Data and variables definition
We used data from DHS conducted in Ethiopia in 2005 and 2011 [
9,
15]. The 2005 and 2011 DHS were conducted on a nationally representative sample of 9,861 and 11,654 households, respectively. The sampling design for both surveys was a two-staged stratified cluster sampling that was not self-weighted at national level. The survey participants/households were stratified into urban or rural groups according to their area of residence. Household’s socioeconomic status was measured using household asset data via a principal components analysis. We used the wealth quintiles as a living standard measure in the subsequent modeling.
Utilization of MCH services was selected for analysis. These were binary variables, where a value of 1 was assigned if care was accessed or a value of 0 if care was not accessed. Both prevention and treatment services were included, where we looked at: medical treatment for diarrhea, skilled birth attendance (SBA), measles immunizations and modern contraceptive usage. We used prevalence of diarrhea, cough, fever and stunting in children as morbidity variables.
Analysis
Inequality in outcomes was measured by calculating a concentration index, where this index quantifies the magnitude of wealth-related inequality that can be compared conveniently across time periods, countries, regions, or other comparators [
18]. The paper by Wagstaff et al provides detailed description of concentration index [
18]. In our analysis concentration index (C) was computed as twice the (weighted) covariance between the health variable (
h) and the fractional rank of the person in the living standard distribution (
r), divided by the mean of the health variable (
μ) [
19] as:
$$ C=\frac{2}{\mu }Cov\left(h,r\right) $$
(1)
Concentration index is restricted to values between −1 and 1 and has a value of zero where there is no income-related inequality in outcomes. If the variable reflects morbidity or mortality, the concentration index will usually be negative, showing that ill health is more prevalent among the poor. For coverage indicators, the concentration index is usually positive, as these tend to be higher among the rich [
19].
Even though concentration index is a measure of income-related inequality in health care utilization, it does not measure the degree of inequity in use since it still includes legitimate income-related differences in use due to differences in need. Therefore, in our analysis, standardization for differences in need for health care in relation to wealth was done using the method of indirect standardization. Standardization adjusts for the need expected distribution as opposed to the observed distribution of use [
20]. To proxy need in health care, the following demographic and morbidity variables were used: age and sex of children under-five years of age and age of women in the reproductive age group (as demographic variables), recent episode of diarrhea (as a morbidity variable in children), history of birth in the past five years (as a proxy of need for SBA) and unmet need for family planning (as a need variable for modern contraceptive usage). Wealth quintile, educational attainment of household head, educational attainment of partner, and area of residence were used as non-need correlates of health care utilization (control variables). Only 0.5 % of the households had health insurance coverage, therefore we did not use it as one of the control variable in our analysis [
9].
After estimating the need-standardized utilization, inequity can be tested by determining whether standardized use is unequally distributed across wealth quintiles. Inequity could be measured by estimating the concentration index of need-standardized health care utilization, which is denoted as the health inequity index. Alternatively, the health inequity index can be calculated as a difference between the concentration index for actual utilization and need-expected utilization of medical care [
20]. A positive (negative) value of horizontal inequity index indicates horizontal inequity that is pro-rich (pro-poor), while an index value of zero shows absence of horizontal inequity.
The decomposition of the concentration index allows the measurement and explanation of inequality in utilization of health care services across income groups. Wagstaff et al [
21] has demonstrated that for any linear regression model of a variable, such as health care use, it is possible to decompose the measured inequality into the contribution of explanatory factors. With this decomposition approach, standardization for need as well as explanation of inequity can be done in one step. Consider the following model:
$$ {y}_i=\alpha +{\displaystyle {\sum}_j{\beta}_j{x}_{ji}+{\displaystyle {\sum}_k{\beta}_k\;{z}_{ki}+{\varepsilon}_i,}} $$
(2)
, where
x
j
denotes the need standardizing variables, that includes demographic and health status/morbidity factors, and
z
k
denotes the non-need variables including socioeconomic status, education, area of residence (urban vs. rural).
α,
β and
ε are the constant, regression coefficients and the error term respectively. The concentration index (C) for utilization of health care can then be written as:
$$ \mathrm{C}={\displaystyle {\sum}_j\left({\beta}_j{\overline{x}}_j/\mu \right)}{C}_j+{\displaystyle {\sum}_k\left({\beta}_k{\overline{z}}_k/\mu \right){C}_k+\raisebox{1ex}{$G{C}_u$}\!\left/ \!\raisebox{-1ex}{$\mu \kern0.5em ,$}\right.} $$
(3)
, where C
j
and C
k
are the concentration indices for the need and non-need variables respectively while μ is the mean of our health variable of interest (y), \( {\overline{x}}_j \) is the mean of x
j
and \( {\overline{z}}_k \) is the mean of z
k
. The components \( \left({\beta}_j{\overline{x}}_j/\mu \right) \) and \( \left({\beta}_k{\overline{z}}_k/\mu \right) \) are simply the elasticity of y with respect to x
j
and z
k
, respectively, that are evaluated at the sample mean. The last term in the equation \( \left(\raisebox{1ex}{$G{C}_u$}\!\left/ \!\raisebox{-1ex}{$\mu $}\right.\right) \) captures the residual component that reflects the inequality in health that is not explained by systematic variation across income groups in the need and non-need variables.
Decomposition for non-linear models can only be applied using linear approximation which can introduce errors and is complex. Therefore, even if our health variable of interest is a binary variable, we used the linear model. It has been found elsewhere that decomposition results differ little between ordinary least squares and non-linear estimators [
22].
Time trends for changes in mean levels of MCH service utilization were assessed using logistic regression model. MCH service utilizations were used as dependent variables while time of survey as independent variables. We computed the percentage change in excess risk by subtracting one from rate ratio (rate ratio-1), where rate ratio is the incidence in the poorest quintile divided by incidence in the richest quintile (Q1/Q5) [
23].
Data were analyzed using the statistical software package STATA (version 13), taking into account the sampling design characteristics of each survey.