Resource allocation in decision support frameworks

Methods to evaluate and allocate societal investments have evolved over time. Cost–benefit analysis grew from the work of French engineer-economist Jules Dupuit in 1844 [1], later formalized by economist Alfred Marshall [2]. The US government began the specific requirement of cost–benefit analyses for water navigation projects in 1936, further codified in the 1939 Flood Control Act, which embodied into law an operative investment decision rule: Invest when “the benefits to whomever they accrue [be] in excess of the estimated costs” [3]. This illuminates an important limitation of the cost–benefit analysis: it cannot consider the distribution of those benefits and costs, yet issues of distribution and equity are the center of many public policy debates.

Planners and analysts of health care have been reluctant to fully embrace the concept of cost–benefit analysis, since it requires an explicit statement by the analyst of the value of a human life or life-year. Over time, cost-effectiveness emerged as an appealing criterion, wherein the analyst can evaluate the incremental costs and health benefits of various medical interventions and then report their ratio. Decision makers then set the cutoff value for approval of investments.

The proof that this approach flowed directly from a single person’s lifetime utility maximization program came only in 1997 [4]. Until that point, the intuitive appeal of cost-effectiveness was all that supported its legitimacy. The use of cost-effectiveness significantly expanded during the latter part of the twentieth century, most notably within the British National Health Service which—through its National Institute for Health and Care Excellence—evaluates medical interventions using a cutoff value currently set around £30,000 per quality adjusted life-years (QALYs) [5]. The World Health Organization recommends the use of modified cost-effectiveness analysis to evaluate health care interventions: using disability-adjusted life years (DALYs), it recommends a cutoff value of one to three times per-capita gross domestic product to guide resource allocation [6].

Once a cutoff value for an acceptable investment has been made, cost-effectiveness analysis and cost–benefit analysis are virtually equivalent, with the difference being the choice for the value measure, be it lives, life-years, QALYs or DALYs [7]. That said, how does one establish the cost-effectiveness cut-off? A general discussion of this issue appears in the most recent cost-effectiveness “handbook” [8]. A complication arises when a health system announces one cost-effectiveness threshold (e.g., $100,000 per QALY) but establishes a budget that is insufficient to fund all technologies passing the established threshold. This creates an affordability conundrum.

This issue has recently even entered the British court system with a lawsuit over prescription drugs facing a conflict between cost-effectiveness thresholds and affordability [9]. If the budget is too tight to fund all approved technologies, then that implies a more stringent threshold in actual use. In all that follows, we intend to use the constraint that binds more tightly (typically the budget). Embedded in a tight budget the “shadow price” for QALYs—the price that really matters. So if the official cutoff is $100,000 per QALY and the budget only would fund activities with cost-effectiveness ratios of $80,000 per QALY, then we would intend that the $80,000 value be used.

Both cost–benefit and cost-effectiveness approaches share a common defect: they are narrow, and cannot include practical critical factors such as the distribution of benefits and costs, broader impact of societal programs, public values and perceptions, and related matters [10]. The importance of these distributional issues have been considered [8, 11–13]. One model measures the distribution of health benefits and costs across various population subgroups [14] but does not provide a mechanism to synthesize this information into a unified value measure.

More comprehensive decision support systems such as multi-criteria decision analysis can include these issues such as equity and social distribution directly and transparently [15–17]. Multi-criteria approaches have demonstrated their value, especially when decision makers have various—and often competing—priorities [18].

Multi-criteria models differ in an important way from standard economic analyses. Economists typically estimate the structure of people’s preferences from observed choices they make using the formal tools of utility maximization and demand theory. These “revealed preferences,” as economists call it, are inferred from actual choices. Multi-criteria decision analysis does something completely different: it elicits the preferences of the decision makers and the trade-offs that they are willing to make. Subsequently, most of these approaches use a simplified method for approximating the total value of any portfolio, often using linear approximation. These “attributes” might include considerations relating to finances, health gains, social justice, or patient preferences to avoid certain side effects of treatments some of which could (in theory) be included in formal cost-effectiveness models (with relevant data) but often are omitted for simplicity and practicality.

Multi-criteria analyses do come at a cost. In their current form, unlike cost–benefit and cost-effectiveness analyses, multi-criteria models do not explicitly guide resource allocation. No widely accepted rule exists for multi-attribute approaches that match the logical ease and spirit of “invest when the net benefits are positive” (as in cost–benefit analysis) or “approve the project if the cost per unit of health gained falls below some predetermined cutoff” (as in 1X to 3X per capita GDP for cost-effectiveness analysis). A recent task force of the International Society for Pharmaceutical and Outcomes Research (ISPOR) concluded that the best practices to support the use of multi-criteria decision analysis to consider budget constraints is “still unclear, and further research should focus on this topic” [19]. This paper seeks to contribute to that discussion.

As a starting point for discussion, resource allocation relates to how basic measurements are done. With a fixed budget, if all one desires is a prioritized rank order of investments, then ordinal scales (placing choices in the desired order) or interval scales (such as Fahrenheit and Celsius temperatures) suffice. Many forms of multi-criteria decision analysis produce interval scales. In this setting, investments are made until the fixed budget is exhausted.

A more refined approach might allocate a fixed investment budget across scalable investments by choosing how large or small each potential project might be to maximize the overall value of the investments. Assigning appropriate budget shares to each potential investment option requires that the multi-attribute model provide a ratio scale, not just an interval scale. Finally, if one wishes to have a clear decision about whether or not to invest—analogous to the outcome of cost–benefit analysis—then benefits and costs must be measured in the same monetary units (e.g., dollars, euros, yuan or rupees). Since multi-criteria models do not automatically convert benefit measures to monetary units, and often only determine ordinal priority ranks, they do not yet provide generalizable resource allocation rules.

In some settings, resource allocation does not enter the picture. For example, an individual health care patient choosing among insured treatment alternatives need not consider resource costs, but rather selects among the options provided by the patient’s health plan. But in most real decisions—such as insurance coverage decisions and health technology assessment—budget constraints invariably enter the picture. In our own recent work focused on systems analysis for prioritizing new vaccine research and development, the issue of choosing investments within a fixed budget—or determining the level of such a budget—was not a design factor [15, 20, 21]. But in some settings, more guidance about resource allocation is needed.

The recent ISPOR task force assessing multi-criteria decision analysis models discussed this challenge, summarizing previous work on the topic and offering three alternatives (none of which they deemed wholly satisfactory), and urged further research on the issue [19]. The approaches they identified from that literature survey included the following:

Our approach requires that any multi-criteria decision model contain a component of health benefits for which there is at least some agreement regarding a proper cutoff for cost-effectiveness analysis. Suppose that the health benefits measure (e.g., QALY or DALY) has a weight w, and all other attributes combined have a weight of (1 − w). If the agreed upon cost-effectiveness cutoff is to accept any intervention with cost per QALY (or DALY) ≤ K, then the proper cutoff in the multi-criteria model is K/w. K is the more binding of the announced cost-effectiveness threshold or the implicit and more stringent value from a tight budget.

Using QALYs (or DALYs) as a standard of value, we can scale the total willingness to pay for the aggregate benefit by using the fraction of the total benefit attributable to QALYs (or DALYs). Our proposal therefore leverages previous agreement about proper cost-per-QALY threshold into a new threshold for the newly defined portfolio of benefits. The value of QALY serves as the numeraire.

Returning to the affordability conundrum raised earlier, the notion that one should be willing to pay more for an item with greater value seems incontestable. However, if a fixed budget health care system suddenly introduces an expanded multi-criteria measure of value (and logically, a greater willingness to pay for that expanded concept of value) then the budget constraint will likely become more binding, and the gap between the stated willingness to pay and the shadow price in the budget can widen.

To see how this works, suppose that a health care system introduced a multi-criteria model with two attributes of value—QALYs gained and the extent to which disease burden of identified disadvantaged populations is equitably reduced. Some interventions that might not meet a population-wide cost-effectiveness criterion might now have higher priority. Tuberculosis prevention or treatment might provide a good example—low priority in a general population but high priority in a disadvantaged population. Using the new measure of value would increase the desire to fund (in our example) the tuberculosis-treatment program, hence further stressing the overall budget for the health care system.

To bring things into alignment logically one of three things must occur: (a) new resources must be added to the budget (b) some previously funded activities must be defunded, or (c) the threshold for accepting interventions must tighten (or some combination of these options). In using this approach in situations with a fixed budget (or until a budget can be adjusted to accommodate new items of value), it is important to use the appropriate threshold, which may well be more stringent than the announced threshold, and which will change even further as the extra value of non-QALY items is introduced into the analysis.

One can ask under what circumstances our simple extrapolation procedure remains valid beyond a simple linear utility model. As a starting point, the extrapolation of the value for QALYs to the entire multi-criteria model remains valid whenever the decision maker’s assumed utility function has constant budget shares (proportions of the total budget spent on a particular good). Cobb–Douglas utility models have this feature—the budget shares are constant over all incomes and prices. A more general set of utility functions—those with constant elasticity of substitution—assures that the method is globally correct while allowing incomes to change, but holding relative prices of QALYs and the other goods constant.

In more generalized utility structures, budget shares vary with changes in income and relative prices of goods. In such cases, the simple proportional extrapolation from the value of a QALY to the value of a more complex multi-criteria bundle will require adopting a specific functional form for the utility structure and then calculating the appropriate extrapolation method.

Multi-criteria models in general are meant to help structure problems for decision makers and to provide general guidance, not to provide precise measures of value. There is always a tradeoff between accuracy and simplicity, and most practitioners of multi-criteria decision analysis generally opt for simplicity when possible. Under what circumstances our extrapolation method remains valid can and should be a topic for further research.

Since much of the literature on choosing a cutoff for an acceptable cost per QALY has focused on its relationship to income, this suggests that our extrapolation method will be reasonably useful even if ignoring differences in relative prices for QALYs and other goods in the multi-criteria bundle.

We also note that even the standard model of cost-effectiveness analysis and the associated “acceptable technology” cutoff rules are not invariant to changes in economic conditions. The current debate about how to incorporate “affordability” into cost-effectiveness analysis highlights this issue. If a new technology emerges that has widespread use yet its cost-effectiveness ratio is “acceptable” by current norms, the situation can easily arise where the technology is both acceptable and unaffordable (with a fixed budget). If the underlying economic conditions change markedly (income, prices, or technological opportunities), then the original behavioral rules that emerge (e.g., a cost per QALY rule) must be revised. This is true both in a pure QALY-based model and in our more general model that incorporates both QALYs and other goods.

The basic idea of our approach is straightforward: If one knows the value of part of a package of valuable items, and one knows the proportion of overall value of the package attributable to that particular part of the package, then one can readily deduce the overall value of the package. In the realm of health, the most likely components to serve this purpose appear to be QALYs or DALYs. The benefit of using existing cutoff measures such as cost per QALYs is simply that a considerable literature exists on determination of those values. We note—referring to the obvious—that the difficulty in reaching agreement about the proper cost per QALY threshold suggests that reaching consensus about a cutoff for multi-attribute decision models may be even more difficult.