Optimizing a portfolio of health care programs in the presence of uncertainty and constrained resources

Much research has been devoted to handling uncertainty in cost-effectiveness analysis. The current literature suggests summarizing uncertainty in cost-effectiveness analysis using acceptability curves or net health benefits. These approaches, however, focus only on uncertainty associated with costs and effects of the programs under consideration. In the real world, most decision-makers have to fund a portfolio of health care programs. Therefore, a more comprehensive approach would include in the analysis the uncertainty of costs and effects of all programs supported by the fixed budget. This paper extends the decision rule described by Birch and Gafni (J. Health Econ. 11(3) (1992) 279) within the context of a portfolio of programs when costs and effects are uncertain and resources constrained.     

Revisiting the decision rule of cost-effectiveness analysis under certainty and uncertainty

The classical decision rule of cost-effectiveness analysis uses a threshold cost-effectiveness ratio as a cut-off point for resources allocation. One assumption of this decision rule is complete divisibility of health care programs. In this article, we argue that health care programs cannot be completely divisible since individuals are not divisible. Consequently, instead of a linear programming approach, an integer programming approach to budget allocation is suggested. The integer programming framework can be extended to include uncertainty in the analysis. An objective function (expected aggregate effects) is maximised subject to the constraint that the probability of exceeding the budget is limited to an arbitrary level (e.g., 0.05). In case the budget is exceeded, the objective function is penalised in order to account for the opportunity costs of the additional resource requirements.     

A Risk-Adjusted Approach to Comparing the Return on Investment in Health Care Programs

The league table approach to rank ordering health care programs according to the incremental cost-effectiveness ratio is a common method to guide policy makers in setting priorities for resource allocation. In the presence of uncertainty, however, ranking programs is complicated by the degree of variability associated with each program. Confidence intervals for cost-effectiveness ratios may be overlapping. Moreover, confidence intervals may include negative ratios and the interpretation of negative cost-effectiveness ratios is ambiguous. We suggest to rank mutually exclusive health care programs according to their rate of return which is defined as the net monetary benefit over the costs of the program. However, how does a program with a higher expected return but higher uncertainty compare to a program with a lower expected return but lower risk? In the present paper we propose a risk-adjusted measure to compare the return on investment in health care programs. Financing a health care program is treated as an investment in a risky asset. The risky asset is combined with a risk-free asset in order to construct a combined portfolio. The weights attributed to the risk-free and risky assets are chosen in such a manner that all programs under consideration exhibit the same degree of uncertainty. We can then compare the performance of the individual programs by constructing a risk-adjusted league table of expected returns.     

Risk management and health investments

A common feature of production models of health is that they neglect the importance of uncertainty in health investment decisions. I regard this as a deficit. Given the uncertainty of the effect of health investments, the question arises as to how an individual should allocate his scarce resources oftime and money to reach an efficient health behavior. To analyze this central question, the original portfolio theory is applied to health investment decisions. By aportfolio approach to health investments, actions of health care are characterized in terms of bundles of actions. In this way, one can make use of gains of diversification. Since the portfolio theory considers the correlation between the outcome of actions, it introduces new insights into the effect of health investments. This new approach to investments in health has not only consequences for individual health behavior but is important for health policy-making as well.     

Optimal allocation of resources over health care programmes: dealing with decreasing marginal utility and uncertainty

This paper addresses the problem of how to value health care programmes with different ratios of costs to effects, specifically when taking into account that these costs and effects are uncertain. First, the traditional framework of maximising health effects with a given health care budget is extended to a flexible budget using a value function over money and health effects. Second, uncertainty surrounding costs and effects is included in the model using expected utility. Other approaches to uncertainty that do not specify a utility function are discussed and it is argued that these also include implicit notions about risk attitude.     

Understanding the risks associated with resource allocation decisions in health: An illustration of the importance of portfolio theory

While a number of health economists have recently applied portfolio theory to the economic evaluation of health care, its importance for resource allocation and medical decision making has not been well illustrated. Portfolio theory is concerned with optimal investment strategies, based on both return and risk, and demonstrates the potential benefits from pooling different investments into a single portfolio. Portfolio theory differs from other methods that focus on risk in medicine as it focuses on the variance around the mean for a single aggregated health outcome measure. This paper demonstrates the importance of using a portfolio theory framework when evaluating a number of health interventions from the perspective of a representative individual and it expands upon the existing literature on portfolio theory in several ways. First, it highlights the importance of distinguishing between risk and uncertainty. Next, it demonstrates that portfolio theory has implications for all types of statistical analysis of multiple interventions in medicine and not only for issues of resource allocation. Through a number of included simulations, this paper also illustrates the importance of accounting for covariance (the relationship between risks) and synergies (the relationship between outcomes). Finally, possible applications and limitations to implementing portfolio theory in medical and resource decision making are discussed.     

Establishing the Cost-Effectiveness of New Pharmaceuticals under Conditions of Uncertainty—When Is There Sufficient Evidence?

Decisions about which health-care interventions represent adequate value to collectively funded health-care systems are as widespread as they are unavoidable. In the case of new pharmaceuticals, many countries now require formal cost-effectiveness analysis to inform this decision-making process. This requires evidence on parameters associated with health-related utilities, treatment effects, resource use, and costs, for which data from available regulatory trials are invariably absent or highly uncertain. This uncertainty results from a number of factors including the predominance of intermediate end points in the clinical evidence-base and the limited period of follow-up of patients in clinical studies. Despite these imperfections in the evidence base, decisions about whether new pharmaceuticals are sufficiently cost-effective for reimbursement cannot be side-stepped. Data limitations do, however, require the use of rigorous analytical methods to support decision making. Probabilistic decision models and value of information analysis offer a means of structuring decision problems, synthesizing all available data, characterizing the uncertainty in the decision, quantifying the cost of uncertainty, and establishing the expected value of perfect information. This analytical framework is important because it addresses two fundamental questions about new pharmaceuticals. First, is the product expected to be cost-effective on the basis of existing evidence? Second, is additional research concerning the product itself cost-effective? In addressing these questions, the analytical framework can establish when sufficient evidence exists to sustain a claim for a new pharmaceutical to be cost-effective.     

The option value of delay in health technology assessment.

Processes of health technology assessment (HTA) inform decisions under uncertainty about whether to invest in new technologies based on evidence of incremental effects, incremental cost, and incremental net benefit monetary (INMB). An option value to delaying such decisions to wait for further evidence is suggested in the usual case of interest, in which the prior distribution of INMB is positive but uncertain. METHODS: of estimating the option value of delaying decisions to invest have previously been developed when investments are irreversible with an uncertain payoff over time and information is assumed fixed. However, in HTA decision uncertainty relates to information (evidence) on the distribution of INMB. This article demonstrates that the option value of delaying decisions to allow collection of further evidence can be estimated as the expected value of sample of information (EVSI). For irreversible decisions, delay and trial (DT) is demonstrated to be preferred to adopt and no trial (AN) when the EVSI exceeds expected costs of information, including expected opportunity costs of not treating patients with the new therapy. For reversible decisions, adopt and trial (AT) becomes a potentially optimal strategy, but costs of reversal are shown to reduce the EVSI of this strategy due to both a lower probability of reversal being optimal and lower payoffs when reversal is optimal. Hence, decision makers are generally shown to face joint research and reimbursement decisions (AN, DT and AT), with the optimal choice dependent on costs of reversal as well as opportunity costs of delay and the distribution of prior INMB.     

An analysis of optimal resource allocation for prevention of infection with human immunodeficiency virus (HIV) in injection drug users and non-users.

Millions of dollars are spent annually to prevent infection with human immunodeficiency virus (HIV) without a thorough understanding of the most effective way to allocate these resources. The authors' objective was to determine the allocation of new resources among prevention programs targeted to a population of injection drug users (IDUs) and a population of non-injection drug users (non-IDUs) that would minimize the total number of incident cases of HIV infection over a given time horizon. They developed a dynamic model of HIV transmission in IDUs and non-IDUs and estimated the relationship between prevention program expenditures and reductions in HIV transmission. They evaluated three prevention programs: HIV testing with routine counseling, HIV testing with intensive counseling, and HIV testing and counseling linked to methadone maintenance programs. They modeled a low-risk IDU population (5% HIV prevalence) and a moderate-risk IDU population (10% HIV prevalence). For different available budgets, they determined the allocation of resources among the prevention programs and populations that would minimize the number of new cases of HIV infection over a five-year period, as well as the incremental value of additional prevention funds. The study framework provides a quantitative, systematic approach to funding programs to prevent HIV infection that accounts for HIV transmission dynamics, population size, and the costs and effectiveness of the interventions in reducing HIV transmission. The approach is general and can be used to evaluate a broader group of prevention programs and risk populations. This framework thus could enable policy makers and clinicians to identify a portfolio of programs that provide, collectively, the most benefit for a given budget.     

Allocating health care resources when people are risk averse with respect to life time

The criterion of cost-effectiveness in health management may be given a welfare-theoretical justification if people are risk neutral with respect to life years. With risk aversion, the optimal allocation of health expenditures changes: Compared to the cost-effective allocation, more resources should be allocated to health conditions for which the expected outcomes even after treatment are worse than average. The consequences of medical interventions are usually not known with certainty. Given this type of uncertainty, simple application of cost-effectiveness analysis would recommend maximization of expected health benefits given the health budget. We show that when people are risk averse with respect to the number of life years they live, the uncertainty associated with different types of interventions should play a role in allocating the health budget.     

Health burden and funding at the Centers for Disease Control and Prevention

BACKGROUND: The relationship between domestic funding for selected conditions to the Centers for Disease Control and Prevention (CDC) and the burden of disease and disability in the United States was assessed systematically. METHODS: Using mortality, years of potential life lost (YPLLs), disability-adjusted life years (DALYs), hospital days, hospital discharges, and direct medical costs of conditions, 34 high-burden conditions addressed by CDC programs were identified, and information was collected about the funds spent on each by CDC during fiscal year (FY) 2003. The 34 conditions were grouped into 15 categorical areas, and the relationship between budget and burden was analyzed using correlation and regression methods for each of the categorical areas and for each measure of burden. RESULTS: Of CDC's total FY 2003 budget of $6.9 billion, 62% ($4.3 billion) of funding was allocated to one of the 34 conditions studied. A positive relationship between budget and burden was identified for all measures of burden, although the correlations varied for the different conditions. CONCLUSIONS: Although examination of the relationship of CDC's budget to burden measures provides insight into the agency's portfolio of investments, this exercise also highlights a number of limitations with this approach and the currently available burden measures. Assessment of key public health functions such as emergency preparedness and the collection of vital statistics require development of metrics different from the burden measures used in this analysis. Investment in the development of such metrics warrants consideration.     

Paying the piper: investing in infrastructure for patient safety

BACKGROUND: Although the best allocation of resources is unknown, there is general agreement that improvements in safety require an organization-level safety culture, in which leadership humbly acknowledges safety shortcomings and allocates resources at the patient care and unit levels to identify and mitigate risks. Since 2001, the Johns Hopkins Hospital has increased its investment in human capital at the patient care, unit/team, and organization levels to improve patient safety. PATIENT CARE LEVEL: An inadequate infrastructure, both technical and human, has prompted health care organizations to rely on nurses to help implement new safety programs and to enforce new policies because hospital leaders often have limited ability to disseminate or enforce such changes with the medical staff. UNIT OR TEAM LEVEL: At the team or nursing unit level, there is little or no infrastructure to develop, implement, and monitor safety projects. There is limited unit-level support for safety projects, and the resources that are allocated come from overtaxed department budgets. ORGANIZATION LEVEL: HOSPITAL LEVEL AND HEALTH SYSTEM: Infrastructure is needed to design, implement, and evaluate the following domains of work-measuring progress in patient safety, translating evidence into practice, identifying and mitigating hazards, improving culture and communication, and identifying an infrastructure in the organization for patient safety efforts. REFLECTIONS: Fulfilling a commitment to safe and high-quality care will not be possible without significant investment in patient safety infrastructure. Health care organizations will need to determine the cost-benefit ratio of various investments in patient safety. Yet, predicating safety efforts on the mistaken belief in a short-term return on investments will stall patient safety efforts.     

The increasing burden of injuries in Eastern Europe and Eurasia: making the case for safety investments

Injuries are one of the leading causes of death and disability in Europe. Within Europe, death rates due to injuries are 60% higher in Eastern compared to Western Europe. This is especially due to unintentional injuries such as road traffic injuries, which is the 2nd leading cause of death in those 5-29 years. The cost of injuries is estimated at 1-2% of GNP. Compared to the burden, the number and types of programs are limited in the Eastern European region. However, the literature reveals the existence of cost-effective interventions for regional and national policy consideration. This is a need to appreciate this problem and promote investments to prevent the high economic and societal costs due to injuries. Results from selected injury prevention programs have shown considerable success and these, if effectively adopted in this region, will make a significant difference in reducing the heavy toll of injuries on lives of people. This paper calls on aid donor agencies and governments to plan and implement injury prevention programs as part of their portfolio of investments, in the Eastern European region.     

Resolving the “Cost-Effective but Unaffordable” Paradox: Estimating the Health Opportunity Costs of Nonmarginal Budget Impacts

Considering whether or not a proposed investment (an intervention, technology, or program of care) is affordable is really asking whether the benefits it offers are greater than its opportunity cost. To say that an investment is cost-effective but not affordable must mean that the (implicit or explicit) “threshold” used to judge cost-effectiveness does not reflect the scale and value of the opportunity costs. Existing empirical estimates of health opportunity costs are based on cross-sectional variation in expenditure and mortality outcomes by program budget categories (PBCs) and do not reflect the likely effect of nonmarginal budget impacts on health opportunity costs.The UK Department of Health regularly updates the needs-based target allocation of resources to local areas of the National Health Service (NHS), creating two subgroups of local areas (those under target allocation and those over). These data provide the opportunity to explore how the effects of changes in health care expenditure differ with available resources. We use 2008–2009 data to evaluate two econometric approaches to estimation and explore a range of criteria for accepting subgroup specific effects for differences in expenditure and outcome elasticities across the 23 PBCs.Our results indicate that health opportunity costs arising from an investment imposing net increases in expenditure are underestimated unless account is taken of likely nonmarginal effects. They also indicate the benefits (reduced health opportunity costs or increased value-based price of a technology) of being able to “smooth” these nonmarginal budget impacts by health care systems borrowing against future budgets or from manufacturers offering “mortgage” type arrangements.     

Economic considerations in technology assessment: the case of genetic disease.

This paper describes economic issues pertinent to health care technology assessment. Of interest are the allocation of resources between health and other sectors of the economy, between alternative services within the health sectors, and the costs of producing the services that are selected. These issues are discussed and then illustrated by reference to a specific area of health care technology: screening for and intervention against genetic diseases. It is concluded that investments in screening programs for Tay Sachs disease and Down Syndrome are allocatively efficient. Indications are that such investments are also efficient for interventions against Neural Tube Defects; however, there are complex ethical issues involved. There are many genetic diseases for which screening tests have yet to be developed. As such tests become available, each will have to be evaluated on its own merits relative to alternative health sector investments.     

Financial consequences of changes in health care demands related to tobacco consumption in Mexico: information for policy makers

This paper presents the results from a longitudinal study in which the main purpose was to determine the health-care costs and financial consequences of changes in the health care demands related to tobacco consumption in Mexico. Eleven health interventions were selected to conduct this study and four probabilistic models were developed to forecast the expected changes in the epidemiologic profile of selected diseases. The costing method was based on the identification of case management costs using the instrumentation and consensus techniques, probabilistic models were designed using the Box-Jenkins technique and allowed us to identify the expected case trends for the 2001-2003 period. The generation of information on case management costs for the selected interventions is a central instrument in the planning of health programs, above all in that which refers to resource allocation by type of demand. On the other hand, the identification of expected cases and the financial consequences allowed us to know the growing trends of the sums required to satisfy health care demands for the period under study. The three types of information are a relevant resource for decision-makers in the production and financing of health services.     

Fate of Medicaid remains uncertain as showdown nears

A Republican plan to renovate the Medicaid program has been proposed in Congress as one component of an overall budget reconciliation act. President Bill Clinton is expected to veto this proposal. The Republicans combined the budget reconciliation with an increase in the Federal debt ceiling. A showdown between Congress and the President is expected by November 6, 1995. If no agreement is reached at that time, the U.S. Government will shut down or default on financial obligations. AIDS activists and health care providers are striving to ensure that the Congressional Medicaid proposal does not pass, as it would devastate health care protection for the indigent, the elderly, and many AIDS patients. Medicaid is the single largest federally-funded health care program for people with AIDS, with over forty percent of people with AIDS relying on Medicaid for their health insurance. Under the Republican plan, Federal funding for State-run Medicaid programs would be at least nineteen percent lower than the amount necessary to cover medical costs; the shortfall ranges from thirty percent in Washington to two percent in Kansas. States would be able to choose the number of beneficiaries that would be covered, the types of services offered, and the source of health care providers. The President's counter-proposal would eliminate projected spending through increased use of managed choice health-care. His plan retains Medicaid as a means-tested entitlement program.     

An investment appraisal approach to clinical trial design

In this paper, a general investment appraisal model is presented which shows how pharmaceutical companies could take profit considerations into account when making decisions about the design of randomized controlled trials. A general model is presented based on the net present value method of investment appraisal. The approach is illustrated with a hypothetical example which shows how optimal (net present value maximizing) designs can be determined based on choices about sample size and endpoint measurement. The method could be extended to accommodate considerations about other trial design features, and could be used to determine a portfolio of studies which maximizes the expected return on a given development or trial budget. Furthermore, the approach could be used by pharmaceutical companies to evaluate the incremental costs and benefits of incorporating non-clinical objectives into trials, such as quality of life research and economic evaluation studies. A number of practical difficulties would need to be overcome to utilize the approach. Directions for further research are therefore highlighted centred on the key components of the model: a trial cost function, a product demand function, innovation diffusion processes and Bayesian approaches to trial design. © 1998 John Wiley & Sons, Ltd.     

The analysis and assessment of health programs

There is a vast gap between methodology and practice in the analysis and assessment of health programs. This presents an acute problem in developing countries where resource allocation decisions at the tight budgetary margin have important practical consequences. The prospects for improving this primitive situation depend critically on progress in analysis of the affordability and effectiveness of health programs. The analysis of affordability--especially on the recurrent cost side--is a necessary condition which can help ensure that proposed programs are unlikely to be vulnerable to implementation delays or underfinancing of operating costs which may seriously compromise the benefits expected from new investments. Improved analysis of effectiveness is also essential in order to help planners choose the best pattern of resource use from among the various combinations of programs that are affordable. To do this will require the devotion of substantial analytical effort to fill the great void of organized empirical knowledge available to those seeking to assess the effectiveness of health interventions. In particular there must be a shift in focus from single interventions directed at communicable diseases in children to a broader concern with multi-purpose interventions, including those directed against the emerging problems of non-communicable disease in adults.     

Bridging the gap between health and non-health investments: moving from cost-effectiveness analysis to a return on investment approach across sectors of economy

When choosing from a menu of treatment alternatives, the optimal treatment depends on the objective function and the assumptions of the model. The classical decision rule of cost-effectiveness analysis may be formulated via two different objective functions: (i) maximising health outcomes subject to the budget constraint or (ii) maximising the net benefit of the intervention with the budget being determined ex post. We suggest a more general objective function of (iii) maximising return on investment from available resources with consideration of health and non-health investments. The return on investment approach allows to adjust the analysis for the benefits forgone by alternative non-health investments from a societal or subsocietal perspective. We show that in the presence of positive returns on non-health investments the decision-maker’s willingness to pay per unit of effect for a treatment program needs to be higher than its incremental cost-effectiveness ratio to be considered cost-effective.