## 4 Distributed Model Training in a Clinical Study
### Results
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & **Accuracy** & **Bal. Accuracy** & **Precision** & **Recall** & **F1-Score** & **Matt. Cor. Coef.** \\ \cline{2-7}  & **R/S/S1000** & **R/S/S1000** & **R/S/S1000** & **R/S/S1000** & **R/S/S1000** & **R/S/S1000** \\ \hline SST & 92.7/90.9/93.1 & 90.9/88.4/93.9 & 96.4/97.1/86.4 & 83.6/78.1/96.9 & 89.5/86.6/91.3 & 84.5/80.9/86.1 \\ (UKA) & \(\pm\)0.008/0.003/0.006 & \(\pm\)0.008/0.003/0.004 & \(\pm\)0.014/0.011/0.011 & \(\pm\)0.009/0.000/0.000 & \(\pm\)0.011/0.004/0.006 & \(\pm\)0.017/0.008/0.010 \\ \hline SST & 92.1/85.4/90.1 & 90.1/87.5/89.8 & 96.3/73.2/85.4 & 82.0/96.1/88.7 & 88.6/83.1/87.0 & 83.3/72.7/79.0 \\ (UMG) & \(\pm\)0.008/0.02/0.008 & \(\pm\)0.010/0.021/0.007 & \(\pm\)0.001/0.022/0.016 & \(\pm\)0.020/0.027/0.008 & \(\pm\)0.012/0.023/0.010 & \(\pm\)0.016/0.041/0.017 \\ \hline SST & 91.4/89.5/92.1 & 89.5/87.8/92.0 & 94.2/89.7/88.0 & 82.0/81.2/91.4 & 87.7/85.2/89.7 & 81.6/73.7/83.3 \\ (UKK) & \(\pm\)0.007/0.000/0.003 & \(\pm\)0.009/0.000/0.005 & \(\pm\)0.009/0.000/0.001 & \(\pm\)0.016/0.000/0.009 & \(\pm\)0.011/0.000/0.005 & \(\pm\)0.016/0.000/0.008 \\ \hline SST & 93.7/94.0/93.9 & 91.6/94.3/94.5 & 100 /89.4/88.0 & 83.2/95.3/96.9 & 90.8/92.3/92.2 & 87.0/87.5/87.4 \\ (UKL) & \(\pm\)0.003/0.015/0.008 & \(\pm\)0.004/0.014/0.006 & \(\pm\)0.000/0.024/0.016 & \(\pm\)0.008/0.013/0.000 & \(\pm\)0.005/0.018/0.009 & \(\pm\)0.006/0.030/0.014 \\ \hline SST & 93.3/94.7/95.5 & 91.0/93.8/95.2 & 100 /95.5/93.8 & 82.0/90.2/94.1 & 90.1/92.8/94.0 & 86.1/88.7/90.3 \\ (IMISE) & \(\pm\)0.003/0.005/0.003 & \(\pm\)0.005/0.005/0.004 & \(\pm\)0.000/0.008/0.000 & \(\pm\)0.009/0.008/0.008 & \(\pm\)0.005/0.007/0.004 & \(\pm\)0.007/0.010/0.006 \\ \hline SST & 92.7/91.1/93.1 & 91.2/91.8/92.4 & 94.8/83.8/92.0 & 85.2/94.5/89.5 & 89.7/88.8/90.7 & 84.4/81.9/85.3 \\ (HSM) & \(\pm\)0.003/0.003/0.006 & \(\pm\)0.005/0.004/0.007 & \(\pm\)0.001/0.009/0.001 & \(\pm\)0.009/0.016/0.015 & \(\pm\)0.005/0.004/0.008 & \(\pm\)0.007/0.007/0.012 \\ \hline IIIL & 92.8/93.6/95.3 & 91.2/94.5/94.9 & 95.6/86.6/94.1 & 84.8/98.0/93.4 & 89.9/91.9/93.7 & 84.7/87.1/90.0 \\  & \(\pm\)0.007/0.011/0.005 & \(\pm\)0.009/0.010/0.005 & \(\pm\)0.010/0.019/0.008 & \(\pm\)0.015/0.008/0.008 & \(\pm\)0.011/0.013/0.006 & \(\pm\)0.016/0.021/0.010 \\ \hline CIIIL & 92.4/93.7/93.9 & 90.6/94.3/94.5 & 95.9/87.6/87.9 & 83.2/96.9/96.9 & 89.1/92.0/92.2 & 83.8/87.2/87.4 \\  & \(\pm\)0.005/0.009/0.003 & \(\pm\)0.005/0.009/0.003 & \(\pm\)0.009/0.012/0.007 & \(\pm\)0.008/0.013/0.000 & \(\pm\)0.007/0.011/0.004 & \(\pm\)0.011/0.018/0.006 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results in IID setting (equally-sized and balanced class distribution). The meaning of the abbreviations are: real-world data (R), synthetic data (S) and synthetic data with the generation size of 1000 (S1000). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Methods**} & **Accuracy** & **Bal. Accuracy** & **Precision** & **Recall** & **F1-Score** & **Matt. Cor. Coef. ** \\ \cline{2-7}  & **R/S/S1000** & **R/S/S1000** & **R/S/S1000** & **R/S/S1000** & **R/S/S1000** & **R/S/S1000** \\ \hline SST & 92.4/90.1/90.6 & 90.6/88.6/89.8 & 95.5/89.8/88.4 & 83.6/82.8/86.3 & 89.2/86.2/87.3 & 83.8/78.6/79.9 \\ (UKA) & \(\pm\)0.010/0.000/0.010 & \(\pm\)0.010/0.010/0.010 & \(\pm\)0.010/0.000/0.010 & \(  
**Setting 1. ** For SST, the model trained on real IID data has achieved on average (standard deviations in brackets) 92.5 (\(\pm\)0.006)%, 91.2 (\(\pm\)0.007)%, 91.3 (\(\pm\)0.009)%, 89.3 (\(\pm\)0.009)%, 90.0 (\(\pm\)0.008), and 84.5 (\(\pm\)0.013) in accuracy, balance accuracy, precision, recall, F1-score and Matthews correlation coefficient, respectively, and we observe similar performance for IIIL and CIII (Table 2). Nevertheless, we experience an inconsistent relationship between precision and recall, when synthetic data is involved (S and S1000). In some cases, the precision is significantly higher than the recall.