Covid-19 Case Study of Regione Lombardia

Authors: Valeria Insogna, Roberta Pascale, Anna Pederzani, Thomas Verardo

Introduction

• Objective: Modeling the trend of the number of hospitalized people in Lombardia during the Covid-19 spreading outbreak and provide forward predictions given the models built.
• Input dataset: Covid-19 data from the official website of Protezione Civile, Covid-19 Rt data from the Istituto Superiore di Sanità, color of the regions from Ondata.it.
• Variable of interest: totale_ospedalizzati.
• Time reference: 1st October 2020 - 1st February 2021.
• Area of interest: Lombardia.

Exploratory Data Analysis

• Data: 124 observations of 30 variables.
  • 3 variables totally missing: note, note_test, note_casi.
  • 9 variables missing more than 50% of data listed above.
  • 11 variables with no missing data such as ricoverati_con_sintomi, terapia_intensiva, etc.
• Cumulative variables have been converted to per-day metrics like dimessi_guariti_per_day, deceduti_per_day, etc.
• Added extra covariates:
  • color of the region
  • rt_positive
  • dummy variable indicating if the peak has already been reached.

Model Building

Linear Model

• Adopting a forward selection approach, with the main assumptions such as linearity, homoscedasticity, and independence of the observations.
• Evaluation metrics include: R2, F-test, checking for multicollinearity (VIF), and more.

Generalized Linear Models (GLM)

• The GLM allows flexibility in modeling the distribution of the response variable.
  • Assumptions and advantages listed above.

Specific GLM and GAM Models

• GLM Poisson
• GLM QuasiPoisson
• GLM Gamma
• GAM Poisson
• GAM Gamma

Details on the models and their statistics are as follows:

Model Selection

GLM Models

Model Details	Deviance Explained	AIC
totale_ospedalizzati ~ mean_nuovi_positivi + log(mean_dimessi_guariti_per_day)*I(rt^2) + rt + deceduti_per_day, family = poisson	0.969	7715.7
totale_ospedalizzati ~ mean_nuovi_positivi+ sqrt(mean_dimessi_guariti_per_day)*I(rt^2) + rt, quasipoisson	0.948	NA
totale_ospedalizzati ~ mean_nuovi_positivi + log(mean_dimessi_guariti_per_day) * I(rt^2) + rt, family = Gamma(link = "log")	0.943	1966.4

GAM Models

Model Details	Adjusted R2	AIC
totale_ospedalizzati ~ s(mean_nuovi_positivi) + s(mean_dimessi_guariti_per_day), family = poisson(link = log)	0.992	2708.01
totale_ospedalizzati ~ s(mean_nuovi_positivi) + s(mean_dimessi_guariti_per_day) +I(rt^2), family = Gamma(link = log)	0.982	1746.353

Data Prediction

GLM Models

Model Details	Deviance Explained	AIC	RMSE
totale_ospedalizzati ~ mean_nuovi_positivi + log(mean_dimessi_guariti_per_day)*I(rt^2) + rt + deceduti_per_day, family = poisson	0.969	7715.7	658.8
totale_ospedalizzati ~ mean_nuovi_positivi+ sqrt(mean_dimessi_guariti_per_day)*I(rt^2) + rt, family = quasipoisson	0.948	NA	819.2
totale_ospedalizzati ~ mean_nuovi_positivi + log(mean_dimessi_guariti_per_day) * I(rt^2) + rt, family = Gamma(link = "log")	0.943	1966.4	746.6

GAM Models

Model Details	Adjusted R2	AIC	RMSE
totale_ospedalizzati ~ s(mean_nuovi_positivi) + s(mean_dimessi_guariti_per_day), family = poisson(link = log)	0.992	2708.01	152.1
totale_ospedalizzati ~ s(mean_nuovi_positivi) + s(mean_dimessi_guariti_per_day) +I(rt^2), family = Gamma(link = log)	0.982	1746.353	313.3