Using rank data to estimate health state utility models

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Abstract

In this paper we report the estimation of conditional logistic regression models for the Health Utilities Index Mark 2 and the SF-6D, using ordinal preference data. The results are compared to the conventional regression models estimated from standard gamble data, and to the observed mean standard gamble health state valuations.

For both the HUI2 and the SF-6D, the models estimated using ordinal data are broadly comparable to the models estimated on standard gamble data and the predictive performance of these models is close to that of the standard gamble models. Our research indicates that ordinal data have the potential to provide useful insights into community health state preferences. However, important questions remain.

Introduction

As cost effectiveness analysis has become more important in health care decision making processes, the interest in how to value health outcomes has increased. There is a substantial body of research on the relative strengths and weaknesses of alternative methods (e.g. Torrance, 1986, Brazier et al., 1999). Such research has focused primarily on three valuation methods; time trade off (TTO); standard gamble (SG); and visual analogue scales (VAS), also called category scaling.

Work that has attempted to identify a preferred method has tended to support the use of TTO and/or SG (Brazier et al., 1999, National Institute for Clinical Excellence, 2004). VAS has been criticised on a number of points, both theoretical (does VAS capture strength of preference?) and empirical (the data may be subject to end-point and context bias) (Torrance et al., 2001). However, it is widely accepted that TTO and SG have significant limitations (Brazier et al., 1999). What is remarkable is the degree to which the role of ordinal data in health state valuation has been largely ignored; notable exceptions to this observation being the work by Kind, 1982, Kind, 1996.

Ranking exercises are conventionally included in health state valuation interviews as warm-up exercises, in order to familiarise the interviewee with the health state classification system being valued and with the task of considering preferences between hypothetical health states (Furlong et al., 1990). The use of the data from these ranking exercises has generally been limited to checking the degree of consistency between the valuations obtained from the SG or TTO valuation exercises and the ranking exercise.

Kind (1982) identified Thurstone's (1927) model of comparative judgement as a potential theoretical basis for deriving cardinal preferences from rank preference data. Thurstone's method considers the proportion of times that health state A is considered worse than health state B. The preferences over the health states represent a latent cardinal utility function. Individual's stated preferences draw upon this latent function but imperfectly, i.e. there are errors in individual's expression of the latent utility function. The closer two health states, A and B, lie on the latent utility function the greater the likelihood that an individual will incorrectly state that they prefer B to A, when in fact the utility they expect to gain from health state A is greater than the utility they expect to gain from health state B. Thus, there is a relationship between observed ordinal preferences and the underlying cardinal latent utility function. McFadden (1974) proposed the conditional logistic regression model as a means of modelling this latent utility function from ordinal data. The assumptions underlying McFadden's choice model are clearly described by Salomon (2003).

In modelling a population latent utility function from individual rank data, the error is being characterised in terms of the deviation of the individuals’ preferences from the population preferences, i.e. variation in individual preferences within a population is considered analogous to Thurstone's individual level perceptual error.

Recently Salomon (2003) presented work that applied conditional logistic regression models to the rank data collected as part of the measurement and valuation of health study (MVH). Salomon estimated a model equivalent to that reported by Dolan (1997). This model did not produce utilities on the 0–1 scale necessary for use in estimating quality adjusted life years. Salomon rescaled the model coefficients on to the full health–death (1–0) scale, using the mean measured TTO value for the PITS state in the EQ-5D classification (3, 3, 3, 3, 3). In this paper we present an approach that avoids the need for external health state utility data, as in such rescaling, by directly estimating a parameter for the state death, as part of the model. This method is applied to rank data from two health state valuation surveys; a UK based valuation survey for the Health Utilities Index Mark 2 (McCabe et al., 2005a) and the UK valuation survey for the SF-6D (Brazier et al., 2002).

Section snippets

Data

Detailed descriptions of the HUI2 and SF-6D classification systems, and the valuation surveys have been reported in detail elsewhere, thus, we will only provide a brief summary of them here (Brazier et al., 2002, McCabe et al., 2005a) (see Appendix A Health Utilities Index Mark 2 (, Appendix B The Short Form 6D ().

Health Utilities Index Mark 2

The Health Utilities Index Mark 2 is a six-dimension health state classification (sensation, mobility, emotion, cognition, self care and pain) with either four or five levels for each

Health Utilities Index Mark 2

Table 1 reports the original and rescaled coefficients for the rank health state utility models for the HUI2. It also gives the results for each of the diagnostic tests. For comparative purposes the same information is provided for the SG health state valuation model (McCabe et al., 2005a, McCabe et al., 2005b).

The similarity of the rank and SG data models is quite striking. The rank model has one more inconsistency than the SG model, and does not distinguish as clearly between the different

Discussion

In this paper we have reported the estimation of population cardinal health state valuation models for the HUI2 and the SF-6D, from individual ordinal preference data. In both cases the models bear comparison to the health state valuation models estimated from SG (cardinal) data provided by the same respondents.

The impetus for this research was an analysis of rank data for the EQ-5D, presented by Salomon (2003). The predictive performance of the rank EQ-5D model, in relation to the observed

Summary

In this paper we have presented two models of population cardinal health state preferences based upon individual ordinal health state preference data; one for the SF-6D health state classification, the other for the HUI2 health state classification. We have compared these to models estimated on SG valuation data, in terms of the degree of accuracy and bias in predicting mean observed SG health state valuations in the estimation samples.

The ordinal rank models perform much better than might have

Acknowledgements

The authors wish to acknowledge the support and encouragement of their co-workers on the SF-6D and HUI2 valuation projects. In addition, George Torrance from McMaster University and Joshua Salomon from Harvard University provided valuable comments on the work as it progressed. We are grateful to the UK Medical Research Council, who funded the HUI2 valuation project and to GlaxoWellcome, who funded the SF-6D valuation project. We also wish to thank two anonymous referees for the excellent

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