Cost-effectiveness acceptability curves in the dock: case not proven?

Cost-effectiveness of adding oseltamivir to primary care for influenza-like-illness: economic evaluation alongside the randomised controlled ALIC4E trial in 15 European countries

BACKGROUND

Oseltamivir is usually not often prescribed (or reimbursed) for non-high-risk patients consulting for influenza-like-illness (ILI) in primary care in Europe. We aimed to evaluate the cost-effectiveness of adding oseltamivir to usual primary care in adults/adolescents (13 years +) and children with ILI during seasonal influenza epidemics, using data collected in an open-label, multi-season, randomised controlled trial of oseltamivir in 15 European countries.

METHODS

Direct and indirect cost estimates were based on patient reported resource use and official country-specific unit costs. Health-Related Quality of Life was assessed by EQ-5D questionnaires. Costs and quality adjusted life-years (QALY) were bootstrapped (N = 10,000) to estimate incremental cost-effectiveness ratios (ICER), from both the healthcare payers' and the societal perspectives, with uncertainty expressed through probabilistic sensitivity analysis and expected value for perfect information (EVPI) analysis. Additionally, scenario (self-reported spending), comorbidities subgroup and country-specific analyses were performed.

RESULTS

The healthcare payers' expected ICERs of oseltamivir were €22,459 per QALY gained in adults/adolescents and €13,001 in children. From the societal perspective, oseltamivir was cost-saving in adults/adolescents, but the ICER is €8,344 in children. Large uncertainties were observed in subgroups with comorbidities, especially for children. The expected ICERs and extent of decision uncertainty varied between countries (EVPI ranged €1-€35 per patient).

CONCLUSION

Adding oseltamivir to primary usual care in Europe is likely to be cost-effective for treating adults/adolescents and children with ILI from the healthcare payers' perspective (if willingness-to-pay per QALY gained > €22,459) and cost-saving in adults/adolescents from a societal perspective.

Peer-led physical activity intervention for girls aged 13 to 14 years: PLAN-A cluster RCT

Background

Increasing physical activity among girls is a public health priority. Peers play a central role in influencing adolescent behaviour. Peer-led interventions may increase physical activity in adolescent girls, and a feasibility trial had shown that PLAN-A (Peer-led physical Activity iNtervention for Adolescent girls) had evidence of promise to increase physical activity in adolescent girls.

Objective

The objective was to test whether or not PLAN-A can increase adolescent girls’ physical activity, relative to usual practice, and be cost-effective.

Design

This was a two-arm, cluster-randomised controlled trial, including an economic evaluation and a process evaluation.

Participants

State-funded secondary schools in the UK with girls in Year 9 (aged 13–14 years) participated in the trial. All Year 9 girls in participating schools were eligible.

Randomisation

Schools were the unit of allocation. They were randomised by an independent statistician, who was blinded to school identities, to the control or intervention arm, stratified by region and the England Index of Multiple Deprivation score.

Intervention

The intervention comprised peer nomination (i.e. identification of influential girls), train the trainers (i.e. training the instructors who delivered the intervention), peer supporter training (i.e. training the peer-nominated girls in techniques and strategies underpinned by motivational theory to support peer physical activity increases) and a 10-week diffusion period.

Outcomes

The primary outcome was accelerometer-assessed mean weekday minutes of moderate to vigorous physical activity among Year 9 girls. The follow-up measures were conducted 5–6 months after the 10-week intervention, when the girls were in Year 10 (which was also 12 months after the baseline measures). Analysis used a multivariable, mixed-effects, linear regression model on an intention-to-treat basis. Secondary outcomes included weekend moderate to vigorous physical activity, and weekday and weekend sedentary time. Intervention delivery costs were calculated for the economic evaluation.

Results

A total of 33 schools were approached; 20 schools and 1558 pupils consented. Pupils in the intervention arm had higher Index of Multiple Deprivation scores than pupils in the control arm. The numbers randomised were as follows: 10 schools (n = 758 pupils) were randomised to the intervention arm and 10 schools (n = 800 pupils) were randomised to the control arm. For analysis, a total of 1219 pupils provided valid weekday accelerometer data at both time points (intervention, n = 602; control, n = 617). The mean weekday moderate to vigorous physical activity was similar between groups at follow-up. The central estimate of time spent engaging in moderate to vigorous physical activity was 2.84 minutes lower in the intervention arm than in the control arm, after adjustment for baseline mean weekday moderate to vigorous physical activity, the number of valid days of data and the stratification variables; however, this difference was not statistically significant (95% confidence interval –5.94 to 0.25; p = 0.071). There were no between-arm differences in the secondary outcomes. The intervention costs ranged from £20.85 to £48.86 per pupil, with an average cost of £31.16.

Harms

None.

Limitations

The trial was limited to south-west England.

Conclusions

There was no evidence that PLAN-A increased physical activity in Year 9 girls compared with usual practice and, consequently, it was not cost-effective.

Future work

Future work should evaluate the utility of whole-school approaches to promote physical activity in schools.

Trial registration

This trial is registered as ISRCTN14539759.

Funding

This project was funded by the National Institute for Health Research (NIHR) Public Health Research programme and will be published in full in Public Health Research; Vol. 10, No. 6. See the NIHR Journals Library website for further project information. This trial was designed and delivered in collaboration with the Bristol Randomised Trials Collaboration (BRTC), a United Kingdom Clinical Research Commission (UKCRC)-registered Clinical Trials Unit that, as part of the Bristol Trials Centre, is in receipt of NIHR Clinical Trials Unit support funding. The sponsor of this trial was University of Bristol, Research and Enterprise Development www.bristol.ac.uk/red/. The costs of delivering the intervention were funded by Sport England.

Handling Uncertainty in Cost-Effectiveness Analysis: Budget Impact and Risk Aversion

Methods to handle uncertainty in economic evaluation have gained much attention in the literature, and the cost-effectiveness acceptability curve (CEAC) is the most widely used method to summarise and present uncertainty associated with program costs and effects in cost-effectiveness analysis. Some researchers have emphasised the limitations of the CEAC for informing decision and policy makers, as the CEAC is insensitive to radial shifts of the joint distribution of incremental costs and effects in the North-East and South-West quadrants of the cost-effective plane (CEP). Furthermore, it has been pointed out that the CEAC does not incorporate risk-aversion in valuing uncertain costs and effects. In the present article, we show that the cost-effectiveness affordability curve (CEAFC) captures both dimensions of the joint distribution of incremental costs and effects on the CEP and is, therefore, sensitive to radial shifts of the joint distribution on the CEP. Furthermore, the CEAFC also informs about the budget impact of a new intervention, as it can be used to estimate the joint probability that an intervention is both affordable and cost-effective. Moreover, we show that the cost-effectiveness risk-aversion curve (CERAC) allows the analyst to incorporate different levels of risk-aversion into the analysis and can, therefore, be used to inform decision-makers who are risk-averse. We use data from a published cost-effectiveness model of palbociclib in addition to letrozole versus letrozole alone for the treatment of oestrogen-receptor positive, HER-2 negative, advanced breast cancer to demonstrate the differences between CEAC, CEAFC and CERAC, and show how these can jointly be used to inform decision and policy makers.

Generating, Presenting, and Interpreting Cost-Effectiveness Results in the Context of Uncertainty: A Tutorial for Deeper Knowledge and Better Practice

This tutorial aims to help make the best available methods for generating and presenting cost-effectiveness results with uncertainty common practice. We believe there is a need for such type of tutorial because some erroneous practices persist (e.g., identifying the cost-effective intervention as the one with the highest probability to be cost-effective), while some of the more advanced methods are hardly used (e.g., the net loss statistic ‘NL’, expected net loss curves and frontier). The tutorial explains with simple examples the pros and cons of using ICER, incremental net benefit and NL to identify the cost-effective intervention, both with and without uncertainty accounted for probabilistically. A flowchart provides practical guidance on when and how to use ICER, incremental net benefit or NL. Different ways to express and present uncertainty in the results are described, including confidence and credible intervals, the probability that a strategy is cost-effective (as usually shown with cost-effectiveness acceptability curves (CEACs)) and the expected value of perfect information (EVPI). The tutorial clarifies and illustrates why EVPI is the only measure accounting fully for decision uncertainty, and why NL curves and the NL frontier may be preferred over CEACs and other plots for presenting cost-effectiveness results in the context of uncertainty. The easy calculations and a worked-out real-life example will help users to thoroughly understand and correctly interpret key cost-effectiveness results. Examples with mathematical calculations, interpretation, plots and R code are provided.

Probabilistic Sensitivity Analysis in Cost-Effectiveness Models: Determining Model Convergence in Cohort Models

Probabilistic sensitivity analysis (PSA) demonstrates the parameter uncertainty in a decision problem. The technique involves sampling parameters from their respective distributions (rather than simply using mean/median parameter values). Guidance in the literature, and from health technology assessment bodies, on the number of simulations that should be performed suggests a 'sufficient number', or until 'convergence', which is seldom defined. The objective of this tutorial is to describe possible outcomes from PSA, discuss appropriate levels of accuracy, and present guidance by which an analyst can determine if a sufficient number of simulations have been conducted, such that results are considered to have converged. The proposed approach considers the variance of the outcomes of interest in cost-effectiveness analysis as a function of the number of simulations. A worked example of the technique is presented using results from a published model, with recommendations made on best practice. While the technique presented remains essentially arbitrary, it does give a mechanism for assessing the level of simulation error, and thus represents an advance over current practice of a round number of simulations with no assessment of model convergence.

Methods to construct a step-by-step beginner's guide to decision analytic cost-effectiveness modeling

BACKGROUND

Although guidance on good research practice in health economic modeling is widely available, there is still a need for a simpler instructive resource which could guide a beginner modeler alongside modeling for the first time.

AIM

To develop a beginner's guide to be used as a handheld guide contemporaneous to the model development process.

METHODS

A systematic review of best practice guidelines was used to construct a framework of steps undertaken during the model development process. Focused methods review supplemented this framework. Consensus was obtained among a group of model developers to review and finalize the content of the preliminary beginner's guide. The final beginner's guide was used to develop cost-effectiveness models.

RESULTS

Thirty-two best practice guidelines were data extracted, synthesized, and critically evaluated to identify steps for model development, which formed a framework for the beginner's guide. Within five phases of model development, eight broad submethods were identified and 19 methodological reviews were conducted to develop the content of the draft beginner's guide. Two rounds of consensus agreement were undertaken to reach agreement on the final beginner's guide. To assess fitness for purpose (ease of use and completeness), models were developed independently and by the researcher using the beginner's guide.

CONCLUSION

A combination of systematic review, methods reviews, consensus agreement, and validation was used to construct a step-by-step beginner's guide for developing decision analytical cost-effectiveness models. The final beginner's guide is a step-by-step resource to accompany the model development process from understanding the problem to be modeled, model conceptualization, model implementation, and model checking through to reporting of the model results.

Output correlations in probabilistic models with multiple alternatives

A comprehensive cost-effectiveness decision model will often go beyond a one-to-one comparison and will include a number of competing alternatives. Only a simultaneous assessment of all relevant treatment alternatives avoids comparing average cost-effectiveness ratios and allows a truly incremental analysis. Two issues arise if the analysis is probabilistic, namely, the occurrence of output correlations and difficulty in presenting the results. I have examined the role of output correlations using a screening model with eight alternatives and have shown that specifically cost-cost and quality-adjusted life years (QALY)-QALY correlations between alternatives have a major impact on decision uncertainty, as measured by the probability of the cost-effectiveness and expected value of perfect information. In particular, the latter strongly depends on between-alternative output correlations. This analysis shows that both the expected value of perfect information plots and acceptability curves/frontiers are sensitive to output correlations and thus appropriate for presentation of multiple alternatives. To avoid confusing statistical significance and economic importance I propose that acceptability curves be augmented by incremental net-benefit density plots at a given willingness to pay threshold.

Cost-effectiveness acceptability curves revisited

Since the introduction of the cost-effectiveness acceptability curve (CEAC) in 1994, its use as a method to describe uncertainty around incremental cost-effectiveness ratios (ICERs) has steadily increased. In this paper, first the construction and interpretation of the CEAC is explained, both in the context of modelling studies and in the context of cost-effectiveness (CE) studies alongside clinical trials. Additionally, this paper reviews the advantages and limitations of the CEAC. Many of the perceived limitations can be attributed to the practice of interpreting the CEAC as a decision rule while it was not developed as such. It is argued that the CEAC is still a useful tool in describing and quantifying uncertainty around the ICER, especially in combination with other tools such as plots on the CE plane and value-of-information analysis.

Communicating uncertainty in economic evaluations: verifying optimal strategies

BACKGROUND

In cost-effectiveness analysis (CEA), it is common to compare a single, new intervention with 1 or more existing interventions representing current practice ignoring other, unrelated interventions. Sectoral CEAs, in contrast, take a perspective in which the costs and effectiveness of all possible interventions within a certain disease area or health care sector are compared to maximize health in a society given resource constraints. Stochastic league tables (SLT) have been developed to represent uncertainty in sectoral CEAs but have 2 shortcomings: 1) the probabilities reflect inclusion of individual interventions and not strategies and 2) data on robustness are lacking. The authors developed an extension of SLT that addresses these shortcomings.

METHODS

Analogous to nonprobabilistic MAXIMIN decision rules, the uncertainty of the performance of strategies in sectoral CEAs may be judged with respect to worst possible outcomes, in terms of health effects obtainable within a given budget. Therefore, the authors assessed robustness of strategies likely to be optimal by performing optimization separately on all samples and on samples yielding worse than expected health benefits. The approach was tested on 2 examples, 1 with independent and 1 with correlated cost and effect data.

RESULTS

The method was applicable to the original SLT example and to a new example and provided clear and easily interpretable results. Identification of interventions with robust performance as well as the best performing strategies was straightforward. Furthermore, the robustness of strategies was assessed with a MAXIMIN decision rule.

CONCLUSION

The SLT extension improves the comprehensibility and extends the usefulness of outcomes of SLT for decision makers. Its use is recommended whenever an SLT approach is considered.

Presenting evidence and summary measures to best inform societal decisions when comparing multiple strategies

Multiple strategy comparisons in health technology assessment (HTA) are becoming increasingly important, with multiple alternative therapeutic actions, combinations of therapies and diagnostic and genetic testing alternatives. Comparison under uncertainty of incremental cost, effects and cost effectiveness across more than two strategies is conceptually and practically very different from that for two strategies, where all evidence can be summarized in a single bivariate distribution on the incremental cost-effectiveness plane. Alternative methods for comparing multiple strategies in HTA have been developed in (i) presenting cost and effects on the cost-disutility plane and (ii) summarizing evidence with multiple strategy cost-effectiveness acceptability (CEA) and expected net loss (ENL) curves and frontiers. However, critical questions remain for the analyst and decision maker of how these techniques can be best employed across multiple strategies to (i) inform clinical and cost inference in presenting evidence, and (ii) summarize evidence of cost effectiveness to inform societal reimbursement decisions where preferences may be risk neutral or somewhat risk averse under the Arrow-Lind theorem. We critically consider how evidence across multiple strategies can be best presented and summarized to inform inference and societal reimbursement decisions, given currently available methods. In the process, we make a number of important original findings. First, in presenting evidence for multiple strategies, the joint distribution of costs and effects on the cost-disutility plane with associated flexible comparators varying across replicates for cost and effect axes ensure full cost and effect inference. Such inference is usually confounded on the cost-effectiveness plane with comparison relative to a fixed origin and axes. Second, in summarizing evidence for risk-neutral societal decision making, ENL curves and frontiers are shown to have advantages over the CEA frontier in directly presenting differences in expected net benefit (ENB). The CEA frontier, while identifying strategies that maximize ENB, only presents their probability of maximizing net benefit (NB) and, hence, fails to explain why strategies maximize ENB at any given threshold value. Third, in summarizing evidence for somewhat risk-averse societal decision making, trade-offs between the strategy maximizing ENB and other potentially optimal strategies with higher probability of maximizing NB should be presented over discrete threshold values where they arise. However, the probabilities informing these trade-offs and associated discrete threshold value regions should be derived from bilateral CEA curves to prevent confounding by other strategies inherent in multiple strategy CEA curves. Based on these findings, a series of recommendations are made for best presenting and summarizing cost-effectiveness evidence for reimbursement decisions when comparing multiple strategies, which are contrasted with advice for comparing two strategies. Implications for joint research and reimbursement decisions are also discussed.

Comparing methods of data synthesis: re-estimating parameters of an existing probabilistic cost-effectiveness model

BACKGROUND

Cost-effectiveness models should always be amendable to updating once new data on important model parameters become available. However, several methods of synthesizing data exist and the choice of method may affect the cost-effectiveness estimates.

OBJECTIVES

To investigate the impact of the different methods of meta-analysis on final estimates of cost effectiveness from a probabilistic Markov model for chronic obstructive pulmonary disease (COPD).

METHODS

We compared four different methods to synthesize data for the parameters of a cost-effectiveness model for COPD: frequentist and Bayesian fixed-effects (FE) and random-effects (RE) meta-analyses. These methods were applied to obtain new transition probabilities between stable disease states and new event probabilities.

RESULTS

The four methods resulted in different estimates of probabilities and their standard errors (SE). The effects of using different synthesis techniques were most prominent in the estimation of the SEs. We found up to 9-fold differences in SEs of the exacerbation probabilities and up to almost 3-fold differences in SEs of the transition probabilities. We found that the frequentist FE model produced the lowest SEs, whereas the Bayesian RE model produced the highest for all parameters. The estimates of differences between treatments in total costs, QALYs and cost-effectiveness acceptability curves (CEAC) also varied depending on the synthesis method. The CEAC was 15% lower with a Bayesian RE model than with any of the other models.

CONCLUSIONS

Health economic modellers should be aware that the choice of synthesis technique can affect resulting model parameters considerably, which can in turn affect estimates of cost effectiveness and the uncertainty around them.

Cost effectiveness of insulin glargine plus oral antidiabetes drugs compared with premixed insulin alone in patients with type 2 diabetes mellitus in Canada

BACKGROUND

Several treatment options are available for patients with type 2 diabetes mellitus who are making the transition from oral antidiabetes drugs (OADs) to insulin. Two options currently recommended by the Canadian Diabetes Association for initiating insulin therapy in patients with type 2 diabetes who are no longer responsive to OADs alone are insulin glargine plus OADs, and premixed insulin therapy only. Because of differences in efficacy, adverse events (such as hypoglycaemia) and acquisition costs, these two treatment options may lead to different long-term clinical and economic outcomes.

OBJECTIVE

To determine the cost effectiveness of insulin glargine plus OADs compared with premixed insulin without OADs in insulin-naive patients with type 2 diabetes in Canada.

METHODS

Using treatment effects taken from a published clinical trial, the validated IMS-CORE Diabetes Model was used to simulate the long-term cost effectiveness of insulin glargine with OADs, versus premixed insulin. Input treatment effects for the two therapeutic approaches were based on changes in glycosylated haemoglobin A(1c) (HbA(1c)) at clinical trial endpoint, and hypoglycaemia rates. The analysis was conducted from the perspective of the Canadian Provincial payer. Direct treatment and complication costs were obtained from published sources (primarily from Ontario) and reported in $Can, year 2008 values. All base-case costs and outcomes were discounted at 5% per year. Sensitivity analyses were conducted around key parameters and assumptions used in the study. Outcomes included direct medical costs associated with both treatment and diabetes-related complications. Cost-effectiveness outcomes included total average lifetime (35 years) costs, life expectancy (LE), QALYs and incremental cost-effectiveness ratios (ICERs).

RESULTS

Base-case analyses showed that, compared with premixed insulin only, insulin glargine in combination with OADs was associated with a 0.051-year increase in LE and a 0.043 increase in QALYs. Insulin glargine plus OADs showed a very slight increase in total direct costs ($Can 343 +/- 2572), resulting in ICERs of $Can 6750 per life-year gained (LYG) and $Can 7923 per QALY gained. However, considerable uncertainty around the ICERs was demonstrated by insulin glargine having a 50% probability of being cost effective at a willingness-to-pay threshold of $Can 10,000 per QALY, and a 54% probability at a $Can 20,000 threshold. Base-case results were most sensitive to assumed disutilities for hypoglycaemic events, to the assumed effect of insulin glargine plus OADs on HbA(1c), and to its assumed acquisition costs.

CONCLUSIONS

These findings should be interpreted within the context of a large degree of uncertainty and of several study limitations that include a single clinical trial as the source for primary treatment assumptions and a single province as the source for most cost inputs. Under current study assumptions and limitations, insulin glargine plus OADs was projected to be a cost-effective option, compared with premixed insulin only, for the treatment of insulin-naive patients with type 2 diabetes unresponsive to OADs. Additional work is needed to examine the generalizability of the findings to individual jurisdictions of the Canadian healthcare system.

The Adoption of Cost-Effectiveness Acceptability Curves in Cost-Utility Analyses

Background. Cost-effectiveness acceptability curves (CEACs) plot the probability that one health intervention is more cost-effective than alternatives, as a function of societal willingness to pay for additional units of health (e.g., life-years or quality-adjusted life-years gained). Objectives. To quantify the adoption of CEACs in published cost-utility analyses (CUAs), and to identify factors associated with CEAC use. Methods. Data from the Tufts Medical Center Cost-Effectiveness Analysis Registry (www.cearegistry.org), a database with detailed information on approximately 1,400 CUAs published in the peer reviewed literature through 2006, was analyzed. The registry includes data on study origin, study methodology, reporting of results, whether CEACs were presented, and a subjective quality score. Univariate and multivariate logistic regression analyses were used to identify factors predicting CEAC use, from their introduction in 1994 through 2006. Results. Approximately 15% of CUAs published since 1994 present a CEAC. The use of CEACs has increased rapidly in recent years, from 2.1% of published CUAs in 2001 to 32.6% in 2006 (P < 0.0001). The most significant predictors of CEAC use were study quality (odds ratio [OR]: 2.26; 95% confidence interval [CI]: 1.80, 2.85), recent publication (OR: 1.99; 95% CI: 1.73, 2.29), and whether studies pertain to the UK (OR: 5.66; 95% CI: 3.67, 8.72) or Sweden (OR: 3.76; 95% CI: 1.67, 8.44). Conclusions. CEAC use is increasing in the published cost-effectiveness literature, especially in UK-based studies.

Improving efficiency and value in palliative care with net benefit regression: an introduction to a simple method for cost-effectiveness analysis with person-level data

The objective of this article is to illustrate how to do cost-effectiveness analysis (CEA) using net-benefit regression and to explain how this method provides all of the benefits CEA can provide for improving efficiency and value in palliative care. We use a hypothetical data set with person-level data to demonstrate the net-benefit regression framework. Cost and effect data are combined with assumptions about willingness to pay to produce a net-benefit variable for each study participant. This net-benefit variable is the dependent variable in a net-benefit regression. In the simplest formulation, the regression coefficient on the treatment indicator variable estimates the difference in value between extra benefits and extra costs. The estimate and its confidence interval provide policy-relevant information. Net-benefit regression can be used with data from clinical trials or from administrative data sets. The results can be used to help develop policy, with an aim toward improving efficiency and value in health care.

Expected value of perfect information: an empirical example of reducing decision uncertainty by conducting additional research

OBJECTIVE

Value of information (VOI) analysis informs decision-makers about the expected value of conducting more research to support a decision. This expected value of (partial) perfect information (EV(P)PI) can be estimated by simultaneously eliminating uncertainty on all (or some) parameters involved in model-based decision-making. This study aimed to calculate the EVPPI, before and after collecting additional information on the parameter of a probabilistic Markov model with the highest EVPPI.

METHODS

The model assessed the 5-year costs per quality-adjusted life year (QALY) of three bronchodilators in chronic obstructive pulmonary disease (COPD). It had identified tiotropium as the bronchodilator with the highest expected net benefit. Total EVPI was estimated plus the EVPPIs for four groups of parameters: 1) transition probabilities between COPD severity stages; 2) exacerbation probabilities; 3) utility weights; and 4) costs. Partial EVPI analyses were performed using one-level and two-level sampling algorithms.

RESULTS

Before additional research, the total EVPI was Euro 1985 per patient at a threshold value of Euro 20,000 per QALY. EVPPIs were Euro 1081 for utilities, Euro 724 for transition probabilities, and relatively small for exacerbation probabilities and costs. A large study was performed to obtain more precise EQ-5D utilities by COPD severity stages. After using posterior utilities, the EVPPI for utilities decreased to almost zero. The total EVPI for the updated model was reduced to Euro 1037. With an EVPPI of Euro 856, transition probabilities were now the single most important parameter contributing to the EVPI.

CONCLUSIONS

This VOI analysis clearly identified parameters for which additional research is most worthwhile. After conducting additional research on the most important parameter, i.e., the utilities, total EVPI was substantially reduced.

Measuring and illustrating statistical evidence in a cost-effectiveness analysis

Recently, there has been much interest in using the cost-effectiveness acceptability curve (CEAC) to measure the statistical evidence of cost-effectiveness. The CEAC has two well established but fundamentally different interpretations: one frequentist and one Bayesian. As an alternative, we suggest characterizing the statistical evidence about cost-effectiveness using the likelihood function (the key element of both approaches). Its interpretation is neither dependent on the sample space nor on the prior distribution. Moreover, the probability of observing misleading evidence is low and controllable, so this approach is justifiable in the traditional sense of frequentist long-run behaviour. We propose a new graphic for displaying the evidence about cost-effectiveness and explore the strengths of likelihood methods using data from an economic evaluation of a Program in Assertive Community Treatment (PACT).

Cost-effectiveness analyses of vaccination programmes : a focused review of modelling approaches

Cost effectiveness is becoming an increasingly important factor for stakeholders faced with decisions about adding a new vaccine into national immunization programmes versus alternative use of resources. Evaluating cost effectiveness, taking into account the relevant biological, clinical, epidemiological and economic factors of a vaccination programme, generally requires use of a model. This review examines the modelling approaches used in cost-effectiveness analyses (CEAs) of vaccination programmes.After overviewing the key attributes of models used in CEAs, a framework for categorising theoretical models is presented. Categories are based on three main attributes: static/dynamic; stochastic/deterministic; and aggregate/individual based. This framework was applied to a systematic review of CEAs of all currently available vaccines for the period of 1976 to May 2007. The systematic review identified 276 CEAs of vaccination programmes. The great majority (83%) of CEAs were conducted in the setting of high-income countries. Only a few vaccines were widely studied, with 57% of available CEAs being focused on the varicella, influenza, hepatitis A, hepatitis B or pneumococcal vaccine. Several time trends were evident, indicating that the number of vaccine CEAs being published is increasing; the main health outcome measures are moving away from the number of cases prevented towards quality-adjusted and unadjusted life-years gained, and more complex models are beginning to be used. The modelling approach was often not adequately described. Of the 208 CEAs that could be categorized according to the framework, around 90% were deterministic, aggregate-level static models. Although a dynamic transmission model is required to account for herd-immunity effects, only 23 of the CEAs were dynamic. None of the CEAs were individual based. To improve communication about the cost effectiveness of vaccination programmes, we believe the first step is for analysts to be more transparent with each other. A clear description of the model type using consistent terminology and justification for the model choice must begin to accompany all CEAs. As a minimum, we urge modellers to provide an explicit statement about the following attributes: static/dynamic; stochastic/deterministic; aggregate/individual based; open/closed. Where relevant, time intervals (discrete/continuous) and (non)linearity should also be described. Enhanced methods of assessing model performance and validity are also required. Our results emphasize the need to improve modelling methods for CEAs of vaccination programmes; specifically, model choice, construction, assessment and validation.