# Machine Learning for Evaluating Hospital Mobility: An Italian Case Study
## 4 Experimental Results and Discussions
### Evaluating Hospital Efficiency in Healthcare Mobility  
Table 6 presents the general descriptive statistics for the DEA efficiency scores across all hospital facilities involved in the analysis. These results indicate that the DEA efficiency scores do not follow a normal distribution, as confirmed by the significant Shapiro-Wilk test result (\(p\)-value \(<\) 0.001). This non-normality justifies the use of the nonparametric Kruskal-Wallis test to analyze efficiency differences among groups of hospitals categorized according to various criteria. In the DEA efficiency score analysis, base-level hospitals demonstrate high efficiency, with an average score of 0.897 and a median of 0.906, indicating effective use of healthcare characteristics to facilitate patient mobility. In contrast, first-level hospitals have the lowest average score of 0.837, suggesting challenges in resource optimization, possibly due to the complexity of cases handled. IRCCS and private nursing homes excel with average scores of 0.922 and 0.973, respectively, highlighting their superior ability to transform healthcare inputs into high patient mobility, likely due to advanced resources and effective management. On the other hand, second-level hospitals show more variability and lower \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline  & **N** & **Mean** & **Median** & **SD** & **Minimum** & **Maximum** & **Shapiro–Wilk** \\
**DEA EFFICIENCY** & 127 & 0.893 & 0.950 & 0.125 & 0.387 & 1.00 & 0.824 & \textless{}0.001 \\
**SCORES** & & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Descriptive statistics of DEA efficiency scores. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & **LEVEL** & **N** & **Mean** & **Median** & **SD** & **Minimum** & **Maximum** \\
**DEA EFFICIENCY** & **BASE LEVEL** & 37 & 0.897 & 0.906 & 0.094 & 0.669 & 1.00 \\
**SCORES** & **FIRST LEVEL** & 23 & 0.837 & 0.842 & 0.160 & 0.387 & 1.00 \\
**IRCCS** & 8 & 0.922 & 0.969 & 0.129 & 0.620 & 1.00 \\
**PRIVATE NURSING** & & 39 & 0.973 & 0.999 & 0.047 & 0.802 & 1.00 \\
**HOMES** & & & & & & \\
**SECOND LEVEL** & 20 & 0.784 & 0.748 & 0.129 & 0.515 & 1.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: DEA efficiency scores by hospital level. scores, with an average of 0.784, reflecting potential inefficiencies or greater complexities in treatments. Table 8 segregates the DEA efficiency scores based on the hospital management network--private versus public--providing insights into how these networks leverage healthcare characteristics to maximize patient mobility. Private network hospitals showcase significantly higher efficiency, with an average score of 0.936 and a median of 0.977. This superior performance is indicative of their ability to effectively convert healthcare inputs into desirable outputs. The high median and relatively low standard deviation (0.0872) suggest that private hospitals maintain consistent efficiency across the board, possibly due to more flexible management practices and targeted investments in healthcare technologies. Conversely, public network hospitals display a broader range of efficiency scores, evidenced by a lower average of 0.830 and a median of 0.875, along with a higher standard deviation of 0.1453. The minimum score dipping to 0.387 points to significant inefficiencies within some public hospitals. This variability could be attributed to disparate operational challenges, including bureaucratic constraints and varying levels of resource allocation, which may affect their capacity to optimize healthcare inputs effectively. To further delve into the efficiency analysis of hospital facilities in the Apulia and Emilia-Romagna macroregion, we employed the nonparametric Kruskal-Wallis ANOVA test. This method was chosen to compare DEA efficiency scores across different groups of hospitals, particularly suitable given the non-normal distribution of the scores.