Budget allocation and the revealed social rate of time preference for health

Appropriate decisions based on cost-effectiveness evaluations of health care technologies depend upon the cost-effectiveness threshold and its rate of growth as well as some social rate of time preference for health. The concept of the cost-effectiveness threshold, social rate of time preference for consumption and social opportunity cost of capital are briefly explored before the question of how a social rate of time preference for health might be established is addressed. A more traditional approach to this problem is outlined before a social decision making approach is developed which demonstrates that social time preference for health is revealed through the budget allocations made by a socially legitimate higher authority. The relationship between the social time preference rate for health, the growth rate of the cost-effectiveness threshold and the rate at which the higher authority can borrow or invest is then examined. We establish that the social time preference rate for health is implied by the budget allocation and the health production functions in each period. As such, the social time preference rate for health depends not on the social time preference rate for consumption or growth in the consumption value of health but on growth in the cost-effectiveness threshold and the rate at which the higher authority can save or borrow between periods. The implications for discounting and the policies of bodies such as NICE are then discussed.Economic evaluation. Discounting. Cost-effectiveness analysis

Does cost-effectiveness analysis discriminate against patients with short life expectancy? Matters of logic and matters of context

The aim of this paper is to explore the claim of ageism made against the National Institute for Health & Clinical Excellence and like organisations, and to identify circumstances under which ageist discrimination might arise. We adopt a broad definition of ageism as representing any discrimination against individuals or groups of individuals solely on the basis that they have shorter life expectancy than others. A simple model of NICE?s decision making process is developed which demonstrates that NICE?s recommendations do not inherently discriminate on the basis of life expectancy per se but that scope for discrimination may arise in the case of specific technologies having identifiable characteristics. Such discrimination may favour patients with either longer or shorter life expectancy. It is shown that NICE?s policies, procedures and the context in which NICE makes its decisions not only reduce the scope for discriminatory recommendations but also – in the case of “end of life” treatments – increase the likelihood that NICE?s recommendations favour those with shorter, rather than longer, life expectancy.

Does Cost-Effectiveness Analysis Discriminate against Patients with Short Life Expectancy?

Does the use of quality-adjusted life-years (QALYs) in cost-effectiveness analyses (CEAs) of health care interventions necessarily discriminate against patients with short life expectancy compared with others? This paper reviews the arguments both that it does and that it does not, and demonstrates that whether the use of any time-dependent outcome measure in CEA will result in discrimination depends, in the context of any given choice between interventions, upon the choice of cost-effectiveness ‘threshold’ adopted by the decision maker, whether the incremental cost-effectiveness ratio (ICER) of the intervention for a subgroup of patients with relatively short life expectancy lies above the cost-effectiveness threshold, and whether the ICER for a subgroup of patients with longer life expectancy falls below the cost-effectiveness threshold. For discrimination to result against such patients requires that the long term ratio of costs to QALYs associated with the intervention be lower than the short term ratio of costs to QALYs. The implications for agencies which use CEA as part of their decision making are then discussed.

Modelling intransitivity in pairwise comparisons with application to baseball data

In most commonly used ranking systems, some level of underlying transitivity is assumed. If transitivity exists in a system then information about pairwise comparisons can be translated to other linked pairs. For example, if typically A beats B and B beats C, this could inform us about the expected outcome between A and C. We show that in the seminal Bradley-Terry model knowing the probabilities of A beating B and B beating C completely defines the probability of A beating C, with these probabilities determined by individual skill levels of A, B and C. Users of this model tend not to investigate the validity of this transitive assumption, nor that some skill levels may not be statistically significantly different from each other; the latter leading to false conclusions about rankings. We provide a novel extension to the Bradley-Terry model, which accounts for both of these features: the intransitive relationships between pairs of objects are dealt with through interaction terms that are specific to each pair; and by partitioning the $n$ skills into $A+1\leq n$ distinct clusters, any differences in the objects' skills become significant, given appropriate $A$. With $n$ competitors there are $n(n-1)/2$ interactions, so even in multiple round robin competitions this gives too many parameters to efficiently estimate. Therefore we separately cluster the $n(n-1)/2$ values of intransitivity into $K$ clusters, giving $(A,K)$ estimatable values respectively, typically with $A+K<n$. Using a Bayesian hierarchical model, $(A,K)$ are treated as unknown, and inference is conducted via a reversible jump Markov chain Monte Carlo (RJMCMC) algorithm. The model is shown to have an improved fit out of sample in both simulated data and when applied to American League baseball data.Comment: 26 pages, 7 figures, 2 tables in the main text. 17 pages in the supplementary materia

A framework for statistical modelling of the extremes of longitudinal data, applied to elite swimming

We develop methods, based on extreme value theory, for analysing observations in the tails of longitudinal data, i.e., a data set consisting of a large number of short time series, which are typically irregularly and non-simultaneously sampled, yet have some commonality in the structure of each series and exhibit independence between time series. Extreme value theory has not been considered previously for the unique features of longitudinal data. Across time series the data are assumed to follow a common generalised Pareto distribution, above a high threshold. To account for temporal dependence of such data we require a model to describe (i) the variation between the different time series properties, (ii) the changes in distribution over time, and (iii) the temporal dependence within each series. Our methodology has the flexibility to capture both asymptotic dependence and asymptotic independence, with this characteristic determined by the data. Bayesian inference is used given the need for inference of parameters that are unique to each time series. Our novel methodology is illustrated through the analysis of data from elite swimmers in the men's 100m breaststroke. Unlike previous analyses of personal-best data in this event, we are able to make inference about the careers of individual swimmers - such as the probability an individual will break the world record or swim the fastest time next year.Comment: 28 pages, 4 figure

Implications of non-marginal budgetary impacts in health technology assessment: a conceptual model

Objectives This paper introduces a framework with which to conceptualise the decision-making process in health technology assessment for new interventions with high budgetary impacts. In such circumstances, the use of a single threshold based on the marginal productivity of the health care system is inappropriate. The implications of this for potential partial implementation, horizontal equity and pharmaceutical pricing are illustrated using this framework. Results Under the condition of perfect divisibility and given an objective of maximising health, a large budgetary impact of a new treatment may imply that optimal implementation is partial rather than full, even at a given incremental cost-effectiveness ratio that would nevertheless mean the decision to accept the treatment in full would not lead to a net reduction in health. In a one-shot price-setting game, this seems to give rise to potential horizontal equity concerns. When the assumption of fixity of the ICER (arising from the assumed exogeneity of the manufacturer's price) is relaxed, it can be shown that the threat of partial implementation may be sufficient to give rise to an ICER at which cost the entire potential population is treated, maximising health at an increased level, and with no contravention of the horizontal equity principle