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Sierra Leone, which is a low-income country, is approximately 71,740 km2 land area divided into four administrative regions namely Northern, Southern, Eastern provinces and the Western area where the capital Freetown is located. The country has a long historical and geopolitical context of poverty, high illiteracy rate. Sierra Leone is also a country that is recovering from disasters including the prolonged 11-year civil war that ended in 2002, followed by the 2012 Cholera outbreak [19] and of recent the 2014–2016 Ebola Virus disease epidemic [20].

Sierra Leone is a low-income country with a reported Gross National Income (GNI) per capita (current dollar, purchasing power parity (PPP) of $1690 while the gross domestic product (GDP) growth rate was 6% in 2013 and the Human Development Index rank for Sierra Leone is 177 out of 187 countries [21]. It has an estimated 2015 population of 7075,64 [22] and the nature of its geography poses significant challenges for the delivery of health services to the population in some of these districts. Sierra Leone currently faces a triple burden of diseases (communicable diseases, 70%; NCDs, 22% and injuries, 7%) [23] common to a growing number of LMICs with life expectancy for both male and female at 50 years [24].

Data source and sample size

This study was based on the secondary analysis of data obtained from two nationally representative household surveys that interviewed a total of 7374 and 16,658 women of reproductive age (15–49 years) in 2008 [8] and 2013 [25]. Response rates among eligible individuals in the target samples were 94% [8] and 97.2% [25] in 2008 and 2013 respectively.

Sampling method of SLDHS

All the two Sierra Leone Demographic and Health Surveys (SLDHS) used a multi-stage cluster sampling technique [8, 25]. Initially, the Enumeration Areas (EA) — a cluster that conventionally encompasses 85 adjacent households each were selected as primary sampling units from the sampling frame developed based on the 2004 Census [26]. In each of the selected EAs, a complete listing of households was carried out from which secondary sampling units were drawn using systematic random sampling technique. In the two surveys, 353 EAs were sampled of which 145 were urban and 208 were rural, with each EA having 85 households from which 22 were selected in the second stage of the two-stage sampling [8, 25]. For this study, all data collected from women who gave birth in the preceding 5 years of the survey were included. In cases, where women had more than one birth in the reference period, the most recent one was considered. An algorithm of the number of women interviewed in each of the SLDHS and the women included in the final analysis of antenatal care (ANC) & postnatal care (PNC) (Additional file 1).

Data analysis

Data analysis were done using Excel Microsoft Corporation and SPSS Package version 22 (SPSS, Inc. Chicago). This study first explored the background characteristics of study participants and then the analysis of MCH utilization by wealth quintile and other individual characteristics. An unadjusted and adjusted binary logistic regression was run for institutional delivery and a concentration curve with subsequent concentration indices generated for ANC visits and PNC reviews for 2008 and 2013 SLDHS.

For MCH utilization variables, we defined the number of antenatal visits (ANC) and post-natal reviews made (PNC) as discrete variables; we considered the number of visits to be complete if it reached the recommended number of visits as per the WHO guidelines [27, 28] (four or more for ANC and four or more for PNC). For ease of analysis, ANC was transformed into three subcategories (none, up to four and more than four visits) and PNC into two subcategories (incomplete and complete). Complete includes all four reviews: post-delivery, prior to discharge, a week after discharge, and 6 weeks post-delivery. If any of these visits were missed, then that constitutes an incomplete PNC. We defined Institutional delivery as the use of a healthcare institution for delivery for the pregnancy under review, regardless of the package of care provided as a binary categorical variable (Yes vs No). We defined wealth quintiles as poorest (1st quintile); poorer (2nd quintile); middle (3rd quintile); richer (4th quintile); and richest (5th quintile). Additional covariates were defined as categorical i.e. education level, occupation, residence (rural/urban), ethnicity, religion, and mother’s age as well as discreet (number of children) variables. All the independent variables were categorical variables except for number of children, which was a quantitative variable.

The undermentioned operational definitions of the dependent and independent variables (see Additional files 2 and 3) were the same as defined in the DHS dataset except for PNC (a composite variable) ethnicity and religion, which were redefined to suit the study design.

The concentration curves were built using two key variables: the independent wealth index variable on the one hand and maternal & child health services utilization outcome variables on the other hand (ANC& PNC). The concentration indices estimated the magnitude of wealth related inequality in the selected MCH services utilization.

During analysis, the cases were grouped according to wealth quintiles into: Poorest: 1st quintile; Poorer: 2nd quintile; Middle: 3rd quintile; Richer: 4th quintile; Richest: 5th quintile.The sum of each outcome variable noted for the five wealth quintiles and then expressed as a percentage of the total outcome variable of interest. Each curve, therefore, represents the cumulative percent of the outcome variable of interest against the cumulative percent of the wealth quintile of the sample analyzed. If ANC visits or PNC reviews utilization were equally distributed across the different wealth quintiles, a 45-degree line representing perfect equality would be generated. This line known as the line of equality (LOE) runs from the bottom left corner of the graph (0,0) to the upper right corner of the graph (100, 100) [29]. If these services were however utilized more by the rich than the poor, the curve falls below the LOE and the further it is away from the LOE the more the wealth-related inequality in the distribution of the MCH services utilization. Since the aim was to compare the wealth related inequality in ANC visits or PNC reviews utilization across a period using the 2008 and 2013 SLDHS, the concentration curves for each outcome variable were plotted on the same graph. Thus, if the curve of one of the time periods (2008 vs 2013) lies above the other (closer to the LOE), then the former is said to dominate the latter, but the extent is unknown. In order to get an exact measure of the degree of inequality, a concentration index is built from each curve and it is defined as double the area between the curve and the LOE [29]. The concentration indexes obtained were then used to rank these two-time periods by the degree of inequality. If the two curves cross each other, a case of non-dominance may be demonstrated.

In this study, the concentration index was calculated first as twice the area between the curve and the line of equality. However, since the area under-the-curve approach to calculating the confidence interval (CI) does not give the standard error of the curve and hence the CI, the CIs were therefore computed using the convenient regression method. The CI was computed in the convenient regression method as twice the weighted variance of fractional living standard variable squared (δ2) and the health variable (h i = ANC or PNC) divided by the mean of the health variable (μ) based on the left hand of eq. 1 below:

$$ {2\updelta}^2\left({\mathrm{h}}_{\mathrm{i}}/\upmu \right)=\upalpha +{\upbeta \mathrm{r}}_{\mathrm{i}+\upvarepsilon \mathrm{i}} $$ (1)

The computation of the fractional rank of wealth index (r i) was based on equation below for the weighted data.

$$ {\mathrm{r}}_{\mathrm{i}=\Sigma\ \left(\mathrm{Wj}+\mathrm{Wi}/2\right)} $$ (2)

r i was then sorted in ascending order and its variance calculated. β produced during the convenient regression of the CI variable against the fractional rank variable represents the unadjusted estimate of the concentration index generated on the right hand of eq. 1.

The standardized or adjusted estimate of the concentration index was computed using SPSS statistical software using the generated model to predict the health variable (ANC or PNC) based on eq. 3 below:

$$ {\mathrm{Y}}_{\mathrm{i}}={\mathrm{b}}_{\mathrm{o}}+{\mathrm{b}}_1{\mathrm{x}}_1+{\mathrm{b}}_2{\mathrm{x}}_2+{\mathrm{b}}_3{\mathrm{x}}_3 $$ (3)

Yi represents the predicted health variable. During the adjustment or standardization of the wealth variable for the other covariates, the adjusted values were predicted using eq. 3 while keeping all covariates at their mean values.

In order to calculate the standard error of the standardized estimate of the concentration index, the sampling variability was taken into account, and thus the convenient regressions were run without transforming the dependent health variable but instead using the transformed living standard variable (i.e. RWealthi).The standard error of the adjusted concentration index was estimated as the coefficient of the transformed living standard variable (RWealthi).The variance of the fractional rank, which was also used in the transformation, depended only on the sample size and so has no sampling variability. It can be treated as a constant. This way the sampling variability was considered because the estimate and its standard error were written as a function of regression coefficients based on eqs. 4, 5, and 6 below.

$$ {\mathrm{h}}_{\mathrm{i}}={\upalpha}_1+{\upbeta}_1{\mathrm{r}}_{\mathrm{i}}+{\mathrm{u}}_{\mathrm{i}} $$ (4)

$$ {}_{\dot{\mathrm{B}}=}\ {\left({{2\updelta}_{\mathrm{r}}}^2/\upmu \right)}_{\dot{\mathrm{B}}} $$ (5)

$$ {}_{\dot{\mathrm{B}}=}\ {\left[{{2\updelta}_{\mathrm{r}}}^2/\left({\upalpha}_{1+\dot{\mathrm{B}}/2}\right)\right]}_{\dot{\mathrm{B}}} $$ (6)

An unadjusted and adjusted binary logistic regression were run to identify how wealth in relation to the other independent variables serves as a predictor of utilization of healthcare institutions for delivery. The generated model predicts whether a pregnant woman will deliver in a health facility or at home based on her wealth index and other independent variables. Logistic regression models were used to obtain unadjusted and adjusted odds ratios with 95% confidence interval for the associations between the different independent variables and institutional delivery. The significant standardized contribution of each covariate was assessed using the adjusted Wald test to obtain the p-value. All p-values < 0.05 were considered statistically significant.

Ethical considerations

The DHS program-ICF International, (Rockville, USA), granted access to the data after a submission of a written request through their online platform. The Sierra Leone Ethics and Scientific Review Committee granted a waiver since this is a secondary analysis of de-identified data.