A Bayesian decision support tool for efficient dose individualization of warfarin in adults and children

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This is a review of Hamberg, Hellman, Dahlberg, Jonsson, and Wadelius’ 2015 article, A Bayesian decision support tool for efficient dose individualization of warfarin in adults and children.[1]


Warfarin is one of the most commonly prescribed anticoagulants in both adults and children, with over 33 million prescriptions in 2011. Dose individualization to minimize the risk for over- or under-dosing can be made:

  • Before starting therapy (a priori) and/or
  • After therapy has been initiated (a posteriori)

The therapy may range in complexity from body size based dosing to utilization of advanced mechanism based mathematical and statistical models.[1]

The authors in this journal article presented a warfarin dose decision tool that can be used a priori to predict the most probable dose to reach a given target International Normalized Ratio (INR), or to predict the most probable INR response to a given dose. It can also be used a posteriori to guide dose revisions using a Bayesian forecasting method which is used to determine probability often times for decision making purposes.


The model was developed on longitudinal data from more than 1,500 warfarin treated adults, and then bridged theoretically to children through the use of physiological principles.

One of the published warfarin models was transferred from NONMEM to a new graphical user interface built with Java Swing components using NetBeans. The differential equations in the Java application are solved using Heun’s method, a second-order Runge-Kutta method, which is a numerical procedure for solving ordinary differential equations that is both fast and easy to implement using vectors. The end result is a Java application that, for a subject with a given set of covariates, can estimate the maintenance dose for a pre-specified target INR or predict the INR response for a pre-specified dose regimen.[1] There are two main windows in the application, one for a priori predictions and one for a posteriori predictions.


The computational performance of the Java-based tool was evaluated by comparing the output with the POSTHOC function in NONMEM version 7 as the reference. This was done using treatment data (one to three INR observations) from a total of 49 children.

A priori predicted maintenance doses and empirical Bayes estimates of individual parameters and a posteriori predictions of maintenance doses from the tool and from NONMEM were compared. There were no differences in a priori maintenance dose predictions with the Java based tool compared to NONMEM, but a mean difference in a posteriori maintenance dose predictions of 5.0% (SD 6.7%).[1]

Employing CDS to avoid morbidity due to medication has shown variable results. Such an example is this paper by McCoy et al., (2012) “Real-time pharmacy surveillance and clinical decision support to reduce adverse drug events in acute kidney injury – a randomized, controlled trial.


The dose prediction tool incorporates age, bodyweight, baseline and target INR, and CYP2C9 and VKORC1 genotype (defined or assumed) for a priori dose predictions, and uses doses and INRs from ongoing treatment for a posteriori dose revisions.

The warfarin model was developed in NONMEM, which is the most commonly used software for non-linear mixed effects modeling of clinical PK and PD data. Dose optimization could in theory be performed using this software, but there are several reasons for moving to another environment. NONMEM, like other specialized software for non-linear mixed effects modeling, has:[1]

  • A high knowledge threshold for use
  • Specific demands for data input
  • Requires licensing of a program

All these aspects would impede the use of the NONMEM model as a dose decision tool and instead opted for the Java based tool.


The predictive performance of the underlying published warfarin model has been extensively evaluated and shown to perform well in predicting the anticoagulant response in both children and adults. It is important for the dosing tool to be evaluated prospectively before it can be recommended for use routinely in a clinical setting.


The journal article was a very interesting read because the authors were able to take a pre-existing algorithmic function and turn it into a fully functional CDS tool. The authors realize that this is simply a tool that can be used to aid in appropriate dosing measures, but overall physician and medical knowledge still needs to be used.


  1. 1.0 1.1 1.2 1.3 1.4 Hamberg, A., Hellman, J., Dahlberg, J., Jonsson, E., & Wadelius, M. (2015). A Bayesian decision support tool for efficient dose individualization of warfarin in adults and children. BMC Medical Informatics and Decision Making, 15(7).