Comparison of Cost-Effectiveness and Utility of Exercise ECG, Single Photon Emission Computed Tomography, Positron Emission Tomography, and Coronary Angiography for Diagnosis of Coronary Artery Disease
Background To compare cost-effectiveness and utility of four clinical algorithms to diagnose obstructive coronary atherosclerotic heart disease (CAD), we compared exercise ECG (ExECG), stress single photon emission computed tomography (SPECT), positron emission tomography (PET), and coronary angiography.
Methods and Results Published data and a straightforward mathematical model based on Bayes’ theorem were used to compare strategies. Effectiveness was defined as the number of patients with diagnosed CAD, and utility was defined as the clinical outcome, ie, the number of quality-adjusted life years (QALY) extended by therapy after the diagnosis of CAD. Our model used published values for costs, accuracy, and complication rates of tests. Analysis of the model indicates the following results. (1) The direct cost (fee) for each test differs considerably from total cost per ΔQALY. (2) As pretest likelihood of CAD (pCAD) in the population increases, there is a linear increase in cost per patient tested but a hyperbolic decrease in cost per effect and cost per utility unit, ie, increased cost-effectiveness and decreased cost per utility unit. (3) At pCAD<0.70, analysis of the model indicates that stress PET is the most cost-effective test, with the lowest cost per utility, followed by SPECT, ExECG, and angiography, in that order. (4) Above a threshold value of pCAD of 0.70 (for example, middle-aged men with typical angina), proceeding directly to angiography as the first test showed the lowest cost per effect or utility. This quantitative model has the advantage of estimating a threshold value of pCAD (0.70) at which the rank order of cost-effectiveness and cost per utility unit change. The model also allows substitution of different values for any variable as a way to account for the uncertainties of clinical data, ie, changing costs, test accuracy and risk, etc. This procedure, called sensitivity analysis, showed that the rank order of cost-effectiveness did not change despite changes in several variables.
Conclusions (1) Estimation of total costs of diagnostic tests for CAD requires consideration not only of the direct cost of the test per se (eg, test fees) but also of the indirect and induced costs of management algorithms based on the test (eg, cost/ΔQALY). (2) It is essential to consider the clinical history (pCAD) when selecting the clinical algorithm to make a diagnosis with the lowest cost per effect or cost per utility unit. (3) Stress PET shows the lowest cost per effect or cost per utility unit in patients with pCAD<0.70. (4) Angiography shows the lowest cost per effect or cost per utility unit in patients with pCAD>0.70.
Positron emission tomography (PET) has greater sensitivity and specificity to diagnose obstructive coronary artery disease (CAD) than does single photon emission computed tomographic (SPECT) imaging or exercise ECG (ExECG).1 2 Despite the demonstration of greater accuracy of PET, it has not yet replaced other noninvasive approaches to detect CAD.
The limitation of PET is that it is more expensive than other noninvasive tests for CAD. One of the most difficult jobs facing medicine today is to objectively assess the cost relative to effectiveness or utility of health care.3 4 There is an especially urgent need to develop the lowest cost per effect for diagnostic approaches to CAD because the spiraling cost of cardiac care is estimated to be between 1% and 2% of the gross domestic product.5 Analysis of the utility of clinical approaches accounts for the impact of medical care on the quality as well as quantity of life.6 7 We previously reported a mathematical model to compare the cost-effectiveness of exercise ECG, planar thallium, and coronary angiography to diagnose CAD.8 The goal of this study is to use an updated version of that model to compare the cost per effect or cost per utility unit of PET and SPECT myocardial perfusion imaging with ExECG and angiography in different populations of patients. Gould et al9 also proposed a model to assess the cost-effectiveness of PET, and Gleason and Frick10 suggested improvements in that model.
Comparison of cost-effectiveness or cost per utility unit is complex because it needs to account for a wide variety of factors.3 4 5 6 7 8 9 10 The model must be able to account for the cost of diagnostic and therapeutic measures, including those that yield false-positive results and lead to unnecessary further testing, as well as those that yield false-negative results and lead to complications due to inadequate treatment of the disease. The present study used actual data that have been published in the literature about the tests, their complication rates, and their accuracy. The objective of the study was not to assess the impact of diagnostic tests or treatment of CAD on the welfare of society. This more complicated task represents cost-benefit analysis.11 12 Rather, the limited goal of this study is to compare the costs of different clinical diagnostic algorithms to achieve the same effect, outcome, or utility, eg, increasing the quantity and/or quality of life by the same amount. Our model addresses only the problem facing a physician who sees a patient with symptoms or a clinical situation that indicates a need for testing for possible CAD.
A mathematical model8 was developed based on real data to estimate comparative cost-effectiveness of cost per utility unit of four different diagnostic approaches to CAD (Table 1⇓) based on literature values for clinical variables (Table 2⇓).
Effectiveness of Tests: Criteria
The most difficult issue in the assessment of cost-effectiveness is to develop criteria to define effectiveness of health care.5 6 7 8 9 10 13 For the purpose of this study, our first criterion for effectiveness of diagnostic tests was the ability to identify accurately a patient who has CAD when patients are selected for testing from a group presenting to a physician because of possible CAD.
The second criterion for the effectiveness of care attempts to account for several of the clinical variables that influence the outcome of management of CAD, ie, utility.4 5 11 Here, we developed criteria for utility of tests for CAD in terms of the clinical outcome for patients undergoing the tests, ie, an increase (Δ) in the number of quality-adjusted life years (QALY) for a patient over a 10-year follow-up period (Appendix A and Table 3⇓).11 We multiplied the number of years of life extended by therapy (over a 10-year follow-up period) by the adjusted quality of life, expressed as a fraction of full quality of life (1.0). This criterion is imperfect, but it does account for most important clinical variables.12 13 It seemed reasonable for the purpose of this study because it must be emphasized that ΔQALY is used only as a common denominator to compare cost per utility unit of different diagnostic tests. Briefly, we assumed that the diagnosis of CAD increased the number of QALYs by 3 years over a 10-year follow-up period, based on available data.14 15 16 17 18 19 20 21 22 23 24 25 26 We limited this variable to a 10-year follow-up period because the natural history of patients treated with modern medical, percutaneous transluminal coronary angioplasty (PTCA), or coronary artery bypass graft surgery (CABG) therapies is not well known beyond 10 years. If therapies have a sustained long-term effect on the natural history of CAD, then the outcome of therapy (ΔQALY) might be more favorable than our analysis indicates.
Calculations of Cost Per Effect and Cost Per Utility Unit (Appendix B)
Total costs were calculated as direct costs (fees for tests) multiplied by the number of patients tested (as decided by physician’s approach) plus the induced costs (the number of patients who had additional tests, eg, angiography), multiplied by the costs of complications produced by test procedures or by CAD per se.8 It was not necessary to estimate the dollar value of a human life lost to CAD or to complications of test procedures. Instead, mortalities were considered separately and were incorporated into the calculation of QALYs. We calculated (cost-effectiveness)−1 as cost (in dollars) per effect:
Effectiveness was defined as a patient with CAD diagnosed.8 11 Utility was defined as an increment in the number of QALYs added over a 10-year follow-up period.11 Although calculation of ratios of cost to effect can lead to erroneous conclusions, as pointed out by McKean,13 our analysis avoids these pitfalls by focusing on the cost-to-effect ratio in a defined population and by accounting for all patients whether or not they were diagnosed accurately. Calculation of direct and induced costs is outlined briefly here but with detailed equations below (Appendix B, using variables in Table 2⇑). Total direct costs, therefore, were calculated as the fee for each test multiplied by the number of patients having the test and summed for all tests.8 The costs for each test were derived from literature values for fees rather than attempts to estimate incremental costs, with all of the uncertainties involved in that procedure.12 Furthermore, the number of patients who undergo a test is determined by the diagnostic approach, ie, strategy selected by the physician to decide indications for each test (Table 1⇑), and thus becomes the most relevant consideration for physicians.
The induced costs of exercise tests arise from the complications and mortalities associated with each test, including subsequent testing indicated by the results of the first test, for example, angiography after a positive noninvasive test.8 Induced costs also include the complications and mortality associated with CAD that is not treated because of false-negative test results.27 28 Costs of complications are not easy to estimate, and it was necessary to combine actual data for this purpose. We assumed that the usual complication of each test or of CAD would be nonfatal myocardial (or cerebral, for angiography) infarction, requiring 1 week in the hospital and 2 months away from employment at a conservative average cost of $40 000 per complication. We adjusted the annual rate of nonfatal myocardial infarction in patients with CAD to estimate the rate of myocardial infarction in the subgroup of patients with false-negative exercise test results.27 28 Because we required that the patient achieve 85% of age-predicted maximal heart rate or a good hemodynamic response to pharmacological vasodilator stress to interpret the test as negative, many patients with false-negative tests would have good exercise capacity and therefore a low risk of nonfatal myocardial infarction or death.27 On the other hand, patients who had pharmacological rather than exercise stress would have no assessment of exercise capacity, which would have helped predict prognosis. Furthermore, only patients with mild to moderate symptoms are likely to avoid angiography despite negative exercise test results. Thus, we assumed a 20% rate of nonfatal myocardial infarction over 10 years in patients with CAD missed by false-negative exercise test results after adjustment for the good exercise tolerance or response to pharmacological dilation, mild to moderate symptoms, and low likelihood of left main or three-vessel CAD in patients with false-negative exercise test results.27 28
A modification of the equations of Bayes’ theorem was used to calculate the number of patients having each test or experiencing the complications (Appendix B).29 30 31 These calculations were based on literature values of the sensitivities and specificities of each test1 2 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 (Table 2⇑ for values used in this study) and the rates of complications47 48 over the full range of pCAD.
Clinical Algorithms for Use of Diagnostic Tests
Using this model, we tested four straightforward diagnostic algorithms for CAD. The four algorithms represent simplified diagnostic approaches or algorithms for CAD (Table 1⇑). For the first three algorithms, one of the three noninvasive stress tests is performed first, and the patients are referred for angiography only if the noninvasive test is positive or nondiagnostic. The three tests are ExECG, stress SPECT, and stress PET myocardial perfusion imaging. In the other approach, angiography is the first and only diagnostic test.
Many assumptions are required in any model of cost-effectiveness (Tables 2⇑ and 3⇑); therefore, we performed sensitivity analysis of the model by repeating calculations after changing the values of sensitivity, specificity, fees, and rates and costs of complications or mortalities (Tables 2⇑ and 4⇓).8 In particular, the most difficult data to estimate accurately are the clinical outcomes, including rates of complications, and effects of different therapies on prognosis (Table 3⇑).14 15 16 17 18 19 20 21 22 23 24 25 26 Fortunately, the impact of these uncertainties on the calculations in this analysis can be easily tested by changing ΔQALY. It must be emphasized that our analysis focused on comparing different clinical approaches to detection of CAD, and these hard-to-measure clinical variables can be accounted for by changing the value of ΔQALY to assess whether it changed the rank order of different approaches to diagnose CAD.
Pretest Likelihood of CAD: Effect on Costs
First, these results show that the fee for a diagnostic test represents only one small component of the total costs incurred by using a management algorithm based on that diagnostic test (Tables 2⇑ and 3⇑ and Fig 1⇓). Next, when the pretest likelihood of CAD (pCAD) increased in the population, the cost and mortality rate over a 10-year follow-up period also increased linearly (Fig 1⇓). As the pCAD increased, there were hyperbolic decreases in cost per patient with CAD diagnosed and in cost per increased number of QALYs (Fig 1⇓). Although the absolute cost and mortality rates increased with increasing pCAD, cost per effect and cost per utility unit improved. The hyperbolic relation between pCAD and cost per effect or cost per utility unit reveals the very high cost per effect or cost per utility unit at low pCAD and the dramatic differences among the different diagnostic algorithms at lower pCAD (Fig 1⇓).
Comparing Cost Per Effect and Cost Per Utility Unit for Clinical Algorithms
Comparing cost per effect and cost per utility unit of different clinical algorithms may be easiest to understand by using individual patient examples selected to represent varied pCAD (Fig 2⇓). A population of 50-year-old men with no chest discomfort but with two risk factors would have a 10% pCAD, based on clinical data alone (pretest likelihood).30 31 In such patients, PET imaging shows the lowest cost per effect and cost per utility unit, followed by SPECT imaging and ExECG. Performing angiography first is the least cost-effective algorithm at the 10% pCAD. The rank order of cost per effect or cost per utility unit is the same for 50-year-old women with atypical chest discomfort (a 30% pCAD).30 31 For 40-year-old men with atypical chest discomfort (with a 50% pCAD),30 31 PET still maintains the lowest cost per effect or cost per utility unit of any algorithm. Performing angiography first has the highest cost per effect, but differences among policies are less dramatic. On the other hand, at 90% pCAD (typical angina in a 65-year-old woman),30 31 performing angiography first has the lowest cost per effect or cost per utility unit, and ExECG has the greatest cost per effect. Thus, not only the relative differences but, more importantly, the rank order of cost per effect or cost per utility unit of the four different algorithms changes as pCAD increases (Fig 2⇓).
Fig 3⇓ plots cost versus the mortality rate over 10 years for the same four patient examples cited above. For the 50-year-old man with no chest discomfort but with two risk factors (10% pCAD), PET has the lowest cost and has virtually the same low mortality as the approach based on angiography. The mortality rate of ExECG is highest. For the 50-year-old woman with atypical chest discomfort (30% pCAD), the rank order is the same, and angiography remains the most costly, followed by PET and SPECT in these patients. Finally, in 65-year-old women with typical angina pectoris (90% pCAD), performing coronary angiography first becomes least costly and has the lowest mortality. PET has the second lowest mortality rate and approaches that of performing angiography first, but it has the second lowest cost in these patients.
Sensitivity Analysis: Changes in Assumptions Influence Cost Per Effect or Cost Per Utility Unit
Because valid data are not easy to acquire and several assumptions are involved in these calculations, we systematically changed parameters in the equations to test their impact on cost per effect or cost per utility unit (Table 4⇑; Figs 4 and 5).8 We analyzed the effects of changes in the variables shown in Table 4⇑ on the basis of available literature.12 14 15 16 17 18 19 20 21 22 23 24 25 26 Fig 4⇓ shows graphs of cost per utility unit for standard parameters and changes A through H defined in Table 4⇑. All changes are shown for each diagnostic approach considered separately, eg, ExECG, SPECT, PET, and angiography. In general, lowering the fee for a test decreases cost per utility unit (ΔQALY), and raising the fee for a test increases cost per utility unit. Lowering the accuracy of tests increases their cost per utility unit, and lowering the risk because of false-negative diagnostic tests decreases cost per utility unit slightly. As the pCAD rises from P=.2 to P=.8, overall cost per utility unit decreases, but there is little effect on the rank order of cost per utility unit due to various changes in parameters (A through H). More details are indicated in the legend to Fig 4⇓. The greatest change occurred when the benefit of treatment (ΔQALY) was reduced.
Fig 5⇓ shows graphs of cost per utility unit for standard parameters and changes (A through H). All changes (A through H) are grouped to emphasize comparison of the rank order of different diagnostic approaches (ExECG, SPECT, PET, and angiography). In general, there was little impact of changes (A through H) on the rank order of different diagnostic approaches. Greatest impact on rank order occurred with selective changes in the fees or accuracy of a particular test, eg, SPECT and PET. The rank order of diagnostic approaches changed when the pCAD increased from 0.2 (noninvasive tests perform best) to 0.5 (less dramatic differences) to 0.8 (angiography performs best). Sensitivity analysis indicates that the model is robust because it shows that relatively small changes occur in rank order of cost per utility unit despite relatively large changes in test fees, test accuracy, complication rates, and benefits of treatments (A through H).
Estimation of Cost-effectiveness
Measurement of the cost-effectiveness of health care is difficult,4 5 6 7 but current spiraling increases in the cost of cardiac care demand further analyses.8 9 The present study was designed to achieve a specific limited objective, that is, to compare the relative cost per effect and cost per utility unit of four diagnostic algorithms for the patient suspected of having CAD. We focused on one aspect of cost-effectiveness, ie, test selection, which is currently decided primarily by the physician. To compare various clinical policies, a conceptual model was constructed based on real data and the equations of Bayes’ theorem.8 The conclusions were derived strictly from analysis of this model and should not be considered clinical practice guidelines unless they can be confirmed in clinical trials.
The most difficult aspect of assessing cost-effectiveness has been an adequate definition of effectiveness.5 7 To minimize this problem, we used one definition of effectiveness but also calculated cost per utility unit.10 Expression of effectiveness and utility yielded concordant results when the rank order of cost per effect and cost per utility unit of different clinical algorithms were compared and did not require placing a dollar value on human life. It must be emphasized that the agreement of results using effectiveness (cost per patient diagnosed) and utility (cost per ΔQALY) supports the validity of the model. This agreement means that the difficult job of estimating improvement in QALY due to diagnosis and treatment of CAD had little or no effect on the comparison of PET versus other modalities. The model is robust and shows only minimal dependence on the assumptions used to calculate the impact of care on the patient outcome.
The present analysis addressed the use of tests to diagnose the presence or absence of CAD, because this is the indication for which the most information exists. There are other indications for tests that were not addressed by the present study, for example, predicting prognosis, functional significance of a coronary lesion, or myocardial viability.31 The present study did not try to assess cost-effectiveness or utility of the tests when used for these indications.
Controversy continues regarding the comparative cost-effectiveness or utility of medical, angioplasty, and surgical therapies for CAD.12 14 15 16 17 18 19 20 21 22 23 24 25 26 For the purpose of this study, the most important result was that the choices among these therapeutic measures produced little change in the rank order of different clinical diagnostic algorithms but rather that they produced similar changes in the absolute cost of each algorithm. Again, the validity of the model is supported by the concordance of rank orders of cost per ΔQALY and cost per CAD patient diagnosed (Fig 1⇑). When ΔQALY decreased from 3.0 to 1.5, there was less utility for diagnosing CAD, so sensitivity of tests to detect CAD became less important than the test fees (Fig 5H⇑). Finally, we used a simplified approach to calculating costs by using the test fees as the cost of the test instead of a more elaborate and controversial cost-accounting analysis of all the factors that influence incremental costs. Because our analysis of the model depends on the relative rather than the absolute costs of different tests, our use of published fees seems reasonable for the limited objective of this study.
pCAD in the Population
Both absolute costs and mortality rates increased linearly with pCAD, but cost per effect and cost per utility unit decreased. Thus, decreased pCAD leads to increased cost per effect and cost per utility unit. The cost per effect and cost per utility unit were particularly high in populations in which pCAD was below 10% because there were too few patients with CAD to benefit from therapy (Fig 1⇑). This analysis shows that diagnostic testing for CAD in asymptomatic populations is not generally cost-effective and offers little utility for the cost. An exception may be the asymptomatic middle-aged people with multiple risk factors for CAD30 31 (who have pCAD of 0.1 to 0.2, similar to the low-pCAD people in Figs 2 through 5⇑⇑⇑⇑). Thus, some asymptomatic patients have considerable risk for CAD, and testing might have lower cost per effect or cost per utility unit than in lower-risk patients with nonanginal chest discomfort.
Cost-effectiveness increased with increasing pCAD for all clinical algorithms involving noninvasive tests, because more patients with CAD were diagnosed and could benefit from therapy. At low pCAD, negative results of the noninvasive tests reduced the number of coronary angiograms because at low pCAD, most negative tests will be correct to exclude CAD (lower predictive error at lower pCAD). Thus, it is entirely reasonable that the noninvasive tests show lower cost per effect and cost per utility unit than angiography only in populations with low to intermediate pCAD.
In contrast, at higher pCAD (above a threshold value of 70%), the noninvasive tests miss so many patients with CAD that increasing complications of CAD increase cost per effect and cost per utility unit. Decreased cost-effectiveness of noninvasive tests at high pCAD results from the increasing percent of patients with false-negative test results who actually have CAD (high predictive error at high pCAD). Thus, at high pCAD (>70%), performing angiography as the first and only test to diagnose CAD showed the lowest cost per effect or cost per utility unit of any clinical algorithm, according to this model. It should be noted that the accuracy of PET allows it to be used at a somewhat higher threshold than the other noninvasive tests; ie, angiography becomes more cost-effective than SPECT at a lower pCAD than it does for PET (Fig 1⇑).
ExECG Versus Stress SPECT or PET Myocardial Perfusion Imaging
SPECT imaging shows lower cost per effect or cost per utility unit than ExECG to diagnose CAD in populations with a wider range of pCAD, but PET is most cost-effective over this same range of pCAD (Figs 1⇑ and 2⇑). It should be noted that our values of sensitivity and specificity were only slightly higher for SPECT imaging1 2 than for ExECG.32 Part of the advantage of SPECT imaging in the present study seems to result from its lower rate of nondiagnostic tests (P<.05) despite its greater cost. PET showed lower cost per effect or cost per utility unit than the other noninvasive tests over a range of pCAD because of its greater accuracy.
Sensitivity Analysis: How Changes in Assumptions Influence Cost Per Effect and Cost Per Utility Unit
Using a model to evaluate cost-effectiveness offers the advantage that one can substitute any variable into any equation to test its impact (Table 4⇑, Figs 4⇑ and 5⇑). This approach, called sensitivity analysis, is one way to account for the uncertainties of available data for costs, risks, and clinical outcomes. For example, the differences in cost per effect or cost per utility unit of ExECG, SPECT, and PET result from changes in test fees, sensitivity, specificity, and the frequency of nondiagnostic test results when one compares the different algorithms. The most dramatic changes in cost per utility unit, however, resulted from changes in the benefit of treatment on patient outcome (ΔQALY).
The physician whose major concern is the risk of missing CAD in a patient would incur the lowest cost per effect or cost per utility unit if he or she recommended a more sensitive test, eg, angiography or PET rather than ExECG. Similarly, if the physician takes a pessimistic view of the impact of therapy on the natural history of CAD, he or she might assume a decrease in the number of QALYs extended from 3 to 1.5 years. This decrease would increase the cost per utility unit for all tests (Fig 5H⇑). Thus, physicians who have the most aggressive and optimistic view of the results of therapy would be expected to be most aggressive about recommending the more sensitive tests for CAD, because they would yield a more favorable cost per utility unit. In contrast, a physician with a more conservative view of the benefits of therapy for CAD would be expected to recommend fewer tests and would require lower sensitivity.
Implications for Patient Care
The results of our analysis of this model suggest cost-effective algorithms for the clinical use of tests to diagnose CAD. The critical step is for the physician to select a diagnostic approach based on the pCAD in the patient, estimated by symptoms and risk factors. It is possible to estimate the pCAD clinically before and after noninvasive testing by use of any of several sources.30 31 In patients with no symptoms or risk factors, in particular, the pCAD is so low that it is difficult for any testing to yield favorable balances between cost and effect or utility. This analysis deserves consideration by physicians who include exercise stress testing as part of a routine examination, regardless of the patient’s history or risk factors. It is also important for the physician to base indications for test ordering on his or her view of the impact of therapy on CAD. The higher the physician’s estimate of the utility (ΔQALY) of treatment of CAD, the more aggressive he or she should be about ordering tests to detect the disease.
Atypical Chest Discomfort
If the patient has symptoms that are not typical of angina pectoris, then the patient has an intermediate pCAD.30 31 This higher pCAD (compared with asymptomatic people) makes all testing approaches more cost-effective and yields greater utility because it reduces the dramatic cost differences among different clinical algorithms for the use of diagnostic tests. PET imaging remains the most cost-effective first test, but the initial use of angiography becomes more competitive in terms of cost per effect or cost per utility unit as pCAD increases.
Typical Angina Pectoris
If the patient has typical angina pectoris, then the pCAD is high, unless the patient is a young woman or very young man.30 31 In middle-aged men and older women, the most cost-effective approach is to perform angiography as the initial test. Angiography provides the most reliable prognostic information for CAD and is necessary before PTCA or CABG is considered.14 Since functional aerobic capacity for exercise27 28 or evidence of functional significance of lesions or myocardial viability may add useful information about prognosis, noninvasive exercise tests might be indicated after angiography in selected patients to determine indications for invasive therapies.30 To incorporate these indications for tests into the model would require many additional assumptions and use of data that have been less widely tested. Thus, we did not test some potentially important and clinically relevant hypotheses so as to make the conclusion more reliable.
Calculation of the Increase in ΔQALY′ for Patients Based on Whether or Not They Have an Accurate Diagnosis of CAD
The absolute value of the utility unit was the increase in quality-adjusted life years (ΔQALY′) due to diagnosis and treatment of CAD (Table 3⇑). This value is obviously difficult to calculate, but it is used in the present study only as a common denominator to modify the benefit of diagnosing CAD. The goal of the present study was to compare rank order of cost per utility unit of four different clinical algorithms to diagnose CAD rather than computing the exact cost of each individual algorithm. The difference in utility (ΔQALY′) over a 10-year follow-up period is shown in Table 3⇑ for patients in whom CAD was diagnosed accurately (“With Dx,” Table 3A⇑) as well as for the same patients if they had not had an accurate diagnosis of CAD (“Without Dx,” Table 3B⇑). The average length of life over a 10-year follow-up period is shown, as is the subjective quality of life, expressed as a fraction of life at full health (Q/y), to calculate utility. Making the diagnosis of CAD leads to higher ΔQALY′: 7.09−4.09=3.00 years (Table 3A⇑ minus 3B). This calculation is based on a synthesis of available data, as indicated below.
Thirty percent of patients were treated medically (FP=0.3), and 60% of these medical patients were living at 10 years after diagnosis (Table 3A⇑) (FL=0.6). For patients who survived 10 years (FL), multiplying the fraction of patients treated medically (FP=0.3) times the fraction of patients alive at 10 years (0.6) times the average length of life after angiography (10 years for survivors) times Q/y (0.8 in survivors) yielded utility (QALY′) values of 1.44 for survivors. Similar calculations for patients who had died within 10 years yielded QALY′ of 0.36 years. The overall QALY′ for all patients treated medically after diagnosis (1.80 years) was calculated as the sum of QALY′ for 10-year survivors (1.44) plus those who died (0.36). The QALY′ for survivors shown in Table 3A⇑ (1.80) is 20% higher than that estimated for the same group of patients if they had not had angiography to prove the diagnosis of CAD (1.54 years, Table 3B⇑).
Another 30% of patients were treated by PTCA (FP=0.3), and 75% of these PTCA patients were living at 10 years after angiography (Table 3A⇑). Multiplying the fraction of patients who had PTCA (0.3) times the fraction who were alive at 10 years (0.75) times the average length of life after angiography (10 years for survivors) times y (0.9) yielded QALY′ values of 2.02 QALY′ for survivors. Similar calculations yielded QALY′=0.23 years for those who died. The overall ΔQALY′ for all patients treated by PTCA (2.25 QALY′, Table 3A⇑) was calculated as the sum of QALY′ for 10-year survivors (2.02) plus those who died (0.23 years). The overall QALY′ for patients with the diagnosis of CAD and PTCA treatment was 40% higher than that estimated for the same group of patients if they had not had angiography to prove the diagnosis of CAD and begin treatment (1.35).
Finally, 40% of patients with CAD diagnosed would have CABG (FP=0.4) for left main or three-vessel CAD or intractable symptoms (Table 3A⇑).12 These surgical patients would have an 80% survival over 10 years compared with a 33% survival estimated for the same patients treated without surgery (“without diagnosis and treatment of CAD,” Table 3B⇑).12 27 28 29 30 31 Patients who died at some time after surgery had a 4-year average life span after surgery and a lower quality of life (Q/y=0.5) than did patients who lived at least 10 years after surgery (Q/y=0.9). The number of QALYs for surgical patients is calculated by multiplying the fractions of patients having surgery (0.4) by the fraction of patients surviving 10 years (0.8)=0.32 (Table 3A⇑). This figure is multiplied by the number of years survived (10) and the Q/y (0.9) to yield QALY′ as an index of utility. Similar computations for patients who died after surgery yield 0.16 years, which is added to yield ΔQALY′ of 3.04 years for surgical patients versus 1.19 years for the same patients treated without CABG (Table 3B⇑).
For sensitivity analysis, this slight improvement in ΔQALY′ (3.0 years) over a 10-year follow-up period was decreased to 1.5 years at full quality of life as an index of utility. Such a large variation in ΔQALY′ can account for a wide range of variability in outcomes of different types of therapies, which represents the major source of uncertainty in this type of utility analysis. Thus, the particular value of improved utility (ΔQALY′) due to diagnosis of CAD changed the absolute dollar cost but not the relative ranking of different clinical policies. This value of improved ΔQALY′ due to diagnosis of CAD estimated in Table 3⇑ was then applied to each of the four clinical policies by use of the equations in Appendix B. We calculated utility as net QALYs (ΔQALY) for each algorithm, and this reflects not only the effect of diagnosis and therapy (ΔQALY′) but also the outcomes of diagnostic tests per se, the effects of complications and mortality rates due to tests and CAD missed by false-negative tests.
Equations to Calculate Cost-effectiveness and Cost Per Utility Unit for Each Clinical Algorithm
Table 2⇑ shows variables used in calculations. For the first algorithm, ExECG was performed first in all patients, and angiography was performed only if ExECG was positive (+) or nondiagnostic (NonDx).
Cost=NE(FE+REC)+NA(FA+RAC)+NF(RFC) and mortalities=NEME+NAMA+NFMF, where P=pCAD in population.
NE=number of patients having initial test; ExECG=1.0.
NA=number of patients having angiography because of (+) or NonDx ExECG=NE×(1−NDxE)×[P×SnE+(1−P)× (1−SpE)]+NE×NDxE.
NF=number of patients with false-negative (−) ExECG who do not have angiography for CAD Dx=NE× (1−NDxE)×P×(1−SnE).
CAD Dx=patients with CAD diagnosed correctly by the test (first definition of “effectiveness” of algorithms)=NE× (1−NDxE)×P×SnE + NE×P×NDxE.
ΔQALY′=quality-adjusted life years extended by therapy due to the diagnosis of CAD by the algorithm (Appendix A) (definition of “utility” of policy) and Table 3⇑=3.0 years over a 10-year follow-up period.
ΔQALY=net quality-adjusted life years extended by therapy for a particular algorithm, taking into account not only the favorable effect of CAD diagnosis (ΔQALY′) but also the deaths and complications of tests and CAD missed that result from application of the particular algorithm=(CAD Dx)× (ΔQALY′)−10×(NE×ME+NA×MA)−5(NF×MF)−10(0.1) (NE×RE+NA×RA+NF×RF), where deaths due to diagnostic tests subtract 10 years, and deaths due to CAD missed by false-negative tests subtract an average of 5 years. Complications due to tests or CAD missed reduce the quality of life per year (Q/y) by 1/10 per year.
In the next algorithm, exercise or pharmacological SPECT or PET imaging was performed first and angiography was performed only if SPECT or PET was positive or nondiagnostic (equations are identical to the first algorithm, substituting values for fees, test sensitivity, specificity, and rates of nondiagnostic tests of SPECT or PET for ExECG).
In the final algorithm, angiography is the first and only test to diagnose CAD.
1. Costs=NA×FA+RA×C and mortality=NA×MA, where NA=NE from policy 1=1.0 and NF=0.
2. CAD Dx=NA×P and ΔQALY=NA×ΔQALY′×P−10× NA×MA−NA×RA.
- Received March 4, 1994.
- Accepted August 15, 1994.
- Copyright © 1995 by American Heart Association
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