Dataset and sample
The SABE study (Health, Aging, and Well-being) is a nationally representative population-based cross-sectional dataset of 23,694 adults over 60-years, which was collected by the Ministry of Health in Colombia in 2015. The survey used in the SABE study followed the conceptual model of active aging and the social determinants of health (see Additional file 1) [28].
Methodology
In order to analyze inequality in utilization of healthcare among the elderly in Colombia, we followed a two-fold approach. In the first instance, we relied on standard multivariate logistic model regression. We followed this with an analysis of inequality in utilization using the standard Concentration Index (CI).
Logit model analysis of utilization of healthcare services
In modelling the utilization of healthcare, our main dependent variables encompass six variables which fall within three levels of care. Preventive care (use of pap smear and mammogram for women; prostate cancer lab screening in the last 2 years for men), outpatient care (doctor visit in the last 4 months; visit to any health professional—other than a doctor—in the last year), and inpatient care (hospitalizations in the last year). Consequently, we estimated six separate logit models using each of the variables above as a dependent variable, one at a time.
The basis for the modelling exercise was the Anderson’s behavioral model of health services use; it also enabled the selection of independent variables for the modelling exercise [29]. Andersen establishes that utilization of health services depends on three factors: predisposing, enabling, and need factors. Predisposing factors include individual characteristics present before the occurrence of a disease and are related to demographic conditions. Enabling factors describe the means utilized by individuals in order to access the services they need, such as income. Finally, need factors refer to the health conditions—either perceived or evaluated—requiring medical care.
Andersen’s model groups determinants of access in three major groups (need, predisposing and enabling factors). The model can capture drivers of inequality from both an individual’s and health system’s perspective. There are, however, some limitations associated with the model. For example, the model does not explain the relationship between healthcare utilization and quality of services (health outcomes and patient satisfaction) [29, 30].
Against this background, if we assume a linear model, utilization of healthcare services can be analyzed by regressing the relevant utilization variable (yi) on a vector of k medical need indicator variables (xk), predisposing factor variables (uq), and a set of p enabling factor variables (zp) (for example, socioeconomic variables, health insurance, and supply-side variables).
The equation would be as follows:
$$ {y}_i^{\ast }=\alpha +{\sum}_k{\beta}_k{x}_{k,i}+{\sum}_q{\delta}_q{u}_{q,i}+{\sum}_p{\gamma}_{p,i}z+{\varepsilon}_i,\kern0.5em \mathrm{with}\kern0.5em \mathrm{i}=1,\dots \mathrm{N} $$
(1)
Where α, β, γ, δ= parameters and εi = error term.
Assuming that yi* in equation (A) is a latent variable, the logit model is written as:
$$ \left\{\begin{array}{c}1\ if\kern0.5em {y}_i^{\ast }>0\\ {}0, otherwise\end{array}\right. $$
Our dependent variables encompass three levels of healthcare utilization: (i) preventive care (e.g. screening activities); (ii) outpatient care (curative and rehabilitation services provided by a healthcare professional at the primary level (both acute and chronic care), that do not require hospital stay) and (iii) inpatient care (curative and rehabilitation services provided at a hospital, and requiring overnight stay, usually for high-complex care).
To assess medical need factors, multimorbidity and self-rated health (SRH) were used as proxies. The SABE study asked participants if they had ever been diagnosed as having high blood pressure, diabetes, osteoarthritis, ischemic heart disease, cerebrovascular disease, chronic respiratory disease or cancer. Therefore, a categorical variable was created encompassing the following: no presence of chronic disease, presence of one chronic disease, and presence of two or more chronic diseases. SRH measured the subjective health experience of individuals by answering the question: “In general, how would you rate your health in the last 30 days?” Based on this question, a dummy variable was created by taking a value of 1 for answers very good, good, and fair and a value of 0 for answers poor and very poor. We also included as need factors, four variables assessing the functional impairment of individuals: the Barthel index [31], any walking impairment, need of walking help, and presence of any amputation. The Barthel index is a geriatric score evaluating the level of dependency giving a score to each individual. We classified individuals as independent, with mild dependency, with moderate to severe dependency and with total dependency. For any walking impairment, individuals were asked if they found difficult walking 400 m. Individuals were subsequently classified as having no difficulty, mild difficulty, somewhat or significant difficulty. For assessing the need of ‘any walking help’, individuals were also asked if they needed any help walking 400 m. The variable took the value of 1 if an individual needed any walking help and zero if they didn’t need any. The variable ‘any amputation’ took the value of 1 if the individual had any limb amputation and zero if they didn’t have any.
Predisposing factors included age, gender, marital status, level of education, belonging to an ethnic minority and displacement. Four, five-year groups represented the age variable: 60–65, 66–70, 71–74 and 75 and older. A dummy variable capturing ethnicity was created, which took the value of 1 if the respondent belonged to any ethnic minority (mixed, black, islander, palenquero or indigenous), and 0 otherwise. Marital status was proxied by a dummy variable that took a value of 1 (being married/cohabiting and divorced/widowed) or 0 (otherwise). Level of education was captured by a categorical variable among four options: no formal education, primary school, secondary school, or technical education and above. In addition, a dummy variable for displacement was created which took a value of 1 if the respondent was displaced and 0 otherwise.
Enabling factors included wealth index, area of residence, type of health insurance, geographic region and receiving a pension. We created a wealth index for all participants as a proxy of their socio-economic level (see Additional file 2) and classified participants into five different wealth quintiles. Based on the area of residence, we created a dummy variable which took a value of 1 if the respondent lived in an urban area and 0 if they lived in a rural setting. The health insurance type was captured by a categorical variable consisting of four categories: subsidized, contributory, special schemes, and uninsured; and the geographic region variable corresponded to the six regions of the country in which the survey aggregated the participants. Given that the survey did not include supply-side variables (e.g. density of doctors or nurses), this variable was used as a proxy for regional variation in supply-side healthcare variables. Finally, a dummy variable which captured whether the respondent received a pension was included.
We used standard weights in the analysis and reported the results as odds ratios. In addition, we reported the standard Wald (Chi2 test) and the log likelihood. All analyses were conducted in STATA version 14.0.
Concentration index for inequality of utilization
We coupled the logit model exercise with a calculation of concentration index (CI) and decomposition of CI in order to quantify the degree of equality in the utilization of health services and the extent to which each of the three groups of variables above (medical need, predisposing, and enabling) contributed to the inequality of utilization [32].
CI is defined with reference to the concentration curve. It is twice the area between the concentration curve and the line of equality (the 45-degree line). Concentration curves plot the specific health variable in the y–axis against the percentage distribution based on a wealth measure in the x–axis. Therefore, CI takes a value ranging from (− 1, 1) where negative values express pro-poor concentration and positive values express pro-rich concentration. Equation 2 presents the general model for CI:
$$ C=\frac{2\ }{\mu }\ {\mathit{\operatorname{cov}}}_w\left({y}_i,{r}_i\right) $$
(2)
Where C is the CI, yi is the measure of utilization of healthcare services, μ is its mean, and ri is the rank distribution of an individual i according to his wealth index.
The decomposition of the CI shows the contribution of the independent variables in the logit model to the distribution (inequality) of health services based on the wealth rank of the population. It provides more detailed information and raises potential areas for policy intervention. We relied on methodology for the decomposition analysis that used a probit model and its ‘partial effects’ (i.e. the effects of an individual independent variable, ceteris paribus) as eq. 3 depicts:
$$ E\left({y}_i|{x}_i\right)=G\ \left({\sum}_k{\beta}_k{x}_k^i\right) $$
(3)
where G represents the functional form for a nonlinear model. As proposed by van Doorslaer et al. [32], we have restored the mechanics of the decomposition framework by replacing the βk parameters in the equation with the βmk parameters, where the βmk represent the partial effects of the x (the determinants of y) in the linear approximation of the non-linear model expressed by Eq. 4:
$$ {y}_i={\sum}_k{\beta}_k^m{x}_k^i+{\mu}_i $$
(4)
Accordingly, we conducted a decomposition of the socio-economic related inequality affecting healthcare utilization.