Beyond the Gold Standard: Linear Regression and Poisson GLM Yield Identical Mortality Trends and Deaths Counts for COVID-19 in Italy: 2021–2025

While it is undisputed that Poisson GLMs represent the gold standard for counting COVID-19 deaths, recent studies have analyzed the seasonal growth and decline trends of these deaths in Italy using a simple segmented linear regression. They found that, despite an overall decreasing trend throughout the entire period analyzed (2021–2025), rising mortality trends from COVID-19 emerged in all summers and winters of the period, though they were more pronounced in winter. The technical reasons for the general unsuitability of using linear regression for the precise counting of deaths are well-known. Nevertheless, the question remains whether, under certain circumstances, the use of linear regression can provide a valid and useful tool in a specific context, for example, to highlight the slopes of seasonal growth/decline in deaths more quickly and clearly. Given this background, this paper presents a comparison between the use of linear regression and a Poisson GLM with the aforementioned death data, leading to the following conclusions. Appropriate statistical hypothesis testing procedures have demonstrated that the conditions of a normal distribution of residuals, their homoscedasticity, and the lack of autocorrelation were essentially guaranteed in this particular Italian case (weekly COVID-19 deaths in Italy, from 2021 to 2025) with very rare exceptions, thus ensuring the acceptable performance of linear regression. Furthermore, the development of a Poisson GLM definitively confirmed a strong agreement between the two models in identifying COVID-19 mortality trends. This was supported by a Kolmogorov–Smirnov test, which found no statistically significant difference between the slopes calculated by the two models. Both the Poisson and the linear model also demonstrated a comparably high accuracy in counting COVID-19 deaths, with MAE values of 62.76 and a comparable 88.60, respectively. Based on an average of approximately 6300 deaths per period, this translated to a percentage error of just 1.15% for the Poisson and only a slightly higher 1.48% for the linear model.