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Synthesis of "Statistical Innovations for Cost-Effectiveness Analysis"

Prepared by Melford J. Henderson, Program Official, CFACT, Agency for Healthcare Research & Quality

The Agency for Healthcare Research and Quality (AHRQ) continues to be a leader in advancing the use and science of cost-effectiveness analysis (CEA) in health care. AHRQ supports extramural research in CEA and advances the science of clinical economic evaluation. AHRQ has also acted as a facilitator for other agencies within the Federal Government to develop and use CEA for the enhancement of their goals and objectives. Since 1985, approximately 10 percent of extramural research grants have demonstrated explicit cost-effectiveness analysis.

During the period of 1997-2003, Dr. Joseph Gardiner, Ph.D., of Michigan State University College of Human Medicine, was awarded an original grant and continuation to study "Statistical Innovations for Cost-Effectiveness Analysis" (AHRQ Grant Number HS09514). The major goals of this study were to develop new statistical models and methods that fill methodological gaps, and resolve inconsistencies in current cost-effectiveness analysis.

Author's Introduction
Research on Cost-Effectiveness Analysis—Its Need, Direction, and Impact
Components of Cost-Effectiveness Analysis
Specific Research Design: Goals, Aims and Objectives
Methodology for Analysis of Health Care Costs and Outcomes
Analytic Background and Significance
Significant Analytic Research Results

Author's Introduction

The purpose of this document is to synthesize Dr. Gardiner's research developments related to Translating Research into Policy and Practice (TRIPP). As a result of developing and testing new methods and models for cost-effectiveness studies, and demonstrating their application in several ongoing clinical studies, this research not only offers an array of promising techniques, but also bridges the gap between methodological development and implementation.

I have omitted all statistical derivations such as equations and formulae in an effort to synthesize and highlight significant and relevant research findings, as well as applications related to TRIPP. I have also attempted to describe Dr. Gardiner's research in a way that will be useful to health services researchers across all disciplines, as well as other researchers in related fields throughout the world.

My major focus in the presentation of this document is to explicitly demonstrate how new statistical methods and models produced by Dr. Gardiner and his research team are revolutionizing the field of Cost Effectiveness Analysis.

The following are summaries of the experience of the research team:

Joseph C. Gardiner, Ph.D., is Director of the Division of Biostatistics in the Department of Epidemiology, Michigan State University, College of Human Medicine. He has been at the University since 1978 and is also Professor of Statistics & Probability in the College of Natural Science. Dr. Gardiner has collaborated extensively with epidemiologists, health services researchers, and clinicians at MSU and outside of the university. Dr. Gardiner has extensive publications in the peer-reviewed literature. He has served on the editorial boards of Medical Decisionmaking, Statistics & Decisions, and Communications in Statistics, and currently serves on the editorial boards of the American Heart Journal, and ASA-SIAM Series on Statistics and Applied Probability. In 2002, in recognition of his contributions to research, Michigan State University conferred on Dr. Gardiner the Distinguished Faculty Award.

Cathy J. Bradley, Ph.D., is Associate Professor of Medicine in the Department of Medicine, Division of Health Services Research, at Michigan State University College of Human Medicine. She was formally head of Proctor and Gamble Pharmaceutical's Clinical Economics Division where she conducted economic evaluation studies in 13 countries. Her research interests are in health economics and clinical decision analysis. She has experience in conducting clinical trials, cost-effectiveness studies, and cost-utility analysis ranging over several therapeutic areas including cancer, endocrine, cardiovascular, and infectious diseases. She has extensive publications in these areas as well as techniques advancing health care technology assessment. With support from the National Cancer Institute Dr. Bradley is currently investigating disparities by race and gender in cancer care, including costs and types of treatments offered to victims of cancer.

David Rovner, M.D., is founding member of the Society for Medical Decisionmaking. He is Professor Emeritus of Medicine and Endocrinology at MSU's College of Human Medicine, and past recipient of the Distinguished Faculty Award from MSU. His research over the past 20 years has focused on clinical decision analysis and cost-effectiveness analysis. Drs. Rovner and Gardiner have been closely involved in research collaborations since 1994, working on cost-effectiveness in heart disease, the cost-effectiveness of the implantable cardioverter defibrillator (ICD), methods for cost-effectiveness analyses, and analyses of hospital costs. Dr. Rovner is the principal resource person to the research team on all clinical issues.

Hossein Rahbar, Ph.D., is founding Director of the Data Coordinating Center (DCC), in the Institute for Healthcare Studies, and Professor of Epidemiology & Statistics. Dr. Rahbar's collaborative studies include studies of the role of EEG recordings to compare sub-groups of dyslexic children, transmission of hepatitis-C virus, breast-feeding practices, micro-nutrient deficiency and of maternal mortality in Pakistan. With support from the WHO, his study of the extent of environmental lead exposure in children in Karachi, Pakistan has received significant attention. Dr. Rahbar and the DCC are currently engaged in a multi-site study of autism and learning disabilities sponsored by the Centers for Disease Control & Prevention.

Zhehui Luo, Ph.D., is Research Associate in the Department of Epidemiology at Michigan State University. She has been associated with the research team of Drs Bradley and Gardiner since 1998. Her expertise is in econometric modeling, particularly in application to health care resource utilization and costs, and experience with dealing with large administrative data bases such as Medicare and Medicaid. Dr. Luo's research interests are in health care economics with a focus on mental health and obesity.

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Research on Cost-Effectiveness Analysis—Its Need, Direction, and Impact

Introduction

Rapid increases in health care costs continue to concern the public, federal and state agencies, and private industry. Publicly funded insurance programs such as Medicare and Medicaid are continually faced with difficult decisions in allocating health care dollars. Private industries are similarly challenged in providing health care benefits to their employees. Expenditure on health care accounts for nearly 15 percent of the U.S. gross national product.¹

Furthermore, current economic conditions have exacerbated the problem and led to higher health insurance premiums, reduced benefits in employer health plans, as well as an increase in the uninsured. Even the most optimistic projections for economic growth over the next decade suggest that the rate of growth in health care spending will rise well above that of the GDP.

The current cost consciousness in health care is documented in the enormous costs of some medical interventions, technologies, and pharmaceuticals relative to their perceived health benefits. The fastest growing segments of the health care dollar are pharmaceuticals and hospitalizations. The recent debate in Congress on the provision of prescription drug coverage to Medicare beneficiaries, the costs of drugs in Europe and Canada relative to the U.S., as well as efforts to reduce hospital stays, underscore the importance of increased health care spending. The need to contain health care costs forces us to consider which interventions produce the greatest value. CEA offers a structured approach for making economic evaluations of health care programs. It can be used for optimizing health benefits from a specified health care budget, or in finding the lowest cost strategy for a specified health effect.²

Faced with pressures to contain costs while optimizing value, policymakers world-wide have turned to evidence of cost-effectiveness in addition to evidence of health benefit in allocating resources for health care services. In Australia, the Pharmaceutical Benefits Advisory Committee makes recommendations, based on effectiveness and cost-effectiveness evidence, on drug products that should be subsidized and placed in the Pharmaceutical Benefits Scheme.³ In the United Kingdom, the National Institute of Clinical Excellence makes similar requirements for use of new healthcare technologies in the National Health Service, and in Ontario, Canada, the Drug Benefits Plan uses economic data when supporting new additions to its formulary.^4,5 Additionally, the U.S. Preventive Services Task Force and the Panel of Cost-Effectiveness in Health and Medicine have urged consideration of cost-effectiveness in addition to clinical effectiveness to help inform investment of health care dollars.^6,7

Improvement of health is an important objective of social policy. In welfare economics, output is judged according to the extent to which it contributes to overall welfare, as determined by individual preferences over health, relative to other considerations in utility functions.^2,8,9 The perspective of the welfarist calls for judging output of health care according to its contribution to health itself, and therefore requires careful assessment of health outcome as it affects an individual's well-being. By defining health as a state of "complete mental, physical, and social well-being and not merely the absence of disease," the World Health Organization in 1948 endorsed the broader perception of health as it is viewed today. ¹⁰

Need for Cost-effectiveness Analysis

Formal methods for assessing costs and outcomes of health care programs, as well as comparing costs with outcomes of competing interventions are needed to optimize health benefits from a specified budget, or to find the lowest cost strategy for a specified health effect. Appraisal of benefits produced by health interventions along with estimates of their total economic burden is vital to planning health care budgets. Decisionmaking based solely on the evidence of effectiveness and safety of therapies, without consideration of their costs, is not appropriate in an environment of limited resources and demands for their optimal allocation. Use of new therapies and treatments should, in addition to demonstrating clinical efficacy, include economic justification.

Several efforts have sought to standardize the conduct of CEA and strengthen its methodology. In the U.S., the Panel on Cost-Effectiveness in Health and Medicine issued a comprehensive set of guidelines to aid practitioners of CEA.⁷ Based on theoretical principles of welfare economics, the Panel urged adoption of a common set of standards for the conduct of CEA to ensure uniformity and permit comparisons across studies. Detailed information was provided on what constitutes costs of an intervention, how its health benefits should be measured and the role of discounting cost and benefits as they accrue over time. The core of this report was the recognition that both costs and benefits were stochastic in nature and thus summary measures such as the cost-effectiveness ratio would have inherent variability that should be quantified.

By quantifying the trade-offs between resources that need to be deployed and health benefits that accrue from use of alternative interventions, CEA offers guidance in decisionmaking by structuring comparisons between these interventions. A cost-identification analysis is often conducted for treatments and procedures that are believed to be equivalent in their clinical efficacy.¹¹ For example, if two competing programs do not differ in their health benefits, then the one with the lower average cost will be preferred. On the other hand, if the costs of two programs are judged equivalent, the intervention with the greater health benefit will be preferred. A dominant intervention is one that delivers higher benefit at lower cost than its competitor. When one program has both higher cost and greater benefit than its competitor a decision has to be made as to which of the two programs should be adopted. Therefore, a determination has to be made concerning the critical value below which society would consider the more costly intervention still "cost-effective."

In this situation, the cost-effectiveness ratio (CER) becomes a useful summary statistic for ranking competing interventions. Competing interventions are mutually exclusive, as for example, surgery or drug therapy in treating the same condition in the same population of patients. The CER is the ratio of the incremental cost relative to the incremental benefit. With costs measured in dollars and health benefits measured in their natural units such as life expectancy, number of lives saved, or quality-adjusted life years (QALYs), the CER is stated in dollars per unit of effectiveness.¹¹ In CEA conducted with a societal perspective that accounts for all costs of the interventions, whether borne by the recipient of care, the provider or the insurer, the critical value of a CER is the upper limit of what society is willing to pay for an additional unit of health benefit.¹²

In summary, CEA can be a powerful tool for decisionmaking. By structuring comparisons between interventions on their costs and benefits, CEA offers the decision maker objective means in obtaining the greatest health benefit from a specified health care budget.

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Components of Cost-Effectiveness Analysis

Measuring Costs

An important step in CEA is the identification of all relevant cost items followed by their measurement and estimation. The Panel on Cost-Effectiveness in Health and Medicine recommended that costs in economic evaluation studies consist of both direct and indirect costs.⁷ The direct medical costs of an intervention are those incurred in providing care, such as payments for drugs, medical/surgical supplies and professional services from nurses, physicians or other health care providers associated with intervention. These include the costs of treating side effects and complications resulting from the intervention. Direct non-medical costs include costs incurred because of the illness or the need to seek care such as caregiver costs, transportation and child-care expenses incurred by patients and their families. Indirect costs, also called productivity costs, represent costs not associated with the transactions for goods or services, such as morbidity that results in time lost from work, or the inability to participate in leisure activities.

Measuring Benefit

The next component of the CEA is the measurement of health benefit resulting from adoption of a specific treatment or intervention. Depending on the context one could use any clinically meaningful measure such as improvement in life expectancy, deaths averted, or number of toxic side effects prevented. Since the goal of any health care intervention is much broader than simply treating the disease condition or preventing death, the use of quality-adjusted life years (QALYs) in CEA has been advocated. A precursor to CEA was cost-benefit analysis which attempted to quantify in monetary terms the effect of the disease.⁷ Health care programs designed to prevent disease could be compared relative to their costs and benefits on the same scale. However, the difficulty of placing a monetary value on health outcomes has prevented its widespread adoption.

There is an important distinction with regard to relative benefit when comparisons are made between two interventions. In clinical studies of efficacy, the randomized controlled trial (RCT) is the accepted gold standard. Efficacy refers to whether a treatment can be successful in affecting outcome. A RCT is designed to test a hypothesis that a particular treatment, compared to another or a control, has a clinically and statistically significant effect on the outcome or illness being evaluated. Because RCTs are generally conducted under controlled conditions with highly selective patient groups, the estimate of the benefit may be larger than what could be expected in actual practice. The latter is referred to as effectiveness because it goes beyond the efficacy established through RCTs to a broader application in real-world settings where differences in patient comorbidities, compliance and follow-up would influence outcomes.^7,13

Quality-Adjusted Life Years

A quality-adjusted life year represents a patient's perception of the reduction in value of one year in perfect health due to pain, disability, and suffering caused by illness. It can be viewed as the proportional decrement in quality of life in the state of ill health, multiplied by years of expected life. Formally, for each unit of time spent in some health state, a quality weight is the relative value placed on that health state against the state of perfect health. Perfect health has a quality weight of 1, while death (or states judged equivalent to death), get a quality weight of 0. All other health states receive a quality weight between 0 and 1. Quality of life studies seek to measure the impact of health conditions on patients' functional status, including their physical, mental and social functioning, as well as their emotional well-being.^14,15

In CEA, use of the QALY to quantify health outcomes provides a common metric across different diseases. For example, the decision maker facing resource allocation can compare cost-effectiveness of coronary artery bypass surgery versus percutaneous coronary intervention, the cost-effectiveness of lipid lowering therapies for the prevention of cardiovascular disease, and the cost–effectiveness of different regimens of screening women for their susceptibility to breast cancer.

Cost-Effectiveness Ratio

The cost–effectiveness ratio (CER) is an important summary statistic for comparing the costs and effectiveness of competing interventions. The CER is the additional cost at which the new or alternative intervention delivers one unit of additional health benefit, relative to the standard intervention to which the new intervention is being compared. In cost-effectiveness studies, the CER is a useful statistical aid in decisionmaking processes and in the allocation of health care resources.

The cost-effectiveness ratio (CER) is computed as the ratio of the net difference in costs of two interventions relative to the net difference in their effectiveness.¹¹ Since the CER is assessed from inputs on cost and effectiveness that are subject to variation, sensitivity analyses are used to assess the extent of uncertainty in the CER. However, with patient-level data collected on costs and benefits in clinical trials, the CER may be viewed as a function of the parameters of the distribution of cost and effectiveness. Thus, given a probability model for sampling costs and health benefits, the CER can be estimated from available data and formal statistical inference can be applied to assess the variability in the estimated CER.

As a ratio the CER presents some difficulties in its statistical analysis. In addition, problems of interpretation arise with negative values of the ratio, and using the ratio alone can lead to very different conclusions.¹⁶ Several investigators have also cautioned using the CER when the incremental effectiveness is not statistically significant.^17,18 In order to overcome these difficulties another summary measure, the net health cost (NHC) or net health benefit (NHB) has been proposed.¹⁸ The NHC, denominated in monetary units, is the incremental cost minus the incremental benefit. The incremental benefit is converted into monetary units using the maximum value of the CER. The NHB is analogously defined in terms of effectiveness units.¹⁹

Stochastic Variation

A common aspect of cost and benefit measures is their stochastic nature. When measured at the level of the individual patient, cost and health outcome measures will vary across the population of patients. These outcomes will depend on demographic factors such as age, gender, ethnicity, socioeconomic variables such as income and education, lifestyle factors such as smoking, alcohol consumption, physical activity, and health conditions as well as comorbidities. Incorporating stochastic variation in outcomes and covariables involves notions of probabilities. This allows the analyst to express and quantify the degree of uncertainty in estimates of cost and benefit.^11,16

Another important feature of cost and benefit comes is that they accrue longitudinally. When an intervention is deployed costs are incurred through resource use over time.The basic framework that Gardiner, et al. have adopted recognizes that over the course of an intervention, a patient's event history unfolds as transitions between different health states and that sojourns in these states, as well as transitions between health states, are associated with costs. The ending state is usually death or some other terminal state which ends the evolution of the patient's event history. The discounted total cost of the intervention over a finite time horizon is then the net present value (NPV) of all expenditures incurred in transitions between health states, and during sojourn in health states.¹¹ Because costs incurred in the future are valued less than the present costs, all future costs are discounted at a fixed rate. As recommended by the Panel on Cost-Effectiveness, this time horizon must be sufficiently long to capture all costs of the intervention and the health benefits that accrue over time.⁷

The stochastic character of a health history is illustrated in the fact that transition times, the length of sojourn in a health state, the unit cost of sojourn and the cost incurred at transition times are all random. Given the underlying probabilistic mechanisms that govern transitions, such as a Markov process, an appropriate longitudinal model for the analysis of transition and sojourn costs, the NPV can be identified with an expected value. A formal process of statistical estimation can then be developed that would estimate NPV's for each intervention. This has been the focus of Gardiner's research. Moreover, because patient-specific factors such as age, gender, race, and clinical indicators such as comorbidity can influence both costs and health outcome, the stochastic models of Gardiner, et al. have the flexibility to incorporate these effects, and thereby estimate NPVs along specified patient profiles.

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Specific Research Design: Goals, Aims and Objectives

The research by Gardiner and colleagues develop and test new statistical procedures for cost-effectiveness analyses. Guided by an evolving literature on methods appropriate for CEA, introduction of guidelines for conducting and reporting economic analyses, and experience in CEA analyses, Gardiner and colleagues address the development of models that reflect the experience of patients in sustained and changing states of health.^20,21 Their analyses are based on a continuous-time Markov models (both nonhomogeneous and semi-Markov) that describe the evolution of patient histories following an intervention or treatment strategy. Measures widely used in cost-effectiveness analyses such as average-cost effectiveness ratio, or CE ratio, incremental cost-effectiveness ratio (CER), and net health benefit (NHB) are defined as parameters in the Markov model. Effectiveness measures include life expectancy, QALY, median survival time, and survival rates discounted where appropriate at a constant rate. Costs are viewed as the value of resources utilized, and consist of two components: 1) costs due to sojourn in health states, and 2) costs due to transition from one health state to another. Covariates that may influence cost and effectiveness measures are incorporated through semi-parametric regression models into the transition probabilities of the Markov models.²⁰

New statistical methods for estimation of summary measures commonly used in CEA are developed in Gardiner, et al.'s research. They exploit fully data arising from the longitudinal assessment of patients through different health states following an intervention, and quantify variability in estimated summary statistics and their dependence on covariate information from patients. For example, their methodology allows for construction of confidence intervals for CERs and statistical tests of hypothesis for given clinical values of CERs that governing bodies of affected communities may establish. Their goal is to provide a unified framework for statistical inference in CEA.

The specific aims of the study were:

To specify stochastic models for costs and health outcome measures. Longitudinal stochastic models were utilized that reflect the experience of patients in changing states of health. Costs are engendered in random amounts at random times during the course of a health intervention. By compiling these expenditures at the individual level into costs per unit time of sojourn in a health state, and in transition between health states, the researchers estimated the distribution of present value of all expenditures, and summary statistics such as mean and median costs. Using Markov models to describe the evolution of patient histories over time, they were able estimate health outcome measures such as life expectancy, median survival and survival rates, all discounted at a constant rate and adjusted for quality of life.
To assess statistically the impact of exogenous factors on outcomes. The researchers exploited the capability of the proposed models for incorporating concomitant covariate information and develop new procedures for assessing the effects of these exogenous variables on the joint distribution of health care costs and outcomes. Both fully parametric and semiparametric models were studied, including regression models for transformed endogenous variables and Cox regression and multiplicative intensity models that specify covariate effects in transition intensities. For CEA, the proposed methods yielded estimates of intervention effects adjusted for other variables that might have impact on measures of cost and effectiveness. The research team then formulated procedures for statistical inference on summary statistics used in CEA such as cost-effectiveness ratios, net benefit and net cost measures.
To test and validate statistical procedures. Simulation studies were used to assess the sensitivity of the inferential techniques to assumptions made in their specification. Robustness of model-derived estimates of regression parameters to different distributional assumptions on cost and health outcome measures has been assessed. Scenarios for these studies were taken from published cost-effectiveness studies that are often framed under a decision-theoretic model with numerous assumptions on the inputs of utilization and effectiveness. The performance of the competing procedures was studied for estimating cost-effectiveness ratios, net benefit and net cost measures in CEA.
To apply and test procedures on existing data sets. The investigators utilized The Michigan Inter-Institutional Collaborative heart (MICH) study, which is a prospective investigation of health care utilization and patient outcomes in admissions for acute myocardial infarction (AMI) to 5 mid-Michigan hospitals during the period January 1, 1994, through April 30, 1995. A second phase of the study was conducted in 1997 which examined similar outcomes after changes in medical management and treatment options for AMI were instituted in these hospitals. The primary objective of this study was to assess sources of variability by race and gender in the use of invasive cardiac procedures-cardiac catheterization (CATH), percutaneous transluminal coronary angioplasty (PTCA), and coronary artery bypass grafting (CABG), in the treatment of AMI. Analyses have been conducted to detect changes in long term-survival between patients in each phase.²² The same study was also used to analyze hospital charges and length of stay by cardiac procedures, accounting for variations in patient characteristics such as age, gender, race, comorbidities and ejection fraction.^23,24

Using data from previous published studies, the researchers also evaluated the effectiveness and cost-effectiveness of the implantable cardiac defibrillator (ICD). Estimates of life-expectancy of ICD patients have been compared with patients treated under electro-physiology guided therapy.^25-27

The researchers are collaborating with an international team of investigators assembled by the World Health Organization (WHO) in Geneva, Switzerland for a study of depression and substance abuse. They are applying their statistical methods and models in developing and testing primary care-based interventions to reduce the burden associated with depression and substance abuse in several countries across the world.

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Methodology for Analysis of Health Care Costs and Outcomes

Gardiner's research adopts a longitudinal framework which incorporates the dynamics of both costs and health outcomes as they manifest over time. Consider for example, patients undergoing a health care intervention for cancer. One could model the evolution of patient health history by an underlying stochastic process that describes the movement of the cancer patient through different health states. For example, the states of remission and relapse will engender different intensities of treatment dependent upon patient characteristics such as age, gender, and comorbidity. Costs will be incurred through resource use at transition times into states and while sojourning in health states. By combining these expenditure streams over time one can define net present value, a summary measure of cost.^20,21 In general the evolving health history of a patient is described by a finite state process with transitions taking place between various states, except the terminal state, death. The probabilistic mechanisms are those that govern sojourns in states (sojourn times) and transitions between states (transition intensities).

Although more general processes can be utilized, Markov processes have been the main choice in decision analyses and CEA.^20,28-31 Markov models provide a natural setting to describe the evolution of event histories of patients through different health states. The Markov property restricts the dependence of the future evolution of the process given the past, only to the most recent past. It is sufficiently flexible to permit modeling of both observable and unobservable patient-specific characteristics through the transition intensities, and assessing their impact on costs and outcomes.

Using this longitudinal framework, Gardiner, et al. describe stochastic models that reflect the experience of patients in sustained and changing states of health. Costs are engendered in random amounts at random points in time during the course of a health care intervention. By compiling these expenditure streams at the individual level into costs per unit time of sojourn in a health state, and in transition between health states, one can estimate the distribution of present values of all expenditures and summary statistics such as mean and median costs. One then estimates health outcome measures such as life expectancy, median survival and survival rates-all discounted where appropriate at a constant rate and adjusted for quality of life. For cost-effectiveness analyses, these methods yield estimates of intervention effects adjusted for covariates that might have impact on measures of cost and effectiveness and provide a basis for inference on cost-effectiveness ratios and net benefit measures.

In order to be useful in practice, data arising from cost measures and health outcomes must incorporate the dynamics of health care utilization as it manifests over time. There are several advantages of using a longitudinal model. Apart from its accurate description of an evolving patient history, it incorporates many of the critical elements that are needed to carry out cost-effectiveness analyses of interventions. For purposes of mathematical and statistical exposition, a Markov process is used to describe a patient's evolving history, with costs incurred in sustained and changing states of health. The Markov model provides a rigorous basis for quantifying variation in costs and health outcomes.

Another advantage of the approach of Gardiner, et al. is that it separates the time dynamics of transition between health states and costs as they become known over time. From a statistical point of view, this allows for modeling costs using modifications of regression methodology applied to longitudinal correlated data. This also permits analyses of differential covariate effects on costs and transitions between health states.

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Analytic Background and Significance

The Cost-Effectiveness Ratio in the Analysis of Health Care Programs

The cost-effectiveness ratio is a statistical parameter. It is estimated from data on costs and health outcomes that are subject to random variation. Thus, assessing the precision of a computed CER is an important aspect of cost-effectiveness analysis. An interval estimate for the CER or the standard error of its point estimate can be used to assess its precision. Several methods for constructing confidence intervals for the CER have been proposed.^{16,17,25,32-35}

Because the CER is a ratio of parameters, the distribution of its estimate might be skewed. Also one must account for the likely correlation between costs and effects in using the CER for inference. Existence of meaningful confidence intervals for the CER depends on the statistical significance of the difference in effectiveness.^17,36 By exploiting the relationship between confidence intervals and hypothesis tests, Gardiner, et al. describe formal test procedures for the CER.³⁷ They also address two related problems in the design of cost-effectiveness studies-the assessment of sample size and power.³⁸

The need for developing appropriate statistical methods was underscored in the report of the Panel on Cost-Effectiveness in Health and Medicine.⁷ It addressed several methodologically challenging areas, including valuing outcomes, defining the perspective of analyses, estimating components of the cost-effectiveness ratio, and meeting statistical rigor.

One of Gardiner's major objectives is to formulate problems of inference on the cost-effectiveness ratio in the traditional framework of statistical inference. When data on costs and effects are not available at the unit level but only known in aggregate from literature searches, expert opinion, and educated guesses, formal statistical inference on the cost-effectiveness ratio will not be possible because of the absence of a proper probabilistic framework for assessing random variation. Gardiner's work describes how under the guidance of an appropriate framework, uncertainty in estimated parameters can be assessed by their sampling error and conventional inferential techniques applied to problems of estimation, tests of hypotheses, and sample size and power determinations in planning economic evaluation studies of health care programs.

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