Modeling smooth and localized mortality patterns across age, time, and space to uncover small-area inequalities

Small-area mortality estimation is inherently difficult, as random fluctuations from low death counts can obscure real geographic differences. We introduce a flexible model that borrows strength across age, space, and time to estimate mortality schedules and trends in very small populations. The approach ensures smooth patterns across these dimensions while allowing localized breaks from the spatial structure, capturing broad trajectories as well as sharp local contrasts. We implement our model within a Penalized Spline framework and estimate it using Generalized Linear Array Model techniques, resulting in a computationally fast, interpretable, and parsimonious method. Crucially, it can readily incorporate sudden mortality shocks, such as the Covid-19 pandemic, making it highly versatile for real-world demographic and epidemiological challenges. We demonstrate its application by estimating life expectancy and age-specific mortality inequalities in over 4,800 small areas across the Greater London Authority from 2002 to 2024.