2.1. Vaccination coverage data

Geolocated individual-level data on the coverage of MCV1 were obtained from the 2021 Cote d’Ivoire DHS (CDHS) [26]. The survey was designed to be representative at the national and first administrative (14 areas known as districts – S1 Fig) levels, and for urban and rural areas. The sampling design involved a random, stratified two-stage selection, with urban and rural areas of each of the 14 districts constituting separate sampling strata, yielding a total of 28 strata. The first stage involved selecting the primary sampling units known as clusters (or enumeration areas) from a sampling frame, while the second stage involved selecting households within each sampled cluster, with 28 households sampled per cluster. In all, a total of 539 clusters were included in the survey [26].

Routine MCV1 is recommended for administration at 9 months of age in Cote d’Ivoire [28]. Hence, for each eligible child aged 9–35 months, we extracted information on their age, vaccination status (based on health records or caregiver recall) and the (latitude/longitude) geocoordinates of the cluster they were sampled from. Each individual level record was classified into one of three age groups - 9–11 months, 12–23 months or 24–35 months - representing different birth cohorts, and aggregated to the survey cluster level for validation purposes. The data extracted contained a total of 4,236 children, of whom 507, 1,920 and 1,809 belonged to the respective age groups. A summary of the extracted data is displayed in Figs 1 and S2. This includes national survey weighted and unweighted estimates of MCV1 coverage for single age points and age groups, unweighted coverage estimates at the cluster level for age groups and corresponding distribution of cluster level sample sizes for each age group.

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Fig 1. Empirical estimates of measles vaccination coverage for children aged 9 to 35 months at the national (a, b) and survey cluster (c) levels for (a) single age points and (b, c) age groups, according to the 2021 Cote d’Ivoire Demographic and Health Survey.

Panels (a) and (b) show both survey weighted and unweighted estimates, whereas panel (c) shows unweighted estimates only. Boundary data used in panel (c) were obtained from geoBoundaries (www.geoboundaries.org) and are available under a CC BY 4.0 license.

https://doi.org/10.1371/journal.pcbi.1013989.g001

These plots generally reveal a sharp increase in coverage at lower ages, which then appears to stabilize and exhibit random fluctuations randomly in the later ages. The relatively lower coverage among children aged 9–11 months is evident both at the national and cluster levels. Cluster level sample sizes are much smaller for age 9–11 months, limiting the feasibility of a separate analysis for this age group. For the other age groups, cluster level sample sizes are also small (median = 3, interquartile range = 3). The distribution of these cluster-level sample sizes is particularly important for accurately estimating the underlying spatial structure in the data and for obtaining more robust point or grid level predictions of vaccination coverage across age groups.

2.2. Geospatial covariates, gridded population and boundary data

Following previous studies [3,17,19,25], we assembled a wide range of geospatial covariate datasets for the analysis. These include geographic, socioeconomic, remoteness, climate, environmental, conflict and health-related variables, which have either direct or proximate associations with vaccination coverage. While most of the covariates were externally sourced (see WorldPop [29] and S1 Table), others such as ownership of a health card/document were obtained from the 2021 CDHS [26]. These CDHS-derived covariates were first processed at the cluster level using the definitions provided in S1 Table. Kriging interpolation was then used to create their interpolated surfaces at 1x1 km resolution as outlined in previous work [19,30]. Covariate selection was undertaken in a non-spatial framework in R version 4.5.0 [31], using a similar approach as outlined in Utazi et al [17]. This involved examining the relationships between the covariates and vaccination coverage, and applying log transformations to the covariates where appropriate; fitting single-covariate models and ranking the covariates based on their predictive ability (using predictive R² values); assessing multicollinearity and choosing between highly correlated covariates (with correlation > 0.8 or variance inflation factor > 4.0) based on their ranks; and finally, using stepwise regression (backward elimination based on the Akaike Information Criterion) to identify the best model or combination of covariates for modelling the outcome in a non-spatial framework with binomial regression models. A total of 13 covariates were selected for the analysis from an initial set of 38 covariates, including urban and rural areas, elevation, vegetation index (veg_index, average number of wet days (wetdays), urban accessibility (urban_access), elevation, maximum temperature (max_temp), distance to conflict areas (dist_conf), walking travel time to the nearest health facility (walking_tt), malaria prevalence (mal_prev), maternal education (mat_educ), health card/document ownership (health_card), access to media (media) and household wealth (wealth). Detailed definitions and sources of these covariates are provided in S1 Table. These selected covariates are displayed in S3 and S4 Figs.

Gridded population data for children aged under 5 years in 2021 were obtained from WorldPop [32]. These were used as weights when aggregating the grid level estimates to the administrative level [19]. All boundary data sets used in the analysis were obtained from geoBoundaries [33].

2.3. Model development

We begin by introducing the spatially varying coefficient model and its parameterizations for estimating vaccination coverage using the birth cohort approach, and then alternative specifications that enable estimation at single age points and for all eligible individuals.

Let denote the age (in months) of the th eligible individual/child sampled from location , and , the different age groups (or birth cohorts), one of which includes . For example, in our application, , and and . Also, let denote the corresponding binary outcome representing the individual’s vaccination status , and the (unobserved) true probability of being vaccinated. The spatially varying coefficient model can be expressed as

(1)

where is the overall intercept, and are fixed and spatially varying regression coefficients for age cohort , is an indicator function that returns a value of 1 if the specified condition is true and 0 otherwise, and is a vector of geospatial covariates for location , with being the corresponding fixed regression coefficients. Thus, can be viewed as a random spatial adjustment to the average change in the log-odds of vaccination for the th age cohort, , at location . Note that the reference age group, , is omitted from equation (1) as this is absorbed into the intercept terms. In practice, the choice of reference age group - the group against which others are compared - may vary depending on the objective of the analysis. Also, the covariate vector, includes an urban-rural variable which helps to account for the urban-rural stratification used in the survey design. Only cluster-level geospatial covariates are included in the model since the goal of inference is to obtain age-specific coverage estimates at the grid level, typically at 1x1 km resolution.

Furthermore, the terms and are modelled as Gaussian random effects, capturing residual spatial and non-spatial (or between-cluster) variation, respectively. Specifically, represents a random spatial adjustment to the overall intercept, , such that defines a spatially varying intercept process (for the reference age group). We model as an independent and identically distributed (iid) process with mean 0 and variance . The spatial random effect is specified as a zero-mean Gaussian process with covariance function , that is, , where is assumed to follow the Matérn covariance function [34] given by

Here, the notation denotes the Euclidean distance, is the marginal variance of , is a scaling parameter related to the range – the distance at which spatial correlation is close to 0.1 - and is the modified Bessel function of the second kind and order . Following Lindgren et al [35], it is common to set the smoothness parameter equal to one to ensure identifiability.

For each of the spatially varying regression coefficients, , we also assume zero-mean Gaussian processes with Matérn covariance functions denoted by . We denote the corresponding range and marginal variance parameters using and , respectively.

The general model in equation (1) can be further parameterized to yield simpler, more parsimonious models, depending on the nature of the dependencies assumed in the data. For example, if the spatially varying coefficients and the geospatial covariates are deemed sufficient to capture all the spatial dependencies, or more specifically, if the geospatial covariates are assumed to fully account for the spatial variation in the outcome for the reference age group, then model (1) reduces to

(2)

which excludes the spatially correlated residual term, . Other variants of model (2) are also possible. For instance, if prior evidence suggests that the step changes captured by are sufficient to characterise the differences between certain age groups and the reference age group, then the corresponding terms may also be excluded, while retaining . Such specifications may be particularly advantageous in contexts involving a large number of age groups.

Furthermore, if the differences in the odds of vaccination between each age group and the reference age group are assumed not to vary spatially and can be adequately characterised using fixed step changes, then the spatially varying coefficients can be removed entirely from model (1), yielding

(3)

In practice, models (2) and (3) provide alternative model specifications against which to compare model (1) to determine the most appropriate modelling approach for capturing spatial dependencies in the data.

Additionally, when the goal is to predict coverage for single ages (in months), model (3) can be modified to include a smooth function of age, :

(4)

where is modelled using a second-order random walk: , which corresponds to the Bayesian equivalent of a cubic smoothing spline [36]. A sum-to-zero constraint was imposed on for identifiability, since the model includes an intercept term [36]. We note that, as in the birth cohort model, it is possible to model the effect of age in equation (4) using a spatially varying coefficient, such that . However, such parameterization is not ideal for estimating the overall smoothed effect of coverage by age as intended in model (4). Hence, model (4) captures the non-linear effect of age on vaccination but assumes constant residual spatial dependence for all ages as in model (3). Similar to model (3), model (4) can also be used to obtain predictions for age groups if desirable (see discussion section).

Finally, to predict coverage for all eligible age groups combined, the age-specific terms in model (1) can simply be dropped, yielding

(5)

Model (5) aligns with approaches commonly used in previous work to map vaccination coverage [16,19,25], except that it is estimated using individual rather than cluster level data. Note that in equation (5), as in all the models considered here, individual level variation is already accounted for in the binomial likelihood, with the variance of the logistic distribution fixed at [37].

For conciseness, we subsequently refer to the candidate birth cohort model specifications in equations (1) to (3) as MODsvc1, MODsvc2 and MODnosvc, respectively. Similarly, we refer to the single-age and all-age models in equations (4) and (5) as MODsmooth and MODall, respectively.

2.4. Bayesian inference, model fitting and prediction

The proposed models are implemented in a fully Bayesian framework. We place the following prior distributions on the parameters:

(6)

These comprise non-informative priors on the fixed regression parameters and a weakly informative prior on the precision of the second-order random walk in MODsmooth. The priors on the range parameters and the remaining variance parameters are penalized complexity priors, introduced by Simpson et al [38] and used in Fuglstad et al [39] in a spatial modelling context, which penalize deviations from a base (simpler) model, e.g., a constant field. For the range parameters, is chosen to be 5% of the extent of the study area in the longer direction (north-south direction for the Cote d’Ivoire application).

Let denote all the fixed parameters of MODsvc1 in equation (1), , and denote all the observed data. Its joint posterior distribution can be expressed as

(7)

where is the joint prior distribution on . The posterior distributions of the other models can be straightforwardly derived from equation (7).

For parameter estimation, we use the integrated nested Laplace approximation-stochastic partial differential equation (INLA-SPDE) approach [35,40] implemented in the inlabru package in R version 4.5.0 [31]. The INLA approach performs approximate Bayesian inference for latent Gaussian models by using the Laplace method to approximate the marginal posterior distributions of all the unknown quantities in the model, including the parameters and latent variables. The SPDE approach facilitates the estimation of the spatial terms in the models (e.g., and in model (1)). The approach works by representing each of these terms as a Gaussian Markov random field to reduce the computational burden inherent in the estimation of their respective covariance matrices [35].

Of particular interest in the proposed models is the prediction of vaccination coverage for the age groups or single age points of interest at unsampled locations, e.g., 1 km grids, throughout the study area. In a Bayesian framework, the prediction of vaccination coverage for age group at a new location, , proceeds by evaluating the posterior predictive distribution of given by

(8)

where is the linear predictor for MODsvc1, such that

In the inlabru package, equation (8) can be computed post model fitting by using either the or function. We obtained 1,000 posterior samples from equation (8) for each prediction grid location, which were then summarized to produce the grid level estimates and associated uncertainties. Administrative level estimates were also obtained as population-weighted averages over all the grid cells falling within each administrative unit [19], as noted previously, using these posterior samples. Individual level predictions (in- and out-of-sample prediction for validation purposes) and predictions using models (2), (3), (4) and (5) can also be obtained in a similar manner.

2.5. Model choice and validation

To compare the fits of the competing birth cohort models in equations (1) to (3) (and those of MODsmooth and MODall), we employed the Watanabe-Akaike Information Criterion (WAIC) [41,42] which uses the log of the predictive density of each data point to evaluate a model’s out-of-sample predictive performance. We note that a formal statistical comparison of the birth cohort models will be required in most applications, since the best model cannot always be determined a priori and to mitigate the risk of overfitting. The WAIC can be expressed as

where is the posterior predictive density of data point (out of data points), which can be evaluated in practice as with denoting the -th posterior draw from a total of posterior samples. The term represents the effective number of parameters, computed as . The WAIC balances model fit and complexity by penalizing overfitting through , which captures the sensitivity of the model’s fit to individual data points. A lower WAIC indicates better predictive accuracy.

To further evaluate the out-of-sample predictive performance of the proposed models both at the cluster and individual levels, we conducted a -fold cross-validation exercise, creating the cross-validation folds as random and spatially stratified splits of cluster locations and setting . Under random cross-validation, clusters were randomly allocated to one of the folds; in contrast, spatially stratified cross-validation assigned neighbouring cluster locations to the same fold. At the cluster level, we used the following metrics to evaluate predictive performance:

Continuous ranked probability score,

where is the number of cluster-level observations in the th cross-validation set, denotes the observed coverage and the corresponding predicted values (i. e., the posterior means). With the CRPS [43], the entire posterior samples are used to measure the discrepancies between the observed values and the predicted values for each data point rather than using a particular summary as in the other metrics. The smaller the values of these metrics, the better the predictive performance.

At the individual level, we evaluated out-of-sample predictive performance by computing the Brier score, , where is the number of individual level observations in validation set locations and denotes the binary outcomes [44]. A lower BS indicates better model performance. All the metrics were averaged over all cross-validation folds in each case.

3.1. Model choice

Table 1 presents the WAIC values of the candidate birth cohort models (MODsvc1, MODsvc2 and MODnosvc), along with those of MODsmooth and MODall for comparison. Among the three birth cohort models, MODsvc1 had the best predictive performance. All models that account for age clearly outperformed MODall, demonstrating better predictive accuracy at the individual level and substantial variation in coverage by age within the data. Notably, the better performance of MODsmooth relative to MODnosvc suggests that, in the absence of the spatially varying coefficients, the smooth age function in MODsmooth more effectively captured the gradients in age-specific coverage than the step changes in MODnosvc. Also, we observe that although MODsvc1 and MODsvc2 - both incorporating spatially varying coefficients - had the lowest WAIC, these also had the largest effective numbers of parameters relative to other models as expected given their greater flexibility.

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Table 1. WAIC values of the proposed models.

https://doi.org/10.1371/journal.pcbi.1013989.t001

The patterns observed in the WAIC results are corroborated by the BS values reported in S2 Table. These results show that for individual level out-of-sample prediction under the random cross-validation scheme, MODsvc1 and MODsvc2 had the best predictive performance, although the differences between the models were modest. Under stratified cross-validation, the differences between the models were even smaller, with MODsvc1 still ranking among the best-performing models. Consistent with previous findings, for both cross-validation schemes, all models accounting for variation by age (except MODsvc2 under stratified cross-validation) outperformed MODall.

For out-of-sample prediction at the cluster level, Table 2 reports the validation metrics for MODsvc1, MODnosvc and MODsvc2, while S3 Table provides corresponding results for MODall for comparison. Due to sample size limitations, it was not feasible to evaluate cluster-level predictive performance for MODsmooth. Across the three models, out-of-sample predictive performance was broadly similar within each age group, though MODsvc1 performed slightly better overall, particularly for the 9–11 and 24–35 month age groups. For the 12–23 month age group, the differences between the models were marginal, with no model clearly outperforming the others. Importantly, all three models performed better for age groups 12–23 months and 24–35 months compared to 9–11 months (except when considering AVG_BIAS, which poorly differentiated between the models), likely reflecting the relatively larger cluster level sample sizes for both older age groups (Figs 1 and S2). Indeed, for the aggregated 9–35 month age group, the validation metrics reported in S3 Table are consistently lower than those in Table 2, indicating improved predictive performance associated with larger cluster level sample sizes. As expected, predictive performance across all the models was generally poorer under the stratified cross-validation scheme, reflecting the increased difficulty of prediction in this setting.

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Table 2. Results of cluster level k-fold cross-validation.

https://doi.org/10.1371/journal.pcbi.1013989.t002

Overall, our evaluation of the out-of-sample predictive performance of the competing birth cohort models, at both the individual and cluster levels, indicates that MODsvc1 offers the best performance. Accordingly, in the following sections, we discuss the results from MODsvc1 when using the birth cohort approach to estimate vaccination coverage.

3.2. Parameter estimates

In Table 3, we present the estimates of the parameters of the best-fitting birth cohort model, MODsvc1. The covariates significantly associated with the odds of vaccination include: urban versus rural residence, distance to conflict areas, walking travel time to the nearest health facility, maternal education, health card/document ownership, access to media and age group. As expected, the odds of vaccination increased with greater distance to conflict areas, higher proportions of educated mothers, higher proportions of children who owned a health card and greater access to the media within households. Conversely, the odds of vaccination decreased as walking travel time to the nearest health facility increased.

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Table 3. Table of parameter estimates. Estimates corresponding to significant regression coefficients are bolded.

https://doi.org/10.1371/journal.pcbi.1013989.t003

Considering the estimated odds ratios, a unit increase in the proportion of children who owned a health card is associated with a sixfold increase in the odds of vaccination, for example. Notably, children residing in urban areas had 46% lower odds of being vaccinated compared to those in rural areas – a pattern that appears to be specific to the study country [26]. Furthermore, on average, children aged 12–23 months and 24–35 months had approximately twice the odds of being vaccinated compared to those aged 9–11 months, suggesting significant delays in MCV1 vaccination during the first year of life.

The spatial variation in the differences in odds of vaccination between the age groups is illustrated by the maps of and in S5 Fig. The estimated surface for appears much smoother than that for , suggesting greater spatial variability in the differences (in the log-odds of vaccination) between age groups 9–11 months and 12–23 months than between 9–11 months and 24–35 months. This provides a strong justification for the use of spatially varying coefficients in our modelling approach, but it also indicates that to preserve parsimony in the model, the difference in the likelihood of vaccination between ages 9–11 months and 24–35 months could be modelled as a step change, as discussed previously in the methods section. We discuss the spatial patterns in the differences in coverage between the age groups in detail in Section 3.3.

The estimated spatial ranges for the spatially varying coefficients - and - are 78 km and 743 km, respectively, while that of the spatial random effect, , is 94 km. Again, these estimates suggest much greater spatial heterogeneities in the differences in coverage between age groups 9–11 months and 12–23 months than between 9–11 months and 24–35 months. Nevertheless, the corresponding marginal variance estimates for these terms are very close, and the iid residual term, , accounts for nearly twice as much variation in the model as .

Similar patterns are observed in the results of MODsmooth reported in S4 Table and S6 Fig, both in terms of significant covariate effects and the effect of age on vaccination. In particular, the delay in the receipt of MCV1 is evident in the estimated nonlinear effect of age on vaccination, which shows a markedly lower probability of vaccination among children aged < 15 months relative to older ages. We observe a steep increase in the probability of vaccination from age 9 months to about 15 months, which then stabilizes at a high level with minor fluctuations beyond 23 months, suggesting immunity gaps in the 24–35 month birth cohort. The credible intervals for the smooth functions indicate greater uncertainty beyond age 12 months due to greater fluctuations in coverage at older ages (see Fig 1a).

3.3. Predicted 1x1 km maps of vaccination coverage for age groups and single age points

Geographically, considerable heterogeneities in MCV1 coverage are observed across all age groups (Fig 2), with a pronounced effect of walking travel time to the nearest health facility (see S4 Fig). The 1x1 km maps generally reveal lower coverage in the 9–11 month age group relative to other age groups, particularly concentrated in the western and northern districts of the country. The spatial distributions of coverage in these age groups show some interesting similarities, but there are also striking differences. Across all the age groups, coverage levels are consistently higher in and around Lacs, Vallée du Bandama and Yamoussoukro districts. Whilst overall coverage levels do not differ substantially between ages 12–23 months and 24–35 months, the spatial patterns in coverage appear to be more similar between ages 9–11 months and 24–35 months than 12–23 months, with the latter showing more pronounced spatial gradients, as noted previously. The modelled estimates at the national level are 54.1%, 67.9% and 70.9% for the respective age groups. Compared to corresponding direct survey estimates of 51.2%, 60.3% and 65.1%, the model slightly overestimated coverage, especially in the 12–23 month age group. For the combined 9–35 month age group, similar spatial patterns are observed, although aggregating over this wider age range obscures differences in coverage between birth cohorts and is more suitable when interest is in estimating for broader age bands.

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Fig 2. 1x1 km maps of MCV1 coverage and associated uncertainties (95% credible interval widths) for age groups 9-11 months, 12-23 months, 24-35 months (panel a) and 9-35 months (panel b).

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The widths of the 95% credible intervals (CIs) associated with the coverage maps indicate greater uncertainties in areas with sparse survey data (e.g., the Zanzan region; see Fig 1) and in areas of lower coverage, especially for age groups 12–23 months and 24–35 months. Uncertainties for the 9–11 month group show less spatial variation but are slightly higher overall, likely reflecting smaller sample sizes. The median widths of the 95% CIs are 50%, 48%, and 43% for the 9–11, 12–23, and 24–35 month groups, respectively, indicating considerable uncertainties in the grid-level estimates.

At single age points (Fig 3), lower coverage at 9 months is also evident, with very similar spatial patterns observed from ages 12–35 months. (Note that MODsmooth does not capture spatial gradients in the differences between age groups.) The modelled national coverage estimates of 47.6%, 65%, 68.3%, 70%, 70.3% and 68.7% at 9, 12, 15, 18, 24 and 35 months, respectively, further confirm that coverage patterns stabilize and become more similar from age 15 months and above. The corresponding uncertainties, reported in S7 Fig, show similar patterns and ranges as those in Fig 2.

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Fig 3. 1x1 km maps of MCV1 coverage for single age points at 9, 12, 15, 18, 24 and 35 months.

Corresponding uncertainty estimates, obtained as the widths of the 95% credible intervals, are shown in the supplementary file.

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3.4. Estimation of vaccination coverage at the administrative level

At the departmental level, differences in both coverage and spatial prioritization for the 9–11, 12–23, and 24–35 month age groups are shown in Figs 4 and S8. Consistent with the national-level estimates reported earlier, coverage remains suboptimal at the departmental level, with no department reaching the target of 95% coverage in any age group. In particular, for the 9–11 month age group, coverage is estimated to be below 60% in about 70% of departments. For the 24–35 month age group, clusters of departments with lower coverage (<60%) are observed in the neighboring Savanes (M’Bengué, Tengrela, Boundiali, and Kouto) and Denguélé (Kaniasso, Madinani, and Séguélon) districts, despite overall higher coverage at older ages - potentially contributing to the dip in coverage after 23 months noted in S6 Fig.

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Fig 4.

(a) Estimates of MCV1 coverage and (b) corresponding ranks at the departmental level for each age group. The dotted vertical lines differentiate between departments in each of the 14 districts of Cote d’Ivoire. Boundary data used in panel (b) were obtained from geoBoundaries (www.geoboundaries.org) and are available under a CC BY 4.0 license.

https://doi.org/10.1371/journal.pcbi.1013989.g004

Among 9–11 month olds, the highest coverage levels (>67%) are estimated in M’Bahiakro, Daoukro, and Prikro (all in the Lacs district), while the lowest (<44%) are in Dianra, Daloa, and Séguélon departments. For 12–23 months, coverage is highest (>81%) in M’Bahiakro, Tanda, and Transua (Lacs and Zanzan districts), and lowest (<47%) in Daloa, Dianra, and Guitry. In the 24–35 month group, coverage peaks (>85%) in Tanda, Koun-Fao, M’Bahiakro, and Transua (Zanzan and Lacs districts), and is lowest in Séguélon, Kouto, and Dianra. Although there are similarities in the locations of higher and lower coverage across age groups, differences also emerge, as reflected in the departmental rankings shown in Fig 4b. For example, even within Lacs district - where coverage is consistently higher across all age groups – there are differences in the ranks of departments when comparing the age groups. The rankings of the 9–11 and 24–35 month groups are generally more similar, corroborating earlier findings about the resemblance in their spatial coverage patterns. The median absolute differences in departmental ranks between age groups are: 9 (IQR = 12) for 9–11 vs. 12–23 months, 8 (IQR = 11) for 9–11 vs. 24–35 months, and 14 (IQR = 18) for 12–23 vs. 24–35 months. Furthermore, the rankings appear to vary most in the Zanzan, Denguélé, and Montagnes districts (based on the larger IQRs of ranks across all age groups within these districts).

The uncertainties associated with the departmental-level estimates (S9 Fig) are considerably smaller than those of the grid-level estimates, with median 95% CI widths of 23%, 22%, and 18% for the respective age groups.

We also estimated coverage at the district level for the 12–23 month age group to enable comparison with direct survey estimates at this level (S10 Fig). Overall, there is good agreement between the modelled and direct survey estimates; however, the relative overestimation of coverage observed earlier is most pronounced in the Abidjan, Comoé, and Lagunes districts.