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Improvement of anticoagulant treatment using a dynamic decision support algorithm
Thrombosis Research 133 (2014) 375–379
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Thrombosis Research journal homepage: www.elsevier.com/locate/thromres
Regular Article
Improvement of anticoagulant treatment using a dynamic decision support algorithm A Danish Cohort study Peter Brønnum Nielsen a,⁎, Søren Lundbye-Christensen b, Lars Hvilsted Rasmussen a, Torben Bjerregaard Larsen a,b a b
Thrombosis Research Unit, Aalborg University, Aalborg, Denmark Department of Cardiology, Aalborg AF study group, Aalborg University Hospital, Aalborg, Denmark
a r t i c l e
i n f o
Article history: Received 11 September 2013 Received in revised form 21 December 2013 Accepted 30 December 2013 Available online 7 January 2014 Keywords: Computer-assisted drug therapy drug dosage calculation international normalised ratio statistical model warfarin
a b s t r a c t Introduction: Warfarin is the most widely prescribed vitamin K antagonist and in the United States and Europe more than 10 million people are currently in long-term oral anticoagulant treatment. This study aims to retrospectively validate a dynamic statistical model providing dosage suggestions to patients in warfarin treatment. Materials and methods: The model was validated on a cohort of 553 patients with a mean TTR of 83%. Patients in the cohort were self-monitoring and managed by a highly specialised anticoagulation clinic. The predictive model essentially consists of three parts handling INR history, warfarin dosage and biological noise, which allows for prediction of future INR values and optimal warfarin dose to stay on INR target. Further, the model is based on parameters initially being set to population values and gradually individualised during monitoring of patients. Primary outcome: Time in therapeutic range was used as surrogate quality measure of the treatment, and modelsuggested dosage of warfarin was used to assess the accuracy of the model performance. Results: The accuracy of the model predictions measured as median absolute error was 0.53 mg/day (interquartile range from 0.25 to 1.0). The model performance was evaluated by the difference between observed and predicted warfarin intake in the preceding week of an INR measurement. In more than 70% of the cases where INR measurements were outside the therapeutic range, the model suggested a more reasonable dose than the observed intake. Conclusion: Applying the proposed dosing algorithm can potentially further increase the time in INR target range beyond 83%. © 2014 Elsevier Ltd. All rights reserved.
Introduction Warfarin is the most widely prescribed drug in oral anticoagulant treatment (OAT) and more than 6 million patients in Europe and approximately 4 million in the United States are currently living on long-term OAT [1,2]. The most common indications for warfarin treatment are atrial fibrillation (AF), deep venous thrombosis (DVT), pulmonary embolism (PE), post myocardial infarction (MI), and heart valve replacement. The treatment balances between avoiding thrombotic events and bleeding episodes.
Abbreviations: INR, international normalised ratio; OAT, oral anticoagulant treatment; AF, atrial fibrillation; DVT, deep venous thrombosis; PE, pulmonary embolism; MI, post myocardial infarction; VKA, vitamin K antagonists; TR, therapeutic range; TTR, Time in therapeutic range; PST, patient self-testing; PSM, patient self-management; MAE, median absolute error. ⁎ Corresponding author at: Forskningens Hus, Srd. Skovvej 15, DK-9000 Aalborg, Denmark. Tel.: +45 99 32 81 00; fax: +45 99 32 80 99. E-mail address: [email protected] (P.B. Nielsen). 0049-3848/$ – see front matter © 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.thromres.2013.12.042
Anticoagulant monitoring is done by measurement of the International Normalised Ratio (INR). The therapeutic range of INR is 2.0-3.0 or 2.5-3.5 for the majority of the underlying conditions mentioned above. Further, anticoagulation with vitamin K antagonists (VKA) is a complicated task due to food and drug interacting with the effect of VKA [3–5]. A noticeable between patients variation in response to warfarin entails individual dosing and frequent monitoring of the INR. The risk profile for patients undergoing VKA treatment is dependent on the time for which the INR value is within therapeutic range (TR) [6–9]. Time in therapeutic range (TTR) is often used as a quality marker of VKA management [7,10,11], and is recommended as an endpoint when analysing quality of anticoagulation management [12]. A recent study, however, shows that TTR is not the optimal predictor of mortality, stroke, bleeding and hospitalisation in atrial fibrillation patients receiving warfarin therapy [13]. Warfarin therapy is primarily monitored by laboratory determination of INR using plasma from venipuncture. Different settings of treatment management exists, including usual care provided by the general practitioner, hospital outpatient clinics, and highly specialised
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anticoagulation clinics. However, some patients are eligible for patient self-testing (PST) or patient self-management (PSM) using portable point-of-care testing coagulometers and will benefit for this type of management [14,15]. A meta-analysis comparing PSM and PST with usual care proved a significant reduction in thromboembolic events, but neither a reduction in major haemorrhagic events nor reduction in death was shown [16]. Patients younger than age 55 and patients with mechanical heart valve replacement had the largest reduction in thrombotic events in the comparison (hazard ratio of 0.33 and 0.52, respectively). Some PSM patients are using decision aiding electronic tools or online decision support systems that will provide an on-screen dosage advice [17,18]. These meta-analysis favours uses of such systems with an overall improvement across studies of 6% in time in therapeutic INR range. However, no significant difference was found between controls and patients using decision support systems when comparing the risk for major bleeding (risk of thrombotic events was not reported) [19]. A proportion of published warfarin prediction algorithms utilise pharmacogentic dose prediction [20–22]. While they have shown to perform better compared to physician managed warfarin dosing in predicting the initial optimal dose (often measured in the time to reach stable treatment), the genetic information does not persistently improve the warfarin treatment [23–26]. It may be important to consider the intention behind the use of decision aiding tools that includes a prediction model, and such underlying prediction model should perform well in at least two situations. First, the model should attempt to maintain a high TTR by providing a dose adjustment advice. This can only be investigated in a prospective study design. Second, the model should perform properly when a measured INR value is outside the INR target range, in the sense of providing a dose adjustment that will bring the future INR value(s) within the desired range. This can be investigated in a retrospective designed study. For the sake of patient’s safety and prior to a randomized controlled trial, we propose to retrospectively validate such a model bearing in mind that OAT is a potential lethal treatment if inappropriate dosage is provided. In this study we aim to apply a developed dynamic statistical model for decision support [27] in a cohort of PSM patients treated in a highly specialised anticoagulation clinic.
Materials and methods Population Eligible patients were identified from the clinical database of the Thrombosis Research Clinic for PSM Oral Anticoagulation, Department of Cardiology, Aalborg University Hospital, Denmark. This centre includes a highly specialized anticoagulation clinic with approximately 850 patients who are trained in PSM OAT. The centre's functions are handled by specially trained nurses and specialists. The centre handles all matters relating to the patient's anticoagulant therapy including perioperative management when needed (regulation of INR, delivery of low molecular weight heparin, contact to other departments’ etc.). The patients are using an online dosage and decision support tool (AC Shared Care, ACURE, IBM, DK-8240 Risskov, Denmark), which provides dosage suggestions of warfarin for the following week based on the previous INR measurement. The dosage advice is given as a mean tablet (2.5 mg) intake per week, and subsequently calculated as a weekly pattern of daily dosage of warfarin. If an INR measurement typed into the system is not adequately close to or within the therapeutic range, a suggestion to contact the staff at the Thrombosis Research Clinic is given to the patient. The staff can order an instant dose change, e.g. double warfarin intake for a day or suspend the treatment for a day. These changes are registered in the clinical database as additions to the current intake of warfarin that day.
The data for the present study was acquired from January 2010 till December 2012 and consists of 837 patients assigned to PSM. Patients were excluded (N = 284) if the following criteria were met: less than 30 days of warfarin therapy or fewer than 4 INR measurements since onset of PSM (N = 38); registered with an event (thrombosis or minor/major bleeding) in the clinical database (N = 158); interval between INR measurements above 8 weeks (N = 87); no registered clinical information (N = 1). Data for each patient were then prepared to be applicable to the prediction model. The model required at least seven days of warfarin intake before the first INR measurement. Hence, the INR measurements that were performed within this period could not be included in the model and were removed accordingly. Model description The model is fully specified and discussed in details in [27], and is designed to handle time series of daily intake of warfarin and measured INR values. For a given patient, let T denote the target INR value, INRt and INRt-1 be the measured INR value at a given day and the previous day (INR history), and wt-1 and wt-2 be the warfarin intake the previous day and the day before (warfarin dosage). Subjected to optimal dosing, the departure from target at a given day, apart from biological noise, is expected to be smaller than the departure the previous day. If the warfarin intake the previous day and the day before is higher than the optimal dose (to stay on target), the INR is expected to increase, and decrease if the warfarin intake is lower than the optimal dose. The day-to-day dynamics of warfarin and INR is modelled as
INR history
Warfarin dosage
Noise
zfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflffl{ zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{ z}|{ INRt −T ¼ ρðINRt−1 −TÞ þAðwt−1 þ λwt−2 –ð1 þ λÞDt−1 Þ þ εt ; where ρ quantifies the day-to-day dynamics of INR, A is the sensitivity towards changes in warfarin intake, D is the idealised dose to maintain INR target, λ is a constant, and εt is a series of independent noise terms. The day-to-day dynamics of INR is quantified by the constant, ρ, between 0 and 1, leaving an auto-regressive structure of INR measurements when the patient is on optimal dosing. The sensitivity towards changes in warfarin intake, A, is an unknown patient specific parameter, negatively correlated to the dosage. This allows for modelling the individual INR change due to a unit change in warfarin, such that patients on a low warfarin dose are more likely to have a larger INR change compared to patients on a high dose. The idealised warfarin dose, D, is an unknown patient specific parameter. Over time D can exhibit small fluctuations reflecting changes in endogenous or exogenous factors. Warfarin affects INRt through a between-day-profile of intake, (wt−1 + λ wt−2), where λ is common to all patients. The noise sequence, εt, reflecting the biological noise has a patient specific standard deviation. Thus, the full specification of the model contains parameters describing population distributions. Model based monitoring When the model based monitoring of a patient is initiated all parameters are set to population values. Usually patients have a daily warfarin intake whereas INR measurements are less frequent. For each day predictions of INR, sensitivity and idealised dose are extrapolated from previous values. When an INR values becomes available the model parameters are updated. This so-called Kalman filter [28] offers recursive formulae for calculation of these updates, see details in [27]. Hereby the suggested dose at each time point is based on history of warfarin intake and INR measurements of the individual patient. Similarly, the individual sensitivity to changes in dose is updated. Hence the model adopts how the patient should be dosed aiming for a higher TTR.
P.B. Nielsen et al. / Thrombosis Research 133 (2014) 375–379 Table 1 Demographics and clinical characteristics of the patient cohort. Patient characteristics
Total
Number of patients Sex
553
Percent or SD
Females Age Total number of INR measurements Total number of observation days Target INR Target 2.5 Target 3.0 Indication for treatment* VTE AF MI Mechanical heart valve, stenosis or prosthesis Stroke or TIA Other † TTR INR Mean Target 2.5 2.54 Target 3.0 2.98 Warfarin intake (mg) Mean Target 2.5 6.01 Target 3.0 6.44
177 55.5 26,175 203,964
32% ±11.8
501 52
90.60% 9.40%
166 194 3 151
30.02% 35.08% 0.54% 27.31%
32 7 83% SDb ±0.19 ±0.26 SDb ±2.43 ±2.49
5.79% 1.26% SDw ±0.46 ±0.58 SDw ±0.52 ±0.73
*Abbreviations and details: Venous thromboembolism and Thrombophilia (VTE), transient ischemic attack (TIA). SD is standard deviations, SDb is between patient standard deviation and SDw is the within patient standard deviation.TTR† is time in therapeutic range calculated by Rosendaal method.
Model performance evaluation A Matlab (MathWorks Inc., MA) script of the dynamic model was implemented, using population values obtained from previous published work [27]. All predicted INR values and predicted doses are stored for the purpose of comparison with their observed counterparts. Dose predictions were compared with administered doses in two ways. First, simple calculation of median absolute error (MAE) is produced to assess the accuracy of the predictions. Second, the means calculated for the seven previous days of predicted and administered dose for each INR value are evaluated as a function of deviations from INR target. This allows for comparing the suggested dose against the administered for INR values outside INR range. Further, the initiation to model predictions is assessed by regarding MAE in patients with 10 consecutive observations within INR range. Hereby the contribution of model uncertainties can be evaluated. Results Of 837 eligible patients 284 met the exclusion criteria. The baseline characteristics of the remaining 553 patients are shown in Table 1. The accuracy of the model predictions compared to administered dose was within a quarter of a tablet, MAE = 0.53 mg/day (interquartile range from 0.25 to 1.0).
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An approach taken to evaluate the model performance is to report the proportion of dose suggestions “more reasonable” than the administered doses when observed INR is below TR or above TR, as shown in Table 2. It is of notice that the model suggests a more adequate dose in more than 70% of the incidents when INR measurements are outside TR. The distinction between whether or not the suggested dose is above or below the administered may be refined by introducing the category “nearly identical”. If the weekly total of suggested doses differs from the administered by less than one tablet, the two dosages will be considered identical. Furthermore, larger deviations from TR are more severe and would cause clinical intervention. In Fig. 1 we depict the mentioned three warfarin categories versus INR measurements subdivided into five ranges. It is evident that the model performs adequately in these severe situations in more than 60% of the incidents and inferior in less than 18%. A subgroup analysis regarding MAE of warfarin intake for patients with 10 consecutive INR measurements (N = 51) within INR range is depicted in Fig. 2. From inspection it is apparent that the MAE between predicted and administered warfarin intake stabilizes after 3 INR observations when initiating monitoring. Discussion This study reports the outcome of an evaluation of a dynamic decision support algorithm retrospectively applied on a cohort of PSM patients treated by a highly specialised anticoagulant clinic. Two European decision support systems for use in anticoagulation treatment (DAWN AC and PARMA 5) have been clinically validated in a multicenter randomized trial [29]. In comparison with experienced medical staff, the two systems significantly improved the TTR, and reduced the clinical events of DVT and pulmonary embolisms. The TTR reported from the randomized trial was significantly lower (65.9 % for computer assisted group) than the TTR reported in this study. For comparison it would be desirable to apply DAWN AC or PARMA 5 on a cohort of PSM patients with a higher baseline TTR. Further, one recent study shows non-inferiority of DAWN AC compared to a simple warfarin dosing algorithm [30]; the reported mean TTR was approximately 70 %. In Sweden a web-based dosing system, named Auricula (based on an algorithm applying 720 rules), for warfarin treatment is widely used [31]. The system also served as a national quality registry since 2006. In a retrospective analysis of more than 50.000 patients the system performed adequately in most cases. The algorithm is meant to improve over time, as it is retrospectively evaluated and the rules can be changed accordingly. The data in the present study originates from a centre with a high quality OAT that educates patients in PSM. Continuous close monitoring of the quality of the treatment is maintained by specialised staff at the centre. The patients are using an online dosage advisory system to maintain their INR within the designated target INR. When INR measurements are outside TR, the staff can order an instant dose change in the attempt to bring back the future INR within range. This leads to a high TTR of 83%, compared to most European contents published. Despite the high quality OAT, which is achieved by a dosing algorithm supplied with optional interference from experienced staff, our
Table 2 Dosage suggestions provided by the model.
Less warfarin intake than model the suggests More warfarin intake than the model suggests Total
INR below TR
INR within TR
INR above TR
Total
1,589 72.29% 609 27.71% 2,198
10,246 49.01% 10,659 50.99% 20,905
726 23.63% 2,346 76.37% 3,072
12,561 47.99% 13,614 52.01% 26,175
Difference between model-suggested dose of warfarin and administered dose of warfarin in the preceding week grouped in three different intervals of therapeutic range.
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Fig. 1. Dosage suggestions for five ranges of INR measurements. Subgroup analysis of INR measurements divided into five groups as a function of difference between model-suggested dose and administered dose in the preceding week. Difference in administered dose and predicted dose within 2.5 mg/week is considered as approximately equal intake. See details in online supplementary table.
dose suggestions compared to the administered doses demonstrates a potential for further improvement. We consider it plausible that good model performance on a high quality OAT setting will imply good model performance also on a low quality OAT setting. We can, however, merely speculate if a minor (or major) improvement in TTR will benefit the patients in terms of a reduction in thrombotic events or bleedings [13]. An important addition to measuring TTR could be a calculation of INR variation as well as the range of measurements. This enables detection of potential dangerous intervals (e.g. very high or very low INR values) that cannot easily be derived from TTR alone. Due to the retrospective design of this study, it is not possible to assess if INR variations would be introduced by the algorithm.
According to Table 2 in more than 70% of the occasions, where INR is outside TR, our dose suggestions are clinically sound, but the magnitude of the change remains uncertain. However, a more thorough analysis reveals that in situations where clinical intervention can be expected (INR b 1.5 or INR N 3.5 if target is 2.5) the model performs inadequately in some cases. INR below 1.5 is comparable to not being in OAT [32]. Consequently, dose suggestions lower than the administered dose when INR b 1.5, which is seen in 17% of the incidents (see Fig. 1), attract attention. Information on operative procedures or bridging therapy is not available from the clinical database. It is, however, anticipated that such episodes occurs in the data set. The staff at the centre handles the clinical management of those episodes and overrules the dose
Fig. 2. Median absolute error between administered and predicted warfarin. Analysis of the model uncertainty when initiating model predictions based on a subgroup of 51 patients, who had the first 10 INR observations within INR range.
P.B. Nielsen et al. / Thrombosis Research 133 (2014) 375–379
suggestions provided by the algorithm in the current system used by the patients. The warfarin dose stored in the database is not updated or changed, but merely not followed by the patients. This entails faulty inputs of warfarin intake to the model, which could explain part of the 17% of the poor dose predictions when INR is below 1.5. The MAE between administered and predicted warfarin intake, shown in Fig. 2, is provided to entail how the model performs when monitoring is initiated. It was chosen to select the subgroup based on patients who have the first ten INR observations within INR range. This ensures that the treatment is optimal within this time span, and hence the provided predicted warfarin dose should be equal or sufficiently close to the administered warfarin dose. As expected the MAE is declining when INR observations are presented to the model, which is due to adoption of patient specific parameters of required warfarin maintenance dose and warfarin sensitivity towards changes. It should be noted that included patients are not warfarin naïve, and hence it cannot be derived from this analysis how long time it takes after initiation of warfarin until the model has adjusted its parameters. Certain aspects of the potential performance of our model-suggested dosages cannot be evaluated due to the retrospective study design. The most important functionality of a system with a build-in model is to maintain patients within a tight TR. This remains yet to be proven for the present model. It should be thoroughly investigated if replacing the currently used algorithm with the presently discussed algorithm would imply an increased number of possibly unnecessary dose changes, hereby risking oscillating warfarin and INR series [33]. A well designed randomised clinical controlled trial comparing the existing algorithm with the presently discussed, keeping the administrative OAT set-up unchanged, is going to be the next succession in the performance validation. For the sake of patient safety, the present study should in our opinion precede a prospective validation. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.thromres.2013.12.042. Conflict of Interest Statement The following authors have an IPR (application number PA201001130) on the algorithm used in the model: Torben Bjerregaard Larsen, Søren Lundbye-Christensen and Peter Brønnum Nielsen. No conflict of interest: Lars Hvilsted Rasmussen. Acknowledgements We thank Pernille Højbak and Helle Ravnslund Sørensen for their help with preparation and interpretation of values in the clinical database. References [1] ISMAAP. International Self-Monitoring Association of Oral Anticoagulated Patients. We Motiv Patients to Tak Control Their Own Oral Anticoagulation Ther; 2013. [2] Garcia DA, Schwartz MJ. Warfarin therapy: tips and tools for better control. J Fam Pract 2011;60:70–5. [3] De Assis MC, Rabelo ER, Avila CW, Polanczyk CA, Rohde LE. Improved oral anticoagulation after a dietary vitamin k-guided strategy: a randomized controlled trial. Circulation 2009;120:1115–22 [3 pp. following 1122]. [4] Nielsen PB, Eriksen EH, Milthers RT, Hejlesen OK. Assessing importance of dietary data in anticoagulation treatment. Stud Health Technol Inform 2009;150:782–6. [5] Holmes MV, Hunt BJ, Shearer MJ. The role of dietary vitamin K in the management of oral vitamin K antagonists. Blood Rev 2012;26:1–14. [6] Van Walraven C, Jennings A, Oake N, Fergusson D, Forster AJ. Effect of study setting on anticoagulation control: a systematic review and metaregression. Chest 2006;129:1155–66. [7] Rosendaal FR, Cannegieter SC, van der Meer FJ, Briët E. A method to determine the optimal intensity of oral anticoagulant therapy. Thromb Haemost 1993;69:236–9.
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Regular Article
Improvement of anticoagulant treatment using a dynamic decision support algorithm A Danish Cohort study Peter Brønnum Nielsen a,⁎, Søren Lundbye-Christensen b, Lars Hvilsted Rasmussen a, Torben Bjerregaard Larsen a,b a b
Thrombosis Research Unit, Aalborg University, Aalborg, Denmark Department of Cardiology, Aalborg AF study group, Aalborg University Hospital, Aalborg, Denmark
a r t i c l e
i n f o
Article history: Received 11 September 2013 Received in revised form 21 December 2013 Accepted 30 December 2013 Available online 7 January 2014 Keywords: Computer-assisted drug therapy drug dosage calculation international normalised ratio statistical model warfarin
a b s t r a c t Introduction: Warfarin is the most widely prescribed vitamin K antagonist and in the United States and Europe more than 10 million people are currently in long-term oral anticoagulant treatment. This study aims to retrospectively validate a dynamic statistical model providing dosage suggestions to patients in warfarin treatment. Materials and methods: The model was validated on a cohort of 553 patients with a mean TTR of 83%. Patients in the cohort were self-monitoring and managed by a highly specialised anticoagulation clinic. The predictive model essentially consists of three parts handling INR history, warfarin dosage and biological noise, which allows for prediction of future INR values and optimal warfarin dose to stay on INR target. Further, the model is based on parameters initially being set to population values and gradually individualised during monitoring of patients. Primary outcome: Time in therapeutic range was used as surrogate quality measure of the treatment, and modelsuggested dosage of warfarin was used to assess the accuracy of the model performance. Results: The accuracy of the model predictions measured as median absolute error was 0.53 mg/day (interquartile range from 0.25 to 1.0). The model performance was evaluated by the difference between observed and predicted warfarin intake in the preceding week of an INR measurement. In more than 70% of the cases where INR measurements were outside the therapeutic range, the model suggested a more reasonable dose than the observed intake. Conclusion: Applying the proposed dosing algorithm can potentially further increase the time in INR target range beyond 83%. © 2014 Elsevier Ltd. All rights reserved.
Introduction Warfarin is the most widely prescribed drug in oral anticoagulant treatment (OAT) and more than 6 million patients in Europe and approximately 4 million in the United States are currently living on long-term OAT [1,2]. The most common indications for warfarin treatment are atrial fibrillation (AF), deep venous thrombosis (DVT), pulmonary embolism (PE), post myocardial infarction (MI), and heart valve replacement. The treatment balances between avoiding thrombotic events and bleeding episodes.
Abbreviations: INR, international normalised ratio; OAT, oral anticoagulant treatment; AF, atrial fibrillation; DVT, deep venous thrombosis; PE, pulmonary embolism; MI, post myocardial infarction; VKA, vitamin K antagonists; TR, therapeutic range; TTR, Time in therapeutic range; PST, patient self-testing; PSM, patient self-management; MAE, median absolute error. ⁎ Corresponding author at: Forskningens Hus, Srd. Skovvej 15, DK-9000 Aalborg, Denmark. Tel.: +45 99 32 81 00; fax: +45 99 32 80 99. E-mail address: [email protected] (P.B. Nielsen). 0049-3848/$ – see front matter © 2014 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.thromres.2013.12.042
Anticoagulant monitoring is done by measurement of the International Normalised Ratio (INR). The therapeutic range of INR is 2.0-3.0 or 2.5-3.5 for the majority of the underlying conditions mentioned above. Further, anticoagulation with vitamin K antagonists (VKA) is a complicated task due to food and drug interacting with the effect of VKA [3–5]. A noticeable between patients variation in response to warfarin entails individual dosing and frequent monitoring of the INR. The risk profile for patients undergoing VKA treatment is dependent on the time for which the INR value is within therapeutic range (TR) [6–9]. Time in therapeutic range (TTR) is often used as a quality marker of VKA management [7,10,11], and is recommended as an endpoint when analysing quality of anticoagulation management [12]. A recent study, however, shows that TTR is not the optimal predictor of mortality, stroke, bleeding and hospitalisation in atrial fibrillation patients receiving warfarin therapy [13]. Warfarin therapy is primarily monitored by laboratory determination of INR using plasma from venipuncture. Different settings of treatment management exists, including usual care provided by the general practitioner, hospital outpatient clinics, and highly specialised
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anticoagulation clinics. However, some patients are eligible for patient self-testing (PST) or patient self-management (PSM) using portable point-of-care testing coagulometers and will benefit for this type of management [14,15]. A meta-analysis comparing PSM and PST with usual care proved a significant reduction in thromboembolic events, but neither a reduction in major haemorrhagic events nor reduction in death was shown [16]. Patients younger than age 55 and patients with mechanical heart valve replacement had the largest reduction in thrombotic events in the comparison (hazard ratio of 0.33 and 0.52, respectively). Some PSM patients are using decision aiding electronic tools or online decision support systems that will provide an on-screen dosage advice [17,18]. These meta-analysis favours uses of such systems with an overall improvement across studies of 6% in time in therapeutic INR range. However, no significant difference was found between controls and patients using decision support systems when comparing the risk for major bleeding (risk of thrombotic events was not reported) [19]. A proportion of published warfarin prediction algorithms utilise pharmacogentic dose prediction [20–22]. While they have shown to perform better compared to physician managed warfarin dosing in predicting the initial optimal dose (often measured in the time to reach stable treatment), the genetic information does not persistently improve the warfarin treatment [23–26]. It may be important to consider the intention behind the use of decision aiding tools that includes a prediction model, and such underlying prediction model should perform well in at least two situations. First, the model should attempt to maintain a high TTR by providing a dose adjustment advice. This can only be investigated in a prospective study design. Second, the model should perform properly when a measured INR value is outside the INR target range, in the sense of providing a dose adjustment that will bring the future INR value(s) within the desired range. This can be investigated in a retrospective designed study. For the sake of patient’s safety and prior to a randomized controlled trial, we propose to retrospectively validate such a model bearing in mind that OAT is a potential lethal treatment if inappropriate dosage is provided. In this study we aim to apply a developed dynamic statistical model for decision support [27] in a cohort of PSM patients treated in a highly specialised anticoagulation clinic.
Materials and methods Population Eligible patients were identified from the clinical database of the Thrombosis Research Clinic for PSM Oral Anticoagulation, Department of Cardiology, Aalborg University Hospital, Denmark. This centre includes a highly specialized anticoagulation clinic with approximately 850 patients who are trained in PSM OAT. The centre's functions are handled by specially trained nurses and specialists. The centre handles all matters relating to the patient's anticoagulant therapy including perioperative management when needed (regulation of INR, delivery of low molecular weight heparin, contact to other departments’ etc.). The patients are using an online dosage and decision support tool (AC Shared Care, ACURE, IBM, DK-8240 Risskov, Denmark), which provides dosage suggestions of warfarin for the following week based on the previous INR measurement. The dosage advice is given as a mean tablet (2.5 mg) intake per week, and subsequently calculated as a weekly pattern of daily dosage of warfarin. If an INR measurement typed into the system is not adequately close to or within the therapeutic range, a suggestion to contact the staff at the Thrombosis Research Clinic is given to the patient. The staff can order an instant dose change, e.g. double warfarin intake for a day or suspend the treatment for a day. These changes are registered in the clinical database as additions to the current intake of warfarin that day.
The data for the present study was acquired from January 2010 till December 2012 and consists of 837 patients assigned to PSM. Patients were excluded (N = 284) if the following criteria were met: less than 30 days of warfarin therapy or fewer than 4 INR measurements since onset of PSM (N = 38); registered with an event (thrombosis or minor/major bleeding) in the clinical database (N = 158); interval between INR measurements above 8 weeks (N = 87); no registered clinical information (N = 1). Data for each patient were then prepared to be applicable to the prediction model. The model required at least seven days of warfarin intake before the first INR measurement. Hence, the INR measurements that were performed within this period could not be included in the model and were removed accordingly. Model description The model is fully specified and discussed in details in [27], and is designed to handle time series of daily intake of warfarin and measured INR values. For a given patient, let T denote the target INR value, INRt and INRt-1 be the measured INR value at a given day and the previous day (INR history), and wt-1 and wt-2 be the warfarin intake the previous day and the day before (warfarin dosage). Subjected to optimal dosing, the departure from target at a given day, apart from biological noise, is expected to be smaller than the departure the previous day. If the warfarin intake the previous day and the day before is higher than the optimal dose (to stay on target), the INR is expected to increase, and decrease if the warfarin intake is lower than the optimal dose. The day-to-day dynamics of warfarin and INR is modelled as
INR history
Warfarin dosage
Noise
zfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflffl{ zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{ z}|{ INRt −T ¼ ρðINRt−1 −TÞ þAðwt−1 þ λwt−2 –ð1 þ λÞDt−1 Þ þ εt ; where ρ quantifies the day-to-day dynamics of INR, A is the sensitivity towards changes in warfarin intake, D is the idealised dose to maintain INR target, λ is a constant, and εt is a series of independent noise terms. The day-to-day dynamics of INR is quantified by the constant, ρ, between 0 and 1, leaving an auto-regressive structure of INR measurements when the patient is on optimal dosing. The sensitivity towards changes in warfarin intake, A, is an unknown patient specific parameter, negatively correlated to the dosage. This allows for modelling the individual INR change due to a unit change in warfarin, such that patients on a low warfarin dose are more likely to have a larger INR change compared to patients on a high dose. The idealised warfarin dose, D, is an unknown patient specific parameter. Over time D can exhibit small fluctuations reflecting changes in endogenous or exogenous factors. Warfarin affects INRt through a between-day-profile of intake, (wt−1 + λ wt−2), where λ is common to all patients. The noise sequence, εt, reflecting the biological noise has a patient specific standard deviation. Thus, the full specification of the model contains parameters describing population distributions. Model based monitoring When the model based monitoring of a patient is initiated all parameters are set to population values. Usually patients have a daily warfarin intake whereas INR measurements are less frequent. For each day predictions of INR, sensitivity and idealised dose are extrapolated from previous values. When an INR values becomes available the model parameters are updated. This so-called Kalman filter [28] offers recursive formulae for calculation of these updates, see details in [27]. Hereby the suggested dose at each time point is based on history of warfarin intake and INR measurements of the individual patient. Similarly, the individual sensitivity to changes in dose is updated. Hence the model adopts how the patient should be dosed aiming for a higher TTR.
P.B. Nielsen et al. / Thrombosis Research 133 (2014) 375–379 Table 1 Demographics and clinical characteristics of the patient cohort. Patient characteristics
Total
Number of patients Sex
553
Percent or SD
Females Age Total number of INR measurements Total number of observation days Target INR Target 2.5 Target 3.0 Indication for treatment* VTE AF MI Mechanical heart valve, stenosis or prosthesis Stroke or TIA Other † TTR INR Mean Target 2.5 2.54 Target 3.0 2.98 Warfarin intake (mg) Mean Target 2.5 6.01 Target 3.0 6.44
177 55.5 26,175 203,964
32% ±11.8
501 52
90.60% 9.40%
166 194 3 151
30.02% 35.08% 0.54% 27.31%
32 7 83% SDb ±0.19 ±0.26 SDb ±2.43 ±2.49
5.79% 1.26% SDw ±0.46 ±0.58 SDw ±0.52 ±0.73
*Abbreviations and details: Venous thromboembolism and Thrombophilia (VTE), transient ischemic attack (TIA). SD is standard deviations, SDb is between patient standard deviation and SDw is the within patient standard deviation.TTR† is time in therapeutic range calculated by Rosendaal method.
Model performance evaluation A Matlab (MathWorks Inc., MA) script of the dynamic model was implemented, using population values obtained from previous published work [27]. All predicted INR values and predicted doses are stored for the purpose of comparison with their observed counterparts. Dose predictions were compared with administered doses in two ways. First, simple calculation of median absolute error (MAE) is produced to assess the accuracy of the predictions. Second, the means calculated for the seven previous days of predicted and administered dose for each INR value are evaluated as a function of deviations from INR target. This allows for comparing the suggested dose against the administered for INR values outside INR range. Further, the initiation to model predictions is assessed by regarding MAE in patients with 10 consecutive observations within INR range. Hereby the contribution of model uncertainties can be evaluated. Results Of 837 eligible patients 284 met the exclusion criteria. The baseline characteristics of the remaining 553 patients are shown in Table 1. The accuracy of the model predictions compared to administered dose was within a quarter of a tablet, MAE = 0.53 mg/day (interquartile range from 0.25 to 1.0).
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An approach taken to evaluate the model performance is to report the proportion of dose suggestions “more reasonable” than the administered doses when observed INR is below TR or above TR, as shown in Table 2. It is of notice that the model suggests a more adequate dose in more than 70% of the incidents when INR measurements are outside TR. The distinction between whether or not the suggested dose is above or below the administered may be refined by introducing the category “nearly identical”. If the weekly total of suggested doses differs from the administered by less than one tablet, the two dosages will be considered identical. Furthermore, larger deviations from TR are more severe and would cause clinical intervention. In Fig. 1 we depict the mentioned three warfarin categories versus INR measurements subdivided into five ranges. It is evident that the model performs adequately in these severe situations in more than 60% of the incidents and inferior in less than 18%. A subgroup analysis regarding MAE of warfarin intake for patients with 10 consecutive INR measurements (N = 51) within INR range is depicted in Fig. 2. From inspection it is apparent that the MAE between predicted and administered warfarin intake stabilizes after 3 INR observations when initiating monitoring. Discussion This study reports the outcome of an evaluation of a dynamic decision support algorithm retrospectively applied on a cohort of PSM patients treated by a highly specialised anticoagulant clinic. Two European decision support systems for use in anticoagulation treatment (DAWN AC and PARMA 5) have been clinically validated in a multicenter randomized trial [29]. In comparison with experienced medical staff, the two systems significantly improved the TTR, and reduced the clinical events of DVT and pulmonary embolisms. The TTR reported from the randomized trial was significantly lower (65.9 % for computer assisted group) than the TTR reported in this study. For comparison it would be desirable to apply DAWN AC or PARMA 5 on a cohort of PSM patients with a higher baseline TTR. Further, one recent study shows non-inferiority of DAWN AC compared to a simple warfarin dosing algorithm [30]; the reported mean TTR was approximately 70 %. In Sweden a web-based dosing system, named Auricula (based on an algorithm applying 720 rules), for warfarin treatment is widely used [31]. The system also served as a national quality registry since 2006. In a retrospective analysis of more than 50.000 patients the system performed adequately in most cases. The algorithm is meant to improve over time, as it is retrospectively evaluated and the rules can be changed accordingly. The data in the present study originates from a centre with a high quality OAT that educates patients in PSM. Continuous close monitoring of the quality of the treatment is maintained by specialised staff at the centre. The patients are using an online dosage advisory system to maintain their INR within the designated target INR. When INR measurements are outside TR, the staff can order an instant dose change in the attempt to bring back the future INR within range. This leads to a high TTR of 83%, compared to most European contents published. Despite the high quality OAT, which is achieved by a dosing algorithm supplied with optional interference from experienced staff, our
Table 2 Dosage suggestions provided by the model.
Less warfarin intake than model the suggests More warfarin intake than the model suggests Total
INR below TR
INR within TR
INR above TR
Total
1,589 72.29% 609 27.71% 2,198
10,246 49.01% 10,659 50.99% 20,905
726 23.63% 2,346 76.37% 3,072
12,561 47.99% 13,614 52.01% 26,175
Difference between model-suggested dose of warfarin and administered dose of warfarin in the preceding week grouped in three different intervals of therapeutic range.
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Fig. 1. Dosage suggestions for five ranges of INR measurements. Subgroup analysis of INR measurements divided into five groups as a function of difference between model-suggested dose and administered dose in the preceding week. Difference in administered dose and predicted dose within 2.5 mg/week is considered as approximately equal intake. See details in online supplementary table.
dose suggestions compared to the administered doses demonstrates a potential for further improvement. We consider it plausible that good model performance on a high quality OAT setting will imply good model performance also on a low quality OAT setting. We can, however, merely speculate if a minor (or major) improvement in TTR will benefit the patients in terms of a reduction in thrombotic events or bleedings [13]. An important addition to measuring TTR could be a calculation of INR variation as well as the range of measurements. This enables detection of potential dangerous intervals (e.g. very high or very low INR values) that cannot easily be derived from TTR alone. Due to the retrospective design of this study, it is not possible to assess if INR variations would be introduced by the algorithm.
According to Table 2 in more than 70% of the occasions, where INR is outside TR, our dose suggestions are clinically sound, but the magnitude of the change remains uncertain. However, a more thorough analysis reveals that in situations where clinical intervention can be expected (INR b 1.5 or INR N 3.5 if target is 2.5) the model performs inadequately in some cases. INR below 1.5 is comparable to not being in OAT [32]. Consequently, dose suggestions lower than the administered dose when INR b 1.5, which is seen in 17% of the incidents (see Fig. 1), attract attention. Information on operative procedures or bridging therapy is not available from the clinical database. It is, however, anticipated that such episodes occurs in the data set. The staff at the centre handles the clinical management of those episodes and overrules the dose
Fig. 2. Median absolute error between administered and predicted warfarin. Analysis of the model uncertainty when initiating model predictions based on a subgroup of 51 patients, who had the first 10 INR observations within INR range.
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suggestions provided by the algorithm in the current system used by the patients. The warfarin dose stored in the database is not updated or changed, but merely not followed by the patients. This entails faulty inputs of warfarin intake to the model, which could explain part of the 17% of the poor dose predictions when INR is below 1.5. The MAE between administered and predicted warfarin intake, shown in Fig. 2, is provided to entail how the model performs when monitoring is initiated. It was chosen to select the subgroup based on patients who have the first ten INR observations within INR range. This ensures that the treatment is optimal within this time span, and hence the provided predicted warfarin dose should be equal or sufficiently close to the administered warfarin dose. As expected the MAE is declining when INR observations are presented to the model, which is due to adoption of patient specific parameters of required warfarin maintenance dose and warfarin sensitivity towards changes. It should be noted that included patients are not warfarin naïve, and hence it cannot be derived from this analysis how long time it takes after initiation of warfarin until the model has adjusted its parameters. Certain aspects of the potential performance of our model-suggested dosages cannot be evaluated due to the retrospective study design. The most important functionality of a system with a build-in model is to maintain patients within a tight TR. This remains yet to be proven for the present model. It should be thoroughly investigated if replacing the currently used algorithm with the presently discussed algorithm would imply an increased number of possibly unnecessary dose changes, hereby risking oscillating warfarin and INR series [33]. A well designed randomised clinical controlled trial comparing the existing algorithm with the presently discussed, keeping the administrative OAT set-up unchanged, is going to be the next succession in the performance validation. For the sake of patient safety, the present study should in our opinion precede a prospective validation. Supplementary data to this article can be found online at http://dx. doi.org/10.1016/j.thromres.2013.12.042. Conflict of Interest Statement The following authors have an IPR (application number PA201001130) on the algorithm used in the model: Torben Bjerregaard Larsen, Søren Lundbye-Christensen and Peter Brønnum Nielsen. No conflict of interest: Lars Hvilsted Rasmussen. Acknowledgements We thank Pernille Højbak and Helle Ravnslund Sørensen for their help with preparation and interpretation of values in the clinical database. References [1] ISMAAP. International Self-Monitoring Association of Oral Anticoagulated Patients. We Motiv Patients to Tak Control Their Own Oral Anticoagulation Ther; 2013. [2] Garcia DA, Schwartz MJ. Warfarin therapy: tips and tools for better control. J Fam Pract 2011;60:70–5. [3] De Assis MC, Rabelo ER, Avila CW, Polanczyk CA, Rohde LE. Improved oral anticoagulation after a dietary vitamin k-guided strategy: a randomized controlled trial. Circulation 2009;120:1115–22 [3 pp. following 1122]. [4] Nielsen PB, Eriksen EH, Milthers RT, Hejlesen OK. Assessing importance of dietary data in anticoagulation treatment. Stud Health Technol Inform 2009;150:782–6. [5] Holmes MV, Hunt BJ, Shearer MJ. The role of dietary vitamin K in the management of oral vitamin K antagonists. Blood Rev 2012;26:1–14. [6] Van Walraven C, Jennings A, Oake N, Fergusson D, Forster AJ. Effect of study setting on anticoagulation control: a systematic review and metaregression. Chest 2006;129:1155–66. [7] Rosendaal FR, Cannegieter SC, van der Meer FJ, Briët E. A method to determine the optimal intensity of oral anticoagulant therapy. Thromb Haemost 1993;69:236–9.
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