It is well known that safe delivery in a health facility reduces the risks of maternal and infant mortality resulting from perinatal complications. What is less understood are the factors associated with safe delivery practices. We investigated factors influencing health facility delivery practices while adjusting for multiple other factors simultaneously, spatial heterogeneity, and trends over time. We fitted a logistic regression model to Lot Quality Assurance Sampling (LQAS) data from Uganda in a framework that considered individual-level covariates, geographical features, and variations over five time points. We showed that ease of access, maternal age and education are strongly associated with delivery in a health facility; after accounting for this, there remains a significant trend towards greater uptake over time. We used this model together with known demographics to formulate a nascent early warning system that identifies candidate districts expected to have low prevalence of facility-based delivery in the immediate future. We provided a statistical method for using inexpensive and routinely collected monitoring and evaluation data to answer complex epidemiology and public health questions in a resource-poor setting.