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Table 3 Model performance of three regression methods for mapping the PHQ-8 to the EQ-5D-3L utility scores

From: Mapping the PHQ-8 to EQ-5D, HUI3 and SF6D in patients with depression

No Mapping method Number of components and truncation Specification ME MAE RMSE MAE rank RMSE rank ARV
1 BETAMIX M1a 1 component without truncation Probability mass at full health 0.0904 0.2014 0.2621 18 18 18
2 BETAMIX M1b 2 components without truncation Probability mass at full health 0.0130 0.1868 0.2381 15 11 13
3 BETAMIX M1c 2 components with truncation Probability mass at full health −0.0043 0.1839 0.2370 12 9 10.5
4 BETAMIX M1d 2 components with truncation Probability mass at full health and truncation point −0.0024 0.1861 0.2390 13 13 13
5 BETAMIX M2a 1 component without truncation Probability mass at full health 0.0866 0.1962 0.2607 17 17 17
6 BETAMIX M2b 2 components without truncation Probability mass at full health 0.0101 0.1825 0.2349 8 7 7.5
7 BETAMIX M2c 2 components with truncation Probability mass at full health −0.0038 0.1806 0.2341 6 5 5.5
8 BETAMIX M2d 2 components with truncation Probability mass at full health and truncation point −0.0013 0.1813 0.2355 7 8 7.5
9 BETAMIX M3a 1 component without truncation Probability mass at full health 0.0659 0.1864 0.2504 14 16 15
10 BETAMIX M3b 2 components without truncation Probability mass at full health 0.0119 0.1800 0.2321 5 1 3
11 BETAMIX M3c 2 components with truncation Probability mass at full health 0.0020 0.1774 0.2328 2 3 2.5
12 BETAMIX M3d 2 components with truncation Probability mass at full health and truncation point 0.0057 0.1765 0.2326 1 2 1.5
13 OLS M1    0.0000 0.1837 0.2374 11 10 10.5
14 OLS M2    0.0000 0.1798 0.2347 4 6 5
15 OLS M3    0.0000 0.1784 0.2331 3 4 3.5
16 TOBIT M1    −0.0263 0.1870 0.2413 16 15 15.5
17 TOBIT M2    −0.0264 0.1834 0.2389 9 12 10.5
18 TOBIT M3    −0.0264 0.1836 0.2390 10 14 12
  1. NOTE: ME Mean error, MAE Mean absolute error, RMSE Root mean square error, ARV Average ranking values
  2. M1 = Regression model including PHQ as explanatory variable
  3. M2 = Regression model including PHQ, age, gender as explanatory variables
  4. M2 = Regression model including PHQ, PHQ-squared, age, gender as explanatory variables