A note on the nature of utility in time and health and implications for cost utility analysis

Time Trade-Off valuations of health are widely used in economic evaluation of health care. Current approaches to eliciting TTO values, and their use in economic evaluation, rests on specific assumptions about the way utility relates to time and health. Both the assumptions themselves and evidence of violations of them are discussed in the literature - yet the issues appear not to be widely appreciated by those using and applying TTO. This paper adds to that literature by demonstrating both the requirements of TTO and violations of these assumptions in terms of the underlying indifference curve maps and utility functions. The advantage of this approach is that is demonstrates very clearly a number of fundamental problems for the way TTO values are currently elicited and used in Cost Utility Analysis. In essence, it is extremely unwise to assume that the current "tariffs" of TTO values, such as those routinely used by NICE and other organisations, can be applied irrespective of the duration of the health states to which they are assigned. The estimates of QALYs that result will, quite often, simply be wrong. We suggest a number of solutions, including the provision of multiple value sets, for a range of durations

Some integer formula-encodings and related algorithms

We investigate the special class of formulas made up of arbitrary but finite com- binations of addition, multiplication, and exponentiation gates. The inputs to these formulas are restricted to the integral unit 1. In connection with such formulas, we describe two essen- tially distinct families of canonical formula-encodings for integers, respectively deduced from the decimal encoding and the fundamental theorem of arithmetic. Our main contribution is the de- tailed description of two algorithms which efficiently determine the canonical formula-encodings associated with relatively large sets of consecutive integers

Does the value of quality of life depend on duration?

The aims of this study are to investigate the feasibility of eliciting Time Trade Off (TTO) valuations using short durations; to determine the effect of contrasting durations on individuals’ responses to the TTO; to examine variations within and between respondents’ values with respect to duration; and to consider the insights provided by participants’ comments and explanations regarding their reaction to duration in the valuation task. 27 participants provided TTO values using short and long durations for three EQ-5D states. Feedback was sought using a series of open ended questions. Of the 81 opportunities to observe it, strict constant proportionality was satisfied twice. 11 participants had no systematic relationship between duration and value; 11 provided consistently lower valuations in long durations, while 5 had higher valuations in long durations. Comments provided by participants were consistent with the values they provided. Mean TTO values did not differ markedly between alternative durations. We conclude that it is feasible to elicit TTO values for short durations. There is considerable heterogeneity in individuals’ responses to the time frames used to elicit values. Further research is required to ensure that the values used in cost effectiveness analysis adequately represent preferences about quality and length of life

A uniform Time Trade Off method for states better and worse than dead: feasibility study of the ‘lead time’ approach

The way Time Trade Off (TTO) values are elicited for states of health considered ‘worse than being dead’ has important implications for the mean values used in economic evaluation. Conventional approaches to TTO, as used in the UK’s ‘MVH’ value set, are problematic because they require fundamentally different tradeoffs tasks for the valuation of states better and worse than dead. This study aims to refine and test the feasibility of a new approach described by Robinson and Spencer (2006), and to explore the characteristics of the valuation data it generates. The approach introduces a ‘lead time’ into the TTO, producing a uniform procedure for generating values either >0 or <0. We used this lead time TTO to value 10 moderate to severe EQ-5D states using a sample of the general public (n=109). We conclude that the approach is feasible for use in valuation studies, and appears to overcome the discontinuity in values around 0 evident in conventional methods. However, further research is required to resolve the issue of how to handle participants who ‘use up’ all lead time; to develop ways of controlling for individual time preferences; and to better understand the implications for valuations of states better than dead

Developing language skills in second language learners through literature discussions

This study analyzed book discussions of primary aged ESL students and their teacher to examine the benefits to language development. Collected over one school year, data included transcribed audiotapes of the book discussions, class interviews, and personal journal entries of the teacher which described classroom events and interactions. Analysis of the transcripts resulted in the identification of seven categories which illustrated the diversity of types of talk. In addition, changes in the amount of student and teacher talk over time were noted, with student talk increasing, and teacher talk becoming less pronounced. Four students were highlighted to illustrate the benefits of picture book discussions for different English proficiency levels. Finally, the role of the teacher in these discussions was explored. Several benefits of discussing picture books with ESL students are suggested in terms of their importance for language development

Gauge invariance of color confinement due to the dual Meissner effect caused by Abelian monopoles

The mechanism of non-Abelian color confinement is studied in SU(2) lattice gauge theory in terms of the Abelian fields and monopoles extracted from non-Abelian link variables without adopting gauge fixing. Firstly, the static quark-antiquark potential and force are computed with the Abelian and monopole Polyakov loop correlators, and the resulting string tensions are found to be identical to the non-Abelian string tension. These potentials also show the scaling behavior with respect to the change of lattice spacing. Secondly, the profile of the color-electric field between a quark and an antiquark is investigated with the Abelian and monopole Wilson loops. The color-electric field is squeezed into a flux tube due to monopole supercurrent with the same Abelian color direction. The parameters corresponding to the penetration and coherence lengths show the scaling behavior, and the ratio of these lengths, i.e, the Ginzburg-Landau parameter, indicates that the vacuum type is near the border of the type1 and type2 (dual) superconductor. These results are summarized that the Abelian fundamental charge defined in an arbitrary color direction is confined inside a hadronic state by the dual Meissner effect. As the color-neutral state in any Abelian color direction corresponds to the physical color-singlet state, this effect explains non-Abelian color confinement and supports the existence of a gauge-invariant mechanism of color confinement due to the dual Meissner effect caused by Abelian monopoles.Comment: 11 pages, 14 figure