A Bayesian decision support tool for efficient dose individualization of warfarin in adults and children
© Hamberg et al.; licensee BioMed Central. 2015
Received: 13 August 2014
Accepted: 23 December 2014
Published: 7 February 2015
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© Hamberg et al.; licensee BioMed Central. 2015
Received: 13 August 2014
Accepted: 23 December 2014
Published: 7 February 2015
Warfarin is the most widely prescribed anticoagulant for the prevention and treatment of thromboembolic events. Although highly effective, the use of warfarin is limited by a narrow therapeutic range combined with a more than ten-fold difference in the dose required for adequate anticoagulation in adults. An optimal dose that leads to a favourable balance between the wanted antithrombotic effect and the risk of bleeding as measured by the prothrombin time International Normalised Ratio (INR) must be found for each patient. A model describing the time-course of the INR response can be used to aid dose selection before starting therapy (a priori dose prediction) and after therapy has been initiated (a posteriori dose revision).
In this paper we describe a warfarin decision support tool. It was transferred from a population PKPD-model for warfarin developed in NONMEM to a platform independent tool written in Java. The tool proved capable of solving a system of differential equations that represent the pharmacokinetics and pharmacodynamics of warfarin with a performance comparable to NONMEM. To estimate an a priori dose the user enters information on body weight, age, baseline and target INR, and optionally CYP2C9 and VKORC1 genotype. By adding information about previous doses and INR observations, the tool will suggest a new dose a posteriori through Bayesian forecasting. Results are displayed as the predicted dose per day and per week, and graphically as the predicted INR curve. The tool can also be used to predict INR following any given dose regimen, e.g. a fixed or an individualized loading-dose regimen.
We believe that this type of mechanism-based decision support tool could be useful for initiating and maintaining warfarin therapy in the clinic. It will ensure more consistent dose adjustment practices between prescribers, and provide efficient and truly individualized warfarin dosing in both children and adults.
Warfarin is one of the most commonly prescribed anticoagulants in both adults and children , with over 33 million prescriptions in 2011 . In spite of the recent introduction of the new oral anticoagulants (NOACs), i.e. dabigatran, rivaroxaban and apixaban, warfarin still remains the most prescribed anticoagulant with 90% of Swedish patients receiving warfarin and only 10% receiving a NOAC during 2013 . Although it has been in clinical use for over 50 years, warfarin therapy is still challenging due to a narrow therapeutic range and considerable variability in response to a given dose. Known contributing factors to the between- and within-subject variability among adult patients include, age, concurrent medications and/or health conditions, vitamin K intake and genetic polymorphisms in two genes, CYP2C9 and VKORC1 [4-6]. In a systematic review and meta-analysis, patients with atrial fibrillation (AF) receiving warfarin spent 61% of the time within, 13% above, and 26% below the target INR of 2-3 . In a US study that was published in 2011, the frequency of warfarin-induced bleeding was reported to be 15% to 20% per year, with life-threatening or fatal bleeding rates as high as 1% to 3% per year . Annual total health care costs were estimated to be 65% and 49% higher for AF patients with a warfarin-induced intracranial hemorrhage or a major gastrointestinal bleeding, respectively, than the costs for patients with no bleeding events .
Dose individualization to minimize the risk for over- or under-dosing can be made i) before starting therapy (a priori) and/or ii) after therapy has been initiated (a posteriori) and may range in complexity from body size based dosing to utilization of advanced mechanism based mathematical and statistical models. There are several published pharmacogenetic prediction models for a priori dose individualization of warfarin for both adults [4,5,10] and children [11-13]. These dosing algorithms aim to predict the expected maintenance dose. A more refined way to achieve individualized dosing is to combine methods for a priori individualization with methods for a posteriori dose revisions, using a Bayesian approach [14,15]. The latter utilizes knowledge of the population distribution of the model parameters for the drug. The most likely parameters for an individual can be obtained using measurements of drug concentrations [16,17] or drug responses [18,19]. These parameters can be used to calculate the dose that most probably results in the target response in that particular individual. By using a predictive model combined with Bayesian forecasting, warfarin dosing can be truly personalized, resulting in rapid achievement of therapeutic anticoagulation without increasing the risk of over-anticoagulation.
A complete description of the underlying warfarin model can be found in the papers describing the model development in NONMEM [20-22]. NONMEM is the most commonly used software for non-linear mixed effects modeling of PK and PD data .
One of the published warfarin models  was transferred from NONMEM to a new graphical user interface built with Java Swing components using NetBeans . NetBeans refers both to a platform framework for Java applications, and to an open source integrated development environment, supporting development of all types of Java applications. 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. Heun’s method is also stable for this type of differential equations and has a high numerical precision. 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. There are two main windows in the application, one for a priori predictions and one for a posteriori predictions. The rate constant ke is referred to as k10 in the tool.
The tool needs input data regarding the patient in order to operate. Data on age, weight, CYP2C9 and VKORC1 genotype, baseline INR and target INR range are required both for dose estimation and for INR prediction. If genotype information is missing, the tool will use the most common genotype combination, conditioned on ethnicity [25,26]. This means that for CYP2C9 all subjects with missing genotype information will be coded as *1/*1 i.e. the genotype with the highest dose requirement. For VKORC1 the tool will use A/G for Caucasians (intermediate dose requirement), A/A for Asians (low dose requirement) and G/G for Africans (high dose requirement). If baseline INR is missing the tool will use a default value of 1. The dosing interval has a default value of 24 hours, i.e. one dose per day, but this can be changed manually if another dosing interval is preferred. Common to all a priori predictions is that the model will use the typical (mean) parameter estimates conditioned on the patient’s age, bodyweight and CYP2C9 and VKORC1 genotype.
Once treatment has been initiated and one or more INR observations are available, the tool can be used to suggest a tailored maintenance dose based on individualized parameter estimates. This is done in several steps using a Bayesian approach. The first step is to estimate individual model parameters, and this is done using Powell’s method. The tool then uses the individual model parameters in the next step, which can be either dose estimation or INR prediction. As more observations become available, the individual model parameters become more refined and specific to the individual patient. This is expected to increase the accuracy and precision of the dose and INR predictions.
When predicting INRs, the user has to specify a dose and the number of days this dose should be repeated. The output is a plot of the predicted INR curve for the number of days specified, and a text field showing the predicted INR at the end of the treatment period. If steady state conditions have been reached the tool will display the mean INR over the dosing interval. If steady state conditions are not yet reached, the predicted INR at 16 hours after last dose is presented. This function may be useful e.g. in situations where it is not feasible to administer the same dose every day with available formulations. Thus, when different daily doses are required, the tool can visualize the variability in INR response that this regimen is expected to introduce. The tool can also be used to predict when warfarin should be discontinued to reach below a certain INR value at a given point in time, which can be of use e.g. before a planned surgical procedure.
The dose prediction tool is based on a published population warfarin model for adults  that has been theoretically bridged to children through the use of physiological principles . The model 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 i) a high knowledge threshold for use, ii) specific demands for data input, and iii) requires licensing of a program. All these aspects would impede the use of the model as a dose decision tool. An advantage of the tool compared with other warfarin dose algorithms, is that it can be used to adjust warfarin dosing a posteriori due to other known or unknown factors than those specifically included in the prediction model. When the a posteriori function is used, the tool will start by estimating individual model parameters based on the patient’s input data. The individual model parameters can be seen as the patient’s warfarin phenotype, and determines how the patient most likely will respond to therapy. When the individual model parameters are estimated all factors that affect the PK or PD of warfarin, e.g. regular exercise, vitamin K intake, interacting drugs or other medical conditions, will be taken into account and influence dose predictions. Another advantage of the tool is its ability to handle INR observations under non-steady-state conditions. INR observations that are measured during initiation of warfarin therapy or after dose changes give valuable information about an individual patient’s response to warfarin, both concerning rate and extent. The tool can use INR values from start of therapy and provide estimates of the expected INR at steady state. In theory, this means that patients can reach a stable maintenance dose in less time and with fewer dose adjustments and INR measurements than an empirical dosing regimen.
When comparing maintenance dose predictions from NONMEM and the Java based tool, there was a systematic difference with a bias (MPE) of -0.104 mg and an imprecision (RMPE) of 0.192 mg for the tool. These differences are relatively small and are not expected to influence dose recommendations when considering the limitations in available tablet strengths. That there is a difference between the tool and NONMEM may be explained by differences in i) the optimization algorithm used when estimating individual doses, and ii) the definition of target INR at steady state. The Java based tool defines the target INR as the mean INR during a dosing interval whereas NONMEM defines the target INR as the INR at 16 hours post dose.
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 [19,21,22,27]. The dosing tool needs to be evaluated prospectively before it can be recommended for use routinely in a clinical setting. However, even before a formal validation, it is possible to build confidence in the tool by using it for prediction of INR. Irrespective of whether the dose administered to a patient is derived from the tool or if it is an empirical dose, its accuracy can be evaluated by comparing predicted and observed INR values. A major limitation with the tool from a clinical perspective is that it has no save or printing function. However, there is at least one commercial dose-individualization software tool that have our warfarin models implemented, which has both a save and a printing function (www.doseme.com.au). It is important to emphasize that this type of decision support tool is not intended to substitute for the care by a licensed health care professional, such as a clinician, pharmacist or specialized nurse. It should rather be seen as a tool to help ensure efficient and consistent dose adjustment practices between prescribers and between different health care providers, irrespective of target INR or target population.
Project name: Warfarin Dose Calculator 1.0.1
Project home page: www.warfarindoserevision.com
Operating system(s): Platform independent
Programming language: Java
Other requirements: Java Runtime Environment (JRE) 1.7.0 or newer
License: Apache Open source
Any restrictions to use by non-academics: No
drug amount in the body
maximum degree of inhibition
dose rate resulting in 50% of maximum inhibition
International Normalized Ratio
first-order drug elimination rate constant
mean prediction error
mean transit time
relative mean prediction error
volume of distribution
AKH was supported by a personal grant from the Ränk family via the Swedish Heart and Lung Foundation. The development of the tool was supported by grants from the Swedish Research Council (Medicine 521-2011-2440), the Swedish Heart and Lung Foundation and the Clinical Research Support (ALF) at Uppsala University. We also want to thank Joakim Nyberg, researcher at the Department of Pharmaceutical Biosciences, Uppsala University, for providing technical and intellectual support during parts of the development.
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