No abstract

A model's purpose is to inform medical decisions and health care resource allocation. Modelers employ quantitative methods to structure the clinical, epidemiological, and economic evidence base and gain qualitative insight to assist decision makers in making better decisions. From a policy perspective, the value of a model-based analysis lies not simply in its ability to generate a precise point estimate for a specific outcome but also in the systematic examination and responsible reporting of uncertainty surrounding this outcome and the ultimate decision being addressed. Different concepts relating to uncertainty in decision modeling are explored. Stochastic (first-order) uncertainty is distinguished from both parameter (second-order) uncertainty and from heterogeneity, with structural uncertainty relating to the model itself forming another level of uncertainty to consider. The article argues that the estimation of point estimates and uncertainty in parameters is part of a single process and explores the link between parameter uncertainty through to decision uncertainty and the relationship to value of information analysis. The article also makes extensive recommendations around the reporting of uncertainty, in terms of both deterministic sensitivity analysis techniques and probabilistic methods. Expected value of perfect information is argued to be the most appropriate presentational technique, alongside cost-effectiveness acceptability curves, for representing decision uncertainty from probabilistic analysis.

Decision-making in health care is inevitably undertaken in a context of uncertainty concerning the effectiveness and costs of health care interventions and programmes. One method that has been suggested to represent this uncertainty is the cost-effectiveness acceptability curve. This technique, which directly addresses the decision-making problem, has advantages over confidence interval estimation for incremental cost-effectiveness ratios. However, despite these advantages, cost-effectiveness acceptability curves have yet to be widely adopted within the field of economic evaluation of health care technologies. In this paper we consider the relationship between cost-effectiveness acceptability curves and decision-making in health care, suggest the introduction of a new concept more relevant to decision-making, that of the cost-effectiveness frontier, and clarify the use of these techniques when considering decisions involving multiple interventions. We hope that as a result we can encourage the greater use of these techniques.

In trial-based cost-effectiveness analysis baseline mean utility values are invariably imbalanced between treatment arms. A patient's baseline utility is likely to be highly correlated with their quality-adjusted life-years (QALYs) over the follow-up period, not least because it typically contributes to the QALY calculation. Therefore, imbalance in baseline utility needs to be accounted for in the estimation of mean differential QALYs, and failure to control for this imbalance can result in a misleading incremental cost-effectiveness ratio. This paper discusses the approaches that have been used in the cost-effectiveness literature to estimate absolute and differential mean QALYs alongside randomised trials, and illustrates the implications of baseline mean utility imbalance for QALY calculation. Using data from a recently conducted trial-based cost-effectiveness study and a micro-simulation exercise, the relative performance of alternative estimators is compared, showing that widely used methods to calculate differential QALYs provide incorrect results in the presence of baseline mean utility imbalance regardless of whether these differences are formally statistically significant. It is demonstrated that multiple regression methods can be usefully applied to generate appropriate estimates of differential mean QALYs and an associated measure of sampling variability, while controlling for differences in baseline mean utility between treatment arms in the trial.

BackgroundCost-effectiveness analysis involves the comparison of the incremental cost-effectiveness ratio of a new technology, which is more costly than existing alternatives, with the cost-effectiveness threshold. This indicates whether or not the health expected to be gained from its use exceeds the health expected to be lost elsewhere as other health-care activities are displaced. The threshold therefore represents the additional cost that has to be imposed on the system to forgo 1 quality-adjusted life-year (QALY) of health through displacement. There are no empirical estimates of the cost-effectiveness threshold used by the National Institute for Health and Care Excellence.Objectives(1) To provide a conceptual framework to define the cost-effectiveness threshold and to provide the basis for its empirical estimation. (2) Using programme budgeting data for the English NHS, to estimate the relationship between changes in overall NHS expenditure and changes in mortality. (3) To extend this mortality measure of the health effects of a change in expenditure to life-years and to QALYs by estimating the quality-of-life (QoL) associated with effects on years of life and the additional direct impact on QoL itself. (4) To present the best estimate of the cost-effectiveness threshold for policy purposes.MethodsEarlier econometric analysis estimated the relationship between differences in primary care trust (PCT) spending, across programme budget categories (PBCs), and associated disease-specific mortality. This research is extended in several ways including estimating the impact of marginal increases or decreases in overall NHS expenditure on spending in each of the 23 PBCs. Further stages of work link the econometrics to broader health effects in terms of QALYs.ResultsThe most relevant ‘central’ threshold is estimated to be £12,936 per QALY (2008 expenditure, 2008–10 mortality). Uncertainty analysis indicates that the probability that the threshold is < £20,000 per QALY is 0.89 and the probability that it is < £30,000 per QALY is 0.97. Additional ‘structural’ uncertainty suggests, on balance, that the central or best estimate is, if anything, likely to be an overestimate. The health effects of changes in expenditure are greater when PCTs are under more financial pressure and are more likely to be disinvesting than investing. This indicates that the central estimate of the threshold is likely to be an overestimate for all technologies which impose net costs on the NHS and the appropriate threshold to apply should be lower for technologies which have a greater impact on NHS costs.LimitationsThe central estimate is based on identifying a preferred analysis at each stage based on the analysis that made the best use of available information, whether or not the assumptions required appeared more reasonable than the other alternatives available, and which provided a more complete picture of the likely health effects of a change in expenditure. However, the limitation of currently available data means that there is substantial uncertainty associated with the estimate of the overall threshold.ConclusionsThe methods go some way to providing an empirical estimate of the scale of opportunity costs the NHS faces when considering whether or not the health benefits associated with new technologies are greater than the health that is likely to be lost elsewhere in the NHS. Priorities for future research include estimating the threshold for subsequent waves of expenditure and outcome data, for example by utilising expenditure and outcomes available at the level of Clinical Commissioning Groups as well as additional data collected on QoL and updated estimates of incidence (by age and gender) and duration of disease. Nonetheless, the study also starts to make the other NHS patients, who ultimately bear the opportunity costs of such decisions, less abstract and more ‘known’ in social decisions.FundingThe National Institute for Health Research-Medical Research Council Methodology Research Programme.