Twelve SSA countries were selected for this study, based on data availability (Table 1). These countries are diverse in terms of size, population density, and landscape.

Table 1 General statistics of DHS datasets used in this analysisGIS data

Geolocated health facilities were extracted from a database assembled by Maina et al. [19], composed of 98,745 geocoded public health facilities in SSA. They used a data compilation, geocoding, cleaning and validation process based on multiple data sources, with a focus on official sources from Ministries of Health, and completed with non-governmental data when necessary.

Friction maps were necessary to generate travel-time estimations with the cost-distance method. Friction maps represent the ease to travel in a given landscape. More specifically, they are raster grids where every cell contains a value representing the time necessary to cross the pixel. These time values are estimated using geographical variables such as land cover, road network or relief. Friction maps are provided by the “malariaAtlas” package of the R software, which is developed by the Malaria Atlas Project team [21]. From this package, we extracted two 2019 friction maps: one considering that the population has access to motorized transportation, and the other considering walking speed only [26, 27]. Both have a spatial resolution of 30 arc seconds (~ 1 × 1 km at the equator). Administrative unit limits were also extracted from the malariaAtlas R package.

For general accessibility measures, we used gridded population datasets produced by WorldPop (www.worldpop.org), where every cell contains an estimation of population count. These maps are generated by disaggregating population count data from administrative units, provided by official national censuses, into 100 × 100 m raster cells. The disaggregation is done using a semi-automated machine learning method based on a random-forest model, and spatial ancillary data such as road network, built areas, land-cover etc. [23]. We used the continental-wide population map provided at a spatial resolution of 0.00833 decimal degrees (~ 1 km at the equator) in order to match the friction maps and reduce computation needs.

Survey data

The Demographic and Health Surveys (DHS; http://www.dhsprogram.org) are standardized surveys, conducted in 90 countries, that collect data on health, wealth, education and household characteristics. DHS respondents living in the same neighborhood are aggregated by clusters. For the sake of confidentiality, GPS coordinates of the cluster centroid are subject to a displacement of a random value between 0 and 2 km for urban clusters and between 0 and 5 km for rural clusters, in a random direction. One percent of the rural clusters receive an additional displacement of a distance between 0 and 10 km. Those displacements are however constrained within the administrative unit level 2 of the country. For the majority of DHS surveys, GPS coordinates of the dislocated cluster centroid are provided. Here we selected 12 SSA countries where surveys have been conducted after 2015 and for which GPS coordinates are available (Table 1).

For the present study, we are particularly interested in the perceived accessibility to health facilities, collected in the DHS individual surveys for women. The question v467 from that survey asks the following: “When you are sick and that you need medical advice or treatment, are the following elements an obstacle to you, yes or no” and the fourth option, coded as v467d, is “Distance to the health facility”. To estimate the perceived accessibility of the population, we used the proportion of women per cluster who have answered “Yes” at the question v467d. This variable is hereafter called PA (Perceived Access). We identified the respondents having access to personal motorized transportation with the questions hv211 and hv212 from DHS, asking respectively if any member of the household owns a motorcycle or a car. Table 1 presents a summary of the data extracted from the DHS surveys.

Modelled accessibility

The goal of this paper is to compare four commonly used spatial models of accessibility with survey-derived perceived accessibility. Each modelling method produces a raster grid with an accessibility value for every cell.

a)

The Euclidean Distance (ED) method computes the on-the-fly distance value to the closest health facility in meters, for each cell of a raster grid, using the “distanceFromPoints” tool from the “raster” package in the R software [11].

b)

The Cost-Distance Motorized (CD-M) method uses a friction map and a cost-distance algorithm in order to generate a raster grid, with an estimated travel-time value in minutes for each cell. This method uses the friction map considering access to motorized transportation. We used the function “accCost” from the “gdistance” package in R [25], following the method and code from Weiss et al. [27].

c)

The Cost-Distance Walking (CD-W) method is identical to CD-M, except that it is based on the friction map considering walking speed only.

d)

The Kernel Density (KD) method computes a point-density continuous surface based on the geolocated health facilities. It generates a dimensionless accessibility value for each cell, using a common Gaussian impedance function, with a distance threshold fixed at 15 km beyond which the accessibility value will be zero. In the absence of robust analyses on the best distance threshold to use, 15 km seemed reasonable here because it is a rather large distance to walk to obtain health care while avoiding a large proportion of the population being assigned a zero-access value. The accessibility values were then summed up for all health facilities, making the KD method the only one considering multiple health facilities in the vicinity to evaluate accessibility. This method generates values varying between 0 and ~ 1.5. Note that the KD method produces values that are higher when accessibility is also higher, contrarily to the other methods.

The four accessibility maps were cropped and resampled in order to match the same extent and cell size as the population raster grid of their respective country. For each geolocated DHS cluster, we extracted PA and the four modelled accessibility values (MAs), i.e. ED, CD-M, CD-W and KD.

Statistical analyses

First, we measured Spearman correlation coefficients between the different modelling methods, in order to evaluate the degree of similarity of their estimates. Given that Kernel density does not have a linear relationship with the three other methods, the Spearman index, which measures the correlation based on variable ranks, is more appropriate.

We then measured Spearman correlation coefficients between PA and MAs, first taking all data together, and then stratifying them into subgroups: (i) by socio-geographic context, i.e. by isolating respondents living in rural or urban areas, and by isolating respondents having access to motorized transportation or not, (ii) by country. Our exploratory analysis and previous studies suggest that non-linear functions such as logistic function or hyperbolic decline better explain the relationship between distance or travel time and perceived accessibility [13, 16]. Scatterplots representing the statistical relationship between PA and MAs were computed and a local weighted smoothing method was used to help visualizing the shape of the relationships.

Because the displacement of DHS clusters may influence MA values, we estimated the range of variability induced by such displacements by artificially moving cluster points 30 times within buffer zones of the same size, as the ones used by DHS (2 km radius for urban clusters, 5 km radius for rural clusters). For each virtual displacement, new MA values were extracted and new Spearman correlation coefficients were calculated.

Finally, the overall accessibility of the population to health facilities was calculated and compared for the 12 countries by overlaying MA maps with gridded population maps. We extracted the proportion of the population living in different distance classes for the Euclidean distance method or travel-time classes for cost-distance methods. These accessibility measures were not calculated with the Kernel density method because it generates dimensionless values that are not appropriate for this type of analysis.