Subgroups and Heterogeneity in Cost-Effectiveness Analysis

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1 Pharmacoeconomics 2008; 26 (9): BRIEFING PAPER /08/ /$48.00/ Adis Data Information BV. All rights reserved. Subgroups and Heterogeneity in Cost-Effectiveness Analysis Mark Sculpher Centre for Health Economics and NICE Decision Support Unit, University of York, Heslington, York, UK Abstract The National Institute for Health and Clinical Excellence (NICE) is required to consider cost effectiveness when issuing guidance about the use of health technologies within the UK NHS. Cost effectiveness is a means of supporting a system objective of maximizing population health gain from the available budget. There is a range of sources of variation between individuals in disease prognosis, and in the costs and effects of health technologies. It is often possible to explain some of this variation on the basis of the clinical and sociodemographic characteristics of patients. This facilitates subgroup-specific estimates of parameters in decision analytic models and provides a means of assessing heterogeneity in cost effectiveness between different types of patient. Given the objective of the NHS, there is a clear need for NICE, and similar decision makers in other systems, to reflect this heterogeneity by being as specific as possible about the characteristics of the recipients of new treatments. The use of subgroup analysis in cost-effectiveness analysis raises a number of methodological questions that have been given little consideration in the literature. They include a need to define the possible sources of heterogeneity that exist, which extends beyond relative treatment effect (which is the focus of clinical trial analysis) to include, for example, sources relating to baseline event rates. There is also the issue of how heterogeneity in model parameters should be estimated and how uncertainty should be appropriately quantified. A major issue also exists concerning the appropriateness, in terms of equity, of using all or some of the subgroup analyses as a basis of decision making. NICE needed to consider these and other issues when updating its methods guidance. 1. Background cost). [1] This trade-off is assessed by comparing the incremental cost per QALY gained against the cost- The brief of the National Institute for Health and effectiveness threshold, which acts as a proxy for the Clinical Excellence (NICE) to consider the cost opportunity cost. [2] In other words, in assessing cost effectiveness, as well as the clinical effectiveness, of new technologies has some important methodologisions that are consistent with maximizing popula- effectiveness, NICE is concerned with making decical implications. To achieve cost effectiveness, a new technology should generate more health gain to tion health gains subject to NHS budget constraints. NHS patients than it displaces as a result of any Within a given patient population it is possible to additional cost imposed on the system (opportunity estimate the mean cost effectiveness of an interven-

2 800 Sculpher tion compared with relevant comparators. However, it is recognized that patients vary, in a number of different ways, regarding the benefit they achieve from that intervention and/or the cost of delivering it. It is often possible to explain some of this variation in terms of the characteristics of the patient. These characteristics may be known when a decision is taken regarding the appropriate clinical management. These baseline characteristics might be sociodemographic (e.g. age, sex, social class, race) or clinical (e.g. disease severity). Arguably, subgroups have more prominence for cost effectiveness than clinical effectiveness. For the latter, it is a case of establishing whether a treatment remains relatively more effective than its comparators across different types of patients. For cost effectiveness, the absolute degree of benefit from the intervention, as well as its cost, matters. For NICE s decision making, then, it is not sufficient to know that a treatment consistently benefits a population of patients whatever their characteristics: the degree of benefit alongside the cost matters. Therefore, average cost effectiveness can mask important sources of heterogeneity that may be important to reflect in decision making by offering positive guidance for patients with particular characteristics. This is true if the technology is consid- ered cost effective on average because there may be subgroups of patients for whom it is not cost effective. It is also true when the intervention is not cost effective on average because there may be subgroups in whom it is cost effective. 2. What is Gained from Reflecting Subgroups and Heterogeneity in Decisions? Appropriately reflecting subgroups and hetero- geneity in decisions has the potential to increase population health gains by focusing the use of an intervention in patients for whom the health gain is greater than the health outcomes displaced from other programmes and interventions. This is illustrated in figure 1, [3] which shows what health systems can gain from reflecting subgroups in their decisions about technologies (what Net benefit gain from stratification ($US 1000) X 4 X Age and location Location only Age only 1 Anterior >75 y ($US13 410) 2 Inferior >75 y ($US16 246) 3 Anterior y ($US20 601) 4 Inferior y ($US27 783) 5 Anterior y ($US49 877) 6 Inferior y ($US74 816) X5 6 X X 1 0 X Threshold value for a life-year gained ( 1000) Fig. 1. Gains in net monetary benefit from reflecting subgroups and heterogeneity in decisions. The context for the example is a costeffectiveness analysis of streptokinase vs alteplase (recombinant tpa) for acute myocardial infarction. The subgroups (numbered 1 to 6) relate to differences in the relative treatment effect (in terms of mortality) of the therapies according to patient age and location of the infarct (anterior or inferior). Reproduced from Coyle et al. [3] with permission from John Wiley & Sons Ltd. ICER = incremental costeffectiveness ratio; X is the ICER for the age-location cohort (see also figure key). Coyle et al. [3] call stratification ). The metric for this gain is net monetary benefit (the y-axis in the figure). [4] This is the health improvement resulting from the decision that is valued in monetary terms using the cost-effectiveness threshold, minus the cost of the decision (e.g. if a decision generates, for an individual patient, ten QALYs at a cost of , the net monetary benefit, assuming a per QALY threshold, is [ ] = ). This would be multiplied by the number of patients in the relevant (sub)-population to calculate total population net monetary benefits. Another way of interpreting net monetary benefit is that, if the monetary value is divided by the cost-effectiveness threshold, this is the net gain in health (e.g. QALYs), taking into account the gains from the intervention and the opportunity costs. The context for the example is a cost-effective- ness analysis of streptokinase versus alteplase (re-

3 Subgroups and Heterogeneity in CEA 801 As mentioned above, the focus of subgroup ana- lysis for clinical evaluation is whether the relative treatment effect between two interventions is con- stant over different patient characteristics defined at the point at which a treatment is selected (i.e. at baseline); in particular, whether there is a qualita- tive interaction [6] (i.e. where the treatment is more effective than its comparator in one subgroup but less effective in another). However, subgroup differ- ences in cost effectiveness can be a result of several types of heterogeneity, which can be described under a series of headings. combinant tpa) for acute myocardial infarction that used life-years rather than QALYs as the measure of health benefit. [5] The average incremental cost per life-year gained for alteplase across all patients was about $US The subgroups relate to differences in the relative treatment effect (in terms of mortality) of the therapies according to patient age and location of the infarct (anterior or inferior). Figure 1 shows the gain in net monetary benefit, when decisions reflect subgroup cost effectiveness in terms of age, infarct location and both of these characteristics compared with making decisions on the basis of average cost effectiveness. These gains are shown as a function of the cost-effectiveness threshold (shown on the x-axis). At very low costeffectiveness thresholds (<$US per life-year gained when both types of subgroup are considered), there is no gain from using subgroups, as the decision would be not to support the use of alteplase at all, on average or for any subgroups, so no change in decision (or population net benefit) would follow from using subgroups. Similarly, at very high thresholds (in excess of about $US per life-year gained when both types of subgroup are considered), the gains from using subgroups would also be zero, as alteplase would be considered cost effective on average and for all subgroups. As the threshold increases from zero until about $U per life-year gained (the average incremental ratio across all patients), alteplase would be considered cost effective in more subgroups but not on average, so there would be net benefit gains from considering subgroups individu- ally. The function peaks where the threshold equals the average incremental cost-effectiveness ratio because, beyond this point, alteplase would be con- sidered not cost effective in fewer subgroups. Once the threshold is high enough to support the use of alteplase in the least cost-effective subgroup, the gains from making decisions at the subgroup level rather than average population level fall to zero. 3. What are the Various Forms of Subgroup and Heterogeneity? 3.1 Factors Potentially Known at Treatment Selection that are Related to the Treatment The main consideration here is the standard clin- ical subgroup effect: the relative treatment effect (e.g. the hazard ratio or odds ratio of a particular event) systematically varies between patients on the basis of particular baseline characteristics. It would also include situations where the cost of the treat- ment systematically varies between patients, the most obvious case being where dosage (and hence acquisition cost) is related to patient weight. 3.2 Factors Potentially Known at Treatment Selection Related to the Disease but not to the Treatment Perhaps the most prominent consideration here is the rate of particular events (or mean measure of outcome on a continuous scale) with a standard therapy or with no treatment (these are often termed baseline events or effects ). For example, if the probability of an undesirable clinical event on standard therapy is 10% over 5 years in a young- er subgroup and 20% in an older subgroup, and assuming that a new treatment halves the risk in both groups (i.e. a constant relative treatment effect), the absolute risk reduction and hence benefit of the new treatment will be greater in the older subgroup. Additionally the cost of particular clinical events might vary systematically between patients. For ex-

4 802 Sculpher ample, Briggs et al. [7] showed that the cost of various cardiac events varied according to patients characteristics, such as age and presence of diabetes mel- litus. It may also be possible that the health-related quality of life (HR-QOL) impact of an event may vary by patient type. For example, Henriksson et al. [8] showed that the change in patients EQ-5D responses (valued using public preferences) following alternative forms of management for acute coro- nary syndrome partly depended on whether they had experienced an earlier myocardial infarction. An- other relevant factor is that the prognosis associated with a particular event may differ by patient charac- teristic (e.g. future QALYs gained from avoiding a diabetic complication may differ between patients depending on the diabetic events they may have experienced earlier). 3.3 Factors Potentially Known at Treatment Selection Unrelated to the Disease Some patient characteristics influence cost effec- tiveness but are unrelated to disease. An important example is patient age independent of its influence on relative treatment effects and the implications of a disease. This is because age has a strongly negative relationship with patients life expectancy and QOL. The gain in quality-adjusted life expectancy from a treatment with a positive effect on mortality will, all other things being equal, be greater in younger than older patients. 3.5 Preferences It is recognized [11,12] that there is variation in preferences between individuals regarding health. One aspect of this is that a patient s preference may influence the outcome they experience from treat- ment, in which case subgroups might be defined in terms of patient preferences relating to treatment (i.e. an example of a type of subgroup as described in section 3.1). When patients preferences are part of the measure of health benefit (e.g. in a QALY), patients might vary systematically in how they value particular states of health. If this information can be captured when a treatment is selected, preference subgroups can be defined in terms of the QALY effect of a given health state. [11] This may also be possible when public preferences are used to derive the measure of health benefit (as is the case in the NICE reference case). Subgroups in terms of public preferences could be constructed. [12] For example, it could be the case that public preferences for a health state varied according to the respondents age and this could be reflected in cost-effectiveness studies in terms of which individuals are ultimately given access to treatment. However, this would raise a number of political and equity issues. [12] 3.6 Factors Revealed Over Time The sources of heterogeneity considered above all relate to characteristics of patients that are poten- tially observable when treatment decisions are taken. However, the fact that patients respond different- 3.4 Factors Potentially Known at Treatment ly to interventions can, in some instances, be observ- Selection Unrelated to the Patient ed over a relatively short period of time. This gives the opportunity to make decisions about whether or not to change or curtail treatment on the basis of short-term response. Increasingly, treatment stop- ping rules are being considered as one form of therapeutic strategy in cost-effectiveness analysis, to be compared with the full range of treatments avail- able for a given patient group. Although stopping rules relate to heterogeneity in patient response, they do not generate subgroup estimates of cost effective- ness and as a result are fundamentally different from those types of heterogeneity considered above. It is possible to identify sources of heterogeneity in cost effectiveness unrelated to the patient. The most obvious case is when the cost effectiveness of an intervention varies according to where it is provided or who delivers it. For example, it is quite possible that costs and/or effects can vary by clinical centre as evidenced in multi-centre randomized trials. [9] Another example is that the effectiveness of a procedure might vary according to the prior experience and training of the clinician. [10]

5 Subgroups and Heterogeneity in CEA How Should Appropriate Subgroups essentially represent arbitrary hurdles for identifybe Identified? ing meaningful subgroups for decision making. [14] It can be argued that pre-specification of potential Although it may be possible to categorize differ- subgroups prior to data analysis based on clinical ent types of subgroup, criteria are needed to estab- and economic plausibility represents a more approlish when a particular source of heterogeneity priate criterion. should be reflected in an analysis to inform decision In terms of the NICE process, the scoping stage making. A series of issues are relevant to this. (for both multiple and single technology appraisals) is an opportunity to define subgroups, but it is 4.1 Is the Subgroup Likely to be doubtful whether this can be fully achieved at that Operationalized in Routine Practice? stage of the process. A full specification of possible A key criterion for whether the potential existhe technology assessment process itself. sources of heterogeneity is something that is part of tence of cost-effectiveness subgroups should be reflected in decisions is whether the provision of an intervention to one or more specific subgroups can 4.3 How Can Uncertainty Associated with be operationalized in practice. This would require Subgroups be Expressed? that the relevant patient characteristic(s) are easily NICE decisions are informed by estimates of observed or routinely measured (e.g. age, sex, key expected costs and effects and the cost effectiveness clinical characteristics). Of course the cost of underof a technology is not reliant on differences in these taking any such measurements, to the extent that this estimates between options being statistically signifis not currently the case in routine practice, would icant. [15] This approach is also relevant to interpreneed to be included in the subgroup-specific estitation of subgroups. Rather than the arbitrary rules mates of cost effectiveness. Another consideration is of statistical significance, the uncertainty of cost whether the measurement defining the subgroup effectiveness by subgroup can be quantified. In the could be inappropriately influenced by a patient in form of a probabilistic sensitivity analysis and aporder to acquire a preferred treatment to which they propriate scenario analysis, a careful assessment of otherwise would not have access. uncertainty will show the potential trade-off between 4.2 How Can Data Dredging be Avoided? identifying a larger number of subgroups (and hence increasing expected population health gains Uncertainty inevitably arises about whether a as shown in figure 1) and the fact that this draws on particular difference between subgroups in cost efsubgroup-specific smaller amounts of evidence and hence increases fectiveness is genuine or simply reflects random uncertainty. noise in available data. The chance of identifying Some of this quantification of uncertainty has to spurious subgroups is increased if they are searched be undertaken using summary data. For example, it for without any clear scientific rationale (so called is commonplace in cost-effectiveness models to as- data dredging ); that is, some apparent subgroups sume that a relative treatment effect is independent will be found by chance. Decision rules for sub- of baseline risk: this is widely assumed in models group identification (in terms of relative treatment looking at the cost effectiveness of, for example, effects) exist in the field of clinical trial analysis to primary and secondary prevention of coronary arprovide evidence that data dredging has not been tery disease. [7] Although often underpowered, metaconducted. [13] These include the need for statistical regression can be used, based on summary data from significance in appropriately specified subgroup trials, to estimate the mean relationship (and its analysis (i.e. in treatment by co-variate interactions). uncertainty) between event rates in trial control However, these safety rules can be seen as impos- groups (baseline events) and treatment effects. [16] ing costs in terms of health gains because they This relationship can then be reflected in the

6 804 Sculpher parameterization of a cost-effectiveness model. For example, in looking at the cost effectiveness of prophylactic antibacterials used in caesarean section, Cooper et al. [17] used this method within a Bayesian framework to quantify the relationship between the underlying risk of wound infection and the treatment effect of antibacterials. An appropriate quantification of uncertainty in subgroup analysis is usually most easily achieved when individual patient data are available for analysis. This facilitates the use of formal modelling of treatment-co-variate interactions (for relative treatment effects). Regression-based models for other parameters also enables the quantification of parameter values relating to particular patient characteristics including the precision of, and correlation between, those parameters (e.g. baseline risks and costs of events). One important advantage of access to individual patient data is the possibility of assess- ing patient characteristics that predict the baseline risk of particular clinical events. These risk models have been important in economic evaluations in a range of clinical areas including, for example, drugeluting stents. [18] 4.4 What Data Should Inform the Identification of Subgroups? 4.5 When Would a Subgroup be Considered Legitimate for Decision Making? In addition to the practical and statistical issues associated with identifying appropriate cost-effectiveness subgroups, there may be equity/ethical con- The strengths of randomized trial evidence as a means of quantifying relative treatment effects are generally accepted. This is also true when estimat- ing treatment by co-variate interactions (i.e. sub- group differences in relative treatment effects). However, for many of the other types of subgroups discussed in section 3, non-randomized evidence may be appropriate. For example, large longitudinal observational studies including a UK patient popu- lation may be the ideal source of information on heterogeneity in baseline event risks, costs and prognosis. straints on which subgroups are used for decision making. In particular, the use of sociodemographic characteristics such as age, sex, race and social class to determine which subgroups should have access to a particular intervention may be considered inequi- table. However, judgements of this type may depend on what type of subgroup is being considered. For example, it may be considered appropriate to use age as a basis for selecting an appropriate subgroup to receive a treatment if the effect of age is on the relative treatment effect itself (e.g. the treatment is less effective in older patients) or the disease (e.g. older patients are at higher baseline risk of an event so a treatment that reduces risk independent of base- line risk will, all other things being equal, be more cost effective in older patients). In contrast, it may not be considered acceptable to use age as a basis of defining subgroups if it does not reflect an age effect on the treatment or the disease. For example, all other things equal, saving the life of a 30-year-old will be more cost effective than doing so in a 70-year-old because the older patient has fewer QALYs to gain. Similar considera- tions are likely to apply in terms of using sex as a basis of defining subgroups given that women have a greater life expectancy than men. This may also be the case for race and social class, although these characteristics may introduce greater complexities. It is important to be clear about the implications of placing equity constraints on the definition of subgroups. As described in section 2, the use of appropriately specified subgroups can increase the health gains generated from an intervention. Con- versely, failure to use subgroups can impose costs on the system in terms of health gains forgone. In other words, imposing equity constraints will result in lost health gains somewhere in the system. [19] In the context of the Coyle et al. [3] example of the choice of thrombolytic for myocardial infarction, this can be worked out directly from the analysis shown in figure 1. It may be important to present decision makers with implications of imposing equity constraints regarding the patient characteristics considered legitimate to define the various types of subgroups. This would give them the opportunity to

7 Subgroups and Heterogeneity in CEA 805 judge when the costs of imposing such constraints are too great. An alternative approach would be to specify exactly what subgroups are permitted to be used in NICE decisions, and these rules would apply to every technology considered. The NICE Social Value Judgements document [20] could be considered to define some of these rules, although it is not highly prescriptive. 5. Discussion NICE s 2004 Methods Guide [15] dealt with heterogeneity and subgroups at quite a general level. It focussed on the general principles of subgroup analysis. The most important ones were (i) that subgroups should be clearly defined and their clin- ical basis justified (including, where appropriate, biological plausibility); (ii) the methods for con- ducting subgroup analysis should be clearly de- scribed, including the methods for quantifying un- certainty in subgroup measures of effectiveness/cost effectiveness; (iii) there was some discussion of the importance of defining subgroups in the scoping document for an appraisal. This paper is based on a briefing document that was developed to inform NICE in developing their updated methods guidance. Part of the process included holding a workshop with individuals from a range of disciplines and backgrounds, and the brief- ing document provided an overview of issues for that meeting. The document outlined a range of questions for discussion at the workshop. The first of these related to which types of subgroups should be considered in economic evaluation studies under- taken to inform the decisions of the Institute. In particular, are there other sources of heterogeneity that are not described in this document? Is there any role for looking at any forms of preference subgroups that were not explicitly considered in the 2004 Methods Guide? A second question raised was whether there is a role for subgroups defined by the location of treat- ment? For example, costs in some hospitals might make a technology cost effective, but this may not be true in other hospitals; the actual price paid for a device or pharmaceutical may vary by hospital and affect cost effectiveness; appropriately skilled and experienced clinicians may not be available to deliv- er particular interventions in some hospitals. A third question concerned the appropriate iden- tification of subgroups. Particular issues were (i) the stage of the technology appraisal process when sub- group issues should be raised: scoping, protcol de- velopment etc.; (ii) whether there is a case for a further stage in the appraisal process to be developed, such as an analysis plan from the assessment team and/or manufacturer for evidence synthesis and modelling; (iii) how clinical plausability could be justified in defining subgroups, e.g. should assessment teams/manufacturers be expected to des- cribe what relevant clinical opinion has been used in this process, or can the issue of plausability be left to the Appraisal Committee (informed by its experts) to decide?; (iv) when should the question of whether a given subgroup can be operationalized in routine practice be considered: is it something assessment teams and manufacturers should be expected to con- sider explicitly? A fourth question raised in the briefing document related to how subgroup-specific parameters should be estimated. Some specific issues raised were (i) whether NICE should require formal hypothesis tests in the reporting of subgroup-specific parameters, or is a more general estimation approach appropriate; (ii) whether other statistical methods should be specified in the guidance, such as the need for details of model selection, specification and fit in risk-prediction models and the methods used in meta-regression to estimate the relationship between underlying event risks and treatment effect. A final question related to whether any equity constraints should be placed on subgroups. Specific issues included the identification of patient charac- teristics that could, if employed in treatment-allocation decisions, raise issues of equity; the implications of NICE s social value judgements document [20] for methods guidance; and whether the potential costs (in terms of population net benefits) of ignoring subgroups in decision making should be

8 806 Sculpher required as a source of information to inform deci- sion making. Med Decis Making 1998; 18 Suppl.: S Stinnett AA, Mullahy J. Net health benefits: a new framework for the analysis of uncertainty in cost-effectiveness analysis. 6. Conclusions This paper has described some key issues relating to heterogeneity and subgroup analysis in cost effec- tiveness. It has also defined a number of specific questions that NICE considered in developing its 2008 methods guidance update. Given an objective to maximize population EUROPA study. Heart 2007; 93: health gain from available budgets, there is a clear need for NICE, and similar decision makers in other systems, to be as specific as possible about the 2008; 94: characteristics of the recipients of new treatments. 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Stat Meth- The author has no conflicts of interest that are directly ods Med Res 2002; 11: relevant to the content of this article. 18. Bagust A, Grayson A, Palmer N, et al. Cost-effectiveness of a The author gratefully acknowledges Karl Claxton, John drug-eluting coronary artery stenting in a UK setting: costutility study. Heart 2006; 92 (1): Brazier and Alex Sutton for comments on earlier drafts. Any remaining errors are the responsibility of the author alone. References 1. Claxton K, Briggs A, Buxton M, et al. Value based pricing for NHS drugs: an opportunity not to be missed? BMJ 2008; 336: Culyer A, McCabe C, Briggs A, et al. Searching for a threshold, not setting one: the role of the National Institute for Health and Clinical Excellence. J Health Serv Res Pol 2007; 12: Coyle D, Buxton MJ, O Brien BJ. Stratified cost-effectiveness anaylsis: a framework for establishing efficient limited use criteria. Health Econ 2003; 12: Epstein DM, Chalabi Z, Claxton K, et al. Efficiency, equity and budgetary policies: informing decisions using mathematical programming. Med Dec Making 2007; 27: National Institute for Health and Clinical Excellence. Social value judgements: principles for the development of NICE guidance [draft for public consultation]. London: NICE, 2008 Correspondence: Professor Mark Sculpher, Centre for Health Economics, University of York, Heslington, York, YO10 5DD, UK. mjs23@york.ac.uk