## 3 Results
### The Comparison of Patients' Characteristics Distribution
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multicolumn{2}{c}{**Feature Category**} & \multicolumn{2}{c}{**Test Set**} & \multicolumn{2}{c}{**STLNFM Prediction**} & \multicolumn{2}{c}{**MTLNFM Prediction**} \\ \multicolumn{2}{c}{**and Name**} & **Days \textless{}= 10** & **Days \textgreater{} 10** & **Days \textless{}= 10** & **Days \textgreater{} 10** & **Days \textless{}= 10** & **Days \textgreater{} 10** \\ \hline \multirow{6}{*}{Numerical} & CCI & 3.1 (2.3) & 1.7 (1.9) & 6.0 (0.0) & 2.0 (2.1) & 3.4 (2.8) & 2.0 (2.0) \\  & Creat & 150 (181.0) & 136.4 (132.1) & 63.4 (2.2) & 140.9 (147.3) & 169 (227.6) & 137.9 (139.4) \\ \cline{1-1}  & Urea & 60.0 (57.4) & 44.7 (42.9) & 23.2 (25.2) & 49.2 (47.8) & 47.2 (47.4) & 49.1 (47.8) \\ \cline{1-1} Features & Lactate & 10.6 (10.1) & 10.6 (7.6) & 17.0 (0.0) & 10.6 (8.3) & 9.9 (7.8) & 10.7 (8.3) \\ \cline{1-1} Mean (Std) & Apache2 & 13.2 (7.9) & 11.5 (7.9) & 2.0 (0) & 12.1 (7.9) & 9.3 (6.8) & 12.2 (8.0) \\ \cline{1-1}  & sofa & 9.5 & 8.2 & 4.0 & 8.6 & 9.1 & 8.5 \\ \cline{1-1}  & cokd & (4.1) & (4.3) & (0.0) & (4.3) & (5.3) & (4.2) \\ \hline \multirow{6}{*}{
\begin{tabular}{c} Categorical \\ Features \\ Patients (\%) \\ \end{tabular} } & CKD & 6 (10.7\%) & 12 (8.3\%) & 0 (0.0\%) & 18 (9.1\%) & 1 (6.2\%) & 17 (9.2\%) \\ \cline{1-1}  & Obesity & 15 (26.8) & 46 (31.7\%) & 0 (0.0\%) & 61 (31.0\%) & 3 (18.8\%) & 58 (31.4\%) \\ \cline{1-1}  & Dementia & 2 (3.6\%) & 3 (2.1\%) & 0 (0.0\%) & 5 (2.5\%) & 3 (18.8\%) & 2 (1.1\%) \\ \cline{1-1}  & Cancer & 5 (8.9\%) & 12 (8.3\%) & 0 (0.0\%) & 17 (8.6\%) & 1 (6.2\%) & 16 (8.6\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Distribution of features regarding the hospitalization length of stay in the testing set performed by STLNFM and MTLNFM prediction. CCI: Charlson Comorbidity Index; Apache2: Acute Physiology and Chronic Health Evaluation; sofa: Sequential Organ Failure Scale; CKD: Chronic Kidney Disease. Figure 3: Performance comparison based on different tasks using STLNFM and MTLNFM with individual and combined clinical outcome prediction tasks. Task 1 (T1): frailty status prediction; Task 2 (T2): hospital length of stay prediction; Task 3 (T3): mortality prediction. the means of the predicted and true distributions. For categorical features, we calculated the absolute difference between the predicted and true percentage distributions across categories. Here, we take the numerical feature CCI and categorical feature CKD predicted by the STLNFM model as an example to illustrate the process. The deviation for CCI was calculated as \(\left|\right.6.0-3.1\left|\right./3.1=0.935\), and for CKD as \(\left|\right.0.091-0.107\left|\right.=0.016\), respectively. We then averaged the deviations across all features of the same type, i.e., numerical and categorical, and presented the results in Figure 4. In principle, a lower deviation indicates that the model's predicted distribution more closely approximates the true distribution, reflecting better generalization and less bias. As shown in the results, MTLNFM consistently achieved lower average deviation values than STLNFM across all prediction tasks and both feature types. These findings reinforce the conclusion that MTLNFM yields more robust and unbiased predictions, making it more reliable for clinical outcome modeling in diverse patient populations.