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.

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