Conducting EQ-5D Valuation Studies in Resource-Constrained Countries: The Potential Use of Shrinkage Estimators to Reduce Sample Size

Use of a Non-parametric Bayesian Method to Model Health State Preferences: An Application to Polish and Irish EQ-5D-5L Valuations

Valuations of preference-based measures for health are conducted in different countries. There is scope to use results from existing countries' valuations to generate better valuation estimates than analyzing the data from each country separately. We analyse data from two smaller design EQ-5D-5L valuation studies where a sample of 119 Polish migrants and 123 native Irish valued 30 common health states using similar composite time trade-off protocols. We apply a non-parametric Bayesian method to provide better predictions of the Polish (Irish) population utility function when the existing Irish (Polish) results were used as informative priors. The resultant new estimates were then compared to those obtained by analyzing the data from each country by itself via different prediction criterions. The results suggest that existing countries' valuations could be used as potential informative priors to produce better valuation estimates under all prediction criterions used. The implications of these results will be hugely important in countries where valuation studies are expensive and hard to conduct. Future application to other countries and to other preference-based health measures are encouraged.

Sample Size and Model Prediction Accuracy in EQ-5D-5L Valuations Studies: Expected Out-of-Sample Accuracy Based on Resampling with Different Sample Sizes and Alternative Model Specifications

Background. National valuation studies are costly, with ∼1000 face-to-face interviews recommended, and some countries may deem such studies infeasible. Building on previous studies exploring sample size, we determined the effect of sample size and alternative model specifications on prediction accuracy of modeled coefficients in EQ-5D-5L value set generating regression analyses. Methods. Data sets (n = 50 to ∼1000) were simulated from 3 valuation studies, resampled at the respondent level and randomly drawn 1000 times with replacement. We estimated utilities for each subsample with leave-one-out at the block level using regression models (8 or 20 parameter; with or without a random intercept; time tradeoff [TTO] data only or TTO + discrete choice experiment [DCE] data). Prediction accuracy, root mean square error (RMSE), was calculated by comparing to censored mean predicted values to the left-out block in the full data set. Linear regression was used to estimate the relative effect of changes in sample size and each model specification. Results. Results showed that doubling the sample size decreased RMSE by on average 0.012. Effects of other model specifications were smaller but can when combined compensate for loss in prediction accuracy from a small sample size. For models using TTO data only, 8-parameter models clearly outperformed 20-parameter models. Adding a random intercept, or including DCE responses, also improved mean RMSE, most prominently for variants of the 20-parameter models. Conclusions. The prediction accuracy impact of further increases in sample size after 300 to 500 were smaller than the impact of combining alternative modeling choices. Hybrid modeling, use of constrained models, and inclusion of random intercepts all substantially improve the expected prediction accuracy. Beyond a minimum of 300 to 500 respondents, the sample size may be better informed by other considerations, such as legitimacy and representativeness, than by the technical prediction accuracy achievable.

Modeling SF-6D Health Utilities: Is Bayesian Approach Appropriate?

Background: Valuation studies of preference-based health measures like SF6D have been conducted in many countries. However, the cost of conducting such studies in countries with small populations or low- and middle-income countries (LMICs) can be prohibitive. There is potential to use results from readily available countries’ valuations to produce better valuation estimates. Methods: Data from Lebanon and UK SF-6D value sets were analyzed, where values for 49 and 249 health states were extracted from samples of Lebanon and UK populations, respectively, using standard gamble techniques. A nonparametric Bayesian model was used to estimate a Lebanon value set using the UK data as informative priors. The resulting estimates were then compared to a Lebanon value set obtained using Lebanon data by itself via various prediction criterions. Results: The findings permit the UK evidence to contribute potential prior information to the Lebanon analysis by producing more precise valuation estimates than analyzing Lebanon data only under all criterions used. Conclusions: The positive findings suggest that existing valuation studies can be merged with a small valuation set in another country to produce value sets, thereby making own country value sets more attainable for LMICs.

Bayesian modeling of health state preferences: could borrowing strength from existing countries' valuations produce better estimates

BACKGROUND

Valuations of preference-based measure such as EQ-5D and/or SF6D have been conducted in different countries. There is potential to borrow strength from existing countries' valuations to generate better representative utility estimates. This is explored using two case studies modelling UK data alongside Japan samples to generate Japan estimates.

METHODS

Data from two SF-6D valuation studies were analyzed, where using similar standard gamble protocols, values for 241 and 249 states were devised from representative samples of Japan and UK general adult populations, respectively. Two nonparametric Bayesian models were applied to estimate a Japan value set, where the UK results were used as informative priors in the first model and subsets of the Japan data set for 25 and 50 health states were modelled alongside the full UK data set in the second. Generated estimates were compared to a Japan value set estimated using Japan values alone using different prediction criterion.

RESULTS

The results allowed the UK data to provide significant prior information to the Japan analysis by generating better estimates than using Japan data alone. Also, using Japan data elicited for 50 health states alongside the existing UK data produces roughly similar predicted valuations as the Japan data by itself.

CONCLUSION

The promising results suggest that the existing preference data could be combined with data from a valuation study in a new country to generate preference weights, thus making own country value sets more achievable for low-middle income countries. Further research and application to other countries and preference-based measures are encouraged.