Formulation of a Mapping Formula to Estimate Well-Being Utility from Clinical Subjective Well-Being Scales

Figures & data

Table 1 Characteristics of Our Sample

		Total Sample (n=500)	Estimation Sample (n=300)	Validation Sample (n=200)
Age	Mean (SD)	44.0 (11.5)	44.0 (11.3)	44.0 (11.9)
Sex	Male/Female	213 / 287	130 / 170	83 / 117
ICECAP-A	Mean (SD)	0.62 (0.21)	0.62 (0.21)	0.62 (0.20)
	Min. - Max.	0.00–1.00	0.00–1.00	0.00–1.00
SWLS	Mean (SD)	19.8 (7.1)	19.7 (7.0)	19.9 (7.4)
	Min. - Max.	5–35	5–35	5–35
FS	Mean (SD)	32.8 (9.3)	32.4 (9.4)	33.3 (9.3)
	Min. - Max.	8–56	8–56	8–56
SPANE-P	Mean (SD)	19.2 (5.3)	19.3 (5.3)	19.1 (5.3)
	Min. - Max.	6–30	6–30	6–30
SPANE-N	Mean (SD)	18.3 (4.8)	18.1 (4.8)	18.6 (4.8)
	Min. - Max.	6–30	6–30	6–30

Abbreviations: SD, standard deviation; ICECAP-A, the ICEpop CAPability measure for Adults; SWLS, the Satisfaction With Life Scale; FS, Flourishing Scale; SPANE, the Scale of Positive and Negative Experience.

Figure 1 Correlation matrix among age and each score of questionnaires regarding well-being.

Table 2 Modeling and Fitting of Each Model

		Estimation Sample (n = 300)					Validation Sample (n = 200)
Model	Used Questionnaires	Mean (SD)	Min	Max	RMSE	MAE	Mean (SD)	Min	Max	RMSE	MAE
1A	SWLS	0.60 (0.15)	0.26	0.88	0.17	0.13	0.60 (0.16)	0.26	0.88	0.16	0.12
1B	FS	0.60 (0.16)	0.17	0.91	0.16	0.12	0.62 (0.16)	0.17	0.92	0.15	0.12
1C	SPANE-P	0.61 (0.16)	0.17	0.89	0.17	0.13	0.60 (0.16)	0.17	0.90	0.15	0.12
1D	SPANE-N	0.60 (0.10)	0.29	0.85	0.19	0.15	0.59 (0.10)	0.33	0.82	0.17	0.14
2A	SWLS, FS	0.60 (0.17)	0.16	0.90	0.15	0.12	0.61 (0.17)	0.17	0.92	0.14	0.11
2B	SWLS, SPANE-P	0.61 (0.17)	0.16	0.91	0.15	0.12	0.60 (0.18)	0.16	0.92	0.15	0.11
2C	SWLS, SPANE-N	0.60 (0.16)	0.22	0.88	0.16	0.12	0.60 (0.17)	0.20	0.91	0.15	0.12
2D	FS, SPANE-P	0.61 (0.18)	0.12	0.92	0.15	0.12	0.61 (0.17)	0.12	0.94	0.14	0.11
2E	FS, SPANE-N	0.60 (0.17)	0.16	0.93	0.15	0.12	0.61 (0.17)	0.16	0.94	0.14	0.11
2F	SPANE-P&N	0.61 (0.16)	0.15	0.92	0.16	0.12	0.59 (0.17)	0.15	0.93	0.15	0.11
3A	SWLS, FS, SPANE-P	0.61 (0.18)	0.14	0.91	0.15	0.11	0.61 (0.18)	0.13	0.94	0.14	0.11
3B	SWLS, FS, SPANE-N	0.60 (0.17)	0.16	0.92	0.15	0.12	0.61 (0.18)	0.15	0.94	0.14	0.10
3C	SWLS, SPANE-P&N	0.61 (0.17)	0.15	0.91	0.15	0.11	0.60 (0.18)	0.14	0.94	0.14	0.11
3D	FS, SPANE-P&N	0.61 (0.18)	0.11	0.94	0.15	0.11	0.60 (0.18)	0.12	0.95	0.14	0.11
4A	All	0.61 (0.18)	0.13	0.93	0.15	0.11	0.60 (0.18)	0.12	0.95	0.14	0.10
1a	SWLS	0.60 (0.17)	0.17	0.90	0.16	0.13	0.61 (0.18)	0.19	0.88	0.16	0.12
1b	FS	0.60 (0.17)	0.17	0.92	0.16	0.12	0.61 (0.16)	0.18	0.91	0.15	0.11
1c	SPANE-P	0.61 (0.17)	0.17	0.89	0.17	0.13	0.59 (0.16)	0.17	0.90	0.16	0.12
1d	SPANE-N	0.60 (0.12)	0.30	0.87	0.18	0.14	0.60 (0.11)	0.29	0.86	0.18	0.14
2a	SWLS, FS	0.60 (0.19)	0.11	0.93	0.15	0.12	0.61 (0.18)	0.17	0.91	0.15	0.11
2b	SWLS, SPANE-P	0.61 (0.18)	0.10	0.93	0.15	0.12	0.60 (0.19)	0.13	0.91	0.15	0.12
2c	SWLS, SPANE-N	0.60 (0.17)	0.14	0.90	0.16	0.12	0.61 (0.18)	0.17	0.89	0.15	0.12
2s	FS, SPANE-P	0.61 (0.18)	0.13	0.93	0.15	0.12	0.60 (0.18)	0.13	0.93	0.15	0.11
2e	FS, SPANE-N	0.60 (0.18)	0.14	0.95	0.15	0.11	0.60 (0.17)	0.15	0.93	0.15	0.11
2f	SPANE-P&N	0.61 (0.17)	0.15	0.92	0.16	0.12	0.58 (0.18)	0.14	0.93	0.15	0.12
3a	SWLS, FS, SPANE-P	0.61 (0.19)	0.09	0.94	0.15	0.11	0.60 (0.19)	0.14	0.92	0.15	0.11
3b	SWLS, FS, SPANE-N	0.60 (0.19)	0.11	0.94	0.15	0.11	0.61 (0.19)	0.10	0.92	0.16	0.12
3c	SWLS, SPANE-P&N	0.61 (0.19)	0.10	0.94	0.15	0.11	0.60 (0.20)	0.12	0.93	0.15	0.12
3d	FS, SPANE-P&N	0.61 (0.19)	0.11	0.95	0.15	0.11	0.59 (0.19)	0.10	0.94	0.16	0.12
4a	All	0.61 (0.19)	0.10	0.94	0.14	0.11	0.60 (0.20)	0.11	0.93	0.16	0.12

Abbreviations: SD, standard deviation; SWLS, the Satisfaction With Life Scale; FS, Flourishing Scale; SPANE: the Scale of Positive and Negative Experience; RMSE, root mean squared error; MAE, mean absolute error.

Table 3 Estimation of Our Recommended Modelings

Model	1A	1B	2F	3C	3D	4A
RMSE*	0.16	0.15	0.14	0.14	0.14	0.14
MAE*	0.12	0.12	0.11	0.11	0.11	0.10
Intercept	−1.4091	−1.9289	−1.5311	−1.7809	−1.9613	−1.9769
Age	−0.0002	−0.0014	0.0074	0.0055	0.0040	0.0038
Female	−0.1070	−0.2340	−0.0920	−0.1064	−0.1710	−0.1594
SWLS	0.0977	–	–	0.0463	–	0.0231
FS	–	0.0798	–	–	0.0437	0.0337
SPANE-P	–	–	0.1294	0.0933	0.0810	0.0738
SPANE-N	–	–	−0.0423	−0.0352	−0.0341	−0.0327

Notes: *These values are estimated in validation sample. An example formula (1A) was as below. ICECAP-A=1/(1+exp (-(Intercept+Estimate1*Age+Estimate2*Female+Estimate3*SWLS))) =1/(1+exp (-(−1.4091+(−0.0002)*Age+(−0.1070)*Female+(0.0977)*SWLS))).

Abbreviations: SWLS, the Satisfaction With Life Scale; FS, Flourishing Scale; SPANE, the Scale of Positive and Negative Experience; RMSE, root mean squared error; MAE, mean absolute error; ICECAP-A, the ICEpop CAPability measure for Adults.

Table 4 Effect of Socio-Economic Factors on Our Mapping Formula

Model	Socio-Economic Factors	1A	1B	2F	3C	3D	4A
RMSE*	-	0.16	0.15	0.14	0.14	0.14	0.14
	+	0.16	0.15	0.14	0.14	0.14	0.14
MAE*	-	0.12	0.12	0.11	0.11	0.11	0.10
	+	0.13	0.12	0.11	0.11	0.11	0.11

Notes: *These values are estimated in validation sample with or without socio-economic factors (marital status, having children, personal income, and being employed).

Abbreviations: RMSE, root mean squared error; MAE, mean absolute error.