Modelling SF-6D health state preference data using a nonparametric Bayesian method

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Abstract

This paper reports on the findings from applying a new approach to modelling health state valuation data. The approach applies a nonparametric model to estimate SF-6D health state utility 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 derivative of the SF-36) was valued by a representative sample of the UK general population using standard gamble. The paper presents the results from applying the nonparametric model and comparing it to the original model estimated using a conventional parametric random effects model. The two models are compared theoretically and in terms of empirical performance. The paper discusses the implications of these results for future applications of the SF-6D and further work in this field.

Introduction

There has been an increasing use of preference-based measures of health related quality of life in order to calculate quality adjusted life years for use in cost effectiveness analyses. These preference-based measures are standardised multi-dimensional health state classifications with pre-existing preference or utility weights elicited from a sample of the general population. There are currently a number of such preference-based measures, including the EQ-5D (Brooks, 1996), HUI3 (Feeny et al., 2002), 15D (Sintonen, 1994, Sintonen, 1995), AQoL (Hawthorne et al., 2001), QWB (Kaplan and Anderson, 1988) and the SF-6D (Brazier et al., 2002). A key problem for these measures has been the large number of unique health states that they define and the consequent need to model health state values from a valuation of a subset of possible states.

Health state values present a significant challenge for conventional statistical modelling procedures due to their nature, namely: skewed, truncated, non-continuous and hierarchical (Brazier et al., 2002). Attempts to statistically model these data have met with some success in the EQ-5D and SF-6D (Dolan, 1997, Brazier et al., 2002). However, for both instruments there are concerns with the size of the prediction errors, and for the SF-6D there is a problem of non-monotonicity (where some better states are assigned a lower value than worse states) and an apparent systematic pattern in the prediction errors (involving over prediction of the value of the poor health states and under prediction of the value of good health states). This paper presents an alternative approach to estimating health state values using Bayesian methods. It applies a nonparametric method in order to derive an improved health preference measure for the original UK SF-6D and compares the results to a more standard parametric random effects model.

Section 2 of this paper describes the SF-6D valuation study and the data used in this paper. Section 3 sets out the parametric and nonparametric approaches for health state valuations. The results from each approach are presented and compared in terms of their ability to predict actual values. Finally the two approaches are applied to some patient data sets to examine the impact of using the nonparametric model results to estimate mean patient health state values and changes over time. We conclude with a discussion of the results and their implication for future use of the SF-6D and modelling work in this field.

Section snippets

SF-6D data set

The SF-6D, derived from the SF-36, is a generic measure of health (Ware and Sherbourne, 1992). It is composed of six multi-level dimensions of health: physical functioning, role limitation, social functioning, bodily pain, mental health and vitality (Table 1). 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

Modelling

The SF-6D descriptive system describes 18,000 possible health states and the empirical survey could obtain valuations for only a small subset. The aim of modelling is to estimate health state utility values for all states. The utility associated with a health state is 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

Results

The models are compared in terms of their predictive ability in Fig. 1, Fig. 2, where the predicted and actual mean values for the 249 health states valued in the survey have been plotted with health states ordered by predicted health state values.3 Fig. 1 presents the resulting

Applications

The implications of different models have been examined by estimating mean health state values in four patient groups and by estimating mean changes in these groups over time. These studies from which these data are drawn all used the SF-36 to assess health status on at least two occasions. The data sets are as follows.

Discussion

This paper reports on the findings from applying a new approach to modelling health state valuation data. The approach applies a nonparametric model to estimate health state utility values for the SF-6D using Bayesian methods. The nonparametric model has five principal advantages over the conventional parametric random effects model.

  • 1.

    Flexibility: The parametric regression model assumes a particular form for the preference function over health states. In particular, apart from the single

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.

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