The correction of TTO-scores for utility curvature using a risk-free utility elicitation method

Abstract

This paper describes and employs a new method to correct time tradeoff (TTO)-scores for utility of life duration curvature. In contrast to most previous attempts to do so, it uses a risk-free method that corresponds well to the risk-free properties of the TTO-method. In addition, the method is robust to several biases that occur under methods that incorporate risk. Our results show a significant degree of curvature in utility of life duration and therefore a clear bias in TTO-scores. The risk-free method seems to be useful to correct TTO-scores for this influence and leads to significantly higher quality-adjustment factors.

Introduction

The time tradeoff (TTO) method is a popular way of eliciting preferences for health states (e.g. Dolan, 2000). As a consequence, several quality-adjustment factors used in cost-effectiveness analyses are based on TTO-measurements (e.g. Dolan, 1997, Lamers et al., 2006). In a TTO individuals need to make a tradeoff between quality of life and duration of life. A typical TTO-measurement will involve a tradeoff between living in some imperfect health state β for 10 years and living in perfect health for a period less than 10 years. The amount of time people are willing to sacrifice in order to restore perfect health then indicates the quality-adjustment factor belonging to β: u(β) = x/10.

Despite its popularity, the typical TTO-procedure has been shown to be prone to several potential biases. It makes strong assumptions such as linear utility of life duration, no loss aversion and no scale compatibility, which are hard to maintain (e.g. Nord, 1992, Bleichrodt, 2002). Consequently, the quality-adjustment factors elicited by the conventional TTO-procedure are biased. Loss aversion and scale compatibility cause an upward bias in health state values (Bleichrodt, 2002). Moreover, utility of life duration is often found to be nonlinear, which mainly relates to two aspects: (i) diminishing marginal utility of additional lifetime and (ii) discounting. Both are problematic in the context of a TTO, as this method does not take into account the utility curvature, leading to a downward bias in quality-adjustment factors (Bleichrodt, 2002).

A typical respondent having to trade-off future life years in order to restore full health is likely to discount future life years (e.g. Stiggelbout et al., 1994, Stalmeier et al., 1996, Wakker and Deneffe, 1996, Martin et al., 2000, Bleichrodt and Pinto, 2005, van der Pol and Roux, 2005, Abellan-Perpinan et al., 2006). Discounting implies, as Bohm–Bawerk already put it, that: ‘To goods that are destined to meet the wants of the future, we ascribe a value which is really less than the true intensity of their future marginal utility’ (as quoted in Olsen, 1993). Both diminishing marginal utility of additional lifetime and discounting cause a lower value to be attached to the future life years that are traded-off in a TTO-measurement. This immediately indicates the problem that this paper addresses. Simply using the ratio calculation of the type u(β) = x/10 to construct quality-adjustment factors will lead to systematic underestimations (Wakker, 2008). In order to have a better estimate of the true quality-adjustment factor, a correction for the utility of life duration curvature is required, therefore. This is especially true for discounting given the way that resulting quality-adjustment factors are normally used in economic evaluations, i.e. they are discounted to calculate a net present value (e.g. Gravelle et al., 2007). If uncorrected TTO-scores are used to calculate quality-adjustment factors and these are subsequently discounted using some discount rate for health effects, this would amount to double discounting and an underestimation of the utility derived from some health state (MacKeigan et al., 2003).

This paper focuses on the role of nonlinear utility of life duration in TTO-measurements and describes a new method to correct for utility of life duration curvature. This involves a recently proposed risk-free (RF) method that does not need to make specific parametric assumptions about the utility of life duration function (Attema et al., 2007). The main contributions of this paper are to show how this RF-method can be employed to correct TTO-scores for utility of life duration curvature, to compare it with other TTO-correction methods and to present some empirical evidence on the feasibility of the RF-method and the resulting correction factor. Applications of the RF-method to the context of procedural invariance of the TTO-method (Attema and Brouwer, 2008a) and constant proportional tradeoffs (Attema and Brouwer, 2008b) can be found elsewhere.

The structure of the paper is as follows. First, we introduce the theory underlying our study in Section 2. There we also discuss related literature concerning corrected TTO-scores. In Section 3 we explain the method used to elicit utility for life duration and the way to use this information to correct raw TTO-scores. The experimental details are put forward in Section 4, followed by a presentation of the results in Section 5. Finally, Section 6 discusses the results and concludes.