Economics, health and health economics: HYEs versus QALYs

Journal of Health Economics 11 (1993) 325-339. North-Holland

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miram Gafni and Stephen Birch

Centre for Health Economics and Policy Analysis, Department oj Clinical Epidemiobgy and Biostatistics, McMaster Universitv, Hamilton. Ontario, Canada

Abraham Mehrez

Department of brdustria! %gi?reering r-4 !!n~agement and Ben Curion University of the Negev, Beer Sheva, krael

Final version received May 1993

This paper responds to Culyer and Wagstaff’s (CW) and Buckingham’s (B) arguments. We refute their claim about the equivaience of HYEs and QALYs; they fail to distinguish between choice under uncertainty and under certainty CW assume that alI individuals have a specific form of utility function, which yields their conclusion of equivalence. B’s arguments confuse the measurenxnt techniq _ 21 and the utility theory from which it stems; his argument about the normative superiority of iii,: QALY cot’rr*rs~! I; ;trLousistent with economic thinking. The HYE, by being compatible with the principles of economics, is superior to the QALY for economic evaluations of health care interventions.

1. Introduction

The healthy-years-equivalent (HYE) was suggested by Mehrez and Gafni (1989) as an alternative to the most commonly-used measure of preference, the quality-adjusted life-year (QALY). The construct of the HYE is superioe to that of the QALY because it avoids many of the assumptions about an invididual’s utility function Cat underlie the utility-based version of the QALY model. These assumptions are acknowledged to be very strong even by proponents of the QALY mtidel (e.g., lV!lyam~tr, and Eraker, P985; T~;‘ance ;;id Teeny, 1989) and are ;rlot supp~ricd by published empirical evidence (e.g., Loomes and McKenzie, 19SSj. The FRYE approach makes no assumptions about the form of the individual’s utility function and thus better reflects the individual’s preferences. A simple two-stage lotterv pro- cedure is suggested to measure YES for an expected utiiity maximizer (Mehrez and Gafni, 1991).

Correspondence to: Amiram Gafni, Ph D., Departrrleq! Q f CE.&B. (HSC-3H29), McMaster University, 1200 Main Street West, Hamilton, CIxario, Canada, L8N 325.

0167_6296/93/$06_CJO @I ! 993--Eisevier Science 5)erbiSsl;ers B-j’_ Aii rights reserved

326 A. Gafni et al., Economics, h&&h and health economics

Two papers published in this issue challenge the HYE approach. Culyer and Wagstaff (1993) (CW) argue that the HYE is concc*ptually identical to the Q,\LY derived from a time-trade-off experiment alId that the utility function underlying the HYE is therefore as restrictive as that underlying the time-trade-off (TTO) hased QALYs. They also argue that none of the examples described by Gafni and colleagues to demonstrate the potential of QALYs to misrepresent preferences is valid. Buckingham (1993) (B) argues similarly for equivalence between the two-stage lottery procedure to measure HYE and the TTO procedure. He argues further that from a normative perspective, the QALY is superior to the HYE.

f i this paper we refute the claim about the eq\l%alence of the two

measurement methods - a claim which fzils to distingbl;.-h between choice problems under uncertainty and under certainty. We also show that @W’s arguments assume that all individuals have a specific form of utility function, in par;teu!ai the spew&;_\, ,X- form underlying the utility-based QALY model. It is not surprising that their ‘analysjc. leads therefore to a conclusion of equivalence. This assumption, in ixt, drives ~ii the conclusions in the CW paper (including those related to the examples provided by Gafni and colleagues). Similarly the arguments presented by B a*e based on confusion between the measurement technique and the utilitv theory from which it stems. We also show that B’s arl;ument about the iorm.ative superiority of the QALY clr,a?rtrwct is inconsister:: with economic thinking. Finally, we show that the HYE, by being compatible with the principles of e;;onGinics, offers a superior meas?rre to the QALY for use in economic evaluations of health care interventions, when applied to the problem of resource allocation.

2. HYEs and ITO-based QAEYs: Measuring versus assuming preferences

The TTO technique was proposed by Torrance et al. (1972) as an elnpirical substitute to the standard gamble (SG) technique that would offer a simpler measurement approach but (hopefully) would provide the same (or similar) resuiss as the SG technique. Unlike the SG, which is based direc’,ly on the fundamentai axioms of expected utility theory (von Neumann and Morgenstern, 1944), the TTO was not related to any behavioral theory by its proponents. But without such a theoretical basis we are unable to interpret or understand what the technique measures, and why empirical studies report large discrepancies in the ratings obtained by the two methods (e.g., Read et al., 1984; Hornberger et al., 1992).

Following Mehrez and Gafni (1990, 199Jj5 both the two-ctagz le#ttery used to measure HYE and the singie-stage direct comparison used to measure ahe TTO are aimed at identifying two points on an individual’s indifference curve. The difference between the two methods is that the TTO deals with indiKerence curves under certainty (i.e., isovalue curves) but the two-stage

lottery is c” clncerned with indifference curves zrrrdev zrncevtplin~y (i.e., i~~~t~~it~ curves).

Following von Neumann and Morgenstern (vN ), different points OR an individual’s isoutility curve are identified usin lottery questions (e.g., Marless, 1992). For a chronic health state (i.e., a given level of health, Q, for a given time, T) for example, the first stage uses a SG question to identify the utility level of the chronic health state profile and hence all other health profiles (i.e., level-time combination) on the same isoutility curve (i.e., p the indifference probability in the first SG question). In stage 2, knowing the utility level of the curve, the second SG question is used to identify a second point on this isoutility curve - a combination of number of years (H*) in full health (Q*). It follows that because U(Q, 7’) =p* and U(Q*, H*) =p* then

U(Q, T) = U(Q", H”) (1)

H* is the healthy-years-equivalent of (T,Q , i.e., a potential combination of years in full health (Q*) :vhc&z k Py level is equal to another potential health profile of living T years in health state Q.

The TTO tecyrnique, on the other hand, involves a paired compariscn under certainty. As noted by Torrance et al. (1982) ‘Since lotteries are not used in the time-trad+off procedure, the results do not incorporate the subject’s attitude towara uncertainty’ (p. 1052) and hepee the TTO procedure ‘. . . is not derived from the vNM utility model’ (Feeny and Torrance, 1989, p. Sl94). In the TTO the comparison is between being in a chronic health state, i.e., level Q for T years with certainty, and being in full health, Q*, for X years with certainty. Period of time X is varied until the subjd is indilirerent between the two alternatives (i.e., following Mehrez and Gafni (1990) both aye on the same isovalue curve). Denote the number of years in full health at the indifference point as X *. Following Mehrez and 5afni (1990) this means that

V(Q, 7’7 = V(Q", X*1, (2)

where V(a) is a utility finnction ul>der certainty or the value function. Both CW and B argue that H * derived using the two-stage lottery

technique is identical to X * derived using the TTO approach. But this requires that the isoutil!ty curve anderlyin, * the HYE approach is identical to the isovaiue WKW underiving the TTO approach. Both t._. and B base their argument for the equivai:nce of H* and X* on the ansitivity axiom. Although the transitivity axiom undt;ili;~ both approaches, this does not mean that the scores derived from the two distinct methods are the same. Indeed the relationship between these two functions (i.e., utility and value) is complex (e.g., Dyer and Sarin, 1979, 1982) - as ‘red herrings’ go (C p. 5) this claim of equivalence is deepest red.

328 A. GaJni et al., Economics, health and health economics

The following example illustrates our point. Consider the case of an individual with the prospect of living 15 years with chronic renal failure followed by death. Usin,, 0 the 13’0 tei-hnique, suppose we find that the individual is indifferent be~;veerl living 11 years in full health and 15 years with chronic renal failure (i.e., a healthy-years-equivalent under certainty of x* = 11). NOW calculate the healthy-years-equivalent score under uncertainty. Using the two-stage lottery technique suppose we find in srage 1 that the utility of living 15 years with chronic renal kilure is equal to say 0.7 (i.e., p* =OJ). In stage 2 we find that the utility of Living 8 years in full health is also equal to 0.7. Because both points are on the same isoutility curve the healthy-years-equivalent under uncertainty (H*) is equal to 8 years. Note that using the two procedures in this hypothetical example we arrive at two different values (i.e., X* = 11, H* = 8).

$ argues that this type of example cannot occur. More specifically he argues that although ‘... the WE does frame some of its questions in terms of a gamble, the gamble is introduced at one stage, only to be dismissed at the final stage’ (p* 10). In other words, B agrees that the response to the SG questions at each stage will be sensitive to the individual’s risk attitude however he clairtjs that the two lotteries cancel each other out. For this to happen the effects o’ the two lotteries has to be, for example, equal and opposite, neither cf vsru~lc% is supported by either theoretical or empirical proof.

Both CW and B fail to recognize that different preference theories are based on different (but not necessarily mutually exclusive) fundamental axioms. But the chosen theory determines the appropriate methods for measurement as well as the interpretation of the results. Because medical interventiorjs occur under conditions of uncertainty both at the individual and group level (Ben Zion and Gafni, !983), a theory which captures individuals’ preferences under uncertainty is called for. The vNM utility theory (or expected utility theory) has been advocated widely as the ‘gold standard’ for decision making under uncertainty both at the individual (e.g., Pauker and Kassirer, 1987) and group (e.g., Torrance, 8886) level and ‘. . . onig: the standard gamble method directly measures vNM utilities. The other instruments at best can be viewed as approximations’ (Torrance and Fecny, 1989, pa 566). Mehrez and Gafni (1991) use the SG approach for the measurement procedure for HYE. Both CW and B imply that the two-stage iottery used to measure HYEs is a general procedure that always holds, thus confusing again the measurement algorithm and the utility theory that it stems from. Mehrez and Gafni (1991) explain that the suggested measure- ment pmedure is valid only under the assumptions of VNM utility theory. If one wants to use another theory e.g., Alpha-Nu choice theory, Anticipated utility, Lottery dependent utility (see Karnie and Schmeidler, 1991) the procedure described by Mehrez and Gafni (1991) is not u&d, but that does

not invalidate the HYE construct, merely the method currently proposed for its measurement.

I$ one accepts VlVvl utility as the ‘gold standard’, preferences for health tiut~~~s FYIUS~ be measured in a way which is consistent with this theory, i.e., using lottery-based questions (Farquhar, 1984). B misses this important point arguing that <he Z.. roat: or the standard gamble question is just to introduce misunderstanding and error’ (p. lo), and that ‘. . . even if we were quantifying the uncertain health states that exist in the real world, the argument that the standard gamble is the appropriate valuation method is rather like insisting that the appropriate way of expressing the value of copper is in terms of gold, because they are both metals. We do not need to express the value of risky prospects in terms of risk’ (p. t 1) emy>&s added). But B does not explain how vNM utilities can be measured without using lottery-based questions.

CW argue that the TTO approach is based on an implicit assumption about the functional form of the individual’s utility function (equation (1) in CW). This functional form is also the basis of the QALY model (as suggested by Pliskin et al., 1980). This functional form assumes that life-years (7’) and quality of life (Q) are mutually utility independent. Hence ranking of gambles over one of the two attributes (r Q) is independent of the other attribute. It also assumes the proportion of remaining life that one is willing to trade-off for a specified quality improvement is independent of the amount of remaining life (i.e., constant proportional trade-oflj. Finally it assumes risk neutrality with respect to survival duration in all healthy states, i.e., the utility function for life-years is linear. As already mentioned, these assumptions are acknowledged to be very strong, even by proponents of the QALY model (e.g., Pliskin et al., 1980; Miyamoto and Eraker, 1985; Torrance and Feeny, 1989) and were found to be invalid by existing empirical evidence (Loomes and McKenzie, 1989).

These assumptions are necessary and sufIicient to equate the utility- weighted QALY index with utility only for the case of a permanent chronic health state (i.e.p being in the :;ame health state for the rest of their life). Mehrez and Gafni (1991) show that ddi-ihd assumptions are needed for the more general case of a hfcti,mu health profile i.e., ali in&ividual who might experience several differehst health states during his or her remaining life, In this case the QALY index assunes that thz utility fun&on of the individual over his or her lifetime health profile is additive. But intertemporal additivity has neither conceptual, empirical nor even normative support. There are many situations (health included) in which consumption in one point in time influences the marginal utility of consumption at another (Loewenstein and Prelec, 1991). In the context of health \ care evaluations Ha3 et al. (1992)

found that prognosis (i.e., future health state) affected the value 3.ttached to a current health state.

330 A. Gafni et al., Economtcs, health and health eL*onomics

Nevertheless CW show that under all of these assumptions ‘. . . the number of QALYs and the number of HYEs are equal to one another’ (p. 2). But this does not undermine the HYE because the purpose of the HYE development was precisely to relax the assumptions CW require to establish equivalence. Moreover, unlike CW, our concern stems from conceptual and empirical bases, neither of which support these required assumptions.

3. Preferences over time and risk .

The TTO as recommended by Torrance et al. (1972) is, like the HYE, a two-stage procedure which first measures X*, the number of years in full health, Qf, which is of equivalent value to a given T years in health state Q(Q <Qf). At this stage no assumptions are made (or needed) about the functional form of the indivrdual’s value function. This stage is merely used to identify two points on the individual’s isovalue curve (Mehrez and Gafni, 1990). A second stage is required to calculate a weight for health state Q to be used in QALY calculations. As explain in Mehrez and Gafni (1990), to do so Torrance et al. (1972) assume that all individuals have a specific form of value function i.e., V@, 7) = vQ(Q)T where yQ(Q) is the preference value for the health state. Using this assumption and setting YdQ*) = 1 it follows that V,(Q)=X*/K But if this assumed functional form does not hold, the preference value of health state, V$Q), is not necessarily equal to X*/T and cannot be calculated in this simple way.

Note that X* is the healthy-years-equivalent under certainty (or HYE oalue) of (Q, T) i.e., the number of years in full health which is equivalent under certainty to T years in heaith state Q (lt’iehrez and Gafni, 1990). Because the individual is asked to trade-off different time durations. his specific time preference pattern (i.e., positive, neutral or negative) is reflected 1.~ kis answers, As B notes ‘. . . individuals implicitly incorporate time preferences into their response, since it is the entire future time profile of health that is being valued directly’ (p. 8). Turning to the calculation of the QALY score under stage 2, CW argue that ‘This utility function makes no allowance, however, for time pi-eference’ (p. 3). As a result they argue that HYEs (and presumably TTO-based QALYs) need !o be discounted. Their argument demonstrates the problems arising from the assumption of the specific functional form in stage 2. By discounting TTO-based QALYs. time preference is double counted, first in the individual’s response to the TTO questions (stage 1) and second by using the discount rate in the QAlY czlcuI3tions.

i

As demonstrated hv Gafni and ‘I’r?rrance ( 1984),, individuals’ responses t 3 SG yuestions incorporate the individual’s time preference (as well as risk attitudes). This is becaF.asc unlike the outcomes usually studied in econom3cs or decision theory, an individual’s health has time inextricably bound to it.

33t

(To trade years for improved qualit_c; they must be years at the end of life, and the same year can only be traded once.)

CW note that the SG method captures some aspects of the individual”s attitude toward risk. In particular they claim QALY measures derived under the SG approach fully reflect ‘the risk associated with health but insufficiently general to capture risk attitude towards fife-years’ (p. 4). However their arguments stem directly from the specific form of utility function they assume. Pliskin et al. ( 1980) already acknowledged that their chosen functional form (and followed by CW) assumes rkk neutrality with respect to survival duration in all health states i.e., the utility function for life-years is linear. Second, CW confuse risk neutrality with certainty. But risk neutrality does not imply that an individual will make the same choices under conditions of certainty or uncertainty. i.e., risk neutrality is insufficient to render the utility and v&tt iunctions identical.

Once again CW fail to recognize that their arguments emerge from their assumption that all individuals have a utility Function of the same functional form and of a specific funct;anal form. Unlike ihe QALY model, the HYE model does not assume a specific utility functicn and thus allows individuals to reveal their true risk preference toward both health states and survival durations. Given the lack of either conceptual or empirical basis for this assumption it seems to us that their efforts might be better directed at encouraging researchers who use the QALY approach to be explicit about these assumptions as opposed to criticizing those who seek to relax these assumptions in attempting to find a more valid approach to representing individuals’ preferences.

Even the more general QALY model cited by CW (p. 6), which does not assume risk neutrality with respect to survival durations, still assumes utility independence of T and Q and constant proportional trade-off property. Because the HYE model does not require these (or any other) assumptions about the functional form of the utility function it enables us to fully reveal the individual’s preferences (i.e., risk attitude and time preference). As such it is stiprior to this more general QALY model which, interestingly enough, is not used in published cost-utik’ty studies.

4. QALYs, HYEs and hypothetical examples

CW argue that the examples provided by Gafni and colleagues do not demonstrate misrepresentation of preferences. However their arguments are again based on individuals whos.: preferences are represented by the particular functional form assumed iq the utility-based QALY mode?.

GaCYhi and Zylak ( 199G) consider thz economic analysis performed by Goel et al. (1989) in which the new (nonionic) agent is found to produce a cost- effectiveness ratio of about $65,GGG per QALY gained. Under the assump-

tions of their analysis, Gael et al. arrived at a small incremental nefit of ALY from using the nonioric rather than the ionic agent. Thus, th

division of the incremental cost of the nonionic material [%3.15) by such a small incremental benefit resulted in L huge cost-effectiveness ratio. Gafni and Zylak ( ) demonstrate that the ch&e of the QALY as the cutcome measure, an ilctional $brm of the utility function on which it is based, the result of the analysis.

d QALYs make precisely the sa XNMllp-

’ (p. 6). As a result CW nss hat both yiefd the same numerical values. They fail to see that the example demon- strates that the specific functional form underlying the utility-based QALY mode1 aSsumes that small duration effects are negligible from the individual’s

rspective. But these short duration eff&s (i.e., ‘minor reactions’) are the most common outcome in the case of ionic contrast media and the major effect of introducing nonionic contrast media is a reduction it? these short- term side effects. Thus, the assumption of the QALY model that these effects are negligible from a patient’s perspective because they are short term, irrespective of how ‘bad‘ they are, is in fact assuming the result of the econo:Gc analysis and produces a potential misrepresentation of patients’ preferences.

In particular Gafni and Zylak (1990) acknowledged that values adopted by them for outcomes death and major reaction ‘. . . are the same values as (the QALYs) assigned by Goel and associates’, noting further that ‘. . . because the

a m,sior reaction occurring is so low (!/!O,OOO in the ionic arm in the nonionic arm) and in practice (even) major changes in

the assigned values arc unlikely to affect the result of the analysis’ (p. 477). Iiowever, unlike Gael et al., Gafni and Zylak set explicitly a value for minor reaction (for the purpose of illustration) of 29.98 HYE for an individual who has 30 more years to live. CW fail to recognize that it is the functional form of the utility function, and not the assigned scores for the states, that explains the illustrated discrepancies. Because the HYE model does not assume a

ific utility function, it allows the individual to reveal a preference where durations in severe pain 0: discomfort or durability d:e not

n~assaril~ negligible. This, &;s shcwn In Gafni and Zylak ( !990), can make the difference between a bargain and burden!

It is worth noting that Gee! et al. did not use the 7Q (or indeed any oath to measure QALYs, but imposed 2 judg:ment value about

to & assigned to each outcome. But for CW’s claim of Pquivalence to be valid empirically, these judgement values would need to

rovitie equivalent preference scores to the TIa, which CW claim to be uivalent to HYEs, a condition for which they present no conceptual

t and which has been shown to be invalid emp;&:i~ (e.g., rger et al., 1992). To argue (like CW) that HYE should always be

necessarily indicate they woula choose no pain relief even if they

publicly-funded dental care to economists! The purpose of ‘Mehrez and Gafni’s second example’ was ts Szmonstrate

th:-i the QALY model can result in preference reversal for individuals who are expected utility maximizers but who do not behave according to the additional assumptions imposed by the utility-based QALY model. Using SG questions to determine the preference of one profile over the other, the upper bound utility must be identical for both situations (i.e., fuf! health for ten years). The utilities of 0.65 for scenario 1 and 0.5 for scenario 2 represent the utilities of living 5 years in he state Q’ (i.e., V(Q’,5)) and living 10 years in health state Q2 (i.e., U(Q2, respectively. Note that CW’s equation (8) is incorrect. As explained above, in order to be able to compare the two scenarios in a vNM model the upper bound utility should be identical for both situations (i.e., the utility of living 10 years in full health is defined as

both lotteries). Because both are measured using the same scale = 0.0 and full health for 10 years = 1.0) the individual’s answers enable

us to determine rhat a VNM type individual would prefer scenario 1 to scenario 2.

QALi’ proponents use tl- ;cse utilities (i.e., 0.65 and 0.5) as the weights in the QALY calculation. Under the constant proportional trade-off assumption of the QILY model the scale which is used to measure the weights (i.e., utilities) does not affect the QALY weights. For an individual, as in the example, who does not behave according to this assumption (as ~dent~~ed in published empirical evidence) preference reversal situations can emerge as described in Mehrez and Gafni (1989). Ac;c;~rding to utility vahs the individual prefers scenario 1 (U(Q’? 5) > V(Q2? er QALY cahh- tions he prefers scenario 2 (QALY’ = 0.65 x 5 5x i3)

It is interesting to note that in their att to discard the potenti

334 A. Gafni et al., Economics, heaith and health economics

preference reversal example described in Mehrez anti Gafni ( 1989). generated another preference reversal exam following vNM utility theory there is nothing wrong in an individ the preference of equivalence

where, using CW notations, Qr and QD are the health sta es of full healt and death, respectively, in period i and Qi in a health state in between (i.e., QP > Qr > Qn). But CW note that imposing their specific ,Atility function, which underlie; the QALY (but not the HYE) model (ie., equation \I) in CW, 1993, such a preference equivalence cannot exist, because it implies that a healtn state (Q’) which is inferior to full health (Qp has a utility value which is greater than that of full health (i.e., U(Q’) = 1.30> U(Qv = 1.0).

This is another example where the stated preference of a VNM individual disagrees w f p’th the imposed utility function. CW fail to acknowledge tk~! VNM type individuals do not have to subscribe to the specific utility function which underlies the utility based QALY model. Thus, any attempt to interpret a vNM type individual’s answers, assuming that he/she subscribe to such preference pattern, has the potential of creating a preference reversal situation as demonstrated nicely by CW’s example. This is precisely the argument made in Mehrez and Gafni (1989).

5. QALYs versw WEs= A normative perspective

Unlike CW, B acknowledges that the HYE model does not assume a utility function which is additive separable over time.’ However, B claims without providing evidence, that respondents are not likely to be able to value a long-term dealth prospect.

‘We need to know whether the imposition of the QALY assumption does more in-justice to ‘real’ preferences, than asking people to make valuations of future health prospects out of ignorance. It is no defence to reply that we are not entitled to force our judgement of these matters onto the public. These are not questions that the public ask themselves, but questions we ask of the pubhc to assist in the determination of health priorities. It is quite conceivable that the public themselves would be interested to know whether and in il>vhat way they might adjust to long term illr~ 5s’ (p. 9).

Individuals might well be uncertaiii about their preferences for future health states which are likely to be affected by their ability to adjust to long- term illness. But this seems to be a case for improving (probabilistic)

‘It is perhaps worth noting that in earlier work CW also acknowledged th;s point (Culyer and Wagstaff, 1391).

information transfer about the Ion tern of the condition (see

Levke et al., 1992) as opposed t the p&&nces of others for

these consequences. Those with e rience of conditions might be able to provide useful descriptive inform information on their p ~~RKVS for those eor~~zquences appears tc introduce preferences for health states amon empirical support and far from normatively compelling.

Moreover, the assumed intertempo;al additivity that underlies B’s pre- ferred QALY approach ignores c huge body of research on the demand for health (e.g., Grossman, 1972, 1982) where the relationships between con- sumption in different points in time are important in understanding indivi- duals’ behaviour. Moreover, the risk neutrality assumption with respect to survivai duration in all health states implied by B is somewhat inconsistent even from 3 normative perspective. Why should individuals be allowed to express their risk attitudes with respect to health states but not with respect to surviv;al durations?

Whose goals are to be served by forcing ‘.. . our judgments of these matte s onto the public’ (p. 9) especially when empirical evidence shows that this structure does not represent individuals’ own judgments? Unlike Buckingham, we belong to the school of thought in which individuals are taken to be the best judges of their own welfare. Unlike Buckingham, we believe that in asking ‘. . . :he public to assist in the determination of health

riot-i ties . . .’ (p. 9) we should use a measurement technique that allows the public to reveal their true preferences (otherwise why bother asking?). The HYE model is supericr to the QALY model from a welfare economics perspective because it is consistent with the normative assumptions of welfare economic theory.

6. Back to economics: From fwtility to utility?

Following Culyer (198i), we agree that “health economics as a discipline does not exist independently of economics as a discipline (and) that economics is not the on/v discioline applicable to this topic, nnr t&s within . . ___L1.1 the generai topic of health’ (p: 4). But in choosing to use economics as the ‘mcde of thinking’ about resource allocation in health, the principles of the discipline of economics must be either followed rigorously, or challenged within the context of the economic discipline.

Birch and Gfni (1992) show that the stated goal of (but not the decision rules used in) cost-utility analysis (CUA), is consistent with the principles of welfare economic theory and deals with the simultaneous satisfaction of zficiency in both production and product mix. ecause an individual’s preferences are embodied in that individual’s utility function, for a measure

336 A. Gafni et al., Economics, health and health economics

of outcome to be consistent with welfare economic theory, it has to be related to utility theory. Neither CW or B consider the relationship between the principles of economics and the QALY measure. In particular CW provide the impression that a QALY is a QALY is a QALY, regardless of the method used to measure the QALY weights. ‘They fail to recognize that the QALY is a health status index where several different methods are used to measure the weights. They fait to acknowledge that the utility approach is only one method of obtaininq the weights and that only under very restrictive conditions is a utility-weighted QALY a utility. As already stated by proponents of the utility-based QALY ‘These conditions . . . are uncom- mon in practice, and thus generally a utility-weighted QALY is not in i&elf a utility’ (Torrance and Feeny, 1989, p. 569).

Although there is much agreement about the structure of the QALY measure (i.e., duration weighted by a health status preference score) there is no agrccmcnt about +V pI c method to *be us& io measure, the weights. itiany methods have been used to measure the weights but only the SG method is related to any behavioral theory under uncertainty (i.e., vNM utility theory). This makes it dificult to interpret what thes ,e dir”ferent methods measure (as opposed to what they don’t measure) in the context of an economic analysis, or to determine their suitability for use in the context of decision making under uncertainty.

As CW (1992) note ‘For good or bad, much of the interest to date in QALYs, has after all been in QALY league tables’ (p. 4). But the many methods that are used to measure the weights for the QALY calculations cast doubt on the validity of such comparisons, notwithstanding the problem of the basis of the comparison. Hornberger et al. (1992) compared six methods of assessing preferences as a basis for QALY weights (SG, TTO, categorical scaling, Sickness Impact Profile, Campbell Index of Well-being, Kaplan-Bush Index of Well-being). The study reports poor correlations among the six methods. Discrepancies among indices were particularly noticeable when data were evaluated at the individual level. These differences caused substantial variability in the calculated cost-effectiveness ratios. So even ~ithig the QALY framework, a QALY is not a QALY is not a QALY.

In earlier WX~, r;“%?J (1992) recognize that there is more than one type of QALY, dividil2g t:Ca~ W.ZM into oniy two types of QALYs:

‘The first, Which we cali tk K-type QALY (Williams, 1985), seems to he ratio scales and are based OE a sampie of subjects’ relative valuations of descriptive states. The second, which w call the T-type QALY (Torrance, 1986), seem to be interval scales and are ba----: ~L’J 05 what Torrance has termed the ‘gold standard procedure of the standard gamble (SG)’ (p. 1).

No recognition is given to the many other methods to measure the weights Wudi!ng for example TTO), neither do they consider whether these two types of QALYs provide us with the same (or similar) scores. But given that

A. Gafni et al., Economics, health and health economics 337

the methods (and results) differ, which method do they believe should & used, and why?

Gafni and Birch (1993) have examined the W-type QALY. They show that in addition to suffering from all the limitations of the utility-based QALY measure, the W-type QALY (and its proprietary equivalent the EuroQol) is based on deterministic rather than stochastic outcomes. Moreover the proponents of the W-type QALY are unable to identify the assumptions required to equate the measure to utility, and hence are unable to consider its validity for use in economic analysis.

In developing or refining the HYE w;’ seek to enhance the validity of economic evaluation from an economics perspective. Thus we advocate use of an outcome measure derived from utility theory. We relax the restrictive assumptions of the existing utility-based QALY model and develop a measurement procedure based solely on he axioms of vNM utility theory. The definition of the HYE does not require that the individual subscribes to vNM utility theory and it is important therefore to distinguish between the definition of the HYE concept and the specific algorithm suggested to meastlre the mnp-t _--_ ~...~~V~..

This distinction is important given the growing criticism of the VNM utility model. Leading researchers in fields of economics, decision theory and psychology no longer accept this theory as a normative standard (see for example Bell and Farquhar, 1986; Machina, 1987 and Fishburn, 1988) and empirical studies have found that people do not ‘behave in a manner cons&tent with the axioms of expected utility theory. When asked to reconcile their actual behaviour with the axioms, many (while accepting the appeal of these axioms) preferred not to change their original behaviour (Bell and Farquhar, ig86). Researchers in the field of economic evaluation may therefore not want to continue to use the expected utility model.

Other types of utility functions (non-vNM) can be used as the bzlses for generating algorithms to measure HYEs. Although, to the best of our knowledge, no such algorithms have been proposed, that does not imply that a non-vNM algorithm cannot be derived. Such algorithms are likely to be more complex than the two-stage lottery-based procedure, but this might be seen as a reasonable ‘price’ to pay for a measurement method which is less restrictive than the vNM one and allows for even better representation of individuals’ preferences. CW (1993) acknowledge that the potential for misrepresentation of individuals’ preference ‘clearly undermines the QALY approach substantially’ (p. 1). But, they (as well as B), prefer to stay with a concept that in most rxes has nothing to do with utility theory, and at best requires that all indJviduals have the same specific form of utility function. HYEs offer researchers a method generated from and consistent with utility theory, a general measurement procedure in the context of a vNM utility approach and the option to extend the measurement procedure to other, less

338 A. Gafni et al., Economics, health and health economics

restrictive, utility theories. As such it allows co+utility analysis to address economic problems in valid ways, i.e., ways consistent with the discipline of economics.

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