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Cost-benefit analysis (CBA) is a recognised as the economic evaluation technique that accords most with the underlying principles of standard welfare economic theory. However, due to problems associated with the technique, economists evaluating resources allocation decisions in health care have most often used cost-effective analysis (CEA), in which health benefits are expressed in non-monetary units. As a result, attempts have been made to build a welfare economic bridge between cost-benefit analysis (CBA) and cost-effectiveness analysis (CEA). In this paper, we develops these attempts and finds that, while assumptions can be made to facilitate a constant willingness-to-pay per unit of health outcome, these restrictions are highly unrealistic. We develop an impossibility theorem that shows it is not possible to link CBA and CEA if: (i) the axioms of expected utility theory hold; (ii) the quality-adjusted life-year (QALY) model is valid in a welfare economic sense; and (iii) illness affects the ability to enjoy consumption. We conclude that, within a welfare economic framework, it would be unwise to rely on a link between CBA and CEA in economic evaluations.

Welfare economists typically advocate the use of cost-benefit analysis (CBA) when evaluating public sector resource allocation decisions (see Mishan, 1988). Under CBA, the costs and benefits from any given programme are expressed in monetary units, and the sign of the net benefit across all affected individuals is used as the decision criterion. CBA aims to maximise aggregate welfare and is the only methodology that, at least in theory, provides information on the absolute benefit of different programmes. However, potential ethical and methodological problems in attaching a monetary value to non-market benefits (see Hausman, 1993) have led to the development of alternative methods for measuring benefits. In health economics, this has led to the development of cost-effectiveness analysis (CEA), in which health-related benefits are expressed in a single measure, such as gains in life years or quality-adjusted life-years (QALYs).1 Indeed, CEA has been used in most economic evaluations of health care interventions (see Elixhauser et al., 1993). In essence, CEA considers only health-related measures of benefit to be relevant. This has led Kenkel (1997) to conclude, “when we accept the methodology of welfare economics, we should use CBA, not CEA”. Nonetheless, this has not prevented economists from attempting to link CEA with CBA. Such a link would be appealing to many economists since the results from the ever-increasing number of CEAs could be interpreted within a standard welfare economic framework. Johannesson (1995) has argued that where CEA counts all societal costs and uses a cost-per-QALY threshold, it can be interpreted as a CBA since the threshold value can be used to translate the non-monetary benefits in CEA into monetary terms for CBA. To do this, there must be a constant Willingness-to-pay (WTP) per QALY. There have been two main attempts to set out the conditions under which this will hold. First, Johannesson and Meltzer (1998) have claimed that an article by Pratt and Zeckhauser (1996, hereafter PZ) “provides the strongest theoretical evidence to date” for the use of a constant WTP-per-QALY figure. PZ’s model uses a veil of ignorance based on perfectly comparable utility functions. Here, linking CBA and CEA requires that the benefit (in utility terms) from a given health improvement is constant across all individuals, so that maximising expected benefits behind the veil necessarily maximises aggregate health. Section 2 considers the prospects for a CBA–CEA link within PZ’s framework and shows that highly restrictive and counter-intuitive assumptions are required. Second, Bleichrodt and Quiggin (1999) show the conditions under which life-cycle preferences are consistent with QALY maximisation. By arguing that individuals will consume the same amount in each period, they set out the conditions under which all individuals weigh their own QALYs equally, and so form a basis for CEA in welfare theoretic terms. Section 3 discusses the results obtained by Bleichrodt and Quiggin (1999) and argues that they do not in fact link the analyses, even when the conditions they set down are met. In Section 4, we propose a general impossibility theorem for links between CBA and CEA and argue that, as things stand, the link must be based on unrealistic assumptions which either arbitrarily set key variables to be constant (as in Johannesson and Meltzer, 1998), or which rely on special cases that do not exist (as in Bleichrodt and Quiggin, 1999). The impossibility theorem shows the conditions that any link between CBA and CEA must satisfy under expected utility theory, and sets out the extremely stringent restrictions on the utility function that are required. Whilst we acknowledge a potential benefit of linking CBA and CEA, we conclude that it is impossible at present.

CEA is increasingly being used to evaluate resource allocation decisions in health care. Most forms of CEA involve the maximisation of an effect variable for a given budget, which typically involves funding all programmes with a cost-per-unit-outcome below a certain threshold level. Economists have considered the extent to which this form of analysis is compatible with a standard welfare economic framework and, in particular, with CBA. Under welfarist models, individuals are the best judges of their own welfare and individual WTP is taken to be the appropriate monetary valuation of any benefit. CBA sums WTP over all those affected and compares this figure to net costs, implementing only those programmes that increase net benefit (defined in monetary terms). CBA is seen as the welfarist ‘gold standard’, whilst CEA can be argued to lack a theoretical foundation (see Johannesson and Karlsson, 1997). Some economists have attempted to find conditions under which CBA and CEA produce identical results. Here, a constant cost-per-QALY value must be used (Johannesson, 1995). But this is problematic because the use of one societal WTP-per-QALY figure means that differences in individual valuations of a QALY have to be ignored. Simply overriding individual preferences will do this, but this does not sit easily with the welfarist tradition. Alternatively, conditions can be imposed on individual preferences and this is the approach favoured by many economists. We have considered two attempts to link CBA and CEA. The first, by Johannesson and Meltzer (1998), requires that incomes be held constant across individuals for WTP to be proportional to the QALY gain. In relaxing this assumption, we find that health must be additively separable to consumption in the utility function, since a relationship between health and income would influence the ability of an individual to enjoy consumption. However, this ‘link’ does not build a suitable bridge between CBA and CEA in the strict welfarist sense since individual judgements (about the trade-offs between health and income) are overruled in formulating a societal CBA. The second attempt to link CBA and CEA, by Bleichrodt and Quiggin (1999), differs in that individual WTP figures are used. Whilst they find conditions under which individuals would choose to maximise QALYs under a given cost-per-QALY threshold, this threshold will differ across individuals and, without a common threshold, their analysis is not consistent with a single implementation of CEA and so no substantive link exists here either. We have developed an impossibility theorem that shows that it is not possible to link CBA and CEA if: (i) the axioms of EU theory hold; (ii) the QALY model is valid in a welfare economic sense; and (iii) illness hinders the ability to enjoy consumption. Since (iii) is intuitive and (ii) is essential for CEA, the relaxation of (i) is the only real avenue open for a meaningful welfare economic link between CBA and CEA (at least where costs are assessed from a societal perspective). In showing that there is currently no meaningful link between CBA and CEA, we have also shown that CEA is not currently justifiable on strictly welfarist grounds. Instead, CEA would seem to be justifiable only on non-welfarist grounds where the output of health care is judged according to its contribution to health itself, rather than according to the extent to which it contributes to overall welfare (as determined by individual preferences). The normative justification for this focus on people’s objective needs rather than on their subjective demands owes much to Sen’s (1980) concept of ‘basic capabilities’. Culyer (1989) draws heavily on Sen when he argues that health is a crucial characteristic that is important for people’s capability to ‘flourish’ as human beings. It appears to us that CBA and CEA have such fundamentally different ethical underpinnings, that it would seem futile to further attempt to reconcile them within the welfare economic paradigm. Rather than attempting to find a bridge that is able to reconcile the central conflict between utility and health maximisation, attention should instead be focused on the debate about the appropriateness of CBA vis-à-vis CEA. One way forward might be to consider the extent to which people prefer health care to be distributed according to the principle ‘to each according to need’ rather than ‘to each according to willingness (and ability) to pay’ i.e. the extent to which, as citizens, they might be willing to override their preferences as consumers. Whatever the details, future research on the relative merits of CBA and CEA must also consider the relative merits of welfarist and non-welfarist philosophies in the context of allocation decisions in health care (see Brouwer and Koopmanschap, 2000).