Data and sample
Secondary analysis of cross-sectional data from the National Health Survey of Chile (ENS 2016–2017); a nationally representative survey with a random, stratified, and multistage sample of 6233 people aged 15 and over [13]. Being a population survey with a complex sampling design, all estimates of the average design effect were made using weighting and the corresponding expansion factor. We assessed the social gradient of HRQoL in the adult population in Chile by socioeconomic status, particularly ranked household income, through the concentration index. In addition, we explored the potential effect of several covariates as determinants of these inequalities through a decomposition analysis of the concentration index. The ENS 2016–2017 survey is an anonymous database available per request by the Ministry of Health of Chile.
Variables and measures
The dependent variable was HRQoL, measured by EQ-5D-3L and converted into cardinal values (also called health utilities) using the social value set validated for Chile in 2009 [30].
EQ-5D-3L assesses health status according to a descriptive system (questionnaire) and a Visual Analogue Scale (VAS). The dimensions evaluated by this questionnaire are Mobility, Self-Care, Usual Activities, Pain & Discomfort and Anxiety & Depression. Each dimension has 3 levels of severity: No problems, Moderate Problems, and Serious Problems, thus providing a final set of 243 health states [31]. The range of this variable considers negative values, which is a limitation for estimating the concentration index [32]. For this reason, the utilities obtained were transformed into disutilities, representing a decrease in utility (valued quality of life) due to a particular symptom, condition, or complication, as follows:
$${\varvec{D}}{\varvec{i}}{\varvec{s}}{\varvec{u}}{\varvec{t}}{\varvec{i}}{\varvec{l}}{\varvec{i}}{\varvec{t}}{\varvec{y}}\boldsymbol{ }=1-\left(\boldsymbol{ }{\varvec{U}}{\varvec{t}}{\varvec{i}}{\varvec{l}}{\varvec{i}}{\varvec{t}}{\varvec{y}}\right)$$
The independent variable was household income per capita. This was estimated from the ENS 2016–2017 dividing the household income by the number of members of the corresponding household. Control variables included in the decomposition analysis included educational level, household income, sex, age, area of residence (urban or rural), and the belonging to a particular health insurance system (public or private).
Inequality measurement
We analysed income-related health inequalities examining gaps and gradients. First, we calculated the absolute and relative (20:20) gaps. Then, we depicted the inequality gradient using concentration curves. The Concentration Curve (CC) provides a means to evaluate the degree of inequality related to the socioeconomic position in the distribution of a health variable, plotting the cumulative percentage of the health variable on the y-axis (disutilities) against the accumulated percentage of the sample on the x-axis, ordered by their socioeconomic position, starting with the poorest and ending with the richest (as measured in this study by ranked household income per capita) [32]. While the concentration curve is important in depicting income-related inequality at each point in the income distribution for a health outcome of interest, it cannot be used to quantify the magnitude of such income-related inequality.
The magnitude of inequality in HRQoL is estimated using the Concentration Index (CI). The CI quantifies the degree of socioeconomic inequality of a health variable, displaying the health gradient in multiple subgroups with natural ordering or ranking. The CI expresses the extent to which an indicator of health is concentrated among the socially disadvantaged or the favoured [33]. The CI is defined as twice the area between the Concentration Curve and the equality line. The CI takes values between -1 and + 1, where a positive value indicates that a health variable is disproportionately concentrated among the most favoured people. In contrast, a negative value indicates the opposite (the variable is disproportionately concentrated in the most disadvantaged people), whereas a value of zero means that there is no inequality [34]. The sign of the concentration index indicates the direction of the relationship between the health variable and socioeconomic position, and its magnitude reflects both the strength of the relationship and the degree of variability in the health variable. The formula to calculate the concentration index is:
$${\varvec{C}}{\varvec{I}}=\frac{2}{{\varvec{\mu}}}{\varvec{c}}{\varvec{o}}{\varvec{v}}\boldsymbol{ }({{\varvec{\gamma}}}_{{\varvec{i}}}\boldsymbol{ },\boldsymbol{ }{{\varvec{R}}}_{{\varvec{i}}})$$
(1)
where γi denotes the health variable (EQ-5D results) of the i-th individual, μ it is average and Ri denotes the fractional rank of the ith individual concerning the socioeconomic position of their household. Given that we used disutilities instead of utilities, the CC in this analysis is expected to be drawn above the diagonal line and the CI is expected to be negative.
Decomposition approach
According to Wagstaff et al. the CI can be decomposed into individual factors which contribute to -or are associated with- socioeconomic status related health inequality [35]. Each contribution corresponds to the product of the sensitivity of health concerning that factor and the degree of inequality related to income in that factor. In our study, to reveal the association of each explanatory variable to inequality in HRQoL, the approach of an additive linear regression model was used that links the results of the EQ-5D (y) to a set of k determinants:
$${{\varvec{\gamma}}}_{{\varvec{i}}\boldsymbol{ }}=\boldsymbol{ }\boldsymbol{\alpha }\boldsymbol{ }+\boldsymbol{ }\sum_{{\varvec{\kappa}}}{{\varvec{\beta}}}_{{\varvec{\kappa}}\boldsymbol{ }}{{\varvec{\chi}}}_{{\varvec{\kappa}}{\varvec{i}}}+{{\varvec{\varepsilon}}}_{{\varvec{i}}}$$
(2)
where Xki is a set of k determining variables for the i-th individual, βk is the coefficient or regressor and ε is the error term. Given the relationship between γi and Xki in Eq. (2), the concentration index for γ, (CI), can be written as:
$${\varvec{C}}{\varvec{I}}=\boldsymbol{ }{\sum }_{{\varvec{\kappa}}}{({\varvec{\beta}}}_{{\varvec{\kappa}}\boldsymbol{ }}\overline{{{\varvec{\chi}} }_{{\varvec{\kappa}}}}/{\varvec{\mu}})\boldsymbol{ }{{\varvec{C}}}_{{\varvec{\kappa}}}+{\varvec{G}}{{\varvec{C}}}_{\begin{array}{c}\varepsilon \\ \end{array}}/{\varvec{\mu}}$$
(3)
where μ is the mean of γ, \(\overline{{\chi }_{\kappa }}\) is the mean of \({\chi }_{\kappa }\), \({C}_{\kappa }\) is the concentration index for \({\chi }_{\kappa }\) (defined exactly as the concentration index for disutility), \(\frac{{{\varvec{\beta}}}_{{\varvec{\kappa}}}\boldsymbol{ }\overline{{{\varvec{\chi}}}_{{\varvec{\kappa}}}}}{{\varvec{\mu}}}\) is the elasticity of disutility with explanatory variables and \({GC}_{\varepsilon }\) is the generalized concentration index for the residual component εi.