Table 5 Beta regression model for predictors of health-related quality of life summarized into area under the curvea

Coefficientsb (95% confidence interval)
No imputation Multiple imputation
Six months onward One year onward Six months onward One year onward
Intercept 1.26 (0.98, 1.54) 1.91 (1.66, 2.16) 1.31 (1.12, 1.49) 1.39 (1.19, 1.58)
Neuroinvasive disease 0.03 (−0.27, 0.34) 0.04 (−0.23, 0.30) 0.02 (−0.17, 0.22) 0.01 (−0.18, 0.19)
Age per 10 years, centered at 50 years −0.08 (−0.19, 0.03) −0.08 (−0.18, 0.014) −0.03 (−0.10, 0.04) −0.02 (−0.09, 0.05)
Male 0.26 (−0.02, 0.53) 0.02 (−0.29, 0.33) 0.15 (−0.03, 0.33) 0.10 (−0.08, 0.27)
Number of comorbid conditions −0.25 (−0.35, −0.14) −0.46 (−0.62, −0.30) −0.16 (−0.24, −0.09) −0.13 (−0.21, −0.05)
Baseline utility (centred) 1.70 (0.74, 2.67) 0.58 (−0.52, 1.68) 0.84 (0.06, 1.62) 0.29 (−0.61, 1.18)
1. Statistically significant results are in bold
2. aArea under the curve is the integral of the utility-time curve after one year. Areas are time-weighted (Total area after one year ÷ follow-up time)
3. bCoefficients and patient characteristics can be substituted into the following equation to calculate the area under the curve: $${\displaystyle \begin{array}{l} Logit\left( Mean\left( Utility score\right)\right)={\beta}_0+{\beta}_1\left(\mathrm{Neuroinvasive}\ \mathrm{disease}\right)+{\beta}_2\left(\frac{\mathrm{Age}-50\ \mathrm{years}\ \mathrm{old}}{10}\right)+{\beta}_3\left(\mathrm{male}\right)+\\ {}{\beta}_4\left(\mathrm{No}.\mathrm{comorbid}\ \mathrm{conditions}\right)+{\beta}_5\left(\mathrm{Baseline}\ \mathrm{utility}\ \mathrm{score}-0.50\right)\end{array}}$$For example, the regression equation for area under the curve past six months in a 60 year old male with neuroinvasive disease, one comorbid condition and a baseline utility score of 0.60 would be: 1.31 (intercept) + 0.02 (neuroinvasive) – 0.03 (ten years greater than 50 years old) + 0.15 (male) – 0.16 (one comorbid condition) + 0.84 * 0.10 (baseline utility score was 0.10 greater than 0.50) = 1.434. Taking the inverse logit, this particular patient would have a predicted long-term utility score of: $$\frac{e^{1.434}}{1+{e}^{1.434}}$$= 0.81