Assessing the relative potency of (S)- and (R)-warfarin with a new PK-PD model, in relation to VKORC1 genotypes

Abstract

Purpose

The purpose of this study is to develop a new pharmacokinetic-pharmacodynamic (PK-PD) model to characterise the contribution of (S)- and (R)-warfarin to the anticoagulant effect on patients in treatment with rac-warfarin.

Methods

Fifty-seven patients starting warfarin (W) therapy were studied, from the first dose and during chronic treatment at INR stabilization. Plasma concentrations of (S)- and (R)-W and INRs were measured 12, 36 and 60 h after the first dose and at steady state 12–14 h after dosing. Patients were also genotyped for the G>A VKORC1 polymorphism. The PK-PD model assumed a linear relationship between W enantiomer concentration and INR and included a scaling factor k to account for a different potency of (R)-W. Two parallel compartment chains with different transit times (MTT₁ and MTT₂) were used to model the delay in the W effect. PD parameters were estimated with the maximum likelihood approach.

Results

The model satisfactorily described the mean time-course of INR, both after the initial dose and during long-term treatment. (R)-W contributed to the rac-W anticoagulant effect with a potency of about 27% that of (S)-W. This effect was independent of VKORC1 genotype. As expected, the slope of the PK/PD linear correlation increased stepwise from GG to GA and from GA to AA VKORC1 genotype (0.71, 0.90 and 1.49, respectively).

Conclusions

Our PK-PD linear model can quantify the partial pharmacodynamic activity of (R)-W in patients contemporaneously exposed to therapeutic (S)-W plasma levels. This concept may be useful in improving the performance of future algorithms aiming at identifying the most appropriate W maintenance dose.

Appendix A

The PK model is represented by the following equations:

$$ {C}_i=\frac{k_a{D}_i}{V_i\left({k}_a-{K}_{e, i}\right)}\left({e}^{-{K_{e, i}}^t}-{e}^{-{K_a}^t}\right)\kern0.5em i= S, R $$

(1)

where C _i is the (S)- or (R)- W concentration [mg/L]; k _a is the absorption constant, set at 2 h⁻¹ [24]; D _i is the S- or R-W dose [50% that of rac-W], assuming 100% oral bioavailability; k _e is the elimination constant, defined as k _e,i  = CL _i / V _i ; CL _i is clearance; and V _i is compartment volume.

Parameters CL _i and V _i were estimated for each subject by a least squares approach, since the maximum likelihood approach used to estimate PD parameters was considered unsuitable for small sample sizes [25].

The PD model, shown in Fig. 1, may be represented by the following differential and algebraic equations:

$$ \frac{dF_1}{dt}={k}_{\mathrm{tr}1} m\left({C}_s+{ k C}_R\right)-{K}_{\mathrm{tr}1}{F}_1 $$

(2)

$$ \begin{array}{ll}\frac{dF_j}{dt}={k}_{\mathrm{tr}\mathrm{l}}{F}_{J-1}-{k}_{\mathrm{tr}1}{F}_J\hfill & J=2,3,4\hfill \end{array} $$

(3)

$$ \frac{dS_1}{dt}={k}_{\mathrm{tr}2} m\left({C}_s+{ k C}_R\right)-{K}_{\mathrm{tr}2}{S}_1 $$

(4)

$$ \begin{array}{ll}\frac{dS_j}{dt}={k}_{\mathrm{tr}2}{S}_{J-1}-{k}_{\mathrm{tr}2}{S}_J\hfill & J=2,3,4\hfill \end{array} $$

(5)

$$ \mathrm{INR}={\mathrm{INR}}_{\mathrm{base}}+\left({F}_4+{S}_4\right) $$

(6)

where F _j and S _j represent the response to W concentration in each compartment j of the fast and slow chains, respectively; k _tr1 and k _tr2 are rate constants [h⁻¹] governing INR response delay [note that MTT₁ = (k _tr1)⁻¹ and MTT₂ = (k _tr2)⁻¹]; m is the slope of the linear correlation between W concentration and INR response; k is the correction coefficient to account for the different potency of the W R-form with respect to S-one; and INR_base is the basal INR value.

The model identification procedure was carried out iteratively according to a “two-step” maximum likelihood estimate (MLE) method [19, 25].

The procedure was as follows:

• Step 1. MTT₁ and MTT₂ were fixed at reasonable values (4.5 and 27.5 h, respectively); m and k were then estimated for each genotype group, with both single-dose and steady-state clinical data. The K values of the three genotype groups were averaged, weighting the estimates by the number of patients in each group.

• Step 2. K and m were fixed at the values estimated above, and MTT₁ was estimated with single-dose data only, since steady-state data were minimally affected by MTT₁.

The procedure was repeated starting from the estimated value of MTT₁ (keeping MTT₂ fixed at 27.5 h). The parameter estimates stabilized after two iterations. Parameter estimation and model simulations were carried out with the general purpose modelling tools gPROMS® v. 4.1.0 by Process Systems Enterprise (London, UK).