features. A single injection is able to initiate and sustain multifollicular growth for an entire week. If necessary, follicular stimulation can be continued with daily injections of recombinant FSH (recFSH) from Day 8 onwards. Administration of hCG for induction of final oocyte maturation is indicated when 3 follicles of ≥ 17 mm are observed. Both follicle number and size are important parameters of treatment success.
Objectives: To develop a PK-PD model to describe the time profile of the number and size of follicles during treatment with corifollitropin alfa and recFSH.
Methods: In a phase II dose-finding trial and a phase III safety and efficacy trial, 479 subjects were treated with corifollitropin alfa and were evaluable for PK-PD analysis. Data from an absolute bioavailability study (n=16) were used to support PK model development. Ultrasound scans were performed regularly to assess the number of follicles in various size categories: 2-4, 5-7, 8-10 mm (Day 1 only) and 11-14, 15-16, 17+ mm (all days). A transit compartment model was used to describe follicular growth. Each compartment corresponded to a 1-mm size class, starting with follicles of 1 mm (or less) and ending with follicles of 17+ mm. Transit rate constants ktr represented follicular growth and were estimated as an Emax function of the corifollitropin alfa concentration. kout was complementary to ktr (kout = Emax - ktr) and represented follicle decline. PK and PD data were analyzed sequentially using NONMEM VI. FOCE was used for the PK model and the LAPLACIAN method for the PD model.
Results: A 3-compartmental model adequately described the PK profile of corifollitropin alfa. In an initial attempt to describe follicular development, the amount in each transit compartment represented the lambda of a Poisson distribution. Simulations indicated overdispersion: the Poisson model was suitable to describe independent measurements, but the repeated count measurements of follicles were not independent. We did not manage to incorporate Markovian elements in this model. In a second attempt, the amount in each compartment represented the probability of a single follicle to have the corresponding size. Follicles were distributed over the compartments according to a multinomial distribution. Again, Markovian elements could not be incorporated in this model in NONMEM. As a work-around, posthoc estimates were used to perform a Markov simulation in SAS.
Conclusions: Follicular development during controlled ovarian stimulation was assessed by ultrasound scans resulting in repeated dependent multicategorical count measurements. The multicategorical nature of the data prevented flexible incorporation of Markovian elements in Poisson and multinomial models.
Discussion: During the "Stuck in Modeling" session, we would like to discuss how to apply Markovian elements. Is it feasible to develop a Markov model of follicular growth in NONMEM? Alternatively, is it acceptable to use posthoc estimates for Markov simulations in SAS?