Operations Research for Health Care 3 (2014) 91–98

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Operations Research for Health Care

journal homepage: www.elsevier.com/locate/orhc

Are numbers still killing people: And what is being done about it?Penelope M. Mullen ∗

Birmingham, United Kingdom

a r t i c l e i n f o

Article history:Received 1 November 2012Accepted 29 October 2013Available online 4 November 2013

Keywords:PolicyQuantificationAnalysisRationingObjectivesEthics

a b s t r a c t

There is increasing recourse to quantitative approaches in healthcare allocation and prioritisation,frequently using methods from operational research and health economics. Such approaches can provevery attractive and influential, employing what are viewed as scientific, rational, methods. But can high-tech quantitative analysis, taken to its apparently logical conclusion, cause the ethical ‘human’ dimensionin health care to be overridden. This paper develops some of the ethics arguments posed in an earlierpaper by Mullen and Mullen (2006), questioning whether it is ever permissible to kill someone. It thensuggests why numbers might kill and discusses what might prevent this. Some recent developmentsare then reviewed to address the question of whether ‘‘Killing by Numbers’’ has become more or lesslikely. It is concluded that, despite recent developments, the attraction of apparently logical quantitativeapproaches means that numbers probably are still killing people.

© 2013 Elsevier Ltd. All rights reserved.

1. Introduction

There is increasing recourse to quantitative approaches inhealthcare allocation and prioritisation, frequently using meth-ods from operational research and health economics. Such ap-proaches can prove very attractive and influential, employingwhatare viewed as scientific, rational,methods. An earlier paper ‘‘Killingby numbers: could quantitative analysis lead to involuntary ‘eu-thanasia’?’’ [1] argued that pursuit of the superficially-attractiveobjective of health-gain maximisation had resulted in potentiallylife-saving or life-prolonging treatment being denied because it isdeemed not cost-effective. It then asked whether the argumentsunderlying this denial could lead to compulsory euthanasia. Noneof the ethical arguments explored demonstrated convincingly thatthis could not happen. Ensuing papers questioned the appropriate-ness of adopting health-gain maximisation as a principal objectiveof health care systems—as advocated by many health economistsand also implicitly or explicitly by many policy makers in the UK.They also explored what might be appropriate health-system ob-jectives.

More recently, whilst continuing to argue that providing non-cost-effective, albeit needed and potentially efficacious, treat-ments would unfairly deprive others of ‘more efficient’ health careand so reduce aggregate heath gain, some proponents of health-gain maximisation have recognised the potential for inequity and

∗ Correspondence to: 75 Eastern Road, Selly Park, Birmingham, B29 7JX, UnitedKingdom. Tel.: +44 (0) 121 472 0576.

E-mail address: penelope.mullen@btinternet.com.

2211-6923/$ – see front matter© 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.orhc.2013.10.003

‘adverse headlines’ resulting from its pursuit. This has led to a num-ber of proposals, policies and sophisticated analytical approachesto attempt to address the concerns.

This paper reviews the debates on the risk of ‘compulsory eu-thanasia’ and appropriate health-service objectives, examines theextent to which recent analysis, policies and proposals address thevarious concerns and askswhether numbers are still killing people.

2. Is it ever permissible to kill someone?

Obviously, killing people is wrong. Luttrell [2, p. 1709] statesthat ‘‘. . . it has been clear for many years that a doctor who activelytakes steps to end the life of one of his or her patients is actingillegally and is potentially guilty of murder. . . ’’. But the full quo-tation, opening with ‘‘Although’’ and concluding ‘‘there has beenmuch less clarity about the relatively common decision to with-draw or withhold life prolonging medical treatment’’, reminds usthat the position is by no means clear cut.

Many debates in medical ethics are relevant and it is possiblehere only to touch on some of the issues and arguments. Relativelynon-controversial is the right, accepted inmany countries, of men-tally competent adults to refuse treatment. More controversial isthewithdrawal of treatment fromnon-mentally competent adults,even when in a persistent vegetative state (PVS). Possibly less con-troversial is assisted suicide or voluntary euthanasia for the men-tally competent—legal in some countries, but a criminal offence inothers. However, at the far more controversial extreme is compul-sory or involuntary ‘euthanasia’. Could or should compulsory ‘eu-thanasia’, whether formentally competent adults or those deemednot mentally competent, ever be accepted?

A commonly quoted set of moral principles in medical ethicsis: respect for autonomy (a norm of respecting the decision-making

92 P.M. Mullen / Operations Research for Health Care 3 (2014) 91–98

capacities of autonomous persons); non-maleficence (a norm ofavoiding the causation of harm), beneficence (a group of norms forproviding benefits and balancing benefits against risks and costs),justice (a group of norms for distributing benefits, risks, and costsfairly) [3].

It could be argued that the principle of autonomy would ruleout compulsory ‘euthanasia’ for mentally-competent adults. But,unless we assume autonomy overrides all the other principles,1 itis necessary to look further.

Compulsory ‘euthanasia’ could, of course, result either from an‘act’—actively killing someone—or from an ‘omission’—failing totreat, or even to feed. These could, respectively, violate the prin-ciples of non-maleficence and beneficence.

To what extent does beneficence imply a duty to act to savea life? According to Beauchamp and Childress [3, p. 165], benefi-cence requires taking ‘‘positive steps to help others, not merely re-frain fromharmful acts’’. This relates towhat they term ‘‘ObligatoryBeneficence’’: but does that imply an absolute degree of obliga-tion?No, according to BeauchampandChildress [3, p. 170],who ar-gue that a poor swimmer seeing someone drowning is not obligedto risk their life attempting to save that person. However, they con-tinue, ‘‘If the passer-by does nothing (eg fails to alert a nearby life-guard) the failure to help is morally culpable’’.

However, a duty to save a life appears to be qualified whenBeauchamp and Childress [3, p. 165] combine two principles: pos-itive beneficence which ‘‘requires agents to provide benefits’’ andutilitywhich ‘‘requires that agents balance benefits and drawbacksto produce the best overall results’’ and which, they claim, is it-self an ‘‘extension of the principle of positive beneficence’’. ‘‘To beappropriately beneficent’’, they continue [3, p. 166], ‘‘generally re-quires that one determine which actions produce an amount ofbenefit sufficient towarrant their costs’’. From this qualified benef-icence they go on to state the conditions which all need to be satis-fied for person X to have ‘‘a determinate obligation of beneficencetoward person Y’’ [3, p. 171]:

1. Y is at risk of significant loss of or damage to life or health orsome other major interest.

2. X’s action is needed (singly or in concert with others) to preventthis loss or damage.

3. X’s action (singly or in concert with others) has a high probabil-ity of preventing it.

4. X’s action would not present significant risks, costs, or burdensto X.

5. The benefit that Y can be expected to gain outweighs any harms,costs, or burdens that X is likely to incur.

Of course, these conditions refer to the duty of individuals, which isnot necessarily identical to the duty of society. Nevertheless, theseconditions point to the considerable scope for debate especiallyin relation to costs and burdens and the potential implications ofapproaches associated with health-gain maximisation, a form ofutilitarianism.

3. Why might numbers kill?

The main arguments here arise from the pursuit in the EnglishHealth Service (NHS),2 and to a lesser extent in some other coun-tries, of the superficially attractive and apparently scientific utili-tarian objective of health-gainmaximisation. Themain instrument

1 The example of Leslie Burke [4], who lost his legal fight to prevent doctorswithdrawing his artificial nutrition and hydration (ANH) if they were unable tocommunicate with him, suggests it does not.2 These arguments apply most specifically to England rather than the whole of

the UK.

Fig. 1. Equity and QALY Gain.

for operationalising this is the Quality Adjusted Life Year (QALY)—with one QALY equivalent to one year in perfect health. The QALY,whose origins can be found in the OR literature of the 1970s, isextremely valuable in comparing alternative therapies for a sin-gle group of patients where, ceteris parabis, the therapy giving thegreatest number of QALYs for given resources, or with the lowestcost/QALY, will be selected. However, problems arise when QALYmaximisation is used to select between treatments for differentgroups of patients.

For example, there are claims that QALYmaximisation is inher-ently ageist as older people have less scope to gain QALYs. Thustreatments targeted at older people might be valued lower.

QALY maximisation can ignore relative need by favouringthose in a higher initial health state if they can achieve greaterQALY gains, as the simple example in Fig. 1 illustrates. Here twoindividuals (A and B) both would benefit from treatment costingthe same amount. The treatment would move A from 0.3 to 0.6 onthe 0–1 scale and B from 0.6 to 1.0, both maintained for 10 years.3Who should get priority? Treating B produces more Health Gain.However, A has a lower Initial Health State (is worse off). Further,treating A would equalise Health Status.

Another equity-related adverse effect is ‘double jeopardy’,where a person who has a pre-existing disability which meansthat their maximum achievable health status is less than perfectwould be able to gain fewer QALYs from life-saving treatment thana person with no pre-existing disability.

In a further equity scenario, A and B achieve the same QALYgain from treatment, but A costs more to treat than B. On a QALY-maximisation decision rule, priority should go to B. But what ifFemale A costs more to treat than Male B for biological reasons,or non-English-speaking A costs more than B because they needan interpreter? Thus, maximising QALYs could result in systematicdiscrimination against, say, minority ethnic groups, occupants ofpoorer housing needing in-patient stays rather than day surgery,or inhabitants of sparsely populated locations.

A variant of the equity argument, which is especially relevantto our concerns here, arises when considering the individual ver-sus the collective. Inherent in health-gain maximisation is indif-ference between health gain achieved through a small increase fora large number of people and that achieved through a large (evenlife-saving) increase for a small number. Thus, a small gain, say 0.1each year over 10 years for 11 people (total 11 QALYs), is valuedhigher than a gain of 1 (life saving) for 10 years for one person (to-tal 10 QALYs), even if the 11 people start from a health status of

3 It is recognised that it is not strictly appropriate to consider individual casesAlso, the issue of discounting health is ignored here—both in the interests ofsimplicity.

P.M. Mullen / Operations Research for Health Care 3 (2014) 91–98 93

0.9. Combining quality-of-life with length-of-life is, according toadvocates, amajor strength of QALYs, but a source of criticism fromothers. Taurek [5, p. 308] argues, ‘‘Suffering is not additive in thisway. The discomfort of each of a large number of individuals expe-riencing a minor headache does not add up to anyone’s experienc-ing a migraine’’.4 Further, in a rather macabre formulation, Menzel[7, p. 15] observes that the sacrifice of an individual ‘‘to extract vi-tal organs and save four or five other people by transplant’’ would‘‘raise average life expectancy’’, i.e. increase health gain and alsoincrease the number of lives saved.5

Health-gain maximisation in the English NHS has beenadvanced by NICE (National Institute for Health and Clinical Ex-cellence), originally established in 1999. NICE makes recommen-dations for the introduction of new (and, to some extent, the useof existing) therapies and drugs based on both clinical efficacy andcost-effectiveness, the latter usually expressed as cost per QALY.Where the drug or therapy under study costs more but has abetter outcome than existing ‘standard practice’, the IncrementalCost-Effectiveness Ratio (ICER) is computed based on the increasein health likely to accrue from the increased cost [9]. In the ab-sence of special reasons, treatments or drugs which have a cost perQALY higher than a threshold of £20,000–£30,000, which has re-mained unchanged from the outset, are not recommended for usein the publicly-funded NHS. Such ‘‘special reasons’’ have in someinstances included the absence of alternative treatments as well aseffective lobbying. For example, political outcries in the UK overthe refusal to recommend or fund new therapies which potentiallyextend life in terminally ill patients, most commonly those withsome cancers, led to recommendations to adopt a higher thresh-old in such cases and the establishment of a special ‘Cancer DrugsFund’ [10]. Nevertheless, the result can still be that potentially life-saving or life-prolonging treatment is denied on cost-effectivenessgrounds, even where no alternative exists.

This consequence of the apparently logical aim to maximiseQALYs (health)—the failure to save lives which could be saved—can come into conflict with the ‘rule of rescue’—‘‘the strong humanproclivity to provide aid to identified victims of illness or accident’’[11, p. 1454]. For example, this is observed when no expense isspared to attempt amine rescue. It is often claimed that the ‘rule ofrescue’ arises because the public are more sympathetic to a namedindividual in trouble than to unknown statistical individuals. ‘‘Anamed person who is dying now is more visible than an unnamedperson dying in the future’’ [12, p. 173]. Weale [13, p. 186] citesnumerous examples where decisions placed higher valuations onidentified lives in immediate danger, than on unknown lives infuture danger, which he terms the ‘‘statistical lives paradox’’. Thishas led to arguments that we should ‘harden our hearts’ to theplight of the identified individual in order to be fair to the unknownstatistical individuals. However, in a small-scale research project,Jenni and Loewenstein [14] found that whether a victim wasidentified or anonymous did not have a statistically significanteffect on respondents’ rating of their importance.

It is possible that it is the degree of risk and certainty associatedwith outcomes which is important, rather than whether or not in-dividuals are identified. It might thus prove inappropriate to treatsuch risk and uncertainty merely as numerical inputs to the com-putation of QALY gain. In many countries, mass vaccination is ad-vocated even where a small number of individuals will be severelydamaged by the vaccine. The very low risk of severe injury is con-sidered to be outweighed by the much higher risk of the possibly

4 However, in an exchange worth consulting, Parfit [6] takes on Taurek anddisputes this argument.5 An interesting article by Hill [8] explores why such action would not be ethical,

even in some fairly extreme circumstances.

life-threatening disease againstwhich the vaccination is given. But,Mullen and Spurgeon [15] asked, would a vaccination programme,with the same net health gain, be advocated if it was known inadvance which specific individuals were going to suffer severedamage from the vaccine but it was impossible to exclude any in-dividual from the programme. If the answer is no, is that becausethe sufferers are identified individuals, or is it because the originalvery low risk of severe injury for everyone is now a 100% certaintyfor a few and 0% risk for the many?—‘‘Inequality of Risk’’ [16]. Theresearch by Jenni and Loewenstein [14, p. 253], cited above, sup-ports the latter explanation, concluding ‘‘the major cause of theidentifiable victim effect is the relative size of the reference groupcompared to the number of people at risk. Identified victims con-stitute their own reference group, 100% of whom will die if stepsare not taken to save them’’. In our second scenario, those at riskalso constitute 100% of the reference group—the group of individ-uals known to be going to suffer severe damage.

Further, can results based on computations of probabilities ap-plied to individuals be compared with those for populations? Taketwo cases. In the first, a prevention programme for a populationof 10,000 against a disease, which will affect 1% of that populationand reduce their quality of life from 1.0 to 0.8 for one year, pro-duces a health gain of 20 QALYs. In the second, an individual has a10% chance of surviving for 20 years in perfect health with treat-ment, but without treatment will die immediately. Can that treat-ment be deemed to produce 2 QALYs (20x0.1) (and if so are thoseQALYs commensurate with the QALYs above?). On a strict compu-tation, if the costs were the same, say £100,000, the cost/QALY forthe prevention programmewould be £5000 but for the individual’streatment would be £50,000. Is it legitimate to compare ratios inthat way, since for the individual there is a 100% probability of dy-ing without treatment? And would any resulting decision be dif-ferent if the probability of cure were 1% or 0.1%? This appears to beanother area where rational quantitative analysis might ignore thehuman dimension.

4. Could we move from failure to save a life to actively killing?

As discussed above, pursuit of health-gain maximisation as ahealth service objective can lead to denying potentially life-savingtreatment deemed to cost too much per QALY. It could be arguedthat such denial can be justified ethically under Beauchamp andChildress’s [3, p. 165] principles of positive beneficence and utility,despite the fact that the consequence is still death regardless of thewishes of the patient (Quadrant 3 in Fig. 2). This justification hasbeen criticised from a number of quarters, but has not preventedsuch a policy being pursued. Indeed, it is strongly defended bysome claiming that providing treatment which falls above thecost/QALY threshold ignores opportunity costs and would unfairlydeprive others of ‘more efficient’ health care and so reduceaggregate heath gain. But could arguments justifying withholdingpotential life-saving treatments from mentally competent adultswho wish to receive it (Quadrant 3) lead to arguments in favour ofthe active termination of life of thosewho are judged too expensiveto be allowed to live (Quadrant 4)?

In other words, could pursuit of health-gain maximisation,which can lead to refusing to provide, on the grounds of cost,life-saving/prolonging treatment wanted by mentally competentadults, lead logically to compulsory ‘euthanasia’ for both thementally competent and mentally incompetent—on the groundsthat they are too expensive to allow to live? That is, is entry tothe fourth quadrant feasible and does quantitative analysis makeit more likely?

4.1. Ethical barriers to Quadrant 4

What could prevent the transition, from failing to save a life onthe grounds of cost/QALY, to taking a life on the same grounds?

94 P.M. Mullen / Operations Research for Health Care 3 (2014) 91–98

Fig. 2. When might life be terminated?

The main candidates appear to be non-maleficence, beneficence,statistical lives and the ‘acts and omissions doctrine’.

Non-maleficence would appear to prevent killing someone fortheir organs. But it is not an absolute principle. According toBeauchamp and Childress [3, p. 168] obligations of beneficencecan ‘‘sometimes override obligations of non-maleficence’’ citing theexample of producing a ‘‘major benefit by causing a minor harm’’.Further, non-maleficence does not appear to prevent withholdinglifesaving treatment on the grounds of cost.

The beneficence principle evokes Harris’s question [17, p. 48]‘What is society’s obligation to care for and protect its citizens?’As noted earlier, Beauchamp and Childress qualify the obligationof beneficence by weighing benefits against harms, costs andburdens. At a societal level, can those benefits, burdens, costs andharms be fed into a cost-effectiveness ratio and justify withholdinglifesaving treatment on the grounds of cost? If yes, why shouldthese principles logically stop the deliberate ending of a lifebecause it is deemed too expensive?

Could the Statistical Lives paradox prevent progression fromwithholding treatment to active killing? As discussed earlier, massvaccinationmight be undertaken even if there is a small probabilitythat some, as yet unidentified; individuals will be harmed or evenkilled by the vaccine. Would a ‘mirror’ of the ‘Rule of Rescue’,which prioritises treating an individual in immediate dangerover saving unidentified ‘statistical’ individuals, deem that whilstkilling unspecified ‘statistical’ individuals might be acceptableunder certain circumstances, this should not extend to killing anidentified individual? However, whilst this argument might byaccepted by adherents of the rule of rescue, it would not satisfythe tenets of unconstrained utilitarianismwhich are used to justifywithholding treatment from an identified individual.

4.2. Acts and omissions

Is the distinction between Omission (failure to save life) andAct (actively ending life) sufficient to prevent the latter? The ‘actsand omissions doctrine’ appears to be the subject of perennialdebate. According to Glover [18, p. 92], this doctrine claims ‘‘that incertain contexts failure to performan act,with certain foreseen badconsequences of that failure, is morally less bad than to perform adifferent act which has the identical foreseen bad consequences’’.Or, as expressed by McLachlan [19, p. 636] ‘‘To kill is not the sameas to let die’’. However, Glover [18, p. 94] asserts we ought to rejectthis doctrine, arguing that the view ‘‘that an act and deliberateomission with identical consequences (i.e. with no differences inside effects) can vary in moral value should be rejected’’. Similarly,Coggon [20, p. 578] suggests that ‘‘When we assess the moralityof a measure (act or omission) that leads to a death, our concernwill be the culpability of the measure, not on whether we areable to describe it as an act or an omission’’. Glover [18, p. 116]

further claims ‘‘. . . the arguments against killing are equally goodarguments in favour of saving lives’’. Turning this around, couldit suggest that, if society considers it justifiable to fail to save alife (which could be saved) on grounds of cost-effectiveness, itmight be justifiable to terminate a life on the same grounds, ceterisparibus?

Harris [17, p. 53] also blurs the distinction between acts andomissions. He sees failing to act as ‘commission’ ‘‘. . .where wedecide not to treat someone knowing that they will die or suffer asa consequence, or decide not to rescue someone knowing that theywill die or suffer as a consequence, then their death or suffering is,in either case, a consequence of our decision’’.

There are a number of other arguments relating to acts andomissionsmight have relevance here. For example, it is argued thatomitting to save a lifemight differ from the act of killing since in theformer case some harmmust already have been done [21]. Obliga-tion and practicality enter arguments. ‘‘We are obliged to refrainfrom killing each and everyone. We do not have a similar obliga-tion to try to prevent each and everyone from dying’’ [19, p. 636].In a similar vein it is claimed that omitting to save a life is justifi-able if you are not in a position or do not have the power to save it.Most debates focus on the obligations and duties of individuals—itis not always clear how these translate into a collective or soci-etal responsibility, nor the extent they could prevent a move fromQuadrant 3 to Quadrant 4.

However, the outcry raised by the recent publication of a paperentitled ‘‘After-birth abortion: why should the baby live?’’ [22],suggests that extrapolating from existing policies or actions towhat some would claim are their logical ‘analytical’ conclusions—and others their unpalatable, unthinkable ends—means therewould be extreme resistance to any move to Quadrant 4.Nevertheless, a rather less unthinkable development from the logicof Quadrant 3 could be deliberate omission to save the life of thosewith, say pneumonia, where the immediate life-saving treatmentis not expensive, butwhobecause of complex unrelated underlyingproblems will incur high costs in the future well in excess of anythreshold. The risk remains that the power of numbers and theapparent logic of quantitative analysis will prevail.

5. What is being done about it?

Before continuing it is worth asking whether this is just a UK(English) phenomenon. Whilst several countries have explicitlystated that they will not adopt health-gain maximisation as thesole or primary goal of their health services, use of Cost–BenefitAnalysis (CBA) appears to be increasing in the assessment ofhealth-care programmes in a number of countries—and manyinternational analysts exhibit great interest in cost/QALY studies.

Since the original paper [1], from a policy perspective in the En-glish NHS, the position has possibly becomemore polarised. ‘‘Max-imisation of Health Gain’’ has become almost a mantra in somequarters whilst, at the same time, the cut-off threshold range hasremained static in cash terms. Nevertheless, as noted above, po-litical outcries over the refusal to recommend or fund new ther-apies which potentially extend life in terminally ill patients haveled to some specificmitigation in the formof higher thresholds andthe establishment of a special ‘Cancer Drugs Fund’. However, at thesame time, it has been reported that a reduction in the value of thethreshold is to be proposed shortly [23].

Whilst the degree of risk ofmoving intoQuadrant 4 is debatable,Quadrant 3 has unquestionably been entered. Views vary as to theimplications, causes and remedies, if any. These will be consideredhere under three headings: ReassertingMaximising Health Gain asthe Principal Criterion; Mitigating the Adverse Effects; Addressingthe Objectives of Healthcare Systems.

P.M. Mullen / Operations Research for Health Care 3 (2014) 91–98 95

5.1. Reasserting maximising health gain as the principal criterion

Some analysts, whilst promoting and adhering to the solecriterion of maximising health gain within their work, stress that,as analysts, they are only giving advice or information to decision-makers who will weigh up the efficiency (cost per QALY) of theproposal or therapy against other criteria, including equity. This isa familiar line of argument within OR but in this case it ignores anumber of powerful factors. They include the enormous attraction,even dominance, of the apparently scientific quantified measure(cost/QALY), the acceptance and even increasing advocacy of themaximising health gain criterion among many decision-makers inthe English NHS and, of course, its use by NICE as the primarycriterion in recommending the adoption of new technologies.

Nevertheless, analysts who advocate health-gain maximisationas a principal criterion claim that the approach is self-evidentlyobvious and rational—all that is needed is to establish the cor-rect threshold—see discussion below. Notwithstanding the dis-claimer above, they support its use in a policy context, arguing,as noted above, that providing treatment which falls above thestated/chosen cost/QALY threshold takes no account of the oppor-tunity costs and would unfairly deprive others of ‘more efficient’health care and so reduce aggregate heath gain of the population.The claim that violating the cost/QALY threshold would constituteunfairness appears powerful given that fairness and equity are of-ten equated. But both equity and fairness are very complex, con-tested, concepts. However, these ‘unfairness’ arguments appear toignore the ‘unfairness’ in distribution of health-care need as re-flected in the extremely skeweddistribution of health care costs in-curred at an individual level, which appear to be found in all healthcare systems.6 This consistently demonstrates that, whilst the ma-jority incur low or even zero health-care costs, a very few individ-uals incur extremely high costs. If such costs even approximatelyreflect need thiswould suggest that denial of potentially life-savingbut ‘non-cost-effective’ care to those patients would impair soli-darity and any essence of ‘assurance’ within a health care system.

5.2. Mitigating the adverse effects

Concern over adverse affects of the pursuit of ‘pure’ health-gain maximisation has led to a number of proposals and attemptsto mitigate these effects, whilst not necessarily questioning orundermining the basic approach. Three such attempts will beconsidered here.

5.2.1. Equity weighting of QALYsUse of QALYs has been claimed to be equitable by maintaining

that ‘‘a QALY is a QALY is a QALY’’—regardless of who gains (orloses) it. However, the concerns and anomalies apparent fromthe unqualified use of QALY maximisation as a goal, illustratedin the examples above, have led a number of policy makers andanalysts to seekmethods of incorporating equity. Amajor thrust ofthis work has been attempts to ‘weight’ QALYs to reflect (usuallysociety’s) views of the relative merits/claims of different groups.Weightings have been attempted by age, social class, severity ofillness, family responsibilities etc., using increasingly sophisticatedanalytical and other research techniques (see, for example, [27]).The apparent intention is that therapies and technologies will be

6 Precise figures appear hard to find. US figures suggests the top 10% consumed64% of expenditure (top 1%, 22%), with the lowest 50% consuming just 3% of thetotal [24]. A similar distribution (top 10% consuming between 74%–80%) was foundwith members of insurance plans in Australia. [25]. In England for hospital costscovered by tariff alone, the mean cost of the top 1% of patients was about 10 timesthe overall mean and 56 times the mean of the lowest 10% [26].

Fig. 3. Threshold for QALY maximisation.

assessed according to their cost-per-weighted-QALY. But whilstthis might go a little way to mitigate some of the equity issues, itwould still leave the inherent distortions resulting from the pursuitof QALY maximisation.

5.2.2. Valuing QALYs and obtaining the ‘correct’ thresholdMuch recent analysis has focused on the related pursuits of the

‘Value of a QALY’ and the ‘correct’ or most appropriate thresholdto use. As noted above, since its inception in 1999, NICE has useda threshold range of £20,000–£30,000 in its funding recommenda-tions. However, there is no empirical (or apparently ethical) basisfor this threshold level, which has remained static, in cash terms.

A number of studies have attempted (or are attempting) toobtain a monetary value for a QALY—usually a ‘societal’ average(see for example, in a UK context Donaldson et al. [28] and,in a Danish context, Gyrd-Hansen & Kjær [29]). Such attemptshave employed traditional techniques, such as ‘Willingness to Pay’(WTP). However, whilst Gyrd-Hansen and Kjær see WTP per QALYas useful for Cost–Benefit Analysis, the overall purpose or policyobjective of such studies do not always appear to be very clear.

Generally, the literature suggests confusion about the meaningof the threshold, how it should be set (and by whom) and itsinterpretation. In fact, it could be argued that NICE and others usinga threshold are not maximising health gain but using crude CBAby adopting a threshold Cost/Benefit ratio (but encompassing arestricted range of costs and benefits).

The underlying logic of ‘‘Maximising Health Gain’’ would sug-gest that the threshold should reflect themarginal benefit of healthspending at the limit of the current budget (see Fig. 3). Although itmight be claimed that in the long termmarginal will equate to av-erage, it is not entirely apparent how that relates to a value of aQALY obtained by, for example, individuals’ expressed willingnessto pay. However, further clarification might be forthcoming.

As to how the value of a/the threshold should be determined,Culyer et al. [30, p. 56] argue that ‘‘it is not constitutionally ap-propriate for NICE to set such a threshold, which is properly thebusiness of parliament. Instead, the task for NICE is as a ‘threshold-searcher’—to seek to identify an optimal threshold incrementalcost-effectiveness ratio, at the ruling rate of expenditure, that isconsistent with the aim of the health service to maximize popula-tion health’’.

Martin et al. [31] have used Programme Budgeting to estimatethe actual cost (or expenditure) per QALY of different programmes.Their model assumes ‘‘that each PCT (Primary Care Trust) receivesan annual financial lump sum budget from central government’sDepartment of Health (DH) and allocates its resources across the23 programmes of care to maximise the health benefits associatedwith that expenditure’’ [31, p. 8]. This, of course, appears to assume

96 P.M. Mullen / Operations Research for Health Care 3 (2014) 91–98

PCTs are already health-gain maximisers. Their results include es-timates ofmeans andmarginal costs/QALY for the 23 programmes.However, the interpretation of these for circulatory diseases issomewhat difficult, as the marginal cost per QALY appears to belower than themean.Martin et al. [31, p. 48] claim that ‘‘the resultscan . . . inform the decisions of the National Institute for Health andClinical Excellence (NICE) about whether its current threshold foraccepting new technologies is set at an appropriate level’’.

As noted above, Jack [23] reported that analysis, carried out atthe University of York and then scheduled for publication in June2012, suggested ‘‘the threshold for new drugs—based on the costof each additional ‘‘quality adjusted life year’’ (QALY) for patients—should fall from £30,000 today to £20,000 and potentially as lowas £10,000’’.7

An alternative approach is to adopt values from other sec-tors, most notably transport, where values are placed on life andhealth in cost–benefit analyses of road improvements etc. How-ever, notwithstanding the point above that using a cost/QALYthreshold is effectively a form of CBA, a major distinction is thatcurative/personal health services are provided to individuals (whocan be individually included and excluded), but programmes suchas road improvements provide benefits to numbers of (unidenti-fied) individuals, who cannot be individually discriminated for andagainst. In effect this is a variant of the ‘statistical lives’ argument,presented above.

5.2.3. Value-based pricingAs an apparent response to some of the adverse effects of

pursuit of ‘pure’ health-gain maximisation, the UK Government isproposing to introduce Value-Based Pricing (VBP) to determine theprice it will pay for new drugs. In general, the basic principle ofVBP is that selling prices are determined by the perceived valueto the customer, rather than by market prices, costs or historicalprices. In its proposals the DoH [33, Section 4.5] states the ‘‘keyprinciple of value-based pricing is to ensure NHS funds are used togain the greatest possible value for patients’’. It goes beyond cost-effectiveness as value will include ‘‘a wide assessment, alongsideclinical effectiveness, of the range of factors through whichmedicines deliver benefits for patients and society’’ [33, Section3.3]. Nevertheless, ‘‘there would be a basic cost effectivenessthreshold, directly reflecting the health gains displaced when newtreatments are funded. This would set the maximum that theGovernment was prepared to pay for medicines that offered noadditional value in terms of innovation, tackling diseases with ahigh burden of illness or wider societal benefits’’ [33, Section 4.13].Higher thresholds could be set for a number of factors including:

• A greater ‘Burden of Illness’ based on the ‘‘severity of the con-dition and the level of unmet need’’, the latter including caseswhere there is no existing alternative effective treatment. In itsresponse to the consultation the government states it intendsto commission ‘‘research to inform the development of Burdenof Illness weightings’’ [34, Section 5.37].

• Greater Therapeutic Innovation and Improvement:which couldperhaps be summed up as ‘New’ v ‘Me Too’ therapies. Whilstsome responses suggested this factor would anyway be re-flected in high QALY gain, the government is proposing ‘‘a workprogramme to develop theweights for the VBPmodel’’ [34, Sec-tion 5.70].

7 The report of this project, ‘‘Methods for the Estimation of the NICE CostEffectiveness Threshold’’, which adopted an empirical approach using routine data,was published in 2013 and concluded that the ‘‘central or ’best’ threshold isestimated to be £18,317 per QALY’’ [32, p. vi].

• Wider Societal Benefits: Whilst the original government pro-posals put out to consultation suggested ‘‘These might includebenefits related to reduced reliance on carers, and other widersocietal factors’’ [33, Section 4.27], responses widened them to‘‘allowing patients to return towork’’ [34, Section 5.74], ‘‘impacton productivity and environmental sustainability’’ [34, Section5.145]. Again weighting would be used to take account of any‘wider society benefits’.

The Government response states that Rare Diseases/Orphan Drugsand drugs currently covered by the Cancer Drugs Fund and forsome end-of-life conditions might need special arrangementsrather than being covered by VBP. Nevertheless, as currentlyproposed, it would appear that VBPwill effectively be largely basedon a cost/QALY threshold, with either weighted QALYs and/or‘weighted’ thresholds.

5.3. Addressing the objectives of healthcare systems

Many attempts tomitigate the adverse effects of the unqualifiedpursuit of QALY maximisation reflect explicit and de factorecognition that health-gain maximisation might not be the soleobjective of a health-care system.However,most of those attemptsappear to accept health-gain maximisation as the principalobjective, with other objectives acting simply to soften it. Further,many commentators stress that pursuit of alternative objectiveswill result in sacrifice of health gains—reaffirming the primacy ofhealth-gain maximisation.

Mullen [35] suggested that the objectives of a (publicly-mandated?) healthcare system should be revisited with a view todrawingup an ‘objective set’. The following setwas tentatively pro-posed in respect of individual/curative health services (as opposedto population-based collective public health and preventative ser-vices):

(1) to relieve suffering and promote health and security of individ-uals;

(2) to minimise (catastrophic) risk;(3) to promote trust and provide security and certainty health care

will be there when needed;(4) to ensure equity and fairness in access to health care;(5) To be responsive (in terms of quality).

Apparently paradoxically, ‘maximising population health-gain’is not included and, in any case, there is little evidence thatcurative/personal health care is a major determinant of populationhealth.

Objectives 1, 4 & 5 appear explicitly or implicitly in manylistings. Objective 2, to minimise catastrophic (usually financial)risk, is a primary reason for establishing collective health-carefinancing systems—whether public or private—and is reflected inthe WHO objective of ‘fair financing’ [36]. Objective 3 ‘‘to promotetrust and provide security and certainty health care will be therewhen needed’’ is related to risk but would appear to go furtherthan Objective 2. Trust and security, which might be categorisedas the ‘assurance’ aspect of a health-care system, does appear to bean important health-service objective.Whilst it was formerly oftenunder-acknowledged, an increasing number of commentators arerecognising this aspect. For example Wendt et al. [37, p. 212],in presenting a seven-country comparison, state: ‘‘The ability toguarantee security against life risks is a major accomplishment ofmodern health-care systems. As the availability of health servicescan be a matter of life and death, people need the security thatnecessary care will be provided in the case of serious illness orinjury’’. They continue [37, p. 213]: ‘‘The level of confidence inreceivingmedical care is an important indicator of trust that peoplehave in the medical system’’. However, such security does notappear to be compatiblewith a policywhich results in denying care

P.M. Mullen / Operations Research for Health Care 3 (2014) 91–98 97

because it is (expensive and) not cost-effective (from a populationhealth point of view).

In an essay, Vaithianathan and Lewis [38, p. 171] state: ‘‘At-tempts to codify the principles of the (UK) NHS should . . .be mind-ful that it is not only a commissioner and provider of health carefor patients, but also an insurer for the public, since every memberof the population enjoys peace ofmind from knowing that the NHSwill pay for their health care should they become ill’’. They propose[38, p. 172] that ‘‘If the NHS is tomaximize its insurance value thensuch uncertainties may be minimized by making the constitutionmore explicit about what services are and are not available’’.

Smith et al. [39, p. 38], in looking at priority-setting in sevencountries, state: ‘‘Themost fundamental element of priority settingis to ensure that a clear set of goals is articulated for the healthsystem to act as a basis for such optimization. Experience sincetheWorld Health Report 2000 suggests that the principal goals arelikely to include variants of the following:

• Improved health status of the population• Safe, high quality health services• Responsive health services, meeting the expectations of pa-

tients and caregivers• Equitable treatment and outcomes• Financial protection from the expenditure consequences of ill

health• Ensuring a sustainable supply and efficient use of resources’’.

Whilst they stress that it is up to the individual nations to makeprecise formulations, they claim [39, p. 39] that ‘‘In practice, high-level goals do not differ substantially between health systems’’ butthat the ‘‘task of priority setting is to convert the chosen high-levelgoals into targets and operational actions for the health system’’.According to them ‘‘a common form of priority setting in systemsboth of mandated health insurance and of devolved tax fundinginvolves the specification of a set of health services (the healthbasket) to which insurees are entitled [and] increasingly, parts ofthe health basket are being shaped . . .using techniques such ascost-effectiveness analysis’’. Nevertheless, they further note, ‘‘it isquite common to observe other priority setting approaches, oftenrunning alongside the health basket, such as targets for healthimprovement, standards for patient safety, or waiting times andother access guarantees’’.

Smith [40] addresses the insurance principle more explicitly inhis paper ‘‘Incorporating financial protection into decision rulesfor publicly financed healthcare treatments’’. Using sophisticatedmodelling he concludes that ‘‘governments can . . . secure an opti-mal system of statutory health insurance coverage by specifying abenefits package in linewith redistributional goals and nurturing acomplementary voluntary insurance market. Under these circum-stances, the conventional cost-effectiveness ratio is the appropri-ate decision rule for including treatments in the package’’.

6. Conclusions

Have recent analytical and policy developments made it moreor less likely that quantitative analysis, with its apparently com-pelling scientific logic, will lead to actively killing people?

The debates continue on whether or not there is a moraldistinction between acts and omissions. It is possible that the‘defence’ of having a lack of ability to save a life could give supportto arguments that ‘society cannot afford to’ to treat those needingtreatment above the set cost/QALY threshold. Protestations that‘we would never go there’ (i.e. actively killing) are less convincingwhen sometimes the same people readily support withholdinglife-saving treatment that exceeds the cost/QALY threshold.

The extensive work on ‘mitigation’—incorporating equity con-siderations within QALYs, valuing QALYs, establishing the ‘correct’

threshold and incorporating other benefits in VBP—introduces a lotof interesting analyses. However, in general they appear to be ac-cepting the primacy of health-gainmaximisation,whilstmodifyingsome of its consequences. Is this because of the compelling attrac-tiveness of the quantifiable and apparently scientific maximisingQALY gain, or does it reflect the reality of what society wants fromhealth care systems?

Beyond more commonly identified objectives of health caresystems, trust and security (and the related ‘insurance principle’)are important but appear to be threatened by unqualified pursuitof maximising health gain. Some have proposed that ‘assurance’can be given by having an explicit guaranteed package of services.However, Smith’s [40] proposal that the ‘‘cost-effectiveness ratiois the appropriate decision rule for including treatments in thepackage’’ would appear to bring us back to the beginning. Therewould be little trust and security for those unable to take out‘complementary voluntary insurance’, who discover their neededtreatment is excluded from the package on grounds of cost-effectiveness. They would still be deemed ‘too expensive to treat’.Although this exclusion might involve far fewer than 1% ofthe population—those who require expensive life-saving or life-prolonging but ‘non-cost-effective’ health care—is this compatiblewith the objectives of a publicly-mandated health service?

Unfortunately, there is frequently little questioning of the ob-jectives of health-care systems. Further, whilst other objectives aresometimes forwarded, they are often difficult to quantify and thereappears to be little analysis on how they can be operationalised inorder to hold their place against the power of QALY maximisation.

The power and attraction of numbers and ‘high-tech’ analysis issuch that they can override what some dismiss as softer ‘irrational’wishes and objectives. But, in attempting to mitigate this dangerwithout addressing the underlying arguments, we risk tying our-selves into sophisticated analytical knots. The force of ‘high-tech’analysis must not be allowed to eclipse the ‘human touch’. Never-theless, numbers probably are still killing people.

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