A factor VII-based method for the prediction of anticoagulant response to warfarin

Warfarin dosing methods based on existing models for warfarin and the international normalised ratio (INR) give biased maintenance dose predictions at the upper and lower quantiles of dose requirements. The aim of this work is to propose a conceptually different approach to predict INR after warfarin dosing. Factor VII concentration was proposed as the principal driving force for the INR. The time to steady-state INR (tSS,INR) was determined based on the INR response to changes in factor VII concentrations following warfarin initiation, and from this the steady-state INR (INRSS) was derived. The proposed method requires timed, paired blood samples of INR and factor VII. At different simulated warfarin dose rates, the prediction error associated with the proposed method was shown to be within clinically acceptable limits for both the tSS,INR (±2 days) and INRSS (±0.2). The use of the method was demonstrated in two patients who were initiated with 5 mg of warfarin daily. The difference in predicted versus actual steady-state INR were 0.0 and −0.4. The proposed method represents a unique approach to predict the INR. It considers factor VII as the main driver for INR and provides valuable information about the time to steady state INR.


Results:
The results of evaluation of assumptions are summarised in Supplementary Table S2. For all the assumptions, although given the high impact nature of violation, the Probability of violation is low and hence the risk of assumption violation is considered on the whole to be (at worst) minor. Then, since all the assumptions are found to have either insignificant or minor risk of violation, the use of this method for determining after warfarin dosing was considered to be justified. Details of the methods and results of the assumption evaluation is provided below in Supplementary Table S2 Unlikely Critical Minor

Probability of assumption violation
Testability and methods Testable. Isobolograms of pairwise combinations of factors II, VII, and X with respect to the INR were constructed via simulation from the QSP coagulation network model 1 . All points on the same isobologram correspond to the same INR (e.g. INR=2.5). Points that fall below the additivity line indicate supra-additivity interactions whereas points that are located above the additivity line correspond to subadditivity interactions.

Rating and results
Assumption violation = very unlikely. The isobologram analysis showed that simultaneous reduction in two clotting factors leads to less than additive increase in the INR (See Supplementary Figure S1).

Supplementary Figure S1
Isobolograms of pairwise combination of factors II, VII, and X for different INRs.
The black circles correspond to pairwise combination of factors II, VII, or X that gives a predetermined INR. The grey solid line is the additivity line. RF,combi refers to reduction in one clotting factor when another clotting factor is simultaneously reduced, RF reduction in a single clotting factor.

Impact of assumption violation
Rating and results Impact = Major. This was rated based on logical reasoning. If the effects of factors II, VII, and X on the INR are additive or supra-additive, contribution of factors II and X to INR will be significant then monitoring of factor VII alone to inform the INR is unlikely to be adequate.
Overall risk assessment Risk = Insignificant. Even given the high impact nature of violation of this assumption the probability of violation is very low and hence the risk is considered to be negligible.

Interpretation
Of factors II, VII, and X, the most deficient clotting factor is the most important determinant of the INR.

Probability of assumption violation
Testability and methods Testable. Isobolograms of pairwise combination of factors II, VII, and X with respect to the INR was constructed via simulation from the coagulation network model 1 . All points on the same isobologram correspond to the same level of effects (e.g. INR=2.5).

Rating and results
Assumption violation = Very unlikely. At high INR (e.g. INR=2.5 or INR=4.5), vertical and horizontal segments were observed on the isobologram (see Supplementary Figure S1). This showed that if either one of the factors II, VII, and X is sufficiently deficient, then the same INR will occur regardless of the concentration of other clotting factors. Hence, the most deficient clotting factor was considered the principal driving force behind the INR.

Impact of assumption violation Testability and methods
Not-testable. This is because significant structural change to the coagulation network model, which is unlikely to be consistent with known physiology, is required to make all factors II, VII, and X to drive the INR equally.
Rating and results Impact = Major. This was rated based on logical reasoning. If factors II, VII, and X all drive the INR considerably, monitoring factor VII alone to inform the INR is unlikely to be adequate.
Overall risk assessment Risk = Insignificant. Even given the high impact nature of violation of this assumption the probability of violation is very low and hence the risk is considered to be negligible.

Assumption 3: Under non-steady-state INR conditions, factor VII is always the most deficient:
Here, 1 2 . represents the degradation half-life of factors II, VII, or X and is the significance level for hypothesis testing.

Probability of assumption violation Testability and methods
Testable. 1 2 of factors II, VII, and X for 1000 individuals were simulated using relevant parameters (e.g. the degradation rate constant of factors II, VII, and X and the corresponding variance-covariance matrix of between subject variability in parameters) from a published warfarin-clotting factor model 2 . An overarching hypothesis to test was as follows: : Here, 0 is the null hypothesis and is the alternative hypothesis. Independent testing of 0 : 1 2 , ≥ 1 2 , and 0 : 1 2 , ≥ 1 2 , were required. Each of these hypotheses was tested using a Wilcoxon-signed rank test at = 0.025 (one-tailed and with Bonferroni correction).

Rating and results
Assumption violation = Very unlikely.

Impact of assumption violation Testability and methods
Testable. Rating and results Impact = Moderate. When factor X replaced factor VII as the most deficient factor during the non-steady-state INR, the time course of no longer bears similarity to that of the INR. Instead, the time course of appears similar to that of the INR. It appears that what matters is that the for the clotting factor with the shortest degradation half-life is used as it provides the best approximation to the INR.
Overall risk assessment Risk = Insignificant. Even given the high impact nature of violation of this assumption the probability of violation is very low and hence the risk is considered to be negligible.

Assumption 4: Non-steady-state INR is the most sensitive to factor VII:
Interpretation is greater in magnitude compared to both and at all time points during the non-steady-state INR. Testability and methods  Testable.  , , and , respectively, were derived from INR and clotting factors data simulated from the coagulation network model 1 .

Probability of assumption violation
/ / versus time were plotted. At each time point during non-steady-state INR, the magnitude of was compared to that of and , respectively (see left-hand column of Supplementary Figure S2).

Rating and results
Assumption violation = Very unlikely. It was observed that is larger in magnitude compared to and at all time points during the non-steady-state INR.

Impact of assumption violation
Testability and methods Testable. Overall risk assessment Risk = Insignificant. Even given the high impact nature of violation of this assumption the probability of violation is very low and hence the risk is considered to be negligible.

Assumption 5: The QSP coagulation network model 1 is adequate in describing the warfarin-clotting factors-INR relationship: Interpretation
The QSP coagulation network model is able to produce physiologically-sound simulated profiles for factors II, VII, X, and INR following warfarin initiation.

Probability of assumption violation Testability and methods
Testable. Factors II, VII, X, and INR were simulated from the QSP coagulation network model 1 . The simulated data were compared to external data ( =17) 2,3 . Individual observed/simulated data versus time were plotted. It is however, not possible to validate the QSP model and hence it is not possible to fully test this assumption across the whole of the INR generating pathways.

Rating and results
Assumption violation = Unlikely. The simulated data showed reasonably good agreement with the observed data for factors II, VII, X, and INR at the individual level. See Supplementary Figure S3 for the individual fits of all patients.

Impact of assumption violation Testability and methods
Testable. No test was carried out as the outcome is self-evident. Rating and results Impact = Critical. It is axiomatic that if the QSP model is unable to accurately describe the warfarin-clotting factors-INR relationship, the derived is unlikely to be fit for the intended purpose.
Overall risk assessment Risk = Minor. Even given the high impact nature of violation of this assumption the probability of violation is very low and hence the risk is considered to be minor overall.

Assumption 6: The simulated clotting factors-INR time course is representative of that of typical patients initiated with warfarin: Interpretation
The simulated profiles for factors II, VII, X, and INR are representative of the majority of patients initiated with warfarin.

Probability of assumption violation Testability and methods
Testable. Factors II, VII, X, and INR were simulated from the QSP coagulation network model 1 . The simulated data were compared to external data ( = 17) 2,3 . Individual observed/simulated data versus time were plotted.

Rating and results
Assumption violation = Unlikely. The simulated data showed reasonably good agreement with the observed data for factors II, VII, X, and INR at the individual level. See Supplementary Figure S3 above for the individual fits of all patients.

Impact of assumption violation
Testability and methods Testable. No test was carried out as the outcome is self-evident.
Rating and results Impact = Critical. It is axiomatic that generalisability is limited if the simulation results are unrepresentative.
Overall risk assessment Risk = Minor. Even given the high impact nature of violation of this assumption the probability of violation is very low and hence the risk is considered to be minor overall.

Supplementary Table S4
Parameter estimates and goodness-of-fit of the logistic model for the time course of . Both ℎ and are dose-dependent and is considered independent. At different warfarin dosing rates, the estimates for obtained were largely similar i.e. ranging from 0.260 to 0.301 and fixing of to 0.300 resulted in an almost identical model fit.
is the warfarin daily dose for a typical patient, ℎ the upper horizontal asymptote, the magnitude of horizontal shift, the shape parameter, 2 the adjusted coefficient of determination, RSE the relative standard error, and the sensitivity index of INR to factor VII The resulting ROC curve for is shown in Supplementary Figure S4. is the sensitivity index of INR to factor VII. The symbolic solution to the definite integral, ∫ (