VALUE IN HEALTH 17 (2014) 297– 301 Available online at www.sciencedirect.com journal homepage: www.elsevier.com/locate/jval Specification of the Utility Function in Discrete Choice Experiments Marjon van der Pol, PhD, MA1,*, Gillian Currie, PhD, MPhil, MA, BComm2, Seija Kromm, MA, BA3, Mandy Ryan, PhD, MSc, BA1 1Health Economics Research Unit, University of Aberdeen, Abedeen, UK; 2University of Calgary, Calgary, AB, Canada; 3University of Toronto, Toronto, ON, Canada ABSTRACT Background: The specification of the utility function has received across the three different specifications of the utility function. Assum- limited attention within the discrete choice experiment (DCE) liter- ing a linear utility function led to much higher estimates of marginal ature. This lack of investigation is surprising given that evidence from rates of substitution (WTWs) than with nonlinear specifications. The the contingent valuation literature suggests that welfare estimates are goodness-of-fit measures indicated that nonlinear specifications were sensitive to different specifications of the utility function. Objective: superior. This study investigates the effect of different specifications of the Keywords: discrete choice experiments, specification of utility utility function on results within a DCE. Methods: The DCE elicited the function. public’s preferences for waiting time for hip and knee replacement Copyright & 2014, International Society for Pharmacoeconomics and and estimated willingness to wait (WTW). Results: The results showed Outcomes Research (ISPOR). Published by Elsevier Inc. that the WTW for the different patient profiles varied considerably Introduction nonlinear results in relative biases ranging up to 63%. Herriges and Kling [7] and Shonkwiler and Shaw [8] analyzed DCE data to Discrete choice experiments (DCEs) are increasingly used to elicit explore the sensitivity of WTP estimates to alternative utility preferences for health and health care [1]. The technique is used specifications and found differences in WTP estimates. to estimate marginal rates of substitution between attributes of a The aim of this article was to explore the effect of using good or service and, if cost (price proxy) is included, willingness different specifications of the utility function in a case study in to pay (WTP) for changes in attributes. Many methodological the health field. The case study used is a DCE eliciting public’s issues have been addressed in the development of DCEs in health preferences for waiting time for hip and knee replacement. Waiting economics, including choice of included attributes, identification time rather than cost is used as the numeraire because the aim was of appropriate levels for attributes, optimal experimental designs, to estimate acceptable willingness to wait (WTW), not WTP, for use and econometric techniques for data analysis. Surprisingly, little in priority setting. This DCE is particularly suitable for exploring attention has been paid to the functional form of the utility nonlinear utility functions because the waiting time attribute has a function. It is standard practice in the DCE literature to assume relatively large number of levels (eight) and a relatively wide range linear utility functions for attributes [2] (Qualitative variables are of values over which marginal utility is unlikely to be constant. This usually modeled by using effects coding or dummy variables, and is the first study to explore the effect of functional form in health therefore no assumption is made regarding the functional form). and shows that different specifications of the utility function have a Exceptions in the health field are van der Pol et al. [3] who use a substantial effect on the WTW estimates generated. quadratic utility function and McIntosh and Ryan [4] who note in discussion that a quadratic utility function was also estimated but results were not presented. This lack of attention is surprising Methods because evidence from the contingent valuation literature sug- gests that welfare estimates are sensitive to different utility The case study used is a DCE conducted in the context of policy function specifications. By using simulation methods, Kling [5] research using the Western Canada Waiting List (WCWL) hip and shows that incorrect functional forms result in errors in WTP knee priority criteria tool [9]. For details on good DCE practice, see values ranging from 4% to 107%. Within the DCE literature, Torres Bridges et al. [10], and for full details on the DCE and the priority et al. [6] show by using simulation methods that assuming a tool, including development of the attributes and levels, see linear utility function when the true utility specification is Western Canada Waiting List Project [11].Briefly, this tool scores * Address correspondence to: Marjon van der Pol, Health Economics Research Unit, University of Aberdeen, Foresterhill, Aberdeen AB25 2ZD, UK. E-mail: [email protected]. 1098-3015/$36.00 – see front matter Copyright & 2014, International Society for Pharmacoeconomics and Outcomes Research (ISPOR). Published by Elsevier Inc. http://dx.doi.org/10.1016/j.jval.2013.11.009 298 VALUE IN HEALTH 17 (2014) 297– 301 fi patient severity according to seven criteria, each with three or four where Uij is the utility of pro le j for individual i; Xj1 is the waiting ’ α α α levels. The aim of the DCE was to estimate public s preferences for time attribute; Xjz are the other attributes in the DCE; 1, 2, 3, fi fi β waiting time for health pro les as de ned within this tool. The and z are the parameters of the attributes; c1 and c2 are the attributes and levels, adopted directly from the tool, were pain on critical values for the waiting time attribute in the stepwise utility fi ε motion, pain at rest, ability to walk without signi cant pain, other function; and ij is the random error term. The values selected for fi functional limitations, abnormal ndings on physical exam, pro- c1 and c2 were based on attribute levels and were 12 and 36, gression of disease, and ability to fulfill role. In addition, a waiting respectively, allowing marginal utility to vary across shorter time attribute was included such that WTW could be estimated. (Waiting time 1), medium (Waiting time 2), and longer (Waiting The levels for this waiting time attribute represent the range time 3) waiting times. observed in patient data from the earlier WCWL tool development. The WTW is the value of waiting time (Xj1) that would The initial attributes and levels are shown in Appendix 1 in compensate for the utility difference caused by a change in an Supplemental Materials found at http://dx.doi.org/10.1016/j.jval. attribute (Xjz). The WTW is estimated by solving the following 2013.11.009. equations: A challenge when using different clinical dimensions as Linear utility function: attributes is that many of the combinations are unrealistic. Some WTW ¼ α1X ¼ β ðX ÀX Þ of the attributes were therefore nested [12]. Appendix 1 in j1 3 jz1 jz0 1 Supplemental Materials found at http://dx.doi.org/10.1016/j.jval. ¼ β ðX ÀX Þ α 3 jz1 jz0 2013.11.009 shows that pain on motion was nested with pain at 1 rest, and ability to walk without significant pain was nested with Quadratic utility function: other functional limitations. Furthermore, some constraints were 2 WTW ¼ α1X þα2X ¼β ðX À X Þ defined to further rule out unrealistic combinations (see lower j1 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffij1 3 jz1 jz0 2 part of Appendix 1 in Supplemental Materials found at http://dx. Àα1 Ϯ α À4α2Àβ ðX ÀX Þ ¼ 1 3 jz1 jz0 doi.org/10.1016/j.jval.2013.11.009). To reduce the total number of 2α2 choices derived from the experimental design, each of the nested Stepwise utility function: attributes was restricted to eight levels. fi ¼ α ð o Þþα ð r o Þþα ð Z Þ¼β ð À Þ AD-efcient fractional factorial design, using the nested WTW 1 Xj1 c1 2 c1 Xj1 c2 3 Xj1 c2 3 Xjz1 Xjz0 fi attributes, of 72 choices was produced by using SAS (D-ef ciency ¼ 1 β ð À Þ; ¼ o ; ¼ r o ; 3 Xjz1 Xjz0 y 1 if Xj1 c1 y 2 if c1 Xj1 c2 is 72.57% [13]). A four-version blocked design, each with 18 choices, αy was used. Consistency of responses was tested by including two y ¼ 3 if X 4c dominant choices; here, one scenario is clearly superior to another j1 2 and respondents are defined as inconsistent if they do not choose The marginal rate of substitution between changes in the the dominant option. This is the most commonly used test within attributes and waiting time is constant only in the linear utility the DCE literature [1]. Thus, in total there were 20 choices for each specification. In nonlinear specifications, the marginal rate of respondent. For each choice set, respondents were asked to substitution varies depending on the size of the utility difference imagine themselves in the two scenarios and to indicate which caused by the change in attribute Xjz. This means that WTW for situation they thought was worse. Appendix 1 in Supplemental differences in attribute levels is no longer an additive. For Materials found at http://dx.doi.org/10.1016/j.jval.2013.11.009 gives example, WTW for a change in attribute Xjz from 0 to 2 is no an example of a choice. Because it is not possible to remove longer necessarily equal to the summation of WTW for a change fi patients with certain pro les from the waiting list, an opt-out was in attribute Xjz from 0 to 1 and WTW for a change in attribute Xjz not appropriate. That is, all patient profiles need to be prioritized. from 1 to 2. It is therefore crucial to use a constant reference point when comparing WTWs for different patient profiles.