Individualized duration of oral anticoagulant therapy for deep vein thrombosis based on a decision model


Roel Vink, Department of Vascular Medicine, Academic Medical Center, University of Amsterdam, Meibergdreef 9, 1105 AZ Amsterdam, the Netherlands.
Tel.: +31 20 566 2377; fax: +31 20 696 8833; e-mail:


Summary. Background: The optimal duration of oral anticoagulant therapy for patients with a first episode of deep vein thrombosis (DVT) is still a matter of debate. However, according to the ACCP consensus strategy a limited stratification in treatment duration is advocated, i.e. 3 months for patients with a transient risk factor and 1 year or longer for patients with recurrent disease or a consistent risk factor such as thrombophilia or cancer. This consensus strategy is founded on the mean optimal duration of therapy obtained in large cohorts of patients and is mainly based on the risk of recurrent venous thromboembolism (VTE), with only minimal consideration for the patient's bleeding risk. Objective: The aim of this study is to optimize the anticoagulant treatment strategy with vitamin K antagonists for the individual patient with DVT. Methods: Based on an extensive literature study, a mathematical model was constructed to balance the risk of recurrent VTE against the risk of major hemorrhagic complications. The following parameters are incorporated in the model: baseline estimates and risk factors for recurrent VTE and bleeding, clinical course of DVT, and efficacy of treatment with vitamin K antagonists. With the use of these parameters, the risk for a recurrent VTE and a bleeding episode can be calculated for the individual patient. The optimal duration of anticoagulant therapy can be defined as the timepoint at which the benefit of treatment (prevention of VTE) is counterbalanced by its risk (bleeding). Results/conclusions: How long a patient should receive anticoagulant treatment is a matter of balancing the benefits and risks of treatment. The model shows that the optimal treatment duration varies greatly from patient to patient according to the patient's unique bleeding and recurrence risk.


Deep vein thrombosis (DVT) of the lower extremity is a frequently occurring disorder, with an estimated incidence of 2 per 1000 persons per year [1]. The primary objectives of treating patients with venous thromboembolism (VTE) are to prevent death from pulmonary embolism (PE) and to reduce the risk for recurrent thromboembolic events. For this purpose, patients are treated with an initial course of heparin followed by a second phase of vitamin K antagonists [2–4]. According to the ACCP consensus strategy, a limited stratification in treatment duration is advocated, i.e. 3 months for patients with a transient risk factor and 1 year or longer for patients with recurrent disease or a consistent risk factor such as thrombophilia or cancer [5]. This consensus is founded on the mean optimal duration of therapy obtained in large cohorts of patients and is mainly based on the risk of recurrent VTE, with only minimal consideration for the patient's bleeding risk [6–8]. It is a well-documented fact that the cumulative risk of bleeding complications is determined by various risk factors. Major determinants are the length of therapy and the patient's characteristics [9,10]. Therefore, the consensus strategy has two major limitations. First, by not taking into account the bleeding risk, a balanced decision on the duration of anticoagulant therapy cannot be adequately made. Second, decisions based on large cohorts neglect the fact that the risk for bleeding and recurrent VTE are dependent on individual characteristics [11,12]. Thus, rational decisions on the optimal duration of anticoagulant therapy for the individual patient require knowledge of the risk of recurrence after discontinuation of treatment and the risk of bleeding during anticoagulant therapy. Ideally, treatment should be continued until the benefits of treatment (prevention of recurrent VTE events) are offset by the risks (major bleeding), taking into account that each patient has an individual spectrum of risk factors for recurrent events and bleeding.

Sarasin et al. published their decision model in 1994 [13]. They compared risk–benefit tradeoffs for treatment durations between 6 weeks and 6 months. However, in the last decade, several new risk factors for recurrent VTE have been identified, and new insights in the risk for bleeding have become available. Therefore, we constructed a mathematical model based on recent literature, which can be easily applied to individual patients and which balances the risk of recurrent venous thromboembolic events against the risk of hemorrhagic complications.


To construct a model for the individual patient, that balances the risk for recurrent venous thromboembolic events against the risk for major hemorrhagic complications, several parameters have to be taken into consideration: (i) baseline estimates for recurrent VTE; (ii) risk factors for recurrent VTE and their risk estimate; (iii) clinical course of DVT; (iv) baseline estimates for hemorrhage and their risk estimate; (v) risk factors for hemorrhage during anticoagulant therapy; and (vi) efficacy of anticoagulant therapy in preventing recurrent VTE. For this purpose, a systematic review of the literature was performed using a computer-assisted search in the MedLine and EmBase databases over the period 1966–2002. The keywords and textwords used for the search were: thrombosis, venous thrombosis, thromboembolism, pulmonary embolism, risk factor, warfarin, oral anticoagulants, bleeding, hemorrhage, thrombophilia, recurrence, treatment, therapy. The reference lists of all retrieved articles were screened to identify additional papers.

To obtain a solid baseline estimate for the incidence of recurrent VTE, studies were considered eligible when they included a cohort of patients in which all known thrombophilic conditions were excluded. To obtain baseline estimates for major hemorrhage during oral anticoagulant therapy, studies that made reference to the incidence of major bleeding in the thromboembolic population were evaluated. For the identification of significant risk factors for recurrent VTE as well as bleeding during anticoagulant therapy, articles that assessed the relative risk (RR) of such a risk factor were analyzed. Odds ratios (OR) for patients with a specific risk factor were calculated separately and, when appropriate, pooled using the Mantel–Haenszel method [14]. To obtain estimates on efficacy of vitamin K antagonist therapy, data were derived from studies that reported on the incidence of recurrent VTE during vitamin K antagonist therapy. The efficacy was expressed as RR reduction for a thromboembolic event, compared with no treatment. Finally, the clinical course of DVT was assessed by evaluation of clinical studies, which included long-term follow-up.

All eligible studies were weighted for methodological strength, according to Sackett et al. [15]. In order to obtain high-quality data, only those articles with the strongest methodology were selected for construction of the mathematical model.

In order to answer the question of how to balance the adverse events of antithrombotic management strategies, i.e. bleeding complications as a result of anticoagulant therapy and recurrent VTE as manifestation of withholding anticoagulant therapy, we sent out a questionnaire to 30 thrombosis experts in the Netherlands.

The structure of the model is described in the section below. The parameters are summarized in Table 1.

Table 1.  Estimates used in the decision model
VariableRates (95% CI)Reference
  1. 95% CI, 95% confidence interval; *no confidence interval available, relative risks are estimates.

Risk factor for hemorrhage
Age (every 10 years above 40)1.5 (1.2–1.8)39–42
Cancer2.0*12; 43; 44
Risk factor for recurrent VTE
Prothrombin mutation1.4 (0.9–2.0)18–22
Factor V Leiden mutation1.3 (1.0–1.7)16; 18; 19; 23–26
Elevated levels of factor VIII
(>200 IU dL−1)
1.8 (1.0–3.3)27; 28
Hyperhomocysteinemia2.5*33; 34
Antiphospholipid antibodies2.5*8; 18; 31; 32
Antithrombin deficiency2.5*18; 29; 30
Protein C & S deficiency2.5*18; 29; 30
Cancer2.0–4.0*11; 35–37
Transient risk factor (surgery,
0.5*4; 35; 36
Recurrent DVT1.5* (assumption)
Baseline estimate for major
Pbleeding= 0.08339
Baseline estimate for DVTPrecur= 1.2 × e –t/14+ 0.116; 17
Efficacy of treatment90% (86%-97%)4; 6–8
Risk for pulmonary embolism
in DVT


Baseline estimates for recurrent VTE

To determine the baseline estimates for recurrent VTE in patients without oral anticoagulant therapy, two studies in which all known thrombophilic conditions were excluded in a subset of patients were identified [16,17]. Since the methodology of both studies was comparable, both studies were combined to calculate the absolute recurrence rate. As expected, the rate of recurrent events in this population declines exponentially as a function of time. This decline is represented by the formula:


Risk factors for recurrent VTE

The incidence of recurrent VTE in patients with the prothrombin G20210A mutation was reported in five studies [18–22]. The pooled OR, using the Mantel–Haenzel method, was 1.4 (95% CI 0.9–2.0).

Eight studies that report on the incidence of recurrent venous thromboembolism in patients with the factor (F) V Leiden mutation have been published [8,16,18,19,23–26]. In one prospective study, only the decreased risk for recurrent VTE (OR 0.5) was observed; however, data needed for the Mantel–Haenszel method could not be extracted from this study [8]. The calculated pooled OR for the other seven studies, using the Mantel–Haenszel method, was 1.3 (95% CI 1.0–1.7).

Several studies reported on an increased risk of a first episode of venous thromboembolism in patients with elevated plasma levels of FVIII; however, studies reporting on the risk of recurrence are scarce. We have reported on a dose-dependent RR for recurrent VTE, which was confirmed in another study [27,28]. An OR for the risk of recurrence, using the Mantel–Haenszel method, was calculated for FVIII levels exceeding 200 IU dL−1. This common OR was 1.8 (95% CI 1.0–3.3).

Three retrospective studies have assessed the risk for recurrent VTE in patients with antithrombin, protein S or protein C deficiency [18,29,30]. No prospective studies on the risk of recurrence in untreated patients with antithrombin, protein C or S deficiency are available. Data needed for the Mantel–Haenszel method could not be extracted. The estimated RR for a recurrent event based on these retrospective studies was 2.5.

The risk of recurrent VTE in patients with antiphospholipid antibodies has been studied in one retrospective [18] and three prospective studies [8,31,32]. Since the original data did not provide sufficient information for the Mantel–Haenszel method, we estimated the overall risk to be 2.5.

Two studies have shown an increased risk for recurrent events in patients with high levels of homocystein. In a prospective study, the RR was 2.6 [33]. In a case–control study, an OR of 3.1 was found [34]. By combining the results, taking into account that case–control studies tend to overestimate, the RR was estimated to be 2.5.

Cancer is generally considered to increase the risk of recurrent VTE. In two prospective cohort studies, the RR for a recurrent event in cancer patients was 1.7 and 2.2, respectively [35,36]. A higher rate of recurrence was observed in a retrospective study (RR 3.2) [37]. Interestingly, the association with VTE seems to be cancer-specific. The types of malignancy most commonly associated with venous thromboembolism are pancreatic, ovarian, lung and mucin-secreting gastrointestinal carcinoma [11]. Therefore, we varied the RR depending on the type of cancer. The RR for high-risk cancer was estimated to be 4, whereas for the other types of cancer an RR of 2 was used.

Three well-conducted studies (two prospective cohort studies [35,36], one randomized trial [4]) evaluated the incidence of recurrent VTE in patients with a transient risk factor (e.g. surgery, trauma, immobilization). The authors reported RRs varying between 0.3 and 0.7. Thus, these patients are at reduced risk for a recurrence compared with patients with idiopathic thrombosis, with a mean RR of 0.5.

In the absence of data from the literature, it was assumed that recurrent VTE without any underlying thrombophilic disorder was associated with an RR of 1.5.

Finally, other potential risk factors (for example elevated levels of FXI, renal insufficiency, hypertension, smoking, obesity) were excluded from analysis, due to lack of data to estimate the risk of recurrent VTE.

Multiplying the baseline risk

Studies comparing the risk for recurrent VTE in patients with a thrombophilic factor with the risk in patients without a thrombophilic abnormality (our baseline population) show that the exponential decline of VTE events, as described above, is identical for patients with and without a thrombophilic factor [16,31,33]. This means that at any time elapsed since the event, the difference in risk of recurrence between the two groups of patients is represented by a constant factor, i.e. the RR for the specific thrombophilic condition. Therefore, the absolute risk of recurrent VTE at any specific timepoint for the individual patient with a certain thrombophilic abnormality is obtained by multiplying the RR for this thrombophilic condition with the baseline risk for recurrent VTE at this timepoint;


We assumed that the RR is constant at any time elapsed since the first event, and that in the presence of two or more risk factors for recurrent VTE, the risk ratios should be multiplied.

Clinical course of DVT and efficacy of treatment

In patients with DVT, approximately 20% of all recurrent events will be asymptomatic PE [38]. Thus, in order to achieve a curve representing the risk for developing PE following DVT, the baseline curve should be multiplied by 0.2.

To obtain the efficacy of treatment with vitamin K antagonists, a meta-analysis of four randomized trials was performed [4,6–8], which showed an efficacy (i.e. an RR reduction of the occurrence of VTE during oral anticoagulant treatment) of 93% (CI 86–97%). We assumed that the efficacy of treatment remained stable at 90%. In conclusion, the risk for the individual patient of developing a PE following DVT after stopping anticoagulant treatment can be written as a function of baseline risk for DVT multiplied by the RR obtained by a given risk factor and two constant factors [the risk for developing PE after DVT (0.2) and the efficacy of treatment (0.9)];


Baseline estimates for major hemorrhage

To determine the baseline estimate for major bleeding during anticoagulant therapy, we identified one study in which no selection was made in patients using oral anticoagulants, and a long-term follow-up was performed. In this study [39], the patients were categorized according to age, which was shown to be a major risk factor for bleeding during oral anticoagulant therapy. The baseline estimate of hemorrhage was therefore assessed by evaluating the risk of hemorrhage in the youngest category. For this patient category, the baseline risk of major bleeding is consistent over time with an incidence of 1% per year (= 0.083% per month); Pbleeding= 0.083. As an assumption, we ignored the potentially higher risk of bleeding in the period when treatment with anticoagulants is being initiated.

Risk factors for major bleeding

We identified two risk factors for major hemorrhage: increasing age and the presence of cancer. In addition, other risk factors for major hemorrhage such as a history of gastrointestinal bleeding or cerebrovascular accident should be considered, but the quantitative contribution of these factors to the bleeding risk is still unknown. In a study by Van der Meer et al. [39], an RR of 1.5 for every 10 years increase in age above the age of 40 years was observed for major bleeding. An OR of 3.2 for an age above 65 years was found in another cohort study [40], which is comparable with the RR in the study of Van der Meer et al. for this age category. Two other articles with a lower methodological strength show identical results of elevated bleeding risks with increasing age [41,42]. Three cohort studies reported on the risk for major bleeding in patients with malignant disease [12,43,44]. The mean OR for malignancy is approximately 2.0. Whether there is a type of cancer-specific OR for bleeding cannot be inferred from the available literature. The individual risk for major hemorrhage can be defined as a function of the baseline risk for developing a major bleed and the presence of an RR factor; Pbleeding= RRbleeding × 0.083, and is assumed to be constant over time, except for the fact that aging is a risk factor for which the risk should be corrected. In the presence of two risk factors for major bleeding, the risk ratios should be multiplied.

The questionnaire

The results of the questionnaire among thrombosis experts show that DVT is rated equally to minor bleeding, non-fatal PE as a manifestation of a recurrent VTE is rated equally to major bleeding, and death due to PE is rated equally to death due to major bleeding (original data not shown). In our model, the risk for major bleeding is outweighed against the risk for a PE as recurrent event.

Integration of recurrence risk and bleeding risk

Oral anticoagulation treatment should ultimately be stopped at the timepoint at which the benefit of treatment (prevention of recurrent VTE) is counterbalanced by its risk (bleeding). Regarding the individual risk curves for both recurrent VTE and bleeding, the timepoint at which the risk of bleeding is equal to the risk of recurrent VTE is represented by the intersection of these curves (Fig. 1). Mathematically, the timepoint of the ultimate duration of anticoagulant therapy can be calculated by the equalization of the formulas for recurrent VTE and major bleeding:

Figure 1.

The sloping curve depicts the risk per month to develop a PE as a manifestation of recurrent VTE. The horizontal curve represents the bleeding risk and is expressed as percentage per month.


A simple conversion leads to the overall formula:


where t is defined as the optimal individual duration of anticoagulant therapy.

With use of the formula, the optimal timepoint can be calculated for each individual patient, since the RRs for recurrent VTE and major bleeding are incorporated. The exact position of the point of intersection of the two curves, and therefore the optimal treatment duration, depends on the presence and quantity of the ORs. When the patient is treated longer than his calculated optimal treatment duration, the risk of PE is exceeded by the bleeding risk and the oral anticoagulant treatment could be harmful.

To avoid complex calculations and potential calculation errors, we designed a simple nomogram for daily clinical practice (Fig. 2), by which the optimal treatment duration in months can be easily determined with use of the risk factors for both recurrent VTE and bleeding.

Table 2.  Patient scenarios
 Patient APatient BPatient C
Gender, ageF, 23 yearsM, 58 yearsM, 49 years
Risk factor for recurrent VTEFactor V LeidenSurgery, immobilizationPancreatic cancer
Relative risk for recurrent VTE1.30.54.0
Risk factor for bleedingNoneAgeAge and cancer
Relative risk for bleeding1.02.25 (1.5 × 1.5)3.0 (1.5 × 2.0)
Duration of treatment24 months1 month22 months

To illustrate the clinical usefulness of the nomogram, three common clinical scenarios are presented (Table 2).

Patient A, a 23-year-old woman, had an episode of spontaneous DVT. She carries the factor V Leiden mutation (heterozygous). There are no risk factors present for bleeding. Therefore, the advocated duration of treatment with oral anticoagulant treatment using our method is 24 months.

Patient B is a 58-year-old man who developed a DVT after surgery and subsequent immobilization. Due to the advanced age, there is a 2.25 (1.5 × 1.5) times higher risk for developing a bleeding compared with the baseline bleeding risk of a person less than 40 years of age. Since his DVT was secondary to a transient event the RR for a recurrent VTE is 0.5. Therefore, the advocated treatment duration in this patient is 1 month.

Patient C is a 49-year-old man who has pancreatic carcinoma. He had an episode of spontaneous DVT. The active cancer contributes to a 4-fold higher risk for recurrent VTE. Due to his age and the presence of cancer, the bleeding risk is 3.0 (1.5 × 2.0). The advocated treatment duration according to the nomogram is therefore 22 months.


In the ACCP guidelines for antithrombotic therapy, stratification in treatment duration is recommended [5]. According to this consensus, patients with a reversible risk factor should be treated for at least 3 months, patients with a first episode of idiopathic VTE for at least 6 months and patients with recurrent VTE or continuing risk factors for at least 1 year or longer. Two major disadvantages of this strategy are the fact that this strategy is based less on the risk of bleeding and, secondly, that this stratification into only three or four groups is quite arbitrary and generalized for a large subset of patients. We present here a model in which the individual risk for a recurrent VTE is more precisely counterbalanced against the individual risk for bleeding. With the use of this model, a rational and literature-based decision on the optimal duration of anticoagulant therapy can be made for each individual patient. How long a patient should receive oral anticoagulant therapy is a matter of balancing the benefits of treatment, in terms of reduced incidence of thromboembolic recurrences against the risks, in terms of increased incidence of major hemorrhages. Patients with a thrombophilic defect and therefore a higher risk for a recurrent event will benefit from a prolonged duration of therapy. In contrast, for patients with an increased risk of an anticoagulant-related bleeding, this prolonged duration could be harmful.

Several decision analyses on the optimal duration of anticoagulant treatment in venous thromboembolic disease have been published. Sarasin et al. [45]. suggest in their decision analysis that prolonged duration of treatment among FV Leiden carriers, at least beyond 1 year, results in more risks (hemorrhages) than benefits (prevention of PE). Van de Belt et al. [46]. performed a decision analysis for patients with an antithrombin, protein C or S deficiency, yielding recommendations for the duration of treatment varying from 6 months to 3 years of treatment, considering age, type of initial event and time elapsed since the event. Although these decision analyses also address the question of duration, they demonstrate usefulness only in a small subset of patients with a defined thrombophilic factor, whereas our model is applicable for the majority of patients with DVT.

The limitations, in general, of decision analyses are that they are based on data derived from literature. The baseline estimate for major bleeding is a critical element of the model and it is supported by a single study. Indeed, more studies that evaluated the risk of bleeding during anticoagulant therapy are available, but these studies included patients with increasing age, and no adjustment for this considerable risk factor for bleeding was performed. The incidence of recurrent thromboembolic events, one of the other key parameters in our model, is difficult to assess since only a limited number of studies are available. However, a recently published meta-analysis confirmed that the risk of recurrence decreases over time [47]. Some studies that evaluated the RR of recurrence in patients with a thrombophilic factor, especially carriers of the FV Leiden mutation, show conflicting results and are confined to relatively small number of patients. However, we have only included studies with a sound methodology in our analysis.

Furthermore, in this model we rated PE (as manifestation of a recurrence) equal to major bleeding. Ideally, the patient's perception of the impact of the non-fatal events and the quality of life associated with long-term anticoagulant therapy should also be considered. In some patients, stopping treatment affects quality of life negatively because of a strong fear of a recurrent episode, whereas others experience anticoagulant treatment and its monitoring as a burden. This subjective estimation of quality of life will probably have a great impact on the patient-oriented optimal duration of treatment. Unfortunately, no reliable estimates of these variables are available yet.

One of the assumptions of the model is that in the presence of two or more risk factors for recurrent VTE or major bleeding, these risk ratios should be multiplied. This concurs with Emmerich et al. [48], who described a complete multiplicative effect of the combined FV Leiden and prothrombin mutation for the risk of a first episode of VTE. ORs were 4.9 and and 3.8 for the FV Leiden and prothrombin mutation, respectively. The OR for VTE in double heterozygotes was 20.0. Also for recurrent VTE, a multiplicative effect of a double mutation was observed [18]. This multiplicative effect of risk factors is also described by several other groups [49,50]. We are aware of the fact that this assumption could induce an estimating simplification of reality for some additive instead of multiplicative combinations of risk factors. However, due to the fact that in our model, the number of risk factors for bleeding are outnumbered by the risk factors for VTE, the optimal duration of VKA therapy is more likely to be calculated too long than too short, which is in line with the current ACCP consensus strategy.

Recently, two new factors for the prediction of a recurrent VTE are described. First, in patients with persistent residual thrombosis confirmed by ultrasonography, recurrent disease is more frequent compared with patients with early recanalization [51]. Second, Palareti et al. showed that the presence of increased d-dimer after discontinuation of oral anticoagulant therapy is associated with a higher risk for recurrent VTE [52]. However, more evidence is needed before these elements can be incorporated into the model.

Several developments in therapeutic quality control have improved the safety and efficacy of oral anticoagulant therapy. Monitoring of anticoagulant therapy by a specialized anticoagulation clinic reduces the bleeding and thromboembolic event rates [53]. More recently, home testing of the coagulation status by means of a portable coagulometer that performs an international normalized ratio (INR) measurement on a single drop of capillary blood have become available. INR home testing appears to be a safe and efficient anticoagulation control method, which results in a higher percentage of target range values compared with the conventional laboratory-based testing regimen [54–56].

The limitations of this type of approach thus include the absence of hard data from management trials in which the proposed guidelines have been proven safe and effective, the danger of propagating uncertainty, and the difficulty of assigning individual patients to categories of risk. All these limitations are valid and attempts should be undertaken in the future to reduce them.

In conclusion, since each patient has his own unique bleeding and thrombosis risk, decisions about the duration of treatment should preferably be based on the individual risk of recurrent thromboembolic events and the individual bleeding risk, rather than a predefined treatment duration that is uniform for a large subset of patients and is based primarily on the risk of recurrent VTE, without taking the patients bleeding risk into account. Application of an individual approach results in a balanced duration of treatment for each patient. Theoretically, this will lead to a lower incidence of recurrent DVT and bleeding complications. To verify this statement, a prospective clinical study should be initiated to validate the model.