Innovative Applications of O.R. Estimating the population utility function: A parametric Bayesian approach R. Muzaffer Musal a , Refik Soyer b,⇑ , Christopher McCabe c , Samer A. Kharroubi d a Department of Computer Information Systems and Quantitative Methods, Texas State University-San Marcos, USA b Department of Decision Sciences, The George Washington University, USA c Institute of Health Sciences, University of Leeds, UK d Department of Mathematics, University of York, UK article info Article history: Received 20 April 2009 Accepted 7 November 2011 Available online 13 November 2011 Keywords: Bayesian inference Health services Multi-attribute utility theory OR in societal problem analysis Group decision making abstract In this paper we consider the health utility index mark II for quantifying and describing a population’s health related quality of life over health states composed of multiple attributes. This measure can be used for various purposes such as evaluating the severity of the effect of a disease or comparing different treat- ment methods. We present a Bayesian framework for population utility estimation and health policy evaluation by introducing a probabilistic interpretation of the multi-attribute utility theory (MAUT) used in health economics. In doing so, our approach combines ideas from the MAUT and Bayesian statistics and provides an alternative method of modeling preferences and utility estimation. Ó 2011 Elsevier B.V. All rights reserved. 1. Introduction Preference based evaluation of health policies has become an integral component of public health policy development in coun- tries such as Australia, Canada and United Kingdom. As pointed out by Brazier (2005), use of preference-based measures of health ‘‘have become a common means of generating health state values for calculating quality-adjusted life years (QALY)’’. Use of preference based measures requires quantification of health state preferences by a group of individuals. This preference data is used as a sample to develop an aggregate measure for the population. Authors such as Torrance et al. (1982) liken this pro- cess to the determination of a social preference function and pres- ent a multi-attribute utility theory (MAUT) framework in the sense of Keeney and Kirkwood (1975). The methods used for aggregation of individual preferences in health economics are closely related to those in group decision making; see for example Herrera et al. (2001) and the review by Liberatore and Nydick (2008). Issues such as evaluation of different aggregation methods (Jabeur and Martel, 2007), uncertainty in individual judgments (Basak, 1998; Altuzarra et al., 2007) and use of different scales (Harvey and Osterdal, 2010) that have attracted attention in OR literature are of interest also in health economics. The methods that quantify preference based measurement of health (PBMH) are referred to as the health related quality of life measures (HRQoL). These measures are used to quantify a popula- tion’s preferences over health states as well as a treatment’s effect. Brazier (2005) provided a short list of several common PBMHs and discussed how they are quantified with HRQoL. Most of the re- search in this area focuses on development of PBMHs such as Health Utilities Index (HUI) of Torrance et al. (1995), Quality of Well-Being (QWB) scale discussed in Kaplan et al. (1988) and Short Form (SF-6D) survey discussed in Brazier et al. (2002). As will be discussed in the sequel, the QWB and SF-6D use a composite ap- proach for measurement whereas HUI is based on a decomposed approach. But all the three measures are based on a multi-attribute model for evaluating health states using preference weights and scores. They provide a single index number for each health state. Typically an index value ‘‘1’’ denotes perfect health and ‘‘0’’ de- notes death. In the health economics literature, these index values are referred to as utility. The health states have multiple dimen- sions allowing a multi-attribute utility model. The composite approach, used by QWB and SF-6D for estima- tion of the multi-attribute utility function, involves direct elicita- tion of utility of multidimensional health states. Brazier (2005) points out that the approach requires more health states than that can be evaluated by a single respondent. Therefore, regression models are used to extrapolate the values of health states that are not included in the survey. An alternative for estimation of the utilities for the health states is the decomposed approach employed by the HUI. This method uses the MAUT framework developed by Keeney and Raiffa (1976) and determines a functional form for the multi-attribute utility function of health states. Based on simplifying assumptions such as preferential independence and utility independence, the 0377-2217/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.ejor.2011.11.017 ⇑ Corresponding author. E-mail address: soyer@gwu.edu (R. Soyer). European Journal of Operational Research 218 (2012) 538–547 Contents lists available at SciVerse ScienceDirect European Journal of Operational Research journal homepage: www.elsevier.com/locate/ejor