A spatial regression model for the disaggregation of areal unit based data to high-resolution grids with application to vaccination coverage mapping

Abstract

The growing demand for spatially detailed data to advance the Sustainable Development Goals agenda of 'leaving no one behind' has resulted in a shift in focus from aggregate national and province-based metrics to small areas and high-resolution grids in the health and development arena. Vaccination coverage is customarily measured through aggregate-level statistics, which mask fine-scale heterogeneities and 'coldspots' of low coverage. This paper develops a methodology for high-resolution mapping of vaccination coverage using areal data in settings where point-referenced survey data are inaccessible. The proposed methodology is a binomial spatial regression model with a logit link and a combination of covariate data and random effects modelling two levels of spatial autocorrelation in the linear predictor. The principal aspect of the model is the melding of the misaligned areal data and the prediction grid points using the regression component and each of the conditional autoregressive and the Gaussian spatial process random effects. The Bayesian model is fitted using the INLA-SPDE approach. We demonstrate the predictive ability of the model using simulated data sets. The results obtained indicate a good predictive performance by the model, with correlations of between 0.66 and 0.98 obtained at the grid level between true and predicted values. The methodology is applied to predicting the coverage of measles and diphtheria-tetanus-pertussis vaccinations at 5 × 5 km² in Afghanistan and Pakistan using subnational Demographic and Health Surveys data. The predicted maps are used to highlight vaccination coldspots and assess progress towards coverage targets to facilitate the implementation of more geographically precise interventions. The proposed methodology can be readily applied to wider disaggregation problems in related contexts, including mapping other health and development indicators.

Keywords: Bayesian inference; Demographic and Health Surveys; INLA-SPDE; Vaccination coverage; spatial misalignment.

Figure 1.

Maps of observed measles and DTP3 vaccination coverage for Afghanistan in 2015 (left panel) and Pakistan in 2013 (right panel) at administrative level 1.

Figure 2.

Plots of the grid ($n_p$ = 3600) and areal configurations ($n_{\mathcal{A}}$ = 9,25,100) used in the simulation study. These were generated on the unit (i.e. [0,1] × [0,1]) square.

Figure 3.

One of the simulated data sets for spatial range r = 0.7. Plotted are true simulated probabilities and the corresponding predictions (mean) and their standard deviations for $n_{\mathcal{A}}$ = 9 (top), 25 (middle) and 100 (bottom).

Figure 4.

Predicted measles and DTP3 vaccination coverage at 5 × 5 km² (left panel) in children aged 12–23 months for Afghanistan in 2015, with the associated standard deviation maps (right panel).

Figure 5.

Predicted measles and DTP3 vaccination coverage at 5 × 5 km² (left panel) in children aged 12–23 months for Pakistan in 2013, with the associated standard deviation maps (right panel).

Figure 6.

Maps of Afghanistan (top) and Pakistan (bottom) showing: (a and c) coldspot areas for measles vaccination defined as the lowest 20%, lowest 50% and lowest 80% coverage areas and (b and d) the districts attaining the WHO Global Vaccine Action Plan (GVAP) threshold of 80% coverage (in green colour) with DTP3 vaccination for Afghanistan in 2015 and Pakistan in 2013.

Figure 7.

(a) Distributions of proportions of children aged 12–23 months vaccinated against measles and (b) percentage differences in national estimates of numbers of under 5 year olds unvaccinated between DHS admin estimates and each of the 5 × 5 km² estimates from area-to-grid and cluster-to-grid approaches. Vaccination coverage in children aged 12–23 months was used as a proxy for coverage levels in under 5s in (b).