Affordability and cost-effectiveness: decision-making on the cost-effectiveness plane

HEALTH ECONOMICS

Health Econ. 10: 675–680 (2001)

DOI: 10.1002/hec.639

HEALTH ECONOMICS LETTERS

AFFORDABILITY AND COST-EFFECTIVENESS:DECISION-MAKING ON THE

COST-EFFECTIVENESS PLANE

P. PEDRAM SENDIa AND ANDREW H. BRIGGSb,*a Institute for Medical Technology Assessment, Erasmus Uni�ersity, Rotterdam, The Netherlands

b Health Economics Research Centre, Uni�ersity of Oxford, Oxford, UK

SUMMARY

Much recent research interest has focused on handling uncertainty in cost-effectiveness analysis and in particularthe calculation of confidence intervals for incremental cost-effectiveness ratios (ICERs). Problems of interpretationwhen ICERs are negative have led to two important and related developments: the use of the net-benefit statisticand the presentation of uncertainty in cost-effectiveness analysis using acceptability curves. However, neither ofthese developments directly addresses the problem that decision-makers are constrained by a fixed-budget and maynot be able to fund new, more expensive interventions, even if they have been shown to represent good value formoney. In response to this limitation, the authors introduce the ‘affordability curve’ which reflects the probabilitythat a programme is affordable for a wide range of threshold budgets. The authors argue that the joint probabilityan intervention is affordable and cost-effective is more useful for decision-making since it captures bothdimensions of the decision problem faced by those responsible for health service budgets. Copyright © 2001 JohnWiley & Sons, Ltd.

KEY WORDS — affordability; cost-effectiveness; decision-making analysis

INTRODUCTION

The inclusion of economic outcomes in clinicaltrials is now common [1] and the analysis ofsuch trials has encouraged much research intostatistical methods for so-called stochastic cost-effectiveness analysis [2–4]. The problem of esti-mating confidence limits for cost-effectivenessratios has received much attention and the mostimportant of the recent developments in thisarea are the use of the net-benefit statistic toavoid the problems associated with ratio statis-tics [5] and the use of cost-effectiveness accept-ability curves to summarize uncertainty on thecost-effectiveness plane [6]. Both these ap-

proaches employ a critical threshold value of theICER that represents the maximum society iswilling to pay for health gain in order to distin-guish between what is and what is not cost-effective.

The use of such a critical threshold for thepurposes of decision-making in cost-effectivenessanalysis is widespread; however, there is no con-sensus on what exactly the value of this criticalratio might be. Speculative suggestions havebeen made as to what thresholds might be ap-propriate [7,8], but these have received muchcriticism and it is suggested that commonly usedthresholds may owe more to being convenientround numbers than to being a valid statementconcerning the value of health [9,10].

* Correspondence to: Health Economics Research Centre, University of Oxford, Institute of Health Sciences, Headington,Oxford OX3 7LF, UK. Tel.: +44 1865 226847; fax: +44 1865 226842; e-mail: [email protected]

Copyright © 2001 John Wiley & Sons, Ltd.Recei�ed 4 December 2000

Accepted 23 February 2001

P. PEDRAM SENDI AND A.H. BRIGGS676

More generally, the use of such thresholds fordecision-making in cost-effectiveness analysis hasbeen criticized on the basis that they will lead toan uncontrolled growth in health care expenditure[11]. The problem is that in using such thresholds,no explicit consideration is given to the fact thathealth systems are resource constrained and thatdecision-makers hold budgets, which must bebalanced.

In the next section we introduce an example ofthe posterior joint distribution of incrementalcosts and effects from a published Bayesian cost-effectiveness model that evaluated a prophylacticagent against opportunistic infections in HIV-positive individuals [12]. Using this example weillustrate the problem of using a threshold deci-sion rule in cost-effectiveness analysis and arguethat recent developments for handling uncertaintyin cost-effectiveness analysis are of limited valueto decision-makers because of their failure to ex-plicitly address the resource constraints of thedecision-making process. We then introduce the‘affordability curve’ and ‘cost-effectiveness afford-ability curve’ in order to provide this additionalinformation to decision-makers in a way that mayhelp them to interpret the results of stochasticcost-effectiveness analyses. A final section offerssome concluding comments.

CONVENTIONAL APPROACHES TOHANDLING AND PRESENTING

UNCERTAINTY

The cost-effectiveness (CE) plane [13,14] is now agenerally accepted method of presenting the re-sults of cost-effectiveness analyses. In particularthe presentation of uncertainty as a region in thecost-effectiveness space is widely employed [6,15].Just such a region is illustrated in Figure 1, repre-senting a parametric fit to a large scale MonteCarlo evaluation of the posterior joint distribu-tion of costs and effects of preventing an oppor-tunistic infection in HIV-infected subjects [12].

Cost-effectiveness acceptability curves are usedto summarize the uncertainty on the cost-effec-tiveness plane. They show the probability that anintervention is cost-effective for a wide range ofthreshold (or ceiling) ratios (represented in Figure1 by Rc— the slope of the line passing through theorigin that bisects the plane into the cost-effectiveand cost-ineffective halves). It can be thought ofgeometrically as the region of the cost-effective-ness plane lying below and to the right of the linewith slope Rc as that slope varies from zerotowards infinity. We take a Bayesian viewpointsince the natural interpretation of cost-effective-ness acceptability curves, the probability that an

Figure 1. Joint density of incremental costs and effects for a prophylactic agent for reducing opportunistic infections inHIV-infected patients shown on the CE plane. Ellipses covering an estimated 5, 50 and 95% of the joint density are presentedtogether with lines representing the ceiling ratio Rc and the budget constraint Bc

Copyright © 2001 John Wiley & Sons, Ltd. Health Econ. 10: 675–680 (2001)

AFFORDABILITY AND COST-EFFECTIVENESS 677

Figure 2. Cost-effectiveness acceptability curve showing the probability that the intervention is cost-effective as a function of theceiling ratio

intervention is cost-effective given the data, re-quires a Bayesian perspective [16]. The cost-effec-tiveness acceptability curve in Figure 2 is derivedby plotting the proportion of the joint densitylocated on the acceptable side of the line throughthe origin with slope Rc as this line rotates fromthe horizontal through to the vertical.

The advantage of cost-effectiveness acceptabil-ity curves over confidence intervals for ICERs isthat they unambiguously quantify the probabilityan intervention is cost-effective for different Rc

and they directly address the study question ofwhether the intervention under evaluation is cost-effective. However, they still do not sufficientlyaddress the decision-making problem with respectto the resources required to fund the new pro-gramme under consideration. The fundamentalproblem is that important information about thesize of the programme is being lost by using aone-dimensional measure of outcome, the ceilingratio Rc, to summarize a two-dimensional object,namely the joint distribution of incremental costsand effects. To see the problem, note that aninfinite number of programmes can be found forevery possible ICER. For example, a programmeA with incremental costs of $100 producing 1additional life-year has the same cost-effectivenessratio as a programme B with incremental costs of$1000 and incremental effects of 10 life-years. If

both programmes cannot be funded in smallerincrements (i.e. are not divisible), the ICER aloneis clearly insufficient for decision-making. Indivis-ibilities of programmes are often encountered inprogrammes with high capital costs such as in thefields of radiation oncology and neurosurgery.Furthermore, even at the level of the individual,the treatment under consideration might reflectindivisible units. For example, immunosuppressedHIV-infected patients have to take their medica-tion for the rest of their lifetime— it does notmake sense to fund the treatment for a limitednumber of days.

Note that it is possible for different joint distri-butions to lead to identical cost-effectiveness ac-ceptability curves— just as different magnitudesof cost and effect differences can produce thesame ratio. These joint distributions would varyin terms of incremental costs and effects, butwould have the same correlation between costsand effects and the same coefficients of variation(the ratio of the standard deviation to the mean).The cost-effectiveness acceptability curve, there-fore, does not provide any information about theadditional resources required in order to imple-ment a new programme—however, this is usuallycritical for decision-making within a resource lim-ited health system. In the next section, we suggestan alternative approach to analysing uncertainty



in cost-effectiveness analysis in order to includeinformation concerning possible budget con-straints.

THE AFFORDABILITY ANDCOST-EFFECTIVENESS AFFORDABILITY

CURVES

Just as the ceiling ratio Rc separates the cost-effec-tiveness plane in two areas where the interventionis cost-effective (area A and C in Figure 1) andcost-ineffective (area B and D in Figure 1), theplane can also be divided into affordable andnon-affordable areas. A budget constraint can berepresented by a horizontal line on the CE plane(labelled Bc in Figure 1); below this line (areas Aand B in Figure 1) is where the intervention isaffordable and above this line (area C and D)indicates the intervention is not affordable. Em-ploying an estimate of the number of individualsthat are candidates for treatment allows the con-struction of an affordability curve, i.e. a curvethat plots the probability the intervention is af-fordable, as a function of the budget constraintBc. This approach produces additional and impor-tant information for decision-makers and is ahelpful tool for communicating with policy-

makers, more helpful than the cost-effectivenessacceptability curve alone. One can think of theaffordability curve as the area of the joint distri-bution of incremental costs and effects below theceiling budget (area A and B), accounting for thesize of the programme (number of individuals), asthe horizontal line described by Bc moves fromthe top down to the horizontal axis of the cost-effectiveness plane. Such an affordability curvefor 1000 individuals and the joint distribution ofincremental costs and effects (Figure 1) is shownin Figure 3.

In addition, the ceiling ratio Rc and the ceilingbudget Bc in combination can be used to distin-guish between four areas on the cost-effectivenessplane (Figure 1):

(i) area A where the programme is both afford-able and cost-effective;

(ii) area B where the programme is affordablebut cost-ineffective;

(iii) area C where the programme is not afford-able but cost-effective; and

(iv) area D where the new programme is neitheraffordable nor cost-effective.

Area A reflects the most desirable outcomewhile area D the least desirable. In the presence oflimited resources, areas A and B (programmeis affordable) are of most interest. Most policy-

Figure 3. An affordability curve showing the probability that the intervention is affordable (for 1000 patients) as a function ofthe budget constraint Bc


AFFORDABILITY AND COST-EFFECTIVENESS 679

Figure 4. A cost-effectiveness affordability curve showing the probability that an intervention is simultaneously cost-effectiveand affordable (for 1000 patients) as a function of the ceiling ratio and the budget constraint

makers, we believe, would be interested in area Afor different levels of the ceiling ratio Rc and thebudget constraint Bc. To account for this, we canconstruct a set of ‘cost-effectiveness affordabilitycurves’. Such a set of curves would describe theprobability that the treatment under considerationis both affordable and cost-effective (area A) as afunction of Rc for different values of Bc. Figure 4demonstrates such a set of ‘cost-effectiveness af-fordability curves’ for different budget constraintswith the acceptability curve of Figure 2 as thelimiting case where there is no constraint on theavailable budget.

The decision rules of cost-effectiveness analysishave been widely explored in the literature. Wein-stein [9] has argued that the theoretically correctmethod for obtaining the relevant ceiling ratio isfrom the shadow price of an explicit budget con-straint, while Karlsson and Johannesson [17] havesuggested that either the ceiling ratio is obtainedfrom the budget constraint or the budget is deter-mined from a fixed value for the ceiling ratio. Inpractical application, however, it is often the casethat a fixed decision rule is applied in a con-

strained budget situation and the strength of theapproach described above is that it unambigu-ously quantifies the location of the joint distribu-tion of incremental costs and effects on the CEplane.

The approach described in this paper is basedon several assumptions. First, the approach as-sumes that there is a stream of additionalresources available at a constant marginalopportunity cost. Furthermore, the approach as-sumes that the cost-effectiveness of the pro-gramme is independent of its size. Similarly, it isassumed that affordability is not related to cost-effectiveness— if a therapy were highly cost-effec-tive, but not affordable, it is likely that someother intervention would be displaced whichwould impact on the relevant ceiling ratio fordecision-making. Finally, we assumed that theprogramme is indivisible in order to estimate af-fordability curves. In circumstances where the as-sumptions of constant returns to scale andconstant marginal opportunity costs do not hold,an alternative method for handling uncertainty incost-effectiveness analysis has been suggested [18].



CONCLUSION

Recent developments in handling and presentinguncertainty in cost-effectiveness analysis have notaddressed the issue of a resource constrainedhealth care system where decision-makers holdbudgets from which to fund new health careinterventions. In order to address this problem,we propose the use of affordability curves todirectly quantify the problem of resource con-straints. We believe that this sort of information isespecially important for analyses from the systemand third party payer’s perspective (rather thanthe societal perspective) where the budget for thetreatment under consideration is often given andtherefore easier to determine. We believe that intimes of scarcity of health care resources, infor-mation about both cost-effectiveness and afford-ability is likely to produce more usefulinformation for policy makers.

ACKNOWLEDGEMENTS

Dr Sendi is supported by the Swiss National Science Founda-tion (grant c823B-056512) and the Lichtenstein-Stiftung. DrBriggs is supported by a joint UK MRC/South East RegionTraining Fellowship. The comments of two anonymous refer-ees are gratefully acknowledged.

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Affordability and cost-effectiveness: decision-making on the cost-effectiveness plane