Outbreak detection algorithms based on generalized linear model: a review with new practical examples

Public health surveillance serves a crucial function within health systems, enabling the monitoring, early detection, and warning of infectious diseases. Recently, outbreak detection algorithms have gained significant importance across various surveillance systems, particularly in light of the COVID-19 pandemic. These algorithms are approached from both theoretical and practical perspectives. The theoretical aspect entails the development and introduction of novel statistical methods that capture the interest of statisticians. In contrast, the practical aspect involves designing outbreak detection systems and employing diverse methodologies for monitoring syndromes, thus drawing the attention of epidemiologists and health managers. Over the past three decades, considerable efforts have been made in the field of surveillance, resulting in valuable publications that introduce new statistical methods and compare their performance. The generalized linear model (GLM) family has undergone various advancements in comparison to other statistical methods and models. This study aims to present and describe GLM-based methods, providing a coherent comparison between them. Initially, a historical overview of outbreak detection algorithms based on the GLM family is provided, highlighting commonly used methods. Furthermore, real data from Measles and COVID-19 are utilized to demonstrate examples of these methods. This study will be useful for researchers in both theoretical and practical aspects of outbreak detection methods, enabling them to familiarize themselves with the key techniques within the GLM family and facilitate comparisons, particularly for those with limited mathematical expertise.