Estimation of utility values from visual analog scale measures of health in patients undergoing cardiac surgery

Figures & data

Figure 1 Flowchart describing the inclusion of patients.

Abbreviations: n, number; CABG, coronary artery bypass grafting; EQ-5D, EuroQol 5 Dimensions questionnaire; VAS, visual analog scale.

Table 1 Patients’ baseline and intraoperative characteristics

Variable	Estimation sample n=114	Validation sample n=76	P-value
Age (years), mean ± SD	68.4±9.2	65.9±9.6	0.07
Female, n (%)	25 (21.9)	13 (17.1)	0.42
Redo cardiac surgery, n (%)	2 (1.8)	0 (0)	0.52
Concomitant surgery, n (%)	20 (17.5)	18 (23.7)	0.30

Abbreviations: n, number; SD, standard deviation.

Figure 2 Questionnaire used to assess health on visual analog scales.

Figure 3 Observed EQ-5D utility scores in the complete dataset.

Abbreviaton: EQ-5D, EuroQol 5 Dimensions questionnaire.

Table 2 Mean utility and VAS scores for all observations

Variable	Estimation sample (233 observations)	Validation sample (149 observations)	P-value
EQ-5D utility score, mean ± SD	0.72±0.20	0.73±0.16	0.39
VAS mobility (mm), mean ± SD	26.8±22.4	26.6±20.3	0.91
VAS self-care (mm), mean ± SD	15.5±21.9	15.2±21.5	0.89
VAS usual activity (mm), mean ± SD	44.4±32.7	41.8±29.9	0.43
VAS pain (mm), mean ± SD	22.8±20.6	23.8±22.1	0.65
VAS anxiety and depression (mm), mean ± SD	16.3±20.6	18.2±21.2	0.39
Disease stage proxy			0.87
Preoperative, n (%)	97 (41.6)	66 (44.3)
Postoperative day 5, n (%)	78 (33.5)	47 (31.5)
Postoperative day 40, n (%)	58 (24.9)	36 (24.2)

Abbreviations: EQ-5D, EuroQol 5 Dimensions questionnaire; SD, standard deviation; VAS, visual analog scale; n, number.

Figure 4 Mean observed and predicted EQ-5D utility scores in the validation sample.

Notes: The graph shows the agreement between the observed EQ-5D utility score and the mean of the predicted score. The observed health states are ordered on the x-axis according to their severity as valued by the Danish time trade-off tool.
Abbreviation: EQ-5D, EuroQol 5 Dimensions questionnaire.

Table 3 Results of the estimated mapping-models

Parameter	Random effects
	GLS 1 β (SE)	GLS 2 β (SE)	Tobit β (SE)	CLAD β (SE)
Age	0.000259	0.000255	0.000599	0.00198‡
	(0.00101)	(0.00102)	(0.00106)	(0.000206)
Female	−0.00263	−0.00351	−0.00898	−0.0165‡
	(0.0218)	(0.0220)	(0.0227)	(0.00464)
VAS scores for
Mobility	−0.00177†	0.0000882	−0.000198	−0.00227‡
	(0.000582)	(0.00128)	(0.00140)	(0.000261)
Self-care	−0.000934	−0.00204	−0.00208	−0.00405‡
	(0.000548)	(0.00135)	(0.00146)	(0.000309)
Usual activity	−0.00146‡	−0.00146	−0.00204	0.000328
	(0.000323)	(0.00111)	(0.00121)	(0.000232)
Pain	−0.00158†	−0.00120	−0.00213	−0.000580*
	(0.000543)	(0.00136)	(0.00146)	(0.000274)
Anxiety and depression	−0.00279‡	0.000335	0.000236	−0.00280‡
	(0.000468)	(0.00118)	(0.00128)	(0.000282)
Squared VAS scores for
Mobility		−0.0000255	−0.0000235	0.0000113†
		(0.0000163)	(0.0000177)	(0.0000034)
Self-care		0.0000165	0.0000166	−0.0000429‡
		(0.0000171)	(0.0000185)	(0.0000030)
Usual activity		−0.0000008	0.0000037	−0.0000136‡
		(0.0000105)	(0.0000115)	(0.0000022)
Pain		−0.0000069	0.0000049	0.0000105*
		(0.0000205)	(0.0000222)	(0.0000043)
Anxiety and depression		−0.0000445†	−0.0000442*	0.0000105†
		(0.0000161)	(0.0000175)	(0.0000038)
Constant	0.909‡	0.877‡	0.892‡	0.738‡
	(0.0691)	(0.0721)	(0.0753)	(0.0140)
Overall	0.632	0.652
R-squared
MAE	0.0857	0.0838	0.0871	0.0818
RMSE	0.121	0.119	0.120	0.141

Notes:

* P<0.05

† P<0.01

‡ P<0.001.

Abbreviations: GLS, generalized least squares; CLAD, censored least absolute deviation; SE, standard error; VAS, visual analog scale; MAE, mean absolute error; RMSE, root mean squared error.

Table 4 Mean absolute error of mapping-models at subsets of observed EQ-5D utility scores

Utility subset	GLS 1	GLS 2	Tobit	CLAD
Utility <0	0.601	0.526	0.527	0.796
0≥ utility <0.25	0.216	0.179	0.175	0.376
0.25≥ utility <0.5	0.123	0.122	0.124	0.106
0.5≥ utility <0.75	0.074	0.078	0.082	0.054
0.75≥ utility ≤1	0.074	0.071	0.074	0.072

Abbreviations: EQ-5D, EuroQol 5 Dimensions questionnaire; GLS, generalized least squares; CLAD, censored least absolute deviation.

Figure 5 Bland–Altman plots of agreement between observed and predicted EQ-5D utility scores.

Notes: (A) Agreement in the estimation sample. (B) Agreement in the validation sample. The x-axis depicts the mean of the observed value and the predicted value, and the y-axis shows the difference (observed minus predicted). The lines show the mean difference, ie, the estimated bias, and the 95% limits of agreement (±1.96 SD of the mean difference).
Abbreviations: EQ-5D, EuroQol 5 Dimensions questionnaire; SD, standard deviation.