A Comparison of Japan and UK SF-6D Health-State Valuations Using a Non-Parametric Bayesian Method

Abstract

Background

There is interest in the extent to which valuations of health may differ between different countries and cultures, but few studies have compared preference values of health states obtained in different countries.

Objective

We sought to estimate and compare two directly elicited valuations for SF-6D health states between the Japan and UK general adult populations using Bayesian methods.

Methods

We analysed data from two SF-6D valuation studies where, using similar standard gamble protocols, values for 241 and 249 states were elicited from representative samples of the Japan and UK general adult populations, respectively. We estimate a function applicable across both countries that explicitly accounts for the differences between them, and is estimated using data from both countries.

Results

The results suggest that differences in SF-6D health-state valuations between the Japan and UK general populations are potentially important. The magnitude of these country-specific differences in health-state valuation depended, however, in a complex way on the levels of individual dimensions.

Conclusion

The new Bayesian non-parametric method is a powerful approach for analysing data from multiple nationalities or ethnic groups, to understand the differences between them and potentially to estimate the underlying utility functions more efficiently.

Appendix: Modification to \( \varvec{\beta}_{{\mathbf{0}}} \) and \( \varvec{\beta}_{{\mathbf{1}}} \) vectors given in (2) and (3)

The SF-6D health state descriptive system is exactly the same for the UK [6] and Japan (Table 1) except for the role limitations dimension, i.e. when d = 2. The result is that

$$ x_{2} = \left\{ {\begin{array}{l} {1,\;2,\;3,\;4\;{\text{or}}\;5} \quad{\text{ for Japan}} \\ {1,\;2,\;3\;{\text{or}}\;4} \quad{{\text{for UK}}.} \\ \end{array} } \right. $$

This corresponds to the second parameter in the β - vector, i.e. β _2. To model this we suggest the following:

	1	2	3	4	5
Japan	0	β 2	2β 2	3β 2	4β 2
UK	0	β*	γ*	β* + γ*

Note that this dimension is a bit anomalous in the UK definition of levels. Level 2 is one type of restriction, level 3 is a different type of restriction and level 4 is no type. Therefore, we have two parameters β* and γ* for the loss of quality of life for each type of restriction.

Let β ₀ be the vector of parameters that represent the UK, which comprise the constant term, the slopes for dimensions 1, 3, 4, 5, 6 and the new pair of parameters for dimension 2. Let β ₁ be the extra parameters that we need for Japan, which are increments to the constant terms and to the slopes in dimensions 1, 3, 4, 5, 6 and the new slope in dimension 2. Let β be the combination of these two vectors. Now we write the expectation of $u_{c} ({\mathbf{x}})\;{\text{as}}\;\varvec{\beta}^{{\prime }} {\mathbf{z}}$, where the vector z is a suitable function of the vector x of levels. For instance if x = (1, 2, 3, 4, 2, 1) and c = 0 then ${\mathbf{z}}$ needs to be (1, 1, 1, 0, 3, 4, 2, 1, 0, 0, 0, 0, 0, 0, 0), where the first 1 is multiplying the UK constant term, the second 1 is multiplying the UK slope parameter for dimension 1, the third 1 is multiplying the β* parameter for UK dimension 2, the first 0 is multiplying the γ* parameter for UK dimension 2, the following 3, 4, 2, 1 multiply the UK slope parameters for dimensions 3–6 and the remaining 7 zeroes multiply the Japanese parameters. For the same x and c = 1, z should be (1, 1, 0, 0, 3, 4, 2, 1, 1, 1, 2, 3, 4, 2, 1). This implies that if x = (1, 1, 3, 4, 2, 1), then

$$ z = \left\{ {\begin{array}{l} { ( 1 ,\; 1 ,\; 0 ,\; 0 ,\; 3 ,\; 4 ,\; 2 ,\; 1 ,\; 0 ,\; 0 ,\; 0 ,\; 0 ,\; 0 ,\; 0 ,\; 0 )}\quad {c = 0} \\ { ( 1 ,\; 1 ,\; 0 ,\; 0 ,\; 3 ,\; 4 ,\; 2 ,\; 1 ,\, 1 ,\; 1 ,\; 2 ,\, 3 ,\, 4 ,\; 2 ,\; 1 )}\quad {c = 1} \\ \end{array} } \right. $$

whereas if x = (1, 4, 3, 4, 2, 1), we get

$$ z = \left\{ {\begin{array}{l} { ( 1 ,\; 1 ,\; 1 ,\; 1 ,\; 3 ,\; 4 ,\; 2 ,\; 1 ,\; 0 ,\; 0 ,\; 0 ,\; 0 ,\; 0 ,\; 0 ,\; 0 )} \quad {c = 0} \\ { ( 1 ,\; 1 ,\; 0 ,\; 0 ,\; 3 ,\, 4 ,\; 2 ,\; 1 ,\; 1 ,\; 1 ,\; 4 ,\; 3 ,\; 4 ,\; 2 ,\; 1 )} \quad{c = 1} \\ \end{array} } \right. $$

Therefore, UK level 4 of dimension 2 has expectation β* + γ*.