Bayesian cost-effectiveness analysis. An example using the GUSTO trial.

A desirable element of cost-effectiveness analysis (CEA) modeling is a systematic way to relate uncertainty about input parameters to uncertainty in the computational results of the CEA model. Use of Bayesian statistical estimation and Monte Carlo simulation provides a natural way to compute a posterior probability distribution for each CEA result. We demonstrate this approach by reanalyzing a previously published CEA evaluating the incremental cost-effectiveness of tissue plasminogen activator compared to streptokinase for thrombolysis in acute myocardial infarction patients using data from the GUSTO trial and other auxiliary data sources. We illustrate Bayesian estimation for proportions, mean costs, and mean quality-of-life weights. The computations are performed using the Bayesian analysis software WinBUGS, distributed by the MRC Biostatistics Unit, Cambridge, England.

An elementary introduction to Bayesian computing using WinBUGS.

Bayesian statistics provides effective techniques for analyzing data and translating the results to inform decision making. This paper provides an elementary tutorial overview of the WinBUGS software for performing Bayesian statistical analysis. Background information on the computational methods used by the software is provided. Two examples drawn from the field of medical decision making are presented to illustrate the features and functionality of the software.

The first positive: computing positive predictive value at the extremes.

Computing the positive predictive value (PPV) of a wellknown test for a relatively common disease is a straight-forward exercise. However, in the case of a new test for a rare disorder; the extreme numbers involved-the very low prevalence of the disorder and the lack of previous false-positive results--make it difficult to compute the PPV. As new genetic tests become available in the next decade, more and more clinicians will have to answer questions about PPVs in cases with extreme prevalence, sensitivity, and specificity. This paper presents some tools for thinking about these calculations. First, a standard PPV calculation with rough estimates of the prevalence, sensitivity, and specificity is reviewed. The "zero numerator" problem posed by not having seen any false-positive results is then discussed, and a Bayesian approach to this problem is described. The Bayesian approach requires specification of a prior distribution that describes the initial uncertainty about the false-positive rate. This prior distribution is updated as new evidence is obtained, and the updated expected false-positive rate is used to calculate PPVs. The Bayesian approach provides appropriate and defensible PPVs and can be used to estimate failure rates for other rare events as well.

A time-tradeoff method for cost-effectiveness models applied to radiology.

PURPOSE: The wait tradeoff (WTO) is a simple time-tradeoff method designed for temporary health states that uses a realistic and intuitive interface for the patient/subject. This method was tested by assessing patients' preferences for magnetic resonance angiography (MRA) versus x-ray angiography (XRA). MATERIALS AND METHODS: The WTO was tested by telephone interview in 38 patients with atherosclerotic peripheral vascular disease, all having previously undergone both MRA and XRA. At indifference point, patients were ambivalent about having MRA or XRA and immediate treatment, versus having a waiting period for test results and treatment after a hypothetical "ideal test" that entailed no pain or risk. RESULTS: The patients were willing to wait a mean of 42.1 days after the ideal test for results and treatment, as opposed to XRA. They were willing to wait only 16.1 days as opposed to MRA. This difference in waiting times was significant (p = 0.0001) and indicates a clear preference for MRA, in agreement with known literature. CONCLUSION: The WTO method assesses preferences for these radiologic tests in an intuitive fashion that does not invoke artificial or irrelevant health states. This approach may also prove useful for other testing situations or short-term treatments being evaluated for cost-effectiveness.

Is the societal perspective in cost-effectiveness analysis useful for decision makers?

BACKGROUND: The U.S. Public Health Service's Panel on Cost-Effectiveness in Health and Medicine recommends that cost-effectiveness analyses (CEAs) intended to help allocate health resources in the public interest include a reference case analysis, conducted from the perspective of society as a whole. This perspective requires that an analysis measure all health effects and changes in resource use caused by an intervention. VALUE OF SOCIETAL CEAs: Tensions unavoidably arise among the parties to medical decisions--patients, their families and friends, clinicians, and third-party payers. One common approach to handling these tensions is to ignore some of them, to "solve" them by pretending they do not or should not exist. Patients do this when they demand the best care for themselves without regard to the cost to others, payers when they make coverage decisions that shift costs ot others. But by estimating all gains and losses, calculations that reflect the safety, effectiveness, and side effects of an intervention as well as its costs, societal CEAs can help resolve those tensions and provide the basis for decisions that are fair to all parties, an agenda for negotiating such decisions, and information essential for designing compensation and incentives to support them. MAKING BETTER USE OF SOCIETAL CEAs: Use of the societal perspective asks that all parties be aware of and consider the interests of others. Some process or procedure needs to be developed for presenting CEA information to the parties most likely to be affected by decisions, soliciting their views, and negotiating an acceptable decision. This process could be used by government decision makers or by managed care organizations, professional societies, or payers.

A Bayesian approach to modelling the natural history of a chronic condition from observations with intervention.

To assess the costs and benefits of screening and treatment strategies, it is important to know what would have happened had there been no intervention. In today's ethical climate, however, it is almost impossible to observe this directly and therefore must be inferred from observations with intervention. In this paper, we illustrate a Bayesian approach to this situation when the observations are at separated and unequally spaced time points and the time of intervention is interval censored. We develop a discrete-time Markov model which combines a non-homogeneous Markov chain, used to model the natural progression, with mechanisms that describe the possibility of both treatment intervention and death. We apply this approach to a subpopulation of the Wisconsin Epidemiologic Study of Diabetic Retinopathy, a population-based cohort study to investigate prevalence, incidence, and progression of diabetic retinopathy. In addition, posterior predictive distributions are discussed as a prognostic tool to assist researchers in evaluating costs and benefits of treatment protocols. While we focus this approach on diabetic retinopathy cohort data, we believe this methodology can have wide application.

Treatment choice and quality of life in patients with choroidal melanoma.

OBJECTIVE: To determine if quality of life differs between patients with choroidal melanoma treated with enucleation and those treated with radiation therapy. MATERIALS AND METHODS: Patients treated for choroidal melanoma at 5 Midwest centers were asked to participate. There were 65 participants treated with enucleation and 82 treated with radiation therapy. Quality of life was assessed using the Medical Outcome Study Short Form 36 and the National Eye Institute Visual Function Questionnaire and by the Time-Tradeoff interview method. RESULTS: The average length of follow-up was 4.9 years for the group treated with radiation therapy and 6.3 years for the group treated with enucleation (P = .05). After adjusting for age, sex, years of follow-up, and the number of chronic conditions, there were few differences in any of the quality-of-life measures by treatment status. Participants in the group treated with radiation therapy were more likely to have higher (better) scores on the Vitality and Mental Component subscales of the Medical Outcome Study Short Form 36 than participants treated with enucleation. There were no differences on the National Eye Institute Visual Function Questionnaire or the Time-Tradeoff measures of quality of life. CONCLUSION: Choice of treatment for choroidal melanoma does not seem to be associated with large differences in quality of life in long-term follow-up.

Computing population-based estimates of health-adjusted life expectancy.

Observed health-adjusted life expectancy (HALE) is an indicator of population health. There are a number of ways to compute HALE for a community. The authors surveyed several methods and demonstrate resulting variation in the estimates of HALE. Quality of well-being (QWB) measures from 1,430 participants in the Beaver Dam Health Outcomes Study are taken as weights. Actuarial life-table methods using community mortality data, State of Wisconsin census data from two time frames, and U.S. census data are used with the QWB to estimate HALE. Measurement of community population health using HALE computations can be completed with national, regional, or local data. Community-level estimates may not be well approximated using large-scale mortality experience. A Bayesian method is developed combining the local data with regional data. The Bayesian method creates a smooth set of rates, retains the local flavor of the community, and gives a measure of variability of the estimated HALE.

Disease progression and cost of insulin dependent diabetes mellitus: development and application of a simulation model.

This paper presents the development and application of a Markov model that simulates the onset and progression of insulin dependent diabetes mellitus (IDDM) and its sequelae. The model estimates direct medical costs resulting from different patterns of health states during the course of the disease. The model is user-friendly and allows for changes in the input variables to be specified, thereby providing a frame-work for sensitivity analysis. The Markov process moves a cohort of individuals through six different health states: Healthy, IDDM without chronic microvascular complications, IDDM with retinopathy alone, IDDM with neuropathy alone or with retinopathy, IDDM with nephropathy, and death. Epidemiologic data were obtained from governmental sources as well as the medical literature. Transition probabilities were estimated using data from the Wisconsin Epidemiologic Study of Diabetic Retinopathy (WESDR). Direct medical costs were estimated from actual charges from a local health maintenance organization in Wisconsin. The validity of the model was tested in several ways including a comparison with an independent cost estimate made by the Wisconsin Department of Health and Family Services. The model appears to be useful in estimating the progression and associated costs of IDDM for any large population over any period of time and in allowing changes in the inputs to evaluate their impact thus providing pertinent information to healthcare decision-makers and health planners.

Toward consistency in cost-utility analyses: using national measures to create condition-specific values.

OBJECTIVES: The authors developed an "off-the-shelf" source of health-related quality of life (HRQL) scores for cost-effectiveness analysts unable to collect primary data. METHODS: The authors derived and conducted preliminary validation on a set of health-related quality of life scores for chronic conditions using nationally representative data from the National Health Interview Survey (NHIS) and the Healthy People 2000 Years of Healthy Life measure developed to monitor the health (longevity and health-related quality of life) of Americans during this decade. The measure comprises two domains, role function and self-rated health, and is scaled from 0 (death) to 1 (best health state). Health-related quality of life scores for chronic conditions were calculated using the Years of Healthy Life scores associated with chronic conditions reported in the 1987-1992 National Health Interview Survey. Preliminary validation was examined by comparing the health-related quality of life scores with those obtained in two other studies. RESULTS: Tables provide health-related quality of life scores for persons with and without conditions. The scores had reasonable face validity, ranging from 0.87 for allergic rhinitis to 0.27 for hemiplegia. Correlations of the health-related quality of life condition weight scores with those from two other studies were 0.78 and 0.86. CONCLUSIONS: These condition weights may prove useful to investigators conducting cost-effectiveness analyses using secondary data, where community ratings of health-related quality of life for chronic conditions are required. Use of a standard set of health-related quality of life weights gathered from a national sample can enhance the comparability of cost-effectiveness analyses. Improvements in national data collection techniques, with empirical gathering of preferences, will further strengthen this measure.

Development and application of a model to estimate the impact of type 1 diabetes on health-related quality of life.

OBJECTIVE: To develop a simulation model to assess the impact of type 1 diabetes and its associated complications on health-related quality of life of a population. RESEARCH DESIGN AND METHODS: The methodology builds upon 1) an existing population model of type 1 diabetes progression, 2) an empirical study designed to measure state- and age-specific health statuses of type 1 diabetes, and 3) existing literature to quantify quality of life of the corresponding health status. Health statuses were measured in a group of type 1 diabetic patients using the Medical Outcomes Study short form 36 (SF-36). A published empirical regression equation was then used to predict corresponding Quality of Well-Being Index (QWB) scores from these assessments. The QWB scores were incorporated into a previously developed type 1 diabetes progression and cost simulation model. Sensitivity analyses on key parameters were performed, and the model was found to be robust. RESULTS: The augmented model can estimate quality-adjusted life years (QALYs) as well as costs associated with type 1 diabetes on any population of interest over any period of time. The model is used to compare intensive versus conventional treatment strategies using a simplified set of assumptions regarding the relative effects of these alternative treatments. With these assumptions, intensive strategy produces more QALYs than does conventional strategy and is cost-beneficial after 5 years. CONCLUSIONS: The model enables health planners to perform cost-effectiveness analyses to compare alternative treatment strategies for type 1 diabetes and support subsequent decision making.

Sleep-disordered breathing and self-reported general health status in the Wisconsin Sleep Cohort Study.

OBJECTIVE: To determine the relationship between sleep-disordered breathing and self-reported general health status. breathing status assessed by overnight in-laboratory polysomnography. SETTING: General Community. SUBJECTS: Employed men (n=421) and women (n=316), ages 30-60 years, enrolled in the Wisconsin Sleep Cohort Study. INTERVENTIONS: None. OUTCOME MEASURE: Self-reported general health profile and life satisfaction measured by the Medical Outcomes Survey Short Form-36 and obtained by interview. RESULTS: Sleep-disordered breathing was associated with lower general health status before and after adjustment for age, sex, body mass index, smoking status, alcohol usage, and a history of cardiovascular conditions. Even mild sleep-disordered breathing (apnea-hypopnea index = 5) was associated with decrements in the Medical Outcomes Short Form 36 Survey health constructs comparable to the magnitude of decrements linked to other chronic conditions such as arthritis, angina, hypertension, diabetes, and back problems. CONCLUSIONS: Sleep-disordered breathing is independently related to lower general health status, and this relationship is of clinical significance. Given the growing emphasis of the importance of patients' perceptions of health, these findings are relevant to estimating the overall impact of sleep-disordered breathing.

MR and conventional angiography: work in progress toward assessing utility in radiology.

RATIONALE AND OBJECTIVES: The authors assessed health-related quality of life changes associated with peripheral x-ray angiography and magnetic resonance (MR) angiography. MATERIALS AND METHODS: Utility (the desirability or preference that individuals exhibit for a particular health state) was assessed in 30 patients with peripheral vascular disease referred for angiography by using a rating scale, additional categoric scaling questions to separate preference from experience, a willingness-to-pay technique, functional and cognitive status questions, and a time trade-off technique. All patients underwent both MR angiography and x-ray angiography. RESULTS: Patients reported significantly (P < .05) less anxiety after the test, less pain after the test, fewer new physical limitations, and less effect on performance of daily activities with MR angiography. Findings from the overall rating scale and categoric scaling questions also significantly (P < .05) favored MR angiography. Patients were willing to pay a mean of 2.12% of annual income to avoid MR angiography and a mean of 7.41% to avoid x-ray angiography. The median quality-adjusted life gain required by patients to undergo the procedures was 52.5-60 days for x-ray angiography and 10.5 days for MR angiography, without discounting. CONCLUSION: X-ray angiography has more profound short-term adverse effects on life than does MR angiography. Preference-based measures can be adapted to elicit patient values for short-term health states as seen in radiology.

Dollars may not buy as many QALYs as we think: a problem with defining quality-of-life adjustments.

The scale of health state quality that should be used to compute quality-adjusted life years (QALYs) ranges from 0 (death) to 1.0 (excellent health); this is called the "Q" scale. But many cost-utility analyses (CUAs) in the literature use the upper anchor of the scale to denote only the absence of the particular health condition under investigation, and weight the disease state proportional to this endpoint; these are called "q" scales. Computations using q-scale health-state weights ignore the fact that the average patient is still subject to chronic and acute conditions comorbid with the condition being analyzed; the absence of a particular condition is not in general the same as excellent health, i.e., the Q scale is longer than a q scale. CUAs based on q scales yield "qALYs." Incremental $/qALY ratios are generally lower than $/QALY ratios; in the example presented, $/qALY must be inflated by about 15% to yield $/QALY. Other CUAs correctly weight disease states using the Q scale, but erroneously assign a quality weight of 1.0 to absence of the disease in the CUA computations. The results of such analyses are called "NP-QALYs," as the correction factor to compute QALYs is not a simple proportional adjustment. The authors suggest that analysis doing cost-utility analyses without access to primary data from treated patients use average age-specific health-related quality-of-life weights from population-based studies to represent the state of not having a particular disease. Consumers of CUAs should closely examine the nature of the QALYs in any published analyses before making decisions based on their results.

Predicting Quality of Well-being scores from the SF-36: results from the Beaver Dam Health Outcomes Study.

BACKGROUND: The SF-36 and the Quality of Well-being index (QWB) both quantify health status, yet have very different methodologic etiologies. The authors sought to develop an empirical equation allowing prediction of the QWB from the SF-36. DATA: They used empirical observations of SF-36 profiles and QWB scores collected in interviews of 1,430 persons during the Beaver Dam Health Outcomes Study, a community-based population study of health status, and 57 persons from a renal dialysis clinic. METHOD: The eight scales of the SF-36, their squares, and all pairwise cross-products, were used as candidate variables in stepwise and best-subsets regressions to predict QWB scores using 1,356 interviews reported in a previous paper. The resulting equation was cross-validated on the remaining 74 cases and using the renal dialysis patients. RESULTS: A six-variable regression equation drawing on five of the SF-36 components predicted 56.9% of the observed QWB variance. The equation achieved an R2 of 49.5% on cross-validation using Beaver Dam participants and an R2 of 58.7% with the renal dialysis patients. An approximation for computing confidence intervals for predicted QWB mean scores is given. CONCLUSION: SF-36 data may be used to predict mean QWB scores for groups of patients, and thus may be useful to modelers who are secondary users of health status profile data. The equation may also be used to provide an overall health utility summary score to represent SF-36 profile data so long as the profiles are not severely limited by floor or ceiling effects of the SF-36 scales. The results of this study provide a quantitative link between two important measures of health status.

Preliminary evaluation of a sensory and psychomotor functional test battery for carpal tunnel syndrome: Part 1--Confirmed cases and normal subjects.

Two new computer-controlled functional tests were developed, known as the Wisconsin test battery, for carpal tunnel syndrome (CTS). The gap detection sensory test quantifies tactile thresholds for areas of the hand innervated by the median nerve. The rapid pinch and release psychomotor test measures the initiation and control of specific muscles innervated by the median nerve motor branch. Ten confirmed CTS patients (based on electrophysiological parameters and examination; 18 CTS hands) and eight confirmed normal subjects (16 hands) with a similar average age were administered both tests. The CTS patients showed significant functional deficits for both tactility and psychomotor tests. Average CTS performance was 24 to 104% poorer than for the normal subjects, depending on the performance measure. The results indicated high correlations (r = 0.5 to 0.8) between median nerve electrophysiological parameters and tactility or psychomotor performance variables. No single functional test variable had sufficient sensitivity for detecting CTS among the subject pool. The combination of the two tests using 95% confidence level cutoff points achieved a sensitivity of 0.78 and a specificity of 0.81. Stepwise discriminant analysis resulted in two performance variables capable of a sensitivity of 0.72 and a specificity of 0.94 for differentiating well-defined CTS subjects from normal subjects. Despite these promising results, limitations of the study include small sample size and subject selection bias. Further studies are needed for verifying the utility of the functional test battery for detecting CTS in a general population.

Health status and hypertension: a population-based study.

We describe the relation between self-reported hypertension and measures of health-related quality of life (HRQOL) in a community-dwelling population. In a cross-sectional study, 1430 randomly selected adults, aged 45 to 89 years, were interviewed to obtain a medical history and health status measures, including the SF-36 questionnaire, the Quality of Well Being (QWB) index, and time trade-off (TTO) assessments. A total of 519 participants reported being affected by hypertension (HTN group). The HTN group, compared to the No HTN group, had significantly lower age-adjusted health status scores measured by the General Health scale of the SF-36 and by TTO, with differences between groups for each measure comprising approximately 5% of the total scale. HTNs also had a significant decline in general health status measures associated with increasing numbers of antihypertensive medications but not with specific classes of medications. We conclude that hypertension and hypertension drug therapy are associated with clinically meaningful decreases in reported health status.