Aims: Warfarin acts by inhibiting the reduction of vitamin K (VK) to its active form, thereby decreasing the production of VK-dependent coagulation factors. The effects of warfarin can be overcome by administration of VK but this can lead to transient warfarin resistance. The overarching goal of this work is to quantify the influence of VK on warfarin dose requirements. To this end, the required first step is to understand the quantitative influence of warfarin on the time course of factors II, VII, IX, X, protein C (PC), and protein S (PS).
Methods: Data from 17 atrial fibrillation adults who were initiated with oral daily warfarin were analysed. One blood sample was collected at baseline, and at 1, 2, 3, 4, 5, 8, 15, and 29 days after warfarin initiation. Concentrations of clotting factors were quantified using relevant factor deficient plasma in prothrombin time assay (for factors II, VII, and X) and in activated partial thromboplastin time assay (for factor IX). Concentration of anticoagulation proteins, PC and PS, were quantified using chromogenic and ELISA assays, respectively. The data were modelled in a stepwise manner using NONMEM v.7.2. In the first stage, each of the six concentration-time profiles for the clotting factors and anticoagulation proteins were modelled independently using a kinetic-pharmacodynamic (K-PD) model. In the subsequent step, the six K-PD models were put into a single joint model whereby the six clotting factors and anticoagulation proteins were linked by the correlation in the parameter and residual error space. Structural identifiability issues were explored using the popt_i software.
Results: A K-PD turnover model was used for factors II, VII, IX, X, PC, and PS, respectively. The K-PD model consists of two parts: (a) a one-compartment model with linear absorption and elimination for describing the amount of warfarin in the biophase; and (b) an inhibitory Emax model linked to a turnover model for describing the delayed reduction in various clotting factors and anticoagulation proteins after warfarin initiation. Both the fixed effect and random effect of volume of distribution were fixed to obtain a structurally identifiable model. In the joint model, the estimated degradation half-life of VK-dependent clotting factors and anticoagulation proteins were in agreement with previous published values. Prediction-corrected visual predictive check showed that the joint model developed provided an adequate description of the observed data.
Conclusion: The warfarin exposure-response model developed represents the first work to model the influence of warfarin to all six VK-dependent clotting factors (factors II, VII, IX, X) and anticoagulation proteins (PC, PS) simultaneously. The current model provides an initial framework for subsequent incorporation of the VK cycle as an intermediary step between warfarin exposure and response. This will be useful for predicting the coagulation kinetics in response to exogenously administered VK in warfarinised patients.