Beyond the Smoothed Surface: Combining Bayesian Spatial Modelling and Density-Based Clustering to Detect Hidden Pockets of Incomplete Childhood Vaccination in Mandera and Mombasa Counties, Kenya

Collins Kigen Sing’oei *

Department of Mathematics and Actuarial Science, Catholic University of Eastern Africa, Nairobi, Kenya.

Gladys Njoroge

Department of Pharmacy Practice and Public Health, United States International University – Africa, Nairobi, Kenya.

Hellen Waititu

Department of Mathematics and Actuarial Science, Catholic University of Eastern Africa, Nairobi, Kenya.

*Author to whom correspondence should be addressed.


Abstract

Aims/Objectives: To demonstrate the complementary value of Bayesian spatial modelling and density-based clustering for detecting hidden pockets of incomplete childhood vaccination in contrasting Kenyan county settings.

Study Design: Secondary cross-sectional spatial analysis of household survey data.

Place and Duration of Study: Mandera and Mombasa counties, Kenya, using data from the 2022 Kenya Demographic and Health Survey (KDHS).

Methodology: The descriptive sample included 223 children aged 12–23 months across 61 enumeration areas (Mandera n = 161; Mombasa n = 62). Incomplete vaccination was defined as failure to receive all eight nationally recommended vaccine doses. A Bayesian BYM2 spatial model was fitted using R-INLA and compared with a non-spatial hierarchical baseline using model-fit criteria. Residual spatial autocorrelation was assessed using Moran’s I. HDBSCAN density-based clustering was applied to 193 complete cases, with sensitivity analysis across minimum cluster sizes of 3, 5, 7, and 10.

Results: The BYM2 model improved fit relative to the non-spatial baseline (deviance information criterion 127.40 vs. 203.29) and reduced residual spatial autocorrelation (Moran’s I: 0.402 to −0.075). Smoothed risk was high in Mandera (mean 0.807) and low in Mombasa (mean 0.257). HDBSCAN identified four clusters, including five Mombasa areas with 100% incomplete vaccination, while BYM2 estimated a mean risk of 0.288 for this cluster.

Conclusion: The methods provided complementary information. Their combined use distinguished the broad geographic risk gradient from a local pocket that was not apparent from the smoothed surface alone, supporting joint use for county-level and local prioritisation.

Keywords: Childhood vaccination, incomplete vaccination, spatial epidemiology, Bayesian spatial modelling, BYM2, HDBSCAN, density-based clustering, geospatial analysis, immunisation coverage, Kenya


How to Cite

Sing’oei, Collins Kigen, Gladys Njoroge, and Hellen Waititu. 2026. “Beyond the Smoothed Surface: Combining Bayesian Spatial Modelling and Density-Based Clustering to Detect Hidden Pockets of Incomplete Childhood Vaccination in Mandera and Mombasa Counties, Kenya”. Asian Journal of Probability and Statistics 28 (9):98-110. https://doi.org/10.9734/ajpas/2026/v28i9945.

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