A Tale of Two Models: Linear Regression and Poisson GLM Yield Identical Trends for COVID-19 Mortality in Italy

While it is undisputed that Poisson GLM models 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 model 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 an acceptable performance of linear regression. This was further confirmed by the development of a Poisson GLM model, which showed: a) a 100% correspondence with the linear regression model in identifying the growth or decline trend across all 11 seasonal periods considered; b) that both the simple linear and Poisson models demonstrated a comparable great accuracy in counting COVID-19 deaths, with mean MAE values, per period, respectively of 88.60 and 62.76. Based on an average of approximately 6,630 deaths per period, the Poisson model showed a percentage error of 1.15%, while the linear regression models error was just 1.48%.