Full Bayesian methods to model utility measures using mixture of distributions


There is an ongoing interest for the improvements of economic evaluation methods. Although a typical research field of economists, nowadays it has become an active and growing research area of statisticians, who have been attracted by the potential for interesting modelling, especially in the context of Bayesian statistics.

In a world of potentially infinite medical advances but with only finite resources, decisions are made by the National Institute for Health and Care Excellence (NICE) regarding which interventions worth the value for money. Quality-adjusted life-years (QALYs) are frequently used in economic evaluations and are suggested by the NICE as the recommended measure for the computation of the gained benefits of a medical intervention. The nature of QALYs makes them attractive measures, which can be used to compare the benefits of different feasible interventions and across disease areas.

QALYs are a composite function of the life-years spent in a health state and the quality of life in that state. We are particularly interested in the quality of life, which is expressed in terms of a utility value (the economist’s way of describing the well-being of a condition). It is important to determine the utility values of health states (for example using specific questionnaires, such as the EQ-5D) used to describe the lives of individuals when undertaking economic evaluations.

EQ-5D is a generic questionnaire frequently used in economic evaluations in order to describe the quality of life of individuals. A 1993 UK general population survey aimed at assigning utility values to a comprehensive set of health states using the output of a time trade-off (TTO) exercise and by applying regression techniques. The derived values represent the mean preferences of individuals for that health state, but do not inform us about how the preference values for that state are distributed among the survey participants.

We are exploring the feasibility and benefits of using full Bayesian methods to model these utility measures using appropriate distributions. Moreover, due to the frequent multi-modality in the data, it might be better to use mixtures of distributions to properly account for this issue. These methods also permit the examination of the impact of individuals’ preferences which deviate from the mean. Furthermore, we can investigate whether the use of sampled values from these distributions leads into different economic evaluation decisions than when merely using the estimated means.

Last updated: Friday 13 December 2019
Gianluca Baio
Gianluca Baio
Professor of Statistics and Health Economics