ORIGINAL ARTICLE
Methods for Predicting Warfarin Dose Requirements Shamin M. Saffian, BPharm, PGCertPharm,*† Daniel F. B. Wright, PhD,* Rebecca L. Roberts, PhD,‡ and Stephen B. Duffull, PhD*
Background: The aim of this study was to compare the predictive performance of different warfarin dosing methods.
Key Words: warfarin, INR, dosing algorithm, Bayesian forecasting, pharmacogenetics (Ther Drug Monit 2015;37:531–538)
Methods: Data from 46 patients who were initiating warfarin therapy were available for analysis. Nine recently published dosing tools including 8 dose prediction algorithms and a Bayesian forecasting method were compared with each other in terms of their ability to predict the actual maintenance dose. The dosing tools included 4 algorithms that were based on patient characteristics (2 clinical and 2 genotype-driven algorithms), 4 algorithms based on international normalized ratio (INR) response feedback and patient characteristics (2 clinical and 2 genotype-driven algorithms), and a Bayesian forecasting method. Comparisons were conducted using measures of bias (mean prediction error) and imprecision [root mean square error (RMSE)].
Results: The 2 genotype-driven INR feedback algorithms by Horne et al and Lenzini et al produced more precise maintenance dose predictions (RMSE, 1.16 and 1.19 mg/d, respectively; P , 0.05) than the genotype-driven algorithms by Gage et al and Klein et al and the Bayesian method (RMSE, 1.60, 1.62, and 1.81 mg/d respectively). The dose predictions from clinical and genotype-driven algorithms by Gage et al, Klein et al, and Horne et al were all negatively biased. Only the INR feedback algorithms (clinical and genotype) by Lenzini et al produced unbiased dose predictions. The Bayesian method produced unbiased dose predictions overall (mean prediction error, +0.37 mg/d; 95% confidence interval, 0.89 to 20.15) but overpredicted doses in patients requiring .8 mg/d.
Conclusions: Overall, warfarin dosing methods that included some measure of INR response (INR feedback algorithms and Bayesian methods) produced unbiased and more precise dose predictions. The Bayesian forecasting method produced positively biased dose predictions in patients who required doses .8 mg/d. Further research to assess differences in clinical endpoints when warfarin doses are predicted using Bayesian or INR-driven algorithms is warranted.
Received for publication July 8, 2014; accepted December 3, 2014. From the *School of Pharmacy, University of Otago, Dunedin, New Zealand; †Faculty of Pharmacy, Universiti Kebangsaan Malaysia, Kuala Lumpur; and ‡Department of Surgical Sciences, University of Otago, Dunedin, New Zealand. The authors declare no conflict of interest. Supplemental digital content is available for this article. Direct URL citations appear in the printed text and are provided in the HTML and PDF versions of this article on the journal’s Web site (www.drug-monitoring.com). Correspondence: Shamin M. Saffian, BPharm, PGCertPharm, School of Pharmacy, University of Otago, PO Box 56, Dunedin 9054, New Zealand (e-mail: shamin.mohdsaffi[email protected]). Copyright © 2014 Wolters Kluwer Health, Inc. All rights reserved.
Ther Drug Monit Volume 37, Number 4, August 2015
INTRODUCTION Warfarin is used for the treatment and prevention of venous thromboembolism, pulmonary embolism, thromboembolism associated with atrial fibrillation, and in some patients, for the prophylaxis of clots after myocardial infarction. It is a difficult drug to dose accurately and safely with daily maintenance doses differing by upwards of 10-fold between patients.1 Dosing is further complicated by a narrow therapeutic range and several well-documented drug interactions.2 The physiological response to warfarin therapy is a prolonged clotting time, which is routinely monitored in clinical practice using the international normalized ratio (INR). Patients who are under anticoagulation (INR ,2) are at an increased risk for blood clots, whereas INRs .4 carry an increased risk for major bleeding.3 Not surprisingly, a major challenge faced by prescribers is the accurate prediction of warfarin maintenance doses that will achieve and maintain a therapeutic INR (usually between 2 and 3) in individual patients. There is a large body of literature exploring different strategies for managing warfarin therapy. Several different methods to aid dose prediction have been proposed. These can be broadly categorized based on the clinical information required to predict the warfarin dose, including (1) methods based only on INR response data, (2) methods based only on patient characteristics, (3) methods based on both patient characteristics and INR response data, and (4) methods based on Bayesian forecasting. Dosing tools based on INR response include nomograms4–6 and computerized decision support tools.7–9 These have been reviewed elsewhere10 and will not be discussed further here. Recent publications advocate for the use of multilinear regression methods to identify patient characteristics that determine warfarin dose requirements. The resulting algorithms are intended to provide a guide to the likely maintenance dose required for each patient before the initiation of therapy. This method of predicting dosage is empirical by design, and the algorithms are often developed specifically for particular populations of patients or for certain warfarin indications.11–14 A large number of dosing algorithms for warfarin have been published. A recent review15 identified 32 published algorithms for warfarin therapy, many of which include broadly similar patient characteristics such as body weight,
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age, warfarin indication, interacting drugs (eg, amiodarone), and genetic differences in warfarin metabolism (via the drug metabolizing enzyme CYP2C9) and genetic differences in the recycling of vitamin K [by vitamin K epoxide reductase (VKORC1)]. In addition, a small number of algorithms have been published that include a single INR response measurement, as well as patient characteristics, in the regression analysis.16–18 This is based on the premise that the variability in warfarin response between individuals will be captured by early INR responses. Several Bayesian methods for warfarin therapy have been published,19–22 although few have been developed into dosing tools for use in the clinic. In general, a Bayesian method involves prediction of future INR responses for an individual patient using a pharmacokinetic–pharmacodynamic (PKPD) model, the PKPD parameter values from a prior population and the INR response for an individual patient.23 As more response data become available (ie, more INR measurements are performed), the Bayesian method will provide accurate predictions of future INR values. This then allows the clinician to determine a choice of dose that achieves their INR target. Warfarin dosing algorithms based on patient characteristics, including CYP2C9 and VKORC1 genotype, can account for about 50% of the variability in dosing requirements between patients,24–26 whereas those that also include a single INR response feedback seem to account for about 60% of the dose variability.16,17 This means that about 40%– 50% of the variability in dose requirements between patients will remain unexplained if therapy decision was based on these algorithms alone. In addition, the genotype-driven and INR feedback algorithms require prior knowledge of CYP2C9 and VKORC1 genotype, which is not routinely available in many clinical settings. A Bayesian forecasting method, because it incorporates repeated measures of INR response, will capture all sources of variability in warfarin response between patients. In addition, it can produce individualized dose predictions, which become more specific for each patient as more INR response data become available. Importantly, the Bayesian method should be able to individualize warfarin doses without the need for prior genetic testing. The aim of this article is to compare the predictive performance of 3 warfarin dosing methods: 1. Dosing algorithms based on patient characteristics. This is divided into genotype-driven algorithms (that include VKORC1 and CYP2C9 genotype) and clinical algorithms (algorithms not using genotype). 2. Dosing algorithms based on patient characteristics and a single INR response data (clinical or genotype-driven algorithm). 3. A Bayesian forecasting method.
therapy for any indication at Dunedin Hospital in Dunedin, New Zealand, were enrolled in the study and genotyped for CYP2C9 and VKORC1. Ethical approval for the study was obtained from the Lower South Regional Ethics Committee, New Zealand (LRS/10/11/056). The dosing history and INR response data were collected from baseline (before warfarin initiation) until a stable INR was achieved. The INR measurements were performed as part of normal clinical care. Stable INR (INRs) was used as an approximation of a steady-state INR. INRs was defined as the second consecutive INR observation that lies within 80%–120% of the target INR, following the convention published elsewhere.17 It was required that the 2 INR observations were separated by at least 7 days and that no dose changes had occurred for at least 14 days before the second INR observation.
DNA Extraction, VKORC1, and CYP2C9 Genotyping DNA was collected from peripheral blood samples using guanidine isothiocyanate extraction and stored at 2208C in Tris–EDTA buffer until analysis.28 Genotyping for VKORC1 (rs9923231) and CYP2C9*2 (rs1799853) and *3 (rs1057910) was performed using predesigned SNP TaqMan assays (Assay IDs: C__30403261_20, C__25625805_10, and C__27104892_10) from Applied Biosystems (Carlsbad, CA). Reactions were performed in 384-well format, in a total volume of 5 mL following the recommendations of the manufacturer and run on a Roche LightCycler 480 real-time PCR system (Roche Diagnostics Corporation, Indianapolis, IN). The accuracy of each TaqMan assay was confirmed by repeat analysis of 10% of samples. Concordance between original and repeat genotype calls was 100% for the 2 assays. PLINK software29 was used to test for deviations in Hardy–Weinberg equilibrium. A P value of ,0.05 was considered to indicate a significant deviation from Hardy–Weinberg equilibrium.
Maintenance Dose Prediction Algorithms In total, 8 algorithms from 4 studies were included in the analysis. Each of the 4 studies provided 2 algorithms—1 clinical and 1 genotype-driven algorithm. Clinical algorithms generally include the same patient characteristics as the genotype-driven algorithm but do not include genotype. They were developed by the authors for comparative purposes and therefore will be used for the same purpose here. Four algorithms (2 clinical and 2 genotype-driven) are based only on patient characteristics. Four algorithms (2 clinical and 2 genotype-driven algorithms) are based on patient characteristics and a single INR response feedback. The full algorithms selected for inclusion in this study are provided in Table 1.
Bayesian Forecasting Method
Patient data were sourced from a previous study by Wright and Duffull.27 Briefly, patients who initiated warfarin
A Bayesian forecasting method was recently developed10 and assessed27 by 2 of the authors. It was implemented in the freely available software TCIWorks (www.tciworks. info). The TCIWorks software consisted of a user interface allowing input of patient details, warfarin doses, and INR
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METHODS Patient Data
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Comparison of Warfarin Dosing Methods
TABLE 1. List of Algorithms Included in the Analysis Abbreviation
Description
C1
Clinical algorithm by Gage et al25
G1
Genotypic algorithm by Gage et al25
C2
Clinical algorithm by Klein et al24
G2
Genotypic algorithm by Klein et al24
C3-INR
Clinical algorithm with INR feedback by Lenzini et al17
G3-INR
Genotypic algorithm with INR feedback by Lenzini et al17
C4-INR
Clinical algorithm with INR feedback by Horne et al16
G4-INR
Genotypic algorithm with INR feedback by Horne et al16
Algorithm Dose (mg/d) = exp [0.613 + (0.425 · BSA) 2 (0.0075 · age) + (0.156 · African American race) + (0.216 · target INR) 2 (0.257 · amiodarone) + (0.108 · smokes) + (0.0784 · DVT/PE)] Dose (mg/d) = exp (0.9751 2 0.3238 · VKORC1 2 1639 G.A + 0.4317 · BSA 2 0.4008 · CYP2C9*3 2 0.00745 · age 2 0.2066 · CYP2C9*2 + 0.2029 · target INR 2 0.2538 · amiodarone + 0.0922 · smokes 2 0.0901 · African American race + 0.0664 · DVT/PE) Dose (mg/wk) = [4.0376 2 0.2546 · age (in decades) + 0.0118 · height (in centimeters) + 0.0134 · weight (in kilograms) 2 0.6752 · Asian race + 0.4060 · Black or African American + 0.0443 · missing or mixed race + 1.2799 · enzyme inducer status 2 0.5695 · amiodarone status]2 Dose (mg/wk) = [5.6044 2 0.2614 · age (in decades) + 0.0087 · height (in centimeters) + 0.0128 · weight (in kilograms) 2 0.8677 · VKORC1 A/G 2 1.6974 · VKORC1 A/A 2 0.4854 · VKORC1 genotype unknown 2 0.5211 · CYP2C9*1/*2 2 0.9357 · CYP2C9*1/*3 2 1.0616 · CYP2C9*2/ *2 2 1.9206 · CYP2C9*2/*3 2 2.3312 · CYP2C9*3/*3 2 0.2188 · CYP2C9 genotype unknown 2 0.1092 · Asian race 2 0.2760 · Black or African American 2 0.1032 · missing or mixed race + 1.1816 · enzyme inducer status 2 0.5503 · amiodarone status]2 Dose (mg/wk) = exp [2.8160220.76679 · ln (INR) 2 0.0059 · age + 0.27815 · target INR 2 0.16759 · diabetes + 0.17675 · BSA 2 0.22844 · stroke 2 0.25487 · fluvastatin use + 0.07123 · African origin 2 0.11137 · amiodarone use + 0.03471 · dose_2 + 0.03047 · dose_3 + 0.01929 · dose_4]† Dose (mg/wk) = exp [3.10894 2 0.00767 · age 2 0.51611 · ln (INR) 2 0.23032 · VKORC1-1639 G.A 2 0.14745 · CYP2C9*2 2 0.3077 · CYP2C9*3 + 0.24597 · BSA + 0.26729 · target INR 2 0.09644 · African origin 2 0.2059 · stroke 2 0.11216 · diabetes 2 0.1035 · amiodarone use 2 0.19275 · fluvastatin use + 0.0169 · dose_2 + 0.02018 · dose_3 + 0.01065 · dose_4]† Dose (mg/wk) = exp (2.19023 2 0.66327 · treatment response index‡ 2 0.00379 · age in years + 0.1095 · BSA 2 0.06548 · simvastatin use 2 0.2809 · fluvastatin use 2 0.08761 · amiodarone use + 0.2612 · Inducer use + 0.04189 · target INR 2 0.13717 · stroke + 0.01292 · day of therapy) Maintenance dose (mg/wk) = exp (2.59853 2 0.47578 · treatment response index‡ 2 0.17132 · VKORC1-1639 G.A 2 0.23385 · CYP2C9*3 2 0.10696 · CYP2C9*2 2 0.00549 · age + 0.16491 · BSA 2 0.09091 · simvastatin use 2 0.251 · fluvastatin 2 0.11994 · amiodarone + 0.3319 · inducer + 0.08796 · target INR 2 0.13902 · stroke + 0.01028 · day of therapy)
BSA, body surface area calculated using Du Bois & Du Bois formula.30 Age is in years unless stated. Variables are coded as 1 if present or 0 otherwise. Where genotype is specified, they are coded as 0 for no polymorphism, 1 for heterozygous, and 2 for homozygous. ln is the natural log. †Dose_2, _3, and _4 refers to dose given 2, 3, and 4 days before the INR was measured. ‡Treatment Response Index: ln (INR/effective dose). DVT/PE, deep vein thrombosis/pulmonary embolism.
observations. The method was underpinned by a warfarin dose–response model developed by Hamberg et al.33 In 2 retrospective analyses, the TCIWorks method was shown to provide accurate and precise predictions of INR response in patients who were initiating warfarin.27,34 For the purpose of this study, where the data were gathered retrospectively from dose individualization, the full dosing history and the first 4 INR observations for each patient were entered into TCIWorks. The authors then selected a dose that resulted in a predicted INR that corresponded to the observed INRs. This was then treated as the predicted maintenance dose. The authors chose to use the first 4 INR observations, as 4 INR observations were found to be sufficient to provide unbiased and precise INRs predictions as mentioned previously.27,34 The influence of more than 4 INR observations were not considered in this study.
Measurement of Bias and Imprecision
Calculations of MPE, MSE, and RMSE are given in the following equations: MPE ¼
N 1X PEi : N i¼1
(1)
MPE is the average differences between predicted and observed maintenance dose, where N is the number of patients. PEi is the prediction error of the predicted maintenance dose for ith individual. Prediction error is the difference between the predicted maintenance dose and the observed maintenance dose (predicted dose minus observed dose). If the 95% confidence interval (CI) of the prediction error included 0, no statistically significant bias was concluded. MSE ¼
N 1X ðPEi Þ2 : N i¼1
(2)
The predictive performance of each of the dosing methods was compared using measures of bias [mean prediction error (MPE)] and imprecision [mean square error (MSE) and root mean square error (RMSE)] as described by Sheiner and Beal.33
MSE is the average of the sum of squared differences between predicted and observed maintenance dose. pffiffiffiffiffiffiffiffiffiffi RMSE ¼ MSE: (3)
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RMSE is the square root of MSE. It provides an estimate of the imprecision given in the same units as the predicted dose (in milligrams per day). The imprecision of each method was compared by an analysis of the ratio of the variances. This was performed using an F-test where the ratio of the larger variance over the smaller variance was compared with 1. Variance of the predicted maintenance dose was calculated using the following equation: varianceMD ¼ MSE 2 MPE2 ;
(4)
where varianceMD is the variance of predicted maintenance dose of each dosing method.
RESULTS Data from 55 patients were available for analysis. Nine patients did not consent to genotyping and were excluded, providing a final data set of 46 patients. Patient characteristics are presented in Table 2. Height was missing for 13 patients and was imputed using multilinear regression (see Appendix 1, Supplemental Digital Content 1, http://links.lww.com/TDM/ A101). INR measurements were missing for 11 patients on days 4 or 5 (required for algorithm C3-INR and G3-INR). The missing INR values were imputed by linear interpolation between adjacent measurement days (see Appendix 1, Supplemental Digital Content 1, http://links.lww.com/TDM/A101). A summary of MPE and RMSE results is presented in Table 3. Goodness of fit plots is included in Figure 1. For the 4 algorithms that were based only on patient characteristics (C1, G1, C2, and G2), the incorporation of genotype into the algorithm produced a more precise prediction (P , 0.05) (Table 3). Bias, however, was not improved by the incorporation of
TABLE 2. Patient Characteristics and a Summary of Maintenance Dose and Stable INR (INRs) Patient Characteristics Age (years) Height (cm) Weight (kg) Male/Female (number of patients) Indication for warfarin (number of patients) Concomitant drugs of note (number of patients) Levothyroxine Beta-lactam antibiotics (.3 days) Metronidazole Azole antifungals Time to reach first stable INR (days) Number of INR observations to stable INR INRs value Dose at INRs (mg/d)
n = 46 62 (29–87) 166 (145–192) 81.7 (44–113) 19/27 Atrial fibrillation: 2; deep vein thrombosis: 27; pulmonary embolism: 17
4 1 1 1 38 (11–118) 11 (6–21) 2.4 (2–3.1) 5.5 (1.5–11)
Values are expressed as median (range) unless specified otherwise.
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genotype where all 4 algorithms produced negatively biased dose predictions. The INR feedback algorithms, C3-INR and G3-INR, were found to produce unbiased dose predictions (Table 3). Although the other INR feedback algorithms (C4-INR and G4-INR) produced negatively biased dose predictions. The INR feedback algorithms, G3-INR and G4-INR, were found to produce the lowest RMSE values overall (1.16 and 1.19, respectively) (Table 3). In addition, the predictions from the algorithm G4-INR were significantly more precise than all other dosing tools (P , 0.05) except for G3-INR and C4-INR. The Bayesian method was, on average, unbiased (MPE, +0.37 mg/d; 95% CI, 0.89 to 20.15). Visualization of the data in Figure 1 indicates that the Bayesian method overpredicted maintenance dose in patients who required higher doses (.8 mg/d). All of the INR feedback algorithms except C3-INR produced significantly more precise warfarin dose predictions than the Bayesian method (P , 0.05), and precision was not statistically different between the Bayesian method and most of the algorithms based on patient characteristics (no INR feedback) (Table 3). Overall, the INR-driven algorithms produced better precision, but only algorithms C3-INR and G3-INR produced unbiased warfarin dose predictions. The incorporation of genotype into the algorithm (clinical versus genotype-driven algorithm from the same study) was found to only improve precision in most cases but not bias.
DISCUSSION There is currently no consensus regarding the optimal method for predicting warfarin dose requirements. The evidence to date generally supports the idea that the use of a warfarin dosing tool of some sort by prescribers will result in superior anticoagulant control (eg, time in the therapeutic range or time to reach a stable warfarin dose) compared with traditional, heuristic, dosing practice.34,35 However, the evidence is less clear about how different warfarin dosing tools compare with each other in terms of predictive performance, INR control, and patient outcomes. For example, although genotype-driven algorithms have been shown to improve dosing predictions and clinical endpoints compared with traditional heuristic dosing practice,36 this has not been consistently demonstrated when compared with other dosing tools that did not include genotype37,38 or to dosing methods using only INR response data.39 Importantly, to our knowledge, there are no published studies comparing Bayesian forecasting for warfarin therapy with other dosing methods, despite promising preliminary results in prospective and retrospective studies.27,35 This means that the choice of which dosing method to use in clinical practice cannot be based on robust evidence comparing one method with another and will therefore be driven by other factors such as cost, ease of use, and availability of genotype data. To the author’s knowledge, this is the first study to compare the predictive performance of a Bayesian forecasting method for warfarin dose individualization with genotype-driven and INR feedback dosing algorithms. The authors have shown that the Bayesian forecasting can provide unbiased dose predictions for patients taking ,8 mg/d without Copyright 2014 Wolters Kluwer Health, Inc. All rights reserved.
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Comparison of Warfarin Dosing Methods
TABLE 3. Summary of Bias, Precision, and F-test for the Different Dosing Methods No INR Feedback Parameter MPE (95% CI) RMSE F-test versus C1 F-test versus G1 F-test versus C2 F-test versus G2 F-test versus C3-INR F-test versus G3-INR F-test versus C4-INR F-test versus G4-INR F-test versus Bayesian
C1 20.76 (20.18 to 21.34) 2.12
G1 20.64 (20.21 to 21.07) 1.60 P , 0.05a
C2 21.01 (20.42 to 21.60) 2.26
Algorithms With INR Feedback G2
C3-INR
G3-INR
C4-INR
G4-INR
Bayesian
20.72 (20.30 to 21.15) 1.62 P , 0.05a
0.27 (0.69 to 20.16) 1.49 P , 0.05a
20.18 (0.16 to 20.53) 1.19 P , 0.05a
20.42 (20.08 to 20.76) 1.22 P , 0.05a
20.52 (20.22 to 20.82) 1.16 P , 0.05a
0.37 (0.89 to 20.15) 1.81 P , 0.05a
P , 0.05b
P , 0.05b
P , 0.05c
P , 0.05c
P , 0.05c
P , 0.05a
P , 0.05c
P , 0.05c
P , 0.05c
P , 0.05c
P , 0.05a
P , 0.05c
P , 0.05d
P , 0.05a
P , 0.05c
P , 0.05e
P , 0.05a
P , 0.05c
P , 0.05f P , 0.05f
P , 0.05a
P , 0.05b
P , 0.05c
P , 0.05a
P , 0.05b
P , 0.05c
P , 0.05d
P , 0.05a
P , 0.05e
P , 0.05f P , 0.05f
P , 0.05f
P , 0.05f
For C3-INR and G3-INR, if an INR on day 4 and day 5 was available, INR on day 5 was used preferentially. For C4-INR and G4-INR, INR available on the earliest day between days 6 and 11 was used to calculate predicted maintenance dose. Superscript letters denote the less precise algorithm aC1, bG1, cC2, dG2, eC3-INR, and fBayesian method.
the need for genotype information. Dose predictions from the Bayesian tool were similar to algorithms based on patient characteristics in terms of precision but were significantly less precise than those predicted by INR feedback algorithms. An important difference between the Bayesian forecasting tool and the other dosing methods analyzed in this study is that the Bayesian method is capable of updating the future INR predictions as more INR observation become available. By predicting accurate future INR, a dose can be selected to achieve the desired target INR. Previous publications have used a variety of different criteria to evaluate warfarin dosing tools. Some studies determined the percentage of dose predictions that lie within a prespecified, and presumably clinically acceptable, range, that is, 620%24,40,41 or 61 mg of the observed dose.42 Other authors have reported the coefficient of determination (R2) as a measure of predictive performance.43,44 The authors evaluated predictive performance using MPE and RSME, as suggested by Sheiner and Beal.33 Although a robust method for assessing the predictive performance of warfarin dosing tools, the authors have found it to be insensitive to the apparent bias in dose predictions produced by the Bayesian method in patients taking .8 mg/d (Fig. 1).
The predictive performance of dosing tools for warfarin therapy has been evaluated in several previous studies.12,40,41,44–48 Finkelman et al40 compared the accuracy of dose predictions of 4 dosing tools in 1378 patients who were part of the International Warfarin Pharmacogenetic Consortium (IWPC)24 cohort. The dosing tools compared were the FDA warfarin drug label,49 a genotype table derived from the IWPC cohort, a clinical algorithm, and a genotype-driven algorithm published by Gage et al25 (algorithm C1 and G1). They found that the genotype-driven algorithm by Gage et al (G1)25 predicted a higher percentage of doses (52%, P , 0.001) within 20% of the observed dose compared with the genotype mean table, FDA warfarin label, and clinical algorithm (44%, 43%, and 39%, respectively). In another study, Marin-Leblanc et al44 compared 4 genotype-driven algorithms.24–26,50 The authors found that the algorithms published by Gage et al (G1)25 and Wadelius et al26 predicted a higher percentage of doses within 20% of the observed dose (41.7% and 46.3%, P , 0.05, respectively) compared with the algorithms published by Klein et al (G2)24 (39%) and Michaud et al50 (31.9%). By comparison, using the same metric with our data, algorithms G1 and G2 predicted 47.8% and 56.5%, respectively, of the doses within 20% of the observed dose.
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FIGURE 1. Scatter plots of observed maintenance dose versus predicted maintenance dose for each dosing method. The solid blue line is the line of identity. The red line is a loess fitted function. Top rows are algorithms based only on patient characteristics, middle rows are algorithms based on patient characteristics and INR response, and bottom is a Bayesian method.
Liu et al41 compared 8 genotype-driven algorithms17,24,25,43,51–54 in a prospective cohort of 282 Chinese warfarin patients. The study included algorithms G1, G2, and G3-INR. The goal was to compare the accuracy of warfarin dose predictions produced by the algorithms in Chinese patients who required low-dose therapy (ie, ,1.5 mg/d). The authors reported that overall 52.1% of the dose predictions produced by G3-INR were within 20% of the observed dose. This was statistically higher than G2 (45%), with a reported odds ratio of 1.71 (95% CI, 1.08–2.72; P = 0.0029). It is noteworthy that in patients taking doses ,1.5 mg/d, only 4.5% of the dose predictions were within 20% of the observed dose. Using the same metric with our data, the INR feedback algorithm G3-INR predicted a similar percentage of doses within 20% of the observed dose at 54.4%. A recently published randomized controlled trial (RCT)36 compared the percentage of INRs within in the therapeutic range (2.0–3.0) after either being guided by a genotype-driven algorithm or by heuristic dosing. The authors found that genotype-driven dosing resulted in INRs within the therapeutic range significantly more than heuristic dosing
(67.4% versus 60.3%, P , 0.001). This trial used 2 difficult algorithms to predict warfarin dosing requirements. Initial doses were predicted using a modified version of the algorithm G2, while subsequent dose predictions were updated with an INR measurement on day 4 or 5 of therapy using the INR feedback algorithm G3-INR. By contrast, in another RCT, Kimmel et al38 found no difference in the percentage of time within the INR therapeutic range using doses predicted by genotype-driven dosing compared with clinical algorithms (45.2% versus 45.4%, respectively). Initial doses in this RCT were predicted using algorithms C1 or G1, and subsequent dose predictions were updated using INR feedback algorithms C3-INR or G3-INR, respectively. This finding aligns with the results of this study where the authors did not find substantial differences in predictive performance between clinical and genotype-driven algorithms. Taken together, the results of the 2 RCTs and our study suggest that genotypedriven dosing may improve INR control compared with heuristic dosing but perhaps not compared with clinical algorithms. Indeed, the results of our study seem to suggest that the inclusion of INR response data in the Bayesian and INR
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feedback tools may have a greater impact on INR control than the addition of genotype. The difference in the predictive performance of published warfarin dosing algorithms between the studies summarized above and in our work is noteworthy. The dosing algorithms are empirically derived using multilinear regression methodology so can be expected to provide a good description of the factors that determined warfarin dose requirements in the populations from which they were developed. However, they do not appear to perform as well when extrapolated to new clinical settings or patient populations. This is arguably a problem for all dose prediction tools but may be less so for Bayesian forecasting methods, where dose predictions are dependant not only on prior population estimates for PKPD parameters but also on the repeated measurement of INR response in each patient. In theory, if the prior model used in a Bayesian system was derived from a diverse population and included sufficient mechanistic components to allow extrapolation, then the Bayesian method should perform well across patients groups. In light of this, it is noteworthy that the Bayesian forecasting method assessed in our study had a propensity to overpredict the dose requirements for those patients who require maintenance doses greater than about 8 mg/d. The authors have observed that the overprediction occurs mainly in patients with the GG genotype for a VKORC1 promoter variant (21639 G.A, rs9923231) (Fig. 2). No relationship to CYP2C9 genotype was observed (data not shown). This suggests that the population used to develop the prior model may have been sufficiently different from the population assessed in our study, at least with regard to the influence of VKORC1 genotype, and this may have biased the results. This problem is the subject of ongoing research. There are limitations to this study. Our sample size is small, making generalization of the results to all warfarin users difficult. The data were collected largely from ambulatory patients attending a deep vein thrombosis clinic at Dunedin
Comparison of Warfarin Dosing Methods
Hospital. It is unclear whether the algorithms and the Bayesian method would have performed differently in other patient groups such as those with atrial fibrillation. Height and INR data on days 4 or 5 of therapy (required by algorithms C3-INR and G3-INR) were missing for some patients (n = 13 and n = 11) and were imputed (see Appendix 1, Supplemental Digital Content 1, http://links.lww.com/TDM/A101). Note that height was only found to explain a small amount of dose variability in all of the algorithms, so the impact of including imputed heights is likely to be small.
CONCLUSIONS Warfarin dosing methods that included some measure of INR response (INR-driven algorithms and Bayesian methods) performed favorably, although no single dosing tool was clearly superior in terms of predictive performance based on our results. The INR feedback algorithms generally produced the most precise dose predictions but were inconsistent in terms of bias. Overall, INR feedback algorithm by Lenzini et al (genotype driven) produced the most precise and unbiased dose predictions. The Bayesian forecasting method produced unbiased dose predictions overall but overpredicted in patients who required doses .8 mg/d. The addition of CYP2C9 and VKORC1 genotype in the genotype-driven algorithms was noted to improve the precision of dose predictions in some cases compared with clinical algorithms but did not appreciably impact predictive performance compared with the Bayesian tool. Further research to assess differences in clinical endpoints, such as time in the therapeutic range or bleeding and stroke events, when warfarin doses are predicted using Bayesian or INR-driven algorithms is warranted.
ACKNOWLEDGMENTS The authors are grateful to Hesham Al-Sallami for his assistance with data imputation and to Mr Lionel van den Berg and Professor Carl Kirkpatrick from Monash University for invaluable assistance with TCIWorks. At the time of writing, S. M. Saffian was the recipient of a Malaysian Government Scholarship. REFERENCES
FIGURE 2. Scatter plots of observed maintenance dose versus predicted maintenance dose for the Bayesian method according to VKORC1 genotype (21639 G.A, rs9923231). Red circles represent AA, blue squares represent AG, and green triangles represent GG. The solid black line is the line of identity.
1. Voora D, McLeod HL, Eby C, et al. The pharmacogenetics of coumarin therapy. Pharmacogenomics. 2005;6:503–513. 2. Hirsh J, Fuster V, Ansell J, et al. American Heart Association/American College of Cardiology Foundation guide to warfarin therapy. J Am Coll Cardiol. 2003;41:1633–1652. 3. Hylek EM, Go AS, Chang Y, et al. Effect of Intensity of oral anticoagulation on stroke severity and mortality in atrial fibrillation. N Engl J Med. 2003;349:1019–1026. 4. Fennerty A, Campbell IA, Routledge PA. Anticoagulants in venous thromboembolism. BMJ. 1988;297:1285–1288. 5. Tait RC, Sefcick A. A warfarin induction regimen for out-patient anticoagulation in patients with atrial fibrillation. Br J Haematol. 1998;101: 450–454. 6. Gedge J, Orme S, Hampton KK, et al. A comparison of a low-dose warfarin induction regimen with the modified fennerty regimen in elderly inpatients. Age Ageing. 2000;29:31–34. 7. Ryan PJ, Gilbert M, Rose PE. Computer control of anticoagulant dose for therapeutic management. Br Med J. 1989;299:1207–1209.
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8. Manotti C, Moia M, Palareti G, et al. Effect of computer-aided management on the quality of treatment in anticoagulated patients: a prospective, randomized, multicenter trial of APROAT (Automated PRogram for Oral Anticoagulant Treatment). Haematologica. 2001;86:1060–1070. 9. Poller L, Shiach C, MacCallum P, et al. Multicentre randomised study of computerised anticoagulant dosage. Lancet. 1998;352:1505–1509. 10. Wright DFB, Duffull SB. Development of a bayesian forecasting method for warfarin dose individualisation. Pharm Res. 2011;28:1100–1111. 11. Ramos AS, Seip RL, Rivera-Miranda G, et al. Development of a pharmacogenetic-guided warfarin dosing algorithm for Puerto Rican patients. Pharmacogenomics. 2012;13:1937–1950. 12. You JHS, Wong RSM, Waye MMY, et al. Warfarin dosing algorithm using clinical, demographic and pharmacogenetic data from Chinese patients. J Thromb Thrombolysis. 2011;31:113–118. 13. Perini JA, Struchiner CJ, Silva-Assuncao E, et al. Pharmacogenetics of warfarin: development of a dosing algorithm for brazilian patients. Clin Pharmacol Ther. 2008;84:722–728. 14. Choi JR, Kim JO, Kang DR, et al. Proposal of pharmacogenetics-based warfarin dosing algorithm in Korean patients. J Hum Genet. 2011;56: 290–295. 15. Verhoef TI, Redekop WK, Daly AK, et al. Pharmacogenetic-guided dosing of coumarin anticoagulants: algorithms for warfarin, acenocoumarol and phenprocoumon. Br J Clin Pharmacol. 2014;77:626–641. 16. Horne BD, Lenzini PA, Wadelius M, et al. Pharmacogenetic warfarin dose refinements remain significantly influenced by genetic factors after one week of therapy. Thromb Haemost. 2012;107:232–240. 17. Lenzini P, Wadelius M, Kimmel S, et al. Integration of genetic, clinical, and INR data to refine warfarin dosing. Clin Pharmacol Ther. 2010;87: 572–578. 18. Millican EA, Lenzini PA, Milligan PE, et al. Genetic-based dosing in orthopedic patients beginning warfarin therapy. Blood. 2007;110:1511–1515. 19. Svec JM, Coleman RW, Mungall DR, et al. Bayesian pharmacokinetic/ pharmacodynamic forecasting of prothrombin response to warfarin therapy: preliminary evaluation. Ther Drug Monit. 1985;7:174–180. 20. Pitsiu M, Parker EM, Aarons L, et al. A Bayesian method based on clotting factor activity for the prediction of maintenance warfarin dosage regimens. Ther Drug Monit. 2003;25:36–40. 21. Vadher B, Patterson D, Leaning M. Prediction of the international normalized ratio and maintenance dose during the initiation of warfarin therapy. Br J Clin Pharmacol. 1999;48:63. 22. Boyle DA, Ludden TM, Carter BL, et al. Evaluation of a bayesian regression program for predicting warfarin response. Ther Drug Monit. 1989; 11:276–284. 23. Sheiner LB, Beal SL. Bayesian individualization of pharmacokinetics: simple implementation and comparison with non-bayesian methods. J Pharm Sci. 1982;71:1344–1348. 24. Klein T, Altman R, Eriksson N, et al. Estimation of the warfarin dose with clinical and pharmacogenetic data. N Engl J Med. 2009;360:753–764. 25. Gage BF, Eby C, Johnson JA, et al. Use of pharmacogenetic and clinical factors to predict the therapeutic dose of warfarin. Clin Pharmacol Ther. 2008;84:326–331. 26. Wadelius M, Chen LY, Lindh JD, et al. The largest prospective warfarintreated cohort supports genetic forecasting. Blood. 2009;113:784–792. 27. Wright DFB, Duffull SB. A bayesian dose-individualization method for warfarin. Clin Pharmacokinet. 2013;52:59–68. 28. Ciulla TA, Sklar RM, Hauser SL. A simple method for DNA purification from peripheral blood. Anal Biochem. 1988;174:485–488. 29. Purcell S, Neale B, Todd-Brown K, et al. PLINK: a tool set for wholegenome association and population-based linkage analyses. Am J Hum Genet. 2007;81:559–575. 30. Du Bois D, Du Bois EF. A formula to estimate the approximate surface area if height and weight be known. 1916. Nutrition. 1989;5:303–311; discussion 312–303. 31. Hamberg AK, Wadelius M, Lindh JD, et al. A pharmacometric model describing the relationship between warfarin dose and INR response with respect to variations in CYP2C9, VKORC1, and age. Clinical pharmacology and therapeutics. 2010;87:727–734. 32. Black L, Wright DFB, Thomson AH, et al. The UK Clinical Pharmacy Association National Conference. Manchester, UK, 2014. 33. Sheiner LB, Beal SL. Some suggestions for measuring predictive performance. J Pharmacokinet Biopharm. 1981;9:503–512.
34. Mitra R, Marciello MA, Brain C, et al. Efficacy of computer-aided dosing of warfarin among patients in a rehabilitation hospital. Am J Phys Med Rehabil. 2005;84:423–427. 35. Chatellier G, Colombet I, Degoulet P. Computer-adjusted dosage of anticoagulant therapy improves the quality of anticoagulation. Stud Health Technol Inform. 1997;52:819–823. 36. Pirmohamed M, Burnside G, Eriksson N, et al. A randomized trial of genotype-guided dosing of warfarin. N Engl J Med. 2013;369: 2294–2303. 37. Anderson JL, Horne BD, Stevens SM, et al. Randomized trial of genotype-guided versus standard warfarin dosing in patients initiating oral anticoagulation. Circulation. 2007;116:2563–2570. 38. Kimmel SE, French B, Kasner SE, et al. A pharmacogenetic versus a clinical algorithm for warfarin dosing. N Engl J Med. 2013;369: 2283–2293. 39. Moreau C, Pautas E, Gouin-Thibault I, et al. Predicting the warfarin maintenance dose in elderly inpatients at treatment initiation: accuracy of dosing algorithms incorporating or not VKORC1/CYP2C9 genotypes. J Thromb Haemost. 2011;9:711–718. 40. Finkelman BS, Gage BF, Johnson JA, et al. Genetic warfarin dosing: tables versus algorithms. J Am Coll Cardiol. 2011;57:612–618. 41. Liu Y, Yang J, Xu Q, et al. Comparative performance of warfarin pharmacogenetic algorithms in Chinese patients. Thromb Res. 2012; 130:435–440. 42. Schelleman H, Chen J, Chen Z, et al. Dosing algorithms to predict warfarin maintenance dose in Caucasians and African Americans. Clin Pharmacol Ther. 2008;84:332–339. 43. Sconce EA, Khan TI, Wynne HA, et al. The impact of CYP2C9 and VKORC1 genetic polymorphism and patient characteristics upon warfarin dose requirements: proposal for a new dosing regimen. Blood. 2005; 106:2329–2333. 44. Marin-Leblanc M, Perreault S, Bahroun I, et al. Validation of warfarin pharmacogenetic algorithms in clinical practice. Pharmacogenomics. 2012;13:21–29. 45. Lubitz SA, Scott SA, Rothlauf EB, et al. Comparative performance of gene-based warfarin dosing algorithms in a multiethnic population. J Thromb Haemost. 2010;8:1018–1026. 46. Shin J, Cao D. Comparison of warfarin pharmacogenetic dosing algorithms in a racially diverse large cohort. Pharmacogenomics. 2011;12: 125–134. 47. Cini M, Legnani C, Cosmi B, et al. A new warfarin dosing algorithm including VKORC1 3730 G . A polymorphism: comparison with results obtained by other published algorithms. Eur J Clin Pharmacol. 2012;68: 1167–1174. 48. Wu AHB, Wang P, Smith A, et al. Dosing algorithm for warfarin using CYP2C9 and VKORC1 genotyping from a multi-ethnic population: comparison with other equations. Pharmacogenomics. 2008;9: 169–178. 49. Bristol-Myers Squibb Company. Coumadin tablets (warfarin sodium tablets, USP) crystalline; Coumadin for injection (warfarin sodium for injection, USP) [web site]. Available at: http://www.accessdata.fda.gov/ drugsatfda_docs/label/2010/009218s108lbl.pdf. Accessed April 25, 2014. 50. Michaud V, Vanier MC, Brouillette D, et al. Combination of phenotype assessments and CYP2C9-VKORC1 polymorphisms in the determination of warfarin dose requirements in heavily medicated patients. Clin Pharmacol Ther. 2008;83:740–748. 51. Huang SW, Chen HS, Wang XQ, et al. Validation of VKORCI and CYP2C9 genotypes on interindividual warfarin maintenance dose: a prospective study in Chinese patients. Pharmacogenet Genomics. 2009;19: 226–234. 52. Ohno M, Yamamoto A, Ono A, et al. Influence of clinical and genetic factors on warfarin dose requirements among Japanese patients. Eur J Clin Pharmacol. 2009;65:1097–1103. 53. Takahashi H, Wilkinson GR, Nutescu EA, et al. Different contributions of polymorphisms in VKORC1 and CYP2C9 to intra- and interpopulation differences in maintenance dose of warfarin in Japanese, Caucasians and African-Americans. Pharmacogenet Genomics. 2006; 16:101–110. 54. Zambon C-F, Pengo V, Padrini R, et al. VKORC1, CYP2C9 and CYP4F2 genetic-based algorithm for warfarin dosing: an Italian retrospective study. Pharmacogenomics. 2011;12:15–25.
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Methods for Predicting Warfarin Dose Requirements Shamin M. Saffian, BPharm, PGCertPharm,*† Daniel F. B. Wright, PhD,* Rebecca L. Roberts, PhD,‡ and Stephen B. Duffull, PhD*
Background: The aim of this study was to compare the predictive performance of different warfarin dosing methods.
Key Words: warfarin, INR, dosing algorithm, Bayesian forecasting, pharmacogenetics (Ther Drug Monit 2015;37:531–538)
Methods: Data from 46 patients who were initiating warfarin therapy were available for analysis. Nine recently published dosing tools including 8 dose prediction algorithms and a Bayesian forecasting method were compared with each other in terms of their ability to predict the actual maintenance dose. The dosing tools included 4 algorithms that were based on patient characteristics (2 clinical and 2 genotype-driven algorithms), 4 algorithms based on international normalized ratio (INR) response feedback and patient characteristics (2 clinical and 2 genotype-driven algorithms), and a Bayesian forecasting method. Comparisons were conducted using measures of bias (mean prediction error) and imprecision [root mean square error (RMSE)].
Results: The 2 genotype-driven INR feedback algorithms by Horne et al and Lenzini et al produced more precise maintenance dose predictions (RMSE, 1.16 and 1.19 mg/d, respectively; P , 0.05) than the genotype-driven algorithms by Gage et al and Klein et al and the Bayesian method (RMSE, 1.60, 1.62, and 1.81 mg/d respectively). The dose predictions from clinical and genotype-driven algorithms by Gage et al, Klein et al, and Horne et al were all negatively biased. Only the INR feedback algorithms (clinical and genotype) by Lenzini et al produced unbiased dose predictions. The Bayesian method produced unbiased dose predictions overall (mean prediction error, +0.37 mg/d; 95% confidence interval, 0.89 to 20.15) but overpredicted doses in patients requiring .8 mg/d.
Conclusions: Overall, warfarin dosing methods that included some measure of INR response (INR feedback algorithms and Bayesian methods) produced unbiased and more precise dose predictions. The Bayesian forecasting method produced positively biased dose predictions in patients who required doses .8 mg/d. Further research to assess differences in clinical endpoints when warfarin doses are predicted using Bayesian or INR-driven algorithms is warranted.
Received for publication July 8, 2014; accepted December 3, 2014. From the *School of Pharmacy, University of Otago, Dunedin, New Zealand; †Faculty of Pharmacy, Universiti Kebangsaan Malaysia, Kuala Lumpur; and ‡Department of Surgical Sciences, University of Otago, Dunedin, New Zealand. The authors declare no conflict of interest. Supplemental digital content is available for this article. Direct URL citations appear in the printed text and are provided in the HTML and PDF versions of this article on the journal’s Web site (www.drug-monitoring.com). Correspondence: Shamin M. Saffian, BPharm, PGCertPharm, School of Pharmacy, University of Otago, PO Box 56, Dunedin 9054, New Zealand (e-mail: shamin.mohdsaffi[email protected]). Copyright © 2014 Wolters Kluwer Health, Inc. All rights reserved.
Ther Drug Monit Volume 37, Number 4, August 2015
INTRODUCTION Warfarin is used for the treatment and prevention of venous thromboembolism, pulmonary embolism, thromboembolism associated with atrial fibrillation, and in some patients, for the prophylaxis of clots after myocardial infarction. It is a difficult drug to dose accurately and safely with daily maintenance doses differing by upwards of 10-fold between patients.1 Dosing is further complicated by a narrow therapeutic range and several well-documented drug interactions.2 The physiological response to warfarin therapy is a prolonged clotting time, which is routinely monitored in clinical practice using the international normalized ratio (INR). Patients who are under anticoagulation (INR ,2) are at an increased risk for blood clots, whereas INRs .4 carry an increased risk for major bleeding.3 Not surprisingly, a major challenge faced by prescribers is the accurate prediction of warfarin maintenance doses that will achieve and maintain a therapeutic INR (usually between 2 and 3) in individual patients. There is a large body of literature exploring different strategies for managing warfarin therapy. Several different methods to aid dose prediction have been proposed. These can be broadly categorized based on the clinical information required to predict the warfarin dose, including (1) methods based only on INR response data, (2) methods based only on patient characteristics, (3) methods based on both patient characteristics and INR response data, and (4) methods based on Bayesian forecasting. Dosing tools based on INR response include nomograms4–6 and computerized decision support tools.7–9 These have been reviewed elsewhere10 and will not be discussed further here. Recent publications advocate for the use of multilinear regression methods to identify patient characteristics that determine warfarin dose requirements. The resulting algorithms are intended to provide a guide to the likely maintenance dose required for each patient before the initiation of therapy. This method of predicting dosage is empirical by design, and the algorithms are often developed specifically for particular populations of patients or for certain warfarin indications.11–14 A large number of dosing algorithms for warfarin have been published. A recent review15 identified 32 published algorithms for warfarin therapy, many of which include broadly similar patient characteristics such as body weight,
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age, warfarin indication, interacting drugs (eg, amiodarone), and genetic differences in warfarin metabolism (via the drug metabolizing enzyme CYP2C9) and genetic differences in the recycling of vitamin K [by vitamin K epoxide reductase (VKORC1)]. In addition, a small number of algorithms have been published that include a single INR response measurement, as well as patient characteristics, in the regression analysis.16–18 This is based on the premise that the variability in warfarin response between individuals will be captured by early INR responses. Several Bayesian methods for warfarin therapy have been published,19–22 although few have been developed into dosing tools for use in the clinic. In general, a Bayesian method involves prediction of future INR responses for an individual patient using a pharmacokinetic–pharmacodynamic (PKPD) model, the PKPD parameter values from a prior population and the INR response for an individual patient.23 As more response data become available (ie, more INR measurements are performed), the Bayesian method will provide accurate predictions of future INR values. This then allows the clinician to determine a choice of dose that achieves their INR target. Warfarin dosing algorithms based on patient characteristics, including CYP2C9 and VKORC1 genotype, can account for about 50% of the variability in dosing requirements between patients,24–26 whereas those that also include a single INR response feedback seem to account for about 60% of the dose variability.16,17 This means that about 40%– 50% of the variability in dose requirements between patients will remain unexplained if therapy decision was based on these algorithms alone. In addition, the genotype-driven and INR feedback algorithms require prior knowledge of CYP2C9 and VKORC1 genotype, which is not routinely available in many clinical settings. A Bayesian forecasting method, because it incorporates repeated measures of INR response, will capture all sources of variability in warfarin response between patients. In addition, it can produce individualized dose predictions, which become more specific for each patient as more INR response data become available. Importantly, the Bayesian method should be able to individualize warfarin doses without the need for prior genetic testing. The aim of this article is to compare the predictive performance of 3 warfarin dosing methods: 1. Dosing algorithms based on patient characteristics. This is divided into genotype-driven algorithms (that include VKORC1 and CYP2C9 genotype) and clinical algorithms (algorithms not using genotype). 2. Dosing algorithms based on patient characteristics and a single INR response data (clinical or genotype-driven algorithm). 3. A Bayesian forecasting method.
therapy for any indication at Dunedin Hospital in Dunedin, New Zealand, were enrolled in the study and genotyped for CYP2C9 and VKORC1. Ethical approval for the study was obtained from the Lower South Regional Ethics Committee, New Zealand (LRS/10/11/056). The dosing history and INR response data were collected from baseline (before warfarin initiation) until a stable INR was achieved. The INR measurements were performed as part of normal clinical care. Stable INR (INRs) was used as an approximation of a steady-state INR. INRs was defined as the second consecutive INR observation that lies within 80%–120% of the target INR, following the convention published elsewhere.17 It was required that the 2 INR observations were separated by at least 7 days and that no dose changes had occurred for at least 14 days before the second INR observation.
DNA Extraction, VKORC1, and CYP2C9 Genotyping DNA was collected from peripheral blood samples using guanidine isothiocyanate extraction and stored at 2208C in Tris–EDTA buffer until analysis.28 Genotyping for VKORC1 (rs9923231) and CYP2C9*2 (rs1799853) and *3 (rs1057910) was performed using predesigned SNP TaqMan assays (Assay IDs: C__30403261_20, C__25625805_10, and C__27104892_10) from Applied Biosystems (Carlsbad, CA). Reactions were performed in 384-well format, in a total volume of 5 mL following the recommendations of the manufacturer and run on a Roche LightCycler 480 real-time PCR system (Roche Diagnostics Corporation, Indianapolis, IN). The accuracy of each TaqMan assay was confirmed by repeat analysis of 10% of samples. Concordance between original and repeat genotype calls was 100% for the 2 assays. PLINK software29 was used to test for deviations in Hardy–Weinberg equilibrium. A P value of ,0.05 was considered to indicate a significant deviation from Hardy–Weinberg equilibrium.
Maintenance Dose Prediction Algorithms In total, 8 algorithms from 4 studies were included in the analysis. Each of the 4 studies provided 2 algorithms—1 clinical and 1 genotype-driven algorithm. Clinical algorithms generally include the same patient characteristics as the genotype-driven algorithm but do not include genotype. They were developed by the authors for comparative purposes and therefore will be used for the same purpose here. Four algorithms (2 clinical and 2 genotype-driven) are based only on patient characteristics. Four algorithms (2 clinical and 2 genotype-driven algorithms) are based on patient characteristics and a single INR response feedback. The full algorithms selected for inclusion in this study are provided in Table 1.
Bayesian Forecasting Method
Patient data were sourced from a previous study by Wright and Duffull.27 Briefly, patients who initiated warfarin
A Bayesian forecasting method was recently developed10 and assessed27 by 2 of the authors. It was implemented in the freely available software TCIWorks (www.tciworks. info). The TCIWorks software consisted of a user interface allowing input of patient details, warfarin doses, and INR
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METHODS Patient Data
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Ther Drug Monit Volume 37, Number 4, August 2015
Comparison of Warfarin Dosing Methods
TABLE 1. List of Algorithms Included in the Analysis Abbreviation
Description
C1
Clinical algorithm by Gage et al25
G1
Genotypic algorithm by Gage et al25
C2
Clinical algorithm by Klein et al24
G2
Genotypic algorithm by Klein et al24
C3-INR
Clinical algorithm with INR feedback by Lenzini et al17
G3-INR
Genotypic algorithm with INR feedback by Lenzini et al17
C4-INR
Clinical algorithm with INR feedback by Horne et al16
G4-INR
Genotypic algorithm with INR feedback by Horne et al16
Algorithm Dose (mg/d) = exp [0.613 + (0.425 · BSA) 2 (0.0075 · age) + (0.156 · African American race) + (0.216 · target INR) 2 (0.257 · amiodarone) + (0.108 · smokes) + (0.0784 · DVT/PE)] Dose (mg/d) = exp (0.9751 2 0.3238 · VKORC1 2 1639 G.A + 0.4317 · BSA 2 0.4008 · CYP2C9*3 2 0.00745 · age 2 0.2066 · CYP2C9*2 + 0.2029 · target INR 2 0.2538 · amiodarone + 0.0922 · smokes 2 0.0901 · African American race + 0.0664 · DVT/PE) Dose (mg/wk) = [4.0376 2 0.2546 · age (in decades) + 0.0118 · height (in centimeters) + 0.0134 · weight (in kilograms) 2 0.6752 · Asian race + 0.4060 · Black or African American + 0.0443 · missing or mixed race + 1.2799 · enzyme inducer status 2 0.5695 · amiodarone status]2 Dose (mg/wk) = [5.6044 2 0.2614 · age (in decades) + 0.0087 · height (in centimeters) + 0.0128 · weight (in kilograms) 2 0.8677 · VKORC1 A/G 2 1.6974 · VKORC1 A/A 2 0.4854 · VKORC1 genotype unknown 2 0.5211 · CYP2C9*1/*2 2 0.9357 · CYP2C9*1/*3 2 1.0616 · CYP2C9*2/ *2 2 1.9206 · CYP2C9*2/*3 2 2.3312 · CYP2C9*3/*3 2 0.2188 · CYP2C9 genotype unknown 2 0.1092 · Asian race 2 0.2760 · Black or African American 2 0.1032 · missing or mixed race + 1.1816 · enzyme inducer status 2 0.5503 · amiodarone status]2 Dose (mg/wk) = exp [2.8160220.76679 · ln (INR) 2 0.0059 · age + 0.27815 · target INR 2 0.16759 · diabetes + 0.17675 · BSA 2 0.22844 · stroke 2 0.25487 · fluvastatin use + 0.07123 · African origin 2 0.11137 · amiodarone use + 0.03471 · dose_2 + 0.03047 · dose_3 + 0.01929 · dose_4]† Dose (mg/wk) = exp [3.10894 2 0.00767 · age 2 0.51611 · ln (INR) 2 0.23032 · VKORC1-1639 G.A 2 0.14745 · CYP2C9*2 2 0.3077 · CYP2C9*3 + 0.24597 · BSA + 0.26729 · target INR 2 0.09644 · African origin 2 0.2059 · stroke 2 0.11216 · diabetes 2 0.1035 · amiodarone use 2 0.19275 · fluvastatin use + 0.0169 · dose_2 + 0.02018 · dose_3 + 0.01065 · dose_4]† Dose (mg/wk) = exp (2.19023 2 0.66327 · treatment response index‡ 2 0.00379 · age in years + 0.1095 · BSA 2 0.06548 · simvastatin use 2 0.2809 · fluvastatin use 2 0.08761 · amiodarone use + 0.2612 · Inducer use + 0.04189 · target INR 2 0.13717 · stroke + 0.01292 · day of therapy) Maintenance dose (mg/wk) = exp (2.59853 2 0.47578 · treatment response index‡ 2 0.17132 · VKORC1-1639 G.A 2 0.23385 · CYP2C9*3 2 0.10696 · CYP2C9*2 2 0.00549 · age + 0.16491 · BSA 2 0.09091 · simvastatin use 2 0.251 · fluvastatin 2 0.11994 · amiodarone + 0.3319 · inducer + 0.08796 · target INR 2 0.13902 · stroke + 0.01028 · day of therapy)
BSA, body surface area calculated using Du Bois & Du Bois formula.30 Age is in years unless stated. Variables are coded as 1 if present or 0 otherwise. Where genotype is specified, they are coded as 0 for no polymorphism, 1 for heterozygous, and 2 for homozygous. ln is the natural log. †Dose_2, _3, and _4 refers to dose given 2, 3, and 4 days before the INR was measured. ‡Treatment Response Index: ln (INR/effective dose). DVT/PE, deep vein thrombosis/pulmonary embolism.
observations. The method was underpinned by a warfarin dose–response model developed by Hamberg et al.33 In 2 retrospective analyses, the TCIWorks method was shown to provide accurate and precise predictions of INR response in patients who were initiating warfarin.27,34 For the purpose of this study, where the data were gathered retrospectively from dose individualization, the full dosing history and the first 4 INR observations for each patient were entered into TCIWorks. The authors then selected a dose that resulted in a predicted INR that corresponded to the observed INRs. This was then treated as the predicted maintenance dose. The authors chose to use the first 4 INR observations, as 4 INR observations were found to be sufficient to provide unbiased and precise INRs predictions as mentioned previously.27,34 The influence of more than 4 INR observations were not considered in this study.
Measurement of Bias and Imprecision
Calculations of MPE, MSE, and RMSE are given in the following equations: MPE ¼
N 1X PEi : N i¼1
(1)
MPE is the average differences between predicted and observed maintenance dose, where N is the number of patients. PEi is the prediction error of the predicted maintenance dose for ith individual. Prediction error is the difference between the predicted maintenance dose and the observed maintenance dose (predicted dose minus observed dose). If the 95% confidence interval (CI) of the prediction error included 0, no statistically significant bias was concluded. MSE ¼
N 1X ðPEi Þ2 : N i¼1
(2)
The predictive performance of each of the dosing methods was compared using measures of bias [mean prediction error (MPE)] and imprecision [mean square error (MSE) and root mean square error (RMSE)] as described by Sheiner and Beal.33
MSE is the average of the sum of squared differences between predicted and observed maintenance dose. pffiffiffiffiffiffiffiffiffiffi RMSE ¼ MSE: (3)
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RMSE is the square root of MSE. It provides an estimate of the imprecision given in the same units as the predicted dose (in milligrams per day). The imprecision of each method was compared by an analysis of the ratio of the variances. This was performed using an F-test where the ratio of the larger variance over the smaller variance was compared with 1. Variance of the predicted maintenance dose was calculated using the following equation: varianceMD ¼ MSE 2 MPE2 ;
(4)
where varianceMD is the variance of predicted maintenance dose of each dosing method.
RESULTS Data from 55 patients were available for analysis. Nine patients did not consent to genotyping and were excluded, providing a final data set of 46 patients. Patient characteristics are presented in Table 2. Height was missing for 13 patients and was imputed using multilinear regression (see Appendix 1, Supplemental Digital Content 1, http://links.lww.com/TDM/ A101). INR measurements were missing for 11 patients on days 4 or 5 (required for algorithm C3-INR and G3-INR). The missing INR values were imputed by linear interpolation between adjacent measurement days (see Appendix 1, Supplemental Digital Content 1, http://links.lww.com/TDM/A101). A summary of MPE and RMSE results is presented in Table 3. Goodness of fit plots is included in Figure 1. For the 4 algorithms that were based only on patient characteristics (C1, G1, C2, and G2), the incorporation of genotype into the algorithm produced a more precise prediction (P , 0.05) (Table 3). Bias, however, was not improved by the incorporation of
TABLE 2. Patient Characteristics and a Summary of Maintenance Dose and Stable INR (INRs) Patient Characteristics Age (years) Height (cm) Weight (kg) Male/Female (number of patients) Indication for warfarin (number of patients) Concomitant drugs of note (number of patients) Levothyroxine Beta-lactam antibiotics (.3 days) Metronidazole Azole antifungals Time to reach first stable INR (days) Number of INR observations to stable INR INRs value Dose at INRs (mg/d)
n = 46 62 (29–87) 166 (145–192) 81.7 (44–113) 19/27 Atrial fibrillation: 2; deep vein thrombosis: 27; pulmonary embolism: 17
4 1 1 1 38 (11–118) 11 (6–21) 2.4 (2–3.1) 5.5 (1.5–11)
Values are expressed as median (range) unless specified otherwise.
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genotype where all 4 algorithms produced negatively biased dose predictions. The INR feedback algorithms, C3-INR and G3-INR, were found to produce unbiased dose predictions (Table 3). Although the other INR feedback algorithms (C4-INR and G4-INR) produced negatively biased dose predictions. The INR feedback algorithms, G3-INR and G4-INR, were found to produce the lowest RMSE values overall (1.16 and 1.19, respectively) (Table 3). In addition, the predictions from the algorithm G4-INR were significantly more precise than all other dosing tools (P , 0.05) except for G3-INR and C4-INR. The Bayesian method was, on average, unbiased (MPE, +0.37 mg/d; 95% CI, 0.89 to 20.15). Visualization of the data in Figure 1 indicates that the Bayesian method overpredicted maintenance dose in patients who required higher doses (.8 mg/d). All of the INR feedback algorithms except C3-INR produced significantly more precise warfarin dose predictions than the Bayesian method (P , 0.05), and precision was not statistically different between the Bayesian method and most of the algorithms based on patient characteristics (no INR feedback) (Table 3). Overall, the INR-driven algorithms produced better precision, but only algorithms C3-INR and G3-INR produced unbiased warfarin dose predictions. The incorporation of genotype into the algorithm (clinical versus genotype-driven algorithm from the same study) was found to only improve precision in most cases but not bias.
DISCUSSION There is currently no consensus regarding the optimal method for predicting warfarin dose requirements. The evidence to date generally supports the idea that the use of a warfarin dosing tool of some sort by prescribers will result in superior anticoagulant control (eg, time in the therapeutic range or time to reach a stable warfarin dose) compared with traditional, heuristic, dosing practice.34,35 However, the evidence is less clear about how different warfarin dosing tools compare with each other in terms of predictive performance, INR control, and patient outcomes. For example, although genotype-driven algorithms have been shown to improve dosing predictions and clinical endpoints compared with traditional heuristic dosing practice,36 this has not been consistently demonstrated when compared with other dosing tools that did not include genotype37,38 or to dosing methods using only INR response data.39 Importantly, to our knowledge, there are no published studies comparing Bayesian forecasting for warfarin therapy with other dosing methods, despite promising preliminary results in prospective and retrospective studies.27,35 This means that the choice of which dosing method to use in clinical practice cannot be based on robust evidence comparing one method with another and will therefore be driven by other factors such as cost, ease of use, and availability of genotype data. To the author’s knowledge, this is the first study to compare the predictive performance of a Bayesian forecasting method for warfarin dose individualization with genotype-driven and INR feedback dosing algorithms. The authors have shown that the Bayesian forecasting can provide unbiased dose predictions for patients taking ,8 mg/d without Copyright 2014 Wolters Kluwer Health, Inc. All rights reserved.
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Ther Drug Monit Volume 37, Number 4, August 2015
Comparison of Warfarin Dosing Methods
TABLE 3. Summary of Bias, Precision, and F-test for the Different Dosing Methods No INR Feedback Parameter MPE (95% CI) RMSE F-test versus C1 F-test versus G1 F-test versus C2 F-test versus G2 F-test versus C3-INR F-test versus G3-INR F-test versus C4-INR F-test versus G4-INR F-test versus Bayesian
C1 20.76 (20.18 to 21.34) 2.12
G1 20.64 (20.21 to 21.07) 1.60 P , 0.05a
C2 21.01 (20.42 to 21.60) 2.26
Algorithms With INR Feedback G2
C3-INR
G3-INR
C4-INR
G4-INR
Bayesian
20.72 (20.30 to 21.15) 1.62 P , 0.05a
0.27 (0.69 to 20.16) 1.49 P , 0.05a
20.18 (0.16 to 20.53) 1.19 P , 0.05a
20.42 (20.08 to 20.76) 1.22 P , 0.05a
20.52 (20.22 to 20.82) 1.16 P , 0.05a
0.37 (0.89 to 20.15) 1.81 P , 0.05a
P , 0.05b
P , 0.05b
P , 0.05c
P , 0.05c
P , 0.05c
P , 0.05a
P , 0.05c
P , 0.05c
P , 0.05c
P , 0.05c
P , 0.05a
P , 0.05c
P , 0.05d
P , 0.05a
P , 0.05c
P , 0.05e
P , 0.05a
P , 0.05c
P , 0.05f P , 0.05f
P , 0.05a
P , 0.05b
P , 0.05c
P , 0.05a
P , 0.05b
P , 0.05c
P , 0.05d
P , 0.05a
P , 0.05e
P , 0.05f P , 0.05f
P , 0.05f
P , 0.05f
For C3-INR and G3-INR, if an INR on day 4 and day 5 was available, INR on day 5 was used preferentially. For C4-INR and G4-INR, INR available on the earliest day between days 6 and 11 was used to calculate predicted maintenance dose. Superscript letters denote the less precise algorithm aC1, bG1, cC2, dG2, eC3-INR, and fBayesian method.
the need for genotype information. Dose predictions from the Bayesian tool were similar to algorithms based on patient characteristics in terms of precision but were significantly less precise than those predicted by INR feedback algorithms. An important difference between the Bayesian forecasting tool and the other dosing methods analyzed in this study is that the Bayesian method is capable of updating the future INR predictions as more INR observation become available. By predicting accurate future INR, a dose can be selected to achieve the desired target INR. Previous publications have used a variety of different criteria to evaluate warfarin dosing tools. Some studies determined the percentage of dose predictions that lie within a prespecified, and presumably clinically acceptable, range, that is, 620%24,40,41 or 61 mg of the observed dose.42 Other authors have reported the coefficient of determination (R2) as a measure of predictive performance.43,44 The authors evaluated predictive performance using MPE and RSME, as suggested by Sheiner and Beal.33 Although a robust method for assessing the predictive performance of warfarin dosing tools, the authors have found it to be insensitive to the apparent bias in dose predictions produced by the Bayesian method in patients taking .8 mg/d (Fig. 1).
The predictive performance of dosing tools for warfarin therapy has been evaluated in several previous studies.12,40,41,44–48 Finkelman et al40 compared the accuracy of dose predictions of 4 dosing tools in 1378 patients who were part of the International Warfarin Pharmacogenetic Consortium (IWPC)24 cohort. The dosing tools compared were the FDA warfarin drug label,49 a genotype table derived from the IWPC cohort, a clinical algorithm, and a genotype-driven algorithm published by Gage et al25 (algorithm C1 and G1). They found that the genotype-driven algorithm by Gage et al (G1)25 predicted a higher percentage of doses (52%, P , 0.001) within 20% of the observed dose compared with the genotype mean table, FDA warfarin label, and clinical algorithm (44%, 43%, and 39%, respectively). In another study, Marin-Leblanc et al44 compared 4 genotype-driven algorithms.24–26,50 The authors found that the algorithms published by Gage et al (G1)25 and Wadelius et al26 predicted a higher percentage of doses within 20% of the observed dose (41.7% and 46.3%, P , 0.05, respectively) compared with the algorithms published by Klein et al (G2)24 (39%) and Michaud et al50 (31.9%). By comparison, using the same metric with our data, algorithms G1 and G2 predicted 47.8% and 56.5%, respectively, of the doses within 20% of the observed dose.
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FIGURE 1. Scatter plots of observed maintenance dose versus predicted maintenance dose for each dosing method. The solid blue line is the line of identity. The red line is a loess fitted function. Top rows are algorithms based only on patient characteristics, middle rows are algorithms based on patient characteristics and INR response, and bottom is a Bayesian method.
Liu et al41 compared 8 genotype-driven algorithms17,24,25,43,51–54 in a prospective cohort of 282 Chinese warfarin patients. The study included algorithms G1, G2, and G3-INR. The goal was to compare the accuracy of warfarin dose predictions produced by the algorithms in Chinese patients who required low-dose therapy (ie, ,1.5 mg/d). The authors reported that overall 52.1% of the dose predictions produced by G3-INR were within 20% of the observed dose. This was statistically higher than G2 (45%), with a reported odds ratio of 1.71 (95% CI, 1.08–2.72; P = 0.0029). It is noteworthy that in patients taking doses ,1.5 mg/d, only 4.5% of the dose predictions were within 20% of the observed dose. Using the same metric with our data, the INR feedback algorithm G3-INR predicted a similar percentage of doses within 20% of the observed dose at 54.4%. A recently published randomized controlled trial (RCT)36 compared the percentage of INRs within in the therapeutic range (2.0–3.0) after either being guided by a genotype-driven algorithm or by heuristic dosing. The authors found that genotype-driven dosing resulted in INRs within the therapeutic range significantly more than heuristic dosing
(67.4% versus 60.3%, P , 0.001). This trial used 2 difficult algorithms to predict warfarin dosing requirements. Initial doses were predicted using a modified version of the algorithm G2, while subsequent dose predictions were updated with an INR measurement on day 4 or 5 of therapy using the INR feedback algorithm G3-INR. By contrast, in another RCT, Kimmel et al38 found no difference in the percentage of time within the INR therapeutic range using doses predicted by genotype-driven dosing compared with clinical algorithms (45.2% versus 45.4%, respectively). Initial doses in this RCT were predicted using algorithms C1 or G1, and subsequent dose predictions were updated using INR feedback algorithms C3-INR or G3-INR, respectively. This finding aligns with the results of this study where the authors did not find substantial differences in predictive performance between clinical and genotype-driven algorithms. Taken together, the results of the 2 RCTs and our study suggest that genotypedriven dosing may improve INR control compared with heuristic dosing but perhaps not compared with clinical algorithms. Indeed, the results of our study seem to suggest that the inclusion of INR response data in the Bayesian and INR
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Ther Drug Monit Volume 37, Number 4, August 2015
feedback tools may have a greater impact on INR control than the addition of genotype. The difference in the predictive performance of published warfarin dosing algorithms between the studies summarized above and in our work is noteworthy. The dosing algorithms are empirically derived using multilinear regression methodology so can be expected to provide a good description of the factors that determined warfarin dose requirements in the populations from which they were developed. However, they do not appear to perform as well when extrapolated to new clinical settings or patient populations. This is arguably a problem for all dose prediction tools but may be less so for Bayesian forecasting methods, where dose predictions are dependant not only on prior population estimates for PKPD parameters but also on the repeated measurement of INR response in each patient. In theory, if the prior model used in a Bayesian system was derived from a diverse population and included sufficient mechanistic components to allow extrapolation, then the Bayesian method should perform well across patients groups. In light of this, it is noteworthy that the Bayesian forecasting method assessed in our study had a propensity to overpredict the dose requirements for those patients who require maintenance doses greater than about 8 mg/d. The authors have observed that the overprediction occurs mainly in patients with the GG genotype for a VKORC1 promoter variant (21639 G.A, rs9923231) (Fig. 2). No relationship to CYP2C9 genotype was observed (data not shown). This suggests that the population used to develop the prior model may have been sufficiently different from the population assessed in our study, at least with regard to the influence of VKORC1 genotype, and this may have biased the results. This problem is the subject of ongoing research. There are limitations to this study. Our sample size is small, making generalization of the results to all warfarin users difficult. The data were collected largely from ambulatory patients attending a deep vein thrombosis clinic at Dunedin
Comparison of Warfarin Dosing Methods
Hospital. It is unclear whether the algorithms and the Bayesian method would have performed differently in other patient groups such as those with atrial fibrillation. Height and INR data on days 4 or 5 of therapy (required by algorithms C3-INR and G3-INR) were missing for some patients (n = 13 and n = 11) and were imputed (see Appendix 1, Supplemental Digital Content 1, http://links.lww.com/TDM/A101). Note that height was only found to explain a small amount of dose variability in all of the algorithms, so the impact of including imputed heights is likely to be small.
CONCLUSIONS Warfarin dosing methods that included some measure of INR response (INR-driven algorithms and Bayesian methods) performed favorably, although no single dosing tool was clearly superior in terms of predictive performance based on our results. The INR feedback algorithms generally produced the most precise dose predictions but were inconsistent in terms of bias. Overall, INR feedback algorithm by Lenzini et al (genotype driven) produced the most precise and unbiased dose predictions. The Bayesian forecasting method produced unbiased dose predictions overall but overpredicted in patients who required doses .8 mg/d. The addition of CYP2C9 and VKORC1 genotype in the genotype-driven algorithms was noted to improve the precision of dose predictions in some cases compared with clinical algorithms but did not appreciably impact predictive performance compared with the Bayesian tool. Further research to assess differences in clinical endpoints, such as time in the therapeutic range or bleeding and stroke events, when warfarin doses are predicted using Bayesian or INR-driven algorithms is warranted.
ACKNOWLEDGMENTS The authors are grateful to Hesham Al-Sallami for his assistance with data imputation and to Mr Lionel van den Berg and Professor Carl Kirkpatrick from Monash University for invaluable assistance with TCIWorks. At the time of writing, S. M. Saffian was the recipient of a Malaysian Government Scholarship. REFERENCES
FIGURE 2. Scatter plots of observed maintenance dose versus predicted maintenance dose for the Bayesian method according to VKORC1 genotype (21639 G.A, rs9923231). Red circles represent AA, blue squares represent AG, and green triangles represent GG. The solid black line is the line of identity.
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