Abstract Detecting geographical areas in a territory with excess mortality is a crucial step to understand health disparities and implement effective public health policies. In practice, this means identifying both individual areas and clusters of neighbouring areas where mortality is higher than in the rest of the territory. Mortality clusters are commonly detected using spatial scan statistics, which are tools that scan the territory with moving windows and test the presence of excess mortality. However, these techniques often detect spurious clusters or encompass areas not at risk into existing clusters, leading to unreliable epidemiological results. Here, we propose a data-driven initialisation of a generalised linear model scan statistic that improves its specificity and reduces its computational cost. Our strategy consists of identifying individual areas with a significant mortality excess through an improved version of the Besag–York–Mollié model, and using them to initialise the clustering procedure. We investigate the properties of our method with a series of simulation experiments, showing that our proposed initialisation increases clustering specificity relative to standard approaches and also prevents the erroneous inclusion of areas not at risk within clusters of elevated mortality. Finally, we demonstrate the usefulness of the proposed tool for healthcare authorities using a case study on mortality data from the Padua province in northeastern Italy.

Abstract This paper introduces a novel and extensive framework for addressing linear-circular regression problems, where linear predictors are related to a circular (angular) response variable. The proposed methodology depends on the wrapped technique, a well-established technique for transforming any linear distribution into a circular distribution, to facilitate linear-circular regression analysis. The core of our methodology is the treatment of circular responses as the outcome of a modulo operation applied to unobserved linear responses. This conceptualization leads to a flexible mixture model that combines multiple linear-linear regression models, allowing for the detection of complex relationships between circular outcomes and linear predictors. To estimate the parameters of the proposed mixture model, we use the Expectation–Maximization algorithm for maximum likelihood estimation. We use four numerical examples to evaluate the performance of the suggested models and show how well they handle different types of data. To demonstrate the real-world effectiveness of our approach, we apply it to two challenging problems: estimating wind directions and tracking the movement patterns of blue periwinkles both of which exhibit complex, highly variable behavior.