Managing Chronic Atrial Fibrillation: A Markov Decision Analysis Comparing Warfarin, Quinidine, and Low-Dose Amiodarone

Methods

The Decision Model

We used a Markov model to compare several treatment strategies for patients with atrial fibrillation [31]. In the model, large hypothetical cohorts of patients are followed for a 5-year period. With each “cycle” of the model, patients may move between several defined health states (for example, well, disabled, dead) according to chance clinical events (for example, stroke). The probabilities of these events were determined using the best available data from the medical literature. Patients accumulate utility, measured in terms of quality-adjusted life-years, until “death” is reached or the 5-year simulation is completed. For example, a patient who spends 3 years in the well state (quality adjustment, 1.0), and then 2 years following a disabling stroke (quality adjustment, 0.5), accumulates 4.0 quality-adjusted life-years ([3 years × 1.0] + [2 years × 0.5]). By simulating outcomes in large numbers of identical patients, the average accumulated utility (or expected value) of each treatment strategy may be estimated. We chose a 5-year period because of the relatively short follow-up periods of the studies on which we based estimates of probabilities and the clinical observation that most patients revert to atrial fibrillation after 5 years, despite treatment with antiarrhythmic therapy. The 65- to 70-year age range was chosen as the population of interest and corresponds to that of patients in the randomized controlled trials of warfarin [3-7].

Our decision model Figure 1, based on asymptomatic or minimally symptomatic 65-year-old patients with atrial fibrillation (50% of whom are male), evaluated the following four treatment strategies:

1. No treatment—all patients with atrial fibrillation began the process in the health state of being well and without warfarin.

2. Warfarin therapy—all patients with atrial fibrillation began the process in the health state of being well and receiving warfarin.

3. Quinidine therapy—all patients had cardioversion. With successful cardioversion, patients began the process in the health state of being well with normal sinus rhythm. If not successful, patients entered the process as either well with atrial fibrillation and receiving warfarin or disabled with atrial fibrillation and receiving warfarin (for the small percentage of patients who had a stroke during cardioversion).

4. Amiodarone therapy—as with quinidine therapy, all patients had cardioversion with assignment of the initial health state dependent on the results.

During each cycle of the process (3 months in this analysis), hypothetical patients in any given health state are at risk for several chance events, which may result in transitions to other health states. Patients may have a stroke or a major bleeding event or may die of another cause. We defined a major bleeding event as any intracranial or retroperitoneal hemorrhage or a bleeding event leading directly to hospitalization, transfusion, or death. In addition, patients receiving antiarrhythmic therapy (who are in normal sinus rhythm) may have a fatal toxic reaction, a toxic reaction requiring withdrawal of medication, or a reversion to atrial fibrillation.

Population-based mortality rates, adjusted for age and sex, were obtained from U.S. Vital Statistics data [32]. The transition probabilities (P) of the Markov models were calculated by the exponential transformation, P = 1 -exp^-rt, where t is the cycle length and r is the annual event or mortality rate. Decision Maker software was used for modeling and analysis [33].

Assumptions

In designing the decision model, several important assumptions were made:

1. Patients having a nonfatal, nonhemorrhagic stroke who had normal sinus rhythm (and were receiving antiarrhythmic therapy) were given warfarin and continued receiving antiarrhythmic therapy. Patients having the same event (who had atrial fibrillation) continued receiving warfarin.

2. Patients having a major bleeding event discontinued warfarin permanently.

3. Patients who have had two previous disabling events were assumed not to be able to survive a third event.

4. Warfarin was taken for 3 weeks before and 1 month after cardioversion [9]. During this time, patients were assumed to have the same risk for a major bleeding event as those initially assigned to receive warfarin therapy.

5. Patients who had a toxic reaction requiring withdrawal of an antiarrhythmic agent started receiving warfarin.

6. Patients receiving an antiarrhythmic agent who subsequently reverted to atrial fibrillation started receiving warfarin and stopped receiving the antiarrhythmic agent. To account for delays in diagnosis and initiation of warfarin therapy in these patients, we assumed that each patient spends one half of that cycle (6 weeks) with atrial fibrillation before receiving anticoagulant therapy.

7. Patients were assumed to be either asymptomatic or minimally symptomatic and, therefore, did not have an absolute indication for antiarrhythmic therapy.

8. Systemic non-central nervous system emboli were not considered. These events occur infrequently and most often result in less morbidity and mortality than do strokes.

Probabilities

Table 1 gives the baseline estimates for each variable in the Markov model and gives the ranges from the literature used in the sensitivity analysis. A sensitivity analysis was done by varying the baseline estimate for a particular variable over a range of plausible values to determine at what value (if any) the preferred strategy changed. In general, the ranges given reflect the low and high values of the individual studies.

Strokes and Major Bleeding Events

We based our estimates for these outcomes primarily on data from the five recent randomized controlled trials of warfarin in patients with atrial fibrillation [3-7]. For some variables, data from population-based studies were used.

The rate of stroke in patients with atrial fibrillation is estimated to be 5.0% per year [1, 2]. The yearly incidence in the placebo groups in the randomized controlled trials ranged from 3.0% to 7.0%. The Stroke Prevention in Atrial Fibrillation study [34] identified a subgroup of patients at very low risk (1.0% per year). There were 25 strokes in 1855 patient-years of follow-up in patients receiving warfarin in the randomized controlled trials (1.35% per year). In the baseline analysis, we assumed that patients receiving antiarrhythmic agents (who were not receiving warfarin and were in normal sinus rhythm) had a yearly stroke incidence similar to that of the general population (0.10%) [35-38]. However, we did a sensitivity analysis over a wide range to account for the likelihood that these patients have other risk factors for stroke (for example, hypertension, and congestive heart failure). The risk for a second stroke was assumed to be greater than that for a first stroke (relative risk, 2.0) [39-42].

A 25% case-fatality rate was used, based on the randomized controlled trials and the four population-based studies [43-46]. Previously disabled patients were assumed to be more likely to die of a subsequent event (relative risk, 1.5) [43-46]. The probability of being permanently disabled from a nonfatal stroke was assumed to be 50%, based on the randomized controlled trials [4, 5] and the two population-based studies [47, 48].

Sixteen major bleeding events occurred in control patients in the randomized controlled trials (0.8% per year). There were 27 major bleeding events in patients receiving warfarin during 1855 patient-years of follow-up (1.46% per year). The effect of these greater reported bleeding rates was tested using sensitivity analysis [49, 50]. The risk for a second event was assumed to be greater than that for a first event (relative risk, 1.5) [49].

Six of the 27 major bleeding events in the randomized controlled trials were fatal (22%). Levine and colleagues [51] estimate that 23% of hemorrhages in patients receiving warfarin are fatal. We estimated the probability of being disabled from a nonfatal hemorrhage to be 7%, based on the Stroke Prevention in Atrial Fibrillation trial [6].

The probability of achieving normal sinus rhythm with cardioversion was estimated to be 85% [10, 52, 53]. The risk for stroke with cardioversion was estimated to be 0.5% [54-56]. No deaths occurred in 1304 patients who had elective cardioversion in the four large series we reviewed [52, 54-56]. We used a fatality risk of 0.01%.

Quinidine

We used the six randomized controlled trials reviewed by Coplen and colleagues [10] as well as observational studies and expert clinical opinion, when necessary [57-62]. In the randomized controlled trials, 42% and 50% of patients had reverted to atrial fibrillation at 6 and 12 months, respectively. Byrne-Quinn and Wing [58] found that 55% of patients had reverted to atrial fibrillation at 15 months. We estimated the probability of reverting to atrial fibrillation for patients receiving quinidine within 6 months to be 42%, and 10% per year thereafter. Sensitivity analysis was done over a wide range because of the lack of long-term follow-up data.

The incidence of early quinidine toxicity (side effects requiring discontinuation of therapy during the first 4 weeks of therapy) was estimated to be 25% [63, 64]. We examined the effect of lower risks reported in the randomized controlled trials using sensitivity analysis. We could not find reliable primary data on the incidence of late toxic reactions. It has been estimated that 30% to 40% of all patients given quinidine will have intolerable side effects [65]. Because we assigned an early toxicity rate of 25%, we estimated the subsequent yearly withdrawal rate to be 1.5% per year. We did sensitivity analysis over a wide range.

Coplen and colleagues [10] reported an excess mortality rate of 2.1% per year based on the unadjusted mortality rates for the quinidine-treated and control patients of 2.9% and 0.8% per year, respectively [10]. However, several of these deaths were not directly attributable to quinidine [66]. In our review, only five deaths in patients treated with quinidine could be directly attributed to the drug, an excess mortality of 1.2% per year (5 of 413). We included the higher estimate of Coplen and colleagues' study in our sensitivity analysis.

Low-Dose Amiodarone

No randomized controlled trials have been done for the use of low-dose amiodarone (defined as a maintenance dose of <400 mg/d) in the treatment of atrial fibrillation [15]. We based efficacy rates on longitudinal studies of patients with refractory atrial tachyarrhythmias who were treated with low-dose amiodarone for up to 3 years [12-14, 22]. Toxicity and excess mortality rates were estimated by combining the results of 13 longitudinal studies (2 randomized controlled trials, 11 cohort studies) of low-dose amiodarone in patients with supraventricular or ventricular tachyarrhythmias; the data represented 1755 patients with 4274 patient-years of follow-up Table 2[11-14, 20-28].

Gosselink and colleagues [12] followed 80 patients with chronic refractory atrial fibrillation or atrial flutter who were receiving low-dose amiodarone. They found that 64% of patients remained in normal sinus rhythm at 6 months, whereas 61%, 56%, and 53% remained in normal sinus rhythm at 1, 2, and 3 years, respectively. Our baseline estimates were taken from this study because all patients had chronic atrial tachyarrhythmias and actuarial data were provided for 3 years of follow-up. Sensitivity analysis was done over a wide range for 6-month failure rates (21% to 45%) and yearly failure rates (0% to 10% per year), thereafter to reflect the results of other studies [13, 14, 22].

Table 2 summarizes the 13 studies we reviewed. We included the study by Herre and colleagues [23] because of the large number of patients followed (n = 462), despite the fact that some patients were taking higher doses (range, 250 to 750 mg/d). There were 270 patients who required withdrawal in 4274 patient-years of follow-up (6.32% per year). We defined a major toxic reaction as any pulmonary, gastrointestinal, or cardiac toxic reaction and as any undefined toxic reaction requiring cessation of amiodarone. Of the 270 patients withdrawn from therapy, 123 met this definition (46%).

Four deaths were attributed to amiodarone in 4274 patient-years of follow-up (0.09% per year). Two (pulmonary fibrosis) occurred in the study by Kowey and colleagues [24], 1 (pulmonary fibrosis) in the study by Smith and colleagues [27], and 1 (hepatic failure) in the study by Brodsky and colleagues [20]. We used this weighted, average, yearly mortality rate (0.09%) in the baseline analysis and the 95% confidence interval for the range tested in our sensitivity analysis.

Utilities

We made adjustments for quality of life explicitly, based on published values and the consensus of clinicians at our institutions Table 3[67-73]. In the baseline analysis, we adjusted only for those events associated with substantial short-term morbidity or long-term sequelae, such as major drug toxicity, major bleeding events, and strokes. We did not adjust for relatively minor, transient events (for example, minor quinidine or amiodarone toxicity) or for the inconveniences of individual therapies (for example, frequent blood sampling and minor bleeding events with warfarin, having cardioversion with antiarrhythmic agents) in the baseline analysis. However, we tested the potential effect of these factors in sensitivity analysis.

Results

Baseline Analysis

In the baseline analysis, we compared clinical outcomes after 5 years in large, hypothetical cohorts of 65-year-old patients (Figure 2). Fewer patients had disabling events with amiodarone (1.4%) when compared with quinidine (1.8%), warfarin (2.6%), or no treatment (7.4%). Amiodarone was also associated with the lowest 5-year mortality (13.6%) when compared with warfarin (14.4%), quinidine (15.8%), and no treatment (18.2%). Amiodarone was more effective in maintaining normal sinus rhythm (34.3% at 5 years) than was quinidine (25.8%).

Low-dose amiodarone had the highest expected value (4.75 quality-adjusted life-years) of the four treatment alternatives and was thus the preferred strategy (Table 4). Differences in the expected values of the four strategies can also be expressed in weeks. When compared with no treatment, patients given amiodarone, warfarin, or quinidine can be expected to gain 10.4, 8.8, or 6.8 weeks, respectively, of quality-adjusted life expectancy during a 5-year period.

Sensitivity Analysis

We did a sensitivity analysis, over the ranges given for each of the variables in Table 1 and Table 3, to examine how changing one or several of the baseline values might influence the preferred strategy. There were few variables to which the model was sensitive. Table 5 lists the “threshold” values for each of these variables. A threshold value is that value of a particular variable at which the expected value for two competing strategies is equivalent. For example, the warfarin and quinidine strategies confer equal benefit if the rate of major bleeding for patients receiving warfarin is 4.30% per year. Warfarin is preferred when the rate is below 4.30%, whereas quinidine is favored when the rate is above 4.30%.

Low-dose amiodarone appeared to be the preferred strategy using most plausible scenarios. Two exceptions were noted using univariate sensitivity analysis (Table 5). “No treatment” appeared to be better than amiodarone if the risk for stroke in patients who were not receiving warfarin was less than 1.12% per year (baseline estimate, 5.0% per year). Warfarin therapy appeared to be better than amiodarone if the risk for stroke in patients receiving anticoagulant therapy was less than 0.35% per year (baseline estimate, 1.35% per year). We repeated the analysis using our baseline estimates for stroke risks while allowing several amiodarone-related risks to vary simultaneously, including excess mortality rate, major toxicity rates, and assumptions about quality of life. However, even using plausible worst-case scenarios for these values, amiodarone appeared to be better than warfarin, “no treatment,” and quinidine.

The decision between using quinidine or warfarin therapy was most sensitive to estimates of the risk for major bleeding events in patients receiving warfarin and the excess mortality associated with quinidine (Table 5). Quinidine appears to be better than warfarin if either the risk for a major bleeding event in patients receiving warfarin is greater than 4.30% per year or the excess mortality of quinidine is less than 0.49% per year. The choice between using warfarin therapy or “no treatment” depended most on the risk for major bleeding events in patients receiving warfarin and the risk for stroke in patients who were not receiving warfarin Table 5.

Although we did not adjust for the inconvenience of taking warfarin in the baseline analysis, sensitivity analysis showed this variable to be important (Figure 3). The expected value of the warfarin treatment strategy declines substantially with worsening assumptions about the quality of life for patients receiving warfarin Figure 3. Because many patients initially assigned to receive low-dose amiodarone or quinidine revert to atrial fibrillation (and thus start warfarin), the expected values of these two strategies also decline, although less rapidly. When the quality adjustment for warfarin therapy is 0.98, the warfarin and quinidine approaches have equivalent expected value. Similarly, when the quality adjustment for warfarin therapy is 0.96, warfarin therapy and “no treatment” are equivalent.

Our results did not change when we included quality-of-life adjustments (1 week deducted from life expectancy) for minor, temporary drug toxicity or for having elective cardioversion. Varying the assumptions about the efficacy of antiarrhythmic agents in maintaining normal sinus rhythm also had no effect on the preferred strategy. High rates of reversion to atrial fibrillation made the expected values of amiodarone and quinidine more similar to the expected value of warfarin therapy but did not change the relative rankings.

Discussion

The goals of this analysis were 1) to compare the relative risks and benefits of four management strategies for atrial fibrillation [no treatment, anticoagulation using warfarin, cardioversion followed by quinidine for maintenance of normal sinus rhythm, and cardioversion followed by low-dose amiodarone] and 2) to determine the key variables in deciding among these strategies. We found low-dose amiodarone to be associated with less morbidity and less mortality than the other more commonly used treatments of atrial fibrillation. In terms of quality-adjusted life expectancy, the net benefit of amiodarone was relatively small: 1.6 weeks more than warfarin, 3.6 weeks more than quinidine, and 10.4 weeks more than no treatment. These small differences can be attributed to the limited time frame of the analysis (5 years); the relatively small risks faced by patients with atrial fibrillation, regardless of therapy; and the fact that a large percentage of patients receiving antiarrhythmic therapy fail to maintain normal sinus rhythm and therefore crossover to warfarin. Although these benefits appear small, when applied across a large population in which atrial fibrillation is common, the potential decrease in morbidity and mortality is substantial. In addition, many other widely accepted clinical practices produce benefits of similar magnitude. For example, breast cancer screening with yearly examination and mammography has a life expectancy benefit of 20 days over 10 years [74]. Preoperative autologous blood donation in total joint replacement has a benefit of less than 1 day [75].

Low-dose amiodarone appeared to be the preferred strategy primarily because of the relatively low fatal and nonfatal toxicity rates derived from published studies. In the 13 studies that we reviewed, only 4 of 1755 patients had fatalities attributable to amiodarone, all of which were related to organ toxicity. This excess mortality rate (0.09% per year) is well below the threshold rate (0.52% per year) required for warfarin therapy to have been favored over amiodarone in our analysis. The nonfatal toxicity rate derived from these studies is also relatively low, 6.32% per year. Approximately 50% of amiodarone-related toxicity would be considered major, but no patients had serious irreversible injuries.

Two potential limitations exist for our assessment of amiodarone-related outcomes. First, mean follow-up periods of the 13 studies were limited to 1 to 5 years, which may be too short to address concerns about the potential for cumulative toxicity with long-term amiodarone therapy. However, we could find no evidence in the 13 longitudinal studies that amiodarone toxicity increased with time on the medication. Also, it is important to note that amiodarone remained the preferred strategy in our analysis even when we used substantially higher toxicity rates and relatively pessimistic assumptions about the effect of major and minor toxicities on quality of life. A second limitation is the possibility of selection bias in the observational studies used in this analysis. Many of the patients included in these studies had tachyarrhythmias refractory to multiple previous medications. Although it is unclear what effect this selection bias may have had on observed toxicity rates, the efficacy of amiodarone in maintaining normal sinus rhythm may have been underestimated. Randomized controlled trials involving amiodarone in atrial fibrillation are needed to more clearly define efficacy and toxicity rates.

The relative value of warfarin strongly depends on the residual risk for stroke in patients with atrial fibrillation who receive anticoagulant therapy. In our analysis, warfarin appeared to be better than amiodarone only if the rate of stroke in patients receiving warfarin was less than 0.35% per year. Of the five randomized studies of warfarin in patients with atrial fibrillation, only the Boston Area Anticoagulation Trial for Atrial Fibrillation [5] achieved similar rates (0.40% per year), despite its having the lowest target level of anticoagulation (International Normalized Ratio, 1.5 to 2.7; prothrombin time, 1.2 to 1.5 x control). One possible explanation for the exceptionally low risk for stroke in this study is chance. Another explanation is the high percentage of prothrombin times in the therapeutic range (83%) obtained by the Boston study [5]. Whether or not this level of compliance can be achieved in clinical practice is uncertain.

Amiodarone appeared to be better than warfarin even if the rate of major bleeding events in patients receiving warfarin was zero. This variable was important, however, in deciding between quinidine and warfarin. We found that warfarin appeared to be better than quinidine unless the rate of major bleeding in patients receiving warfarin exceeded 4.30% per year. Although this rate exceeds that of any of the randomized controlled trials [3-7], preliminary results from the Stroke Prevention in Atrial Fibrillation II study [76] suggest that patients older than 75 years may face a risk for major bleeding of 5.0% per year. Thus, elderly patients may represent a subgroup for whom antiarrhythmic strategies are preferable to the warfarin strategy.

Quinidine did not appear to be as beneficial in our analysis, primarily because of its relatively high excess mortality rate. We based our estimates of this important variable on data from randomized controlled trials published in the 1970s to early 1980s. Although these are the best available data, it is unclear whether patients presently face a similar risk for sudden death. Today, more is known about the proarrhythmic potential of quinidine, as well as its interaction with digitalis, and thus patients may be monitored more closely early in the course of therapy. A more recent observational study [77] found that patients without a history of congestive heart failure who received antiarrhythmic therapy for atrial fibrillation (52% of whom received quinidine) had no increase in cardiac mortality.

We found “no treatment” to be the best option only for patients with very low risks for stroke while not receiving warfarin (< 1.12% per year). The Stroke Prevention in Atrial Fibrillation trial [34] identified a subgroup with a risk for stroke of 1.0% per year (patients without a history of hypertension, recent congestive heart failure, or previous thromboembolism and, using echocardiography, without left ventricular dysfunction or left atrial dilatation). These characteristics resemble those for patients with so-called “lone” atrial fibrillation, for whom anticoagulation is not presently recommended [9]. However, such patients make up fewer than 5% of all patients with atrial fibrillation [78].

The quality of life for patients receiving warfarin was an important variable in our analysis. Previous studies [72, 73, 79] have found the decision of whether to give patients long-term anticoagulant therapy to be highly sensitive to this variable. A recent study [80] of patients who participated in the Boston Area Anticoagulation Trial for Atrial Fibrillation found no statistical differences in health perceptions between those receiving warfarin and those receiving placebo, unless they had a minor bleeding episode. However, these findings may have been biased by a selection or “volunteer” bias. For example, of 2546 patients invited to participate in the AFASAK (Copenhagen Atrial Fibrillation, Aspirin, and Anticoagulation Study) study [7], 835 refused (33%). Although the reasons for refusal were not specified, it is likely that a substantial number did so to avoid frequent blood sampling. In addition, 38% of the patients who were randomly assigned to warfarin withdrew, mostly because of the inconvenience of frequent blood sampling and the side effects of treatment [7]. In our analysis, warfarin therapy appeared to be better than “no treatment” only if the quality adjustment for taking warfarin exceeded 0.96 (a quality adjustment less than 0.96 implies that patients would accept a one-time risk for death of 4% to avoid taking warfarin). Warfarin therapy appeared to be better than quinidine only if the quality adjustment exceeded 0.98. Amiodarone appeared to be better than warfarin even without adjustment for the quality of life of patients receiving warfarin.

Several possible advantages exist for maintaining normal sinus rhythm in some patients with atrial fibrillation that were not included in this analysis. These advantages include an improved sense of well-being, better functional capacity because of restoration of atrioventricular synchrony, and avoidance of palpitations from an inappropriately rapid ventricular response. Although these benefits are difficult to quantify, their exclusion may have biased our results against antiarrhythmic therapy.

This study assessed the relative efficacy of the most common approaches to management of atrial fibrillation. Treatment with aspirin was not considered. The randomized controlled trials [3-7] provide conflicting data on the efficacy of aspirin, and a recent decision model found that warfarin appeared to be better than aspirin [72]. Other potential antiarrhythmic agents were also not considered. We did not feel sufficient data were available to evaluate medications such as procainamide, flecainide, sotalol, and propafenone.

This decision analysis suggests that electrical cardioversion followed by attempted maintenance of normal sinus rhythm with low-dose amiodarone appears to be a relatively safe and effective alternative to long-term warfarin therapy in a hypothetical cohort of patients with atrial fibrillation, especially for those who view the minor bleeding events and frequent blood sampling associated with warfarin therapy as substantial detriments to their quality of life. Future randomized controlled trials of low-dose amiodarone and other antiarrhythmic agents, as well as more formal assessments of the quality of life for patients receiving warfarin, should help to further refine clinical decision making for patients with this common condition.