Development of a Bayesian Forecasting Method for Warfarin Dose Individualisation

ABSTRACT

Purpose

The aim of this study was to develop a Bayesian dose individualisation tool for warfarin. This was incorporated into the freely available software TCIWorks (www.tciworks.info) for use in the clinic.

Methods

All pharmacokinetic and pharmacodynamic (PKPD) models for warfarin in the medical literature were identified and evaluated against two warfarin datasets. The model with the best external validity was used to develop an optimal design for Bayesian parameter control. The performance of this design was evaluated using simulation-estimation techniques. Finally, the model was implemented in TCIWorks.

Results

A recently published warfarin KPD model was found to provide the best fit for the two external datasets. Optimal sampling days within the first 14 days of therapy were found to be days 3, 4, 5, 11, 12, 13 and 14. Simulations and parameter estimations suggested that the design will provide stable estimates of warfarin clearance and EC50. A single patient example showed the potential clinical utility of the method in TCIWorks.

Conclusions

A Bayesian dose individualisation tool for warfarin was developed. Future research to assess the predictive performance of the tool in warfarin patients is required.

APPENDIX 1: THE OTAGO WARFARIN PKPD MODEL

Methods

PKPD Modelling

A warfarin PKPD model was developed using data from the O’Reilly dataset. Population PK analysis was carried out with NONMEM VI using the first-order conditional estimation with interaction (FOCEI). One- and two-compartment pharmacokinetic models with first-order absorption were fitted to the warfarin concentration data. An absorption lag time (tlag) was also considered to help describe the apparent absorption delay of warfarin. Total body weight, sex and age were considered as covariates. These were retained in the model if inclusion decreased the objective function value by 3.84 or more (χ ², p ≤ 0.05, d.f. = 1). Model discrimination and covariate inclusion were also assessed using graphical goodness-of-fit analysis. The between-subject variability was assumed to be log-normally distributed, with a mean of zero and a variance of ω². Residual error was modelled using a combined additive and proportional error model.

Once the best PK model had been identified, a simultaneous PKPD model was developed. Graphical inspection of a PCA versus time plot overlayed on a concentration versus time plot suggested a considerable delay between warfarin response and dose. Therefore, only delayed effects models, such as effect compartment and inhibitory turnover (Imax) models, were considered. Candidate PKPD models were evaluated by comparison of the objective function values and by visual inspection of visual predictive checks (VPCs).

Internal and External Model Evaluation

The model was evaluated by simulating 1000 patients under the model and plotting the 10th, 50th, and 90th percentiles of the simulated PCA values. This was compared to the same percentiles from the O’Reilly dataset (VPCi) and the University of Sydney (VPCe).

Results

PKPD Modelling (The Otago Model)

Parameter and error model estimates for the final PKPD model are presented in Table III. A one-compartment pharmacokinetic model with first-order absorption and tlag provided the best fit for the data. Visual inspection of covariate plots suggested a relationship between CL, V and weight. A model for weight, standardised to 70 kg, was applied to clearance and volume. An allometric scaling function was also applied to clearance. The final model for clearance is given by

$$ CL = \mathop \theta \nolimits_{CL} *{\left( {\frac{{wt}}{{70}}} \right)^{0.75}} $$

(1)

and for volume by

$$ V = \mathop \theta \nolimits_V *\left( {\frac{{wt}}{{70}}} \right) $$

(2)

An inhibitory turnover model provided the best fit for the pharmacodynamic (PCA) data (see Eq. 3).

$$ \begin{array}{*{20}{c}} {\frac{{dPCA}}{t} = \left( {Rat{e_{in}}*IC} \right) - {k_{out}}*PCA} \hfill \\{IC = 1 - \frac{{\left( {IMAX*{C_p}} \right)}}{{\left( {EC50 - {C_p}} \right)}}} \hfill \\\end{array} . $$

(3)

where Rate_in is the zero-order production rate for PCA, K_out is PCA elimination rate constant, Imax is the maximum inhibition of PCA, Cp is the plasma concentration (of warfarin), and EC50 is warfarin plasma concentration at 1/2 Imax.

Internal and External Evaluation of the Otago Model

An internal visual predictive check (VPCi) for warfarin response compared to the O’Reilly dataset is presented in the main body of the text (Fig. 1a). The plot suggests good model performance. An external evaluation (VPCe) of the model against the Sydney dataset is presented in the main body of the text (Fig. 2a). The model appears to under-predict anticoagulant response somewhat. This is discussed further in the main body of the paper.

Table 3 Warfarin PKPD Parameter Estimates for the final Otago Model