Mapping algorithms to predict EuroQol-5D-3L utilities from chronic obstructive pulmonary disease assessment test

The Institutional Review Board of National Cheng Kung University Hospital (NCKUH) approved this study prior to initiation (IRB number: B-ER-98-289 and B-ER-111-254). Informed consent was obtained from all subjects and all methods were performed in accordance with relevant research ethics board guidelines and regulations.

In this study, 323 patients were enrolled who were diagnosed with COPD in the Cheng Kung National University Medical Center Ambulatory Pulmonary Medicine Clinic from April 2017 to December 2020. All patients were enrolled in the pay-for-performance program COPD and had been receiving regular medical treatment for COPD for more than three months. These COPD cases were defined according to the GOLD guidelines and diagnostic criteriaseven. All pulmonary function tests were performed according to a joint consensus of the American Thoracic Society and the European Respiratory Society11. Patients who did not want to participate, could not benefit from the pay-for-performance program (eg, bedridden), or had advanced lung cancer and pulmonary fibrosis were excluded.

Participants were graded according to the GOLD 2017 classification and were divided into four stages (mild to very severe), which corresponded to GOLD 2017 grades 1 to 4, based on post-bronchodilator forced expiratory volume in one second (FEV1): grade 1 or mild stage (VEM1≥ 80%), grade 2 or moderate stage (50% ≤ FEV11< 80%), grade 3 or severe stage (30% ≤ FEV11< 50%) and grade 4 or very severe stage (FEV11< 30%)seven. In this study, participants with FEV1<50% were categorized as 'severe' to obtain a sufficient number in the sample for the estimate.

The quality of life of COPD patients was monitored consistently with EQ-5D-3L and CAT to develop an algorithm to estimate EQ-5D equivalent utilities from CAT. The validated Taiwanese version of the EQ-5D-3L and the Chinese version of the CAT questionnaires were used in this study12.13.

The questionnaires were administered by the pay-for-performance program case manager in the outpatient department.

Development of a model

The COPD patient dataset was randomly divided into a training group of 160 patients and a validation group of 163 patients. While the predictive model was built, the final model coefficients were derived based on the full sample (all 323 patients) to obtain the most accurate estimates. In this study, we considered two OLS-based procedures to build predictive models for patients with COPD. The first was the model recommended by Hoyle et al.9. They regressed EQ-5D utility on 8 CAT scores and chose 4 CAT scores (chest tightness, activities, confidence, and energy) with p-values ​​less than 0.05 to build the final model. We created modified versions of the Hoyle et al. and Lim et al. which correspond better to the Taiwanese population. A backward elimination procedure was applied to obtain a final parsimonious model with a Type I error rate of 0.05 when the statistical hypothesis tests were performed.

Response mapping is another feasible approach that can be used for utility prediction.14.15. While OLS aims to predict EQ-5D utility, response mapping aims to predict five EQ-5D scores, each taking values ​​of 1, 2, or 3. The five predicted scores are then transformed into utility. The transformation formula varies according to the different underlying populations. In this study, the formula, which is based on the Taiwanese population obtained from Lee et al. has been applied16. The formula was: EQ-5D-3L Utility = 1–0.185–0.123*Mobility at level 2–0.272*Mobility at level 3–0.167*Self-heal at level 2–0.276*Self-heal at level 3–0.085*Usual activities at level 2–0.208*usual activities at level 3–0.121*pain/discomfort at level 2–0.261*pain/discomfort at level 3–0.154*anxiety/depression at level 2–0.282*anxiety/depression at level 3–0.190 *Any dimension at level 3.

Additionally, since the EQ-5D score takes on discrete values, a multinomial logistic regression (MLR) is a relevant model to use to identify the association between the score and the covariates, 8 CAT scores, age, and gender. In our dataset, most patients completed the EQ-5D and CAT questionnaires multiple times during the follow-up period. In other words, the experiment consisted of repeated measurements. Therefore, a Generalized Estimating Equation (GEE) was applied with an independent working correlation for estimation and hypothesis testing.17. For each EQ-5D score prediction, the final multinomial logistic regression was chosen such that the resulting QIC is minimized18. The GEE models were made using the SAS GEE procedure.

We also applied the Mean Rank Method (MRM), developed by Wee et al.19, as another method to develop a predictive model for mapping EQ-5D utilities from CAT. The MRM takes into account the nonparametric correspondence between EQ-5D and CAT scores, preventing potentially erroneous model assumptions and providing less interpretive information.


Among all the applied methods, OLS, MLR and MRM, the training data was used to build predictive models, while the validation data was used to evaluate the performance of these models via both mean squared error (RMSE) and the mean absolute error (MAE). Moreover, the models of Hoyle et al. and Lim et al. were modified by re-estimating their coefficients using the training group and validated by the validation group for comparison.

In this study, as expected, the model with the best predictive ability should have the smallest RMSE and MAE. Additionally, to visualize potential prediction biases, we suggest the bubble chart drawn with R statistical software version 4.2.1, R Core Team (2021). A: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL in this article. The best model should locate a majority of bubbles on the diagonal line of the bubble chart. For statistical comparisons between groups, continuous variables were analyzed by t-test and categorical variables were analyzed by chi-square. All statistical analyzes were performed using SAS statistical software version 9.4 (SAS Institute Inc., Cary, NC, USA).

Ethics approval

The Institutional Review Board of National Cheng Kung University Hospital (NCKUH) approved this study prior to initiation (IRB number: B-ER-98-289 and B-ER-111-254).