# To Swab or Not to Swab? The Lesson Learned in Italy in the Early Stage of the COVID-19 Pandemic
## 3 Results  
In Table 1, the weekly number of total positive cases of COVID-19, and the total hospitalizations, swabs, and individuals in isolation at home are reported for both Piemonte and Veneto. A first Poisson regression model (Model 1) was fitted for the daily cumulative hospitalization data count in Veneto with a temporal trend and the daily number of positive COVID-19 cases as explanatory variables. Overdispersion was detected; hence, the model was fitted with a suitable multiplicative factor in the variance function. The goodness-of-fit test in Table 2 showed that the time trend and the number of positive cases alone could not explain the variation of the number of hospitalized patients (\(p=0.026\)). The same model applied to the data of Piemonte (Figure 1A) does not fit the observed data, confirming that the daily counts of positive COVID-19 cases do not explain the differences in the number of hospitalized patients between the two regions. The observed data for Piemonte and Veneto are plotted in Figure 1A as points. The continuous lines correspond to a local linear smoothing for the data from Veneto and the values predicted by the Poisson model applied to the data from Piemonte. The predicted hospitalization \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Week**} & \multicolumn{4}{c}{**Piemonte**} & \multicolumn{4}{c}{**Veneto**} \\ \cline{2-10}  & **No. of Positive** & **No. of** & **No. of Individuals** & **No. of Positive** & **No. of** & **No. of Individuals** \\  & **COVID-19 Cases** & **Hospitalizations** & **Swabs** & **in Isolation** & **COVID-19 Cases** & **Hospitalizations** & **Swabs** & **in Isolation** \\ \hline
01/03/2020 & 11 & 7 & 308 & 4 & 191 & 35 & 8659 & 154 \\
08/03/2020 & 207 & 148 & 1046 & 54 & 543 & 164 & 14,429 & 341 \\
15/03/2020 & 873 & 688 & 3680 & 126 & 1937 & 485 & 26,980 & 1290 \\
22/03/2020 & 3952 & 2277 & 10,701 & 1229 & 4617 & 1191 & 53,642 & 3023 \\
29/03/2020 & 7671 & 3533 & 21,511 & 3318 & 7930 & 1903 & 89,380 & 5010 \\
05/04/2020 & 11,109 & 3891 & 37,318 & 5802 & 10,824 & 2015 & 133,289 & 7078 \\
12/04/2020 & 16,008 & 3819 & 62,577 & 8351 & 13,768 & 1716 & 190,912 & 9033 \\
14/04/2020 & 17,690 & 3762 & 71,678 & 9293 & 14,432 & 1660 & 208,878 & 9076 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Weekly number of positive COVID-19 cases, hospitalizations, swabs performed, and individuals in isolation at home in Piemonte and Veneto. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Index** & **Model 1** & **Model 2** \\ \hline Goodness-of-fit-indexes & & \\ \hline Goodness-of-fit test, \(p\)-value & 0.026 & 0.454 \\ Analysis of deviance, \(p\)-value & - & \textless{}0.001 \\ Pseudo \(R^{2}\) & 0.412 & 0.988 \\ AIC & 488.73 & 471.27 \\ \hline Prediction accuracy index & & \\ \hline RMSE & 1401.331 & 294.732 \\ Scatter Index & 0.710 & 0.149 \\ sMAPE & 0.388 & 0.203 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Goodness-of-fit and prediction accuracy indexes. The goodness-of-fit indexes were computed on the model built on Veneto data. The prediction accuracy indexes were computed on the predictions of the number of hospitalizations over time in Piemonte. Model 1 considers the daily number of positive Covid19 cases and time as explanatory covariates for the daily number of hospitalizations; Model 2 considers the daily number of positive Covid19 cases and the daily number of swabs with time-interaction as explanatory covariates for the daily number of hospitalizations. counts in Piemonte were significantly lower than the real observed ones, as confirmed by the measures of the prediction accuracy (RMSE = 1401.3, SI = 70%, and sMAPE = 39%). A second Poisson model was developed including the interaction between time and the number of swabs as the further predictor. No overdispersion was detected and the number of swabs was highly significant, as well as its interaction with time (\(p<0.001\) for both).