Table 1.

Main characteristics of the three models chosen to compare excess mortality estimates during COVID-19 pandemic years in Italy from 2020–2021.

	Model 1	Model 2	Model 3
Models compared (reference)	(Generalized mixed effects models; Maruotti A, et al.).	(Generalized additive models; Dorrucci M, et al.).	(Time-series with temperatures distributions; Scortichini M, et al.).
Statistical model/approach	Negative binomial mixed model with seasonal patterns.	Negative binomial model/epidemiological approach.	Quasi-Poisson time-series regression model/time-series.
Type of time modelling and time unit	Time (weeks) modelled by Fourier series; number of terms chosen by goodness of fit criteria (AIC; BIC).	Time (weeks) modelled by quadratic splines, with one knot per month.	A linear term corresponding to time to model long-term trends, a cyclic cubic B-spline with three equally spaced knots for the day of the year used to model seasonality, and indicators for day of the week to account for weekly variations in mortality.
Estimate of the number of expected deaths	Mortality baseline estimated over (2011–2019). The weekly predictions of mortality data for years 2020 and 2021 are based on the 2019 year-specific conditional best linear unbiased predictions of the generalized linear mixed model.	Mean number of deaths during pre-pandemic years (2015–19).	Smooth functions that define a baseline risk accounting for temporal trends and variation in temperature distribution.
Estimate of excess deaths	Difference from the estimated baseline along with 95% prediction intervals. If zero is included in the intervals, no difference from the expected number of deaths is hypothesized.	Difference in the number of deaths in 2020/21 adjusted by seasonality with the number of expected deaths.	The excess risk In mortality during the COVID-19 outbreak defined through a constrained quadratic B-spline with four equally spaced knots.
Strengths of the model	Simple interpretation and very good in-sample fitting performance are obtained for all Italian regions.	Simple interpretation.	Presence of covariates containing the information regarding mean temperatures.
Limitation of the model	Socio-demographic and hospital-related information may improve the accuracy of the estimates and may contribute to explaining heterogeneity across regions. No harvesting effect is considered.	No secular trend estimate.	Low number of cases prevents the full application of the two-stage modelling process in age groups <50 years old.