A bivariate copula-geostatistical model for binary outcomes: joint spatial risk mapping of zero-dose and under-immunized children in Malawi, 2015–2016 MDHS

Zero-dose and under-immunized children remain vulnerable, hindering progress toward Immunization Agenda 2030 and Sustainable Development Goals (SGDs). Although these outcomes are closely related, they are often analyzed independently, and conventional spatial models do not adequately capture their joint distribution and spatial dependencies. This study applies a copula-based geospatial model for binary outcomes to analyze these data in Malawi. Using 2015–2016 Malawi DHS data, we examined immunization status (zero-dose and under-immunization) among children aged 12–35 months. Covariates included maternal age, education, wealth, residence, and district. Exploratory spatial analysis mapped distributions, while copula-based joint modelling, through generalized joint regression model (GJRM) assessed dependencies. Markov Random Fields smoothed district-level estimates, and splines modelled maternal age effects. Among the 5,668 children included in the analysis, 2.33% were zero-dose and 4.59% were under-immunized. The joint model revealed that children from the poorest families and those with parents having no education had higher odds of being zero-dose or under-immunized. Conversely, children from the northern region and rural residences had lower odds of being zero-dose or under-immunized. The spatial analysis revealed districts with more proportions of zero-dose and under-immunized children which included: Nsanje, Chikwawa, Thyolo, Phalombe. The joint modelling, using Frank copula, further revealed strong positive correlation between zero-dose and under-immunized. The copula-based geospatial modelling framework provided a flexible approach for jointly analyzing zero-dose and under-immunization while accounting for their spatial dependence. The findings identified geographical hotspots and socioeconomic inequalities in childhood immunization, providing evidence to support geographically targeted and equity-focused interventions aimed at improving vaccine initiation and completion in Malawi.