Poulimenos, Spyridon; (2020) Bayesian models for health related quality of life data: propagating uncertainty in data from the EQ-5D-3L questionnaire. Doctoral thesis (Ph.D), UCL (University College London).

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Abstract

The EQ-5D-3L is a tool that is used for the measurement and valuation of the health of populations for research. It is a self-reported questionnaire, with five questions and describes 243 distinct health states. Each state has been assigned a score (or utility score) that reflects the relative ranking. These scores can then be used to estimate quality-adjusted life-years in economic evaluations. The derived utility scores of the UK EQ-5D-3L were estimated based on a regression model using standard classical (frequentist) statistical techniques. The scores represent point estimates of the quality of life associated with each health state. These point estimates tacitly ignore the uncertainty of the estimates due to the variability inherent in the underlying data. In order to address this, the objective of this thesis is to extend the original analysis and propagate the uncertainty of the UK EQ-5D-3L scores by constructing a Bayesian model, which assigns appropriate posterior probability distributions to each of the EQ-5D-3L health states. The data used are from a 1993 UK-representative survey in which respondents evaluated EQ-5D-3L health states. A Bayesian hierarchical model is built, which accounts for model-misspecification and the responses of the survey participants in order to assign a probability distribution to the utility score of every feasible EQ-5D-3L state experienced by a group of people such as clinical trial subjects. My methods are applied on the CoBalT trial as well as on simulated data. Markov Chain Monte Carlo (MCMC) samples of simulations are derived for the utility values of the EQ-5D-3L health states. The posterior utility distributions of the EQ-5D-3L health states are summarised as approximate three-component Normal distributions using numerical optimisation and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm. The cost-effectiveness results of the proposed model are compared with those obtained under the regular approach and differences are observed especially for the results of the simulated data. I recommend the use of the presented approach in order to properly propagate the underlying uncertainty, as otherwise an important layer of uncertainty is not taken into consideration and this can lead to the wrong inference when conducting cost-effectiveness analysis. Furthermore, this approach provides the useful advantage of doing sensitivity analysis without making any further distributional assumptions about the utility scores of the EQ-5D-3L health states experienced by the clinical trial subjects. Similar methods can be applied to the EQ-5D-3L scores of other countries and to other health instruments such as the SF-6D. Other extensions include applications in the context of model-based economic evaluations and in the area of mapping utility scores across health instruments.

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