Elsevier

Social Science & Medicine

Volume 64, Issue 6, March 2007, Pages 1242-1252
Social Science & Medicine

Modelling covariates for the SF-6D standard gamble health state preference data using a nonparametric Bayesian method

https://doi.org/10.1016/j.socscimed.2006.10.040Get rights and content

Abstract

It has long been recognised that respondent characteristics can impact on the values they give to health states. This paper reports on the findings from applying a non-parametric approach to estimate the covariates in a model of SF-6D health state values using Bayesian methods. The data set is the UK SF-6D valuation study, where a sample of 249 states defined by the SF-6D (a derivate of the SF-36) was valued by a sample of the UK general population using standard gamble. Advantages of the nonparametric model are that it can be used to predict scores in populations with different distributions of characteristics and that it allows for an impact to vary by health state (whilst ensuring that full health passes through unity). The results suggest an important age effect, with sex, class, education, employment and physical functioning probably having some effect, but the remaining covariates having no discernable effect. Adjusting for covariates in the UK sample made little difference to mean health state values. The paper discusses the implications of these results for policy.

Introduction

The increasing use of preference-based measures in deriving quality adjusted life years (QALYs), for populating models of cost effectiveness for informing purchasers of health care, inevitably raises questions about whose values should be used to value health states. A number of key agencies around the world have followed the Washington Panels on Cost Effectiveness of Medicines recommendation to use a representative sample of the general population (Gold, Siegel, Russell, & Weinstein, 1996; NICE, 2004; Torrance et al., 1996). This raises an important policy question as to whether there should be an allowance for any systematic variation in health state values between sub-groups of the population. Our paper examines the impact of respondent background characteristics on the values they give to health states.

Previous research into the impact of respondent covariates on their valuation of health states has been based on small sample sizes and/or has lacked a coherent approach to exploring the impact of background characteristics (Hadorn & Uebersax, 1995). Furthermore, past studies have often used rating scales (Badia, Fernandez, & Segura, 1995; Hadorn & Uebersax, 1995) rather than one of the choice-based methods, such as time trade-off (TTO) or standard gamble (SG). A full exploration of the impact of covariates requires a multi-variate approach and a comparatively large valuation data set over many health states. A published analysis of the comparatively large UK EQ-5D valuation data set found some systematic variation of TTO values by age, sex and marital status (Dolan & Roberts, 2002). The most important of these was age, but this finding may have been partly the result of an artefact of the TTO variant used for states worse than death, since 50% of respondents over 60 regarded the scenario as implausible. Furthermore, the results may not translate to other valuation methods like standard gamble.

The application of multi-variate techniques to exploring the impact of covariates on the valuation of a descriptive system like the EQ-5D, where only a sub-set of states has been valued, is potentially impeded by the nature of such data, namely: skewed, truncated, non-continuous and hierarchical (Brazier, Roberts, & Deverill, 2002). These types of data have been analysed with some success using conventional parametric methods, but these methods are limited in the way they are able to model the impact of covariates on health state values. The main limitation is that covariates are modelled only in terms of their impact on the intercept. This results in the intercept deviating from unity, which contravenes the requirement that full health equals one on the conventional full health-death scale used to estimate QALYs. Secondly, it means that the impact of a covariate is assumed to be the same regardless of the state; so for example the impact is the same regardless of the severity of the state. This is an unrealistic assumption.

This paper presents an alternative approach to estimating health state values using nonparametric Bayesian methods (Kharroubi, O’Hagan, & Brazier, 2005). It applies a nonparametric approach in order to provide a more flexible method to taking into account the impact of covariates, that: (1) enables the estimation of the impact of covariates on the state as whole and not just the intercept term, and (2) allows for the fact that each individual values several states, by incorporating individual random effects that can be linked to covariates and retaining the feature that perfect health should have a value of one.

The next section briefly describes the SF-6D valuation study and the data used in this paper. Section 3 sets out the nonparametric approach and how it offers a better way to estimate the impact of covariates compared to conventional parametric approaches. The results are presented in Section 4. The implications of these results for further research and health policy are discussed in Section 5.

Section snippets

SF-6D data set

The SF-6D, derived from the SF-36, is a generic measure of health (Ware & Sherbourne, 1992). It is composed of six multi-level dimensions of health: physical functioning, role limitation, social functioning, bodily pain, mental health and vitality. It was constructed from a sample of 11 items selected from the SF-36 to minimise the loss of descriptive information (Brazier et al., 2002). The six dimensions have between four and six levels. An SF-6D health state is defined by selecting one

Modelling

The aim of modelling is to estimate health state utility values for all states from the sample of 249 states valued in the survey. The utility associated with a health state is usually assumed to be a function of that state, hence by estimating a relationship between the descriptive system and the observed values we can infer values for all states. Valuation surveys generate data with a complex structure creating a number of problems for estimation and a variety of techniques have been used to

Reporting of results

The results from running these models are reported in a number of different ways. Firstly, the posterior probabilities, means and standard deviations are presented for all covariates examined in the model where the posterior probability of being positive is over 0.8 or under 0.2 (i.e. a 0.8 chance of being negative). These cut-offs are more relaxed than the usual levels of probabilities used in frequentist analysis, because it was felt valuable to show variables that could have an influence.

Results

Table 3 reports the inferences for covariates meeting the cut-off values of a posterior probability of <0.2 or >0.8. Out of the covariates examined in the model age and age squared, sex, having a degree, social class, being employed, being a student, own physical functioning, own social functioning, degree of difficulty with ranking task and understanding of ranking task made these cut-offs. Nine of these 11 covariates achieved a posterior probability of being positive of <0.1 or >0.9.

These

Discussion

This paper has examined the role of respondent characteristics in explaining variation in SG valuations of SF-6D health states from a survey of 611 members of the UK general population. It has presented a new approach to modelling which allows for a more flexible way to model the impact of covariates. A wide range of background variables has been examined to explain variation in SG health state values, including age, sex, education, class, living circumstances, employment, retirement,

Acknowledgements

We would like to thank GlaxoSmithKline for funding the original study and Roger Thomas and Roger Sturgis for conducting the valuation survey. John Brazier is funded by the MRC HSRC. The views represented here are the authors’ and are not necessarily representative of the funding bodies.

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