## 2 Materials and Methods
### Convolutional Neural Network Training and Testing  
A residual neural network (ResNet), a type of convolutional neural network (CNN), was used in this study. The ResNet model was selected after training and testing several other common ML frameworks due to its increased performance and speed. ResNets utilize \"skip connections\" between the blocks of convolutional, max-pooling, and fully connected layers that function to mute upstream layers within the neural network framework and amplify the subsequent downstream layers [24]. This functions to reduce the occurrence of vanishing gradients and accuracy saturation, and allow for faster, deeper models to be created with lower training error [24]. ResNet50 architecture from the TensorFlow Python package was used to implement the ResNet model [25]. A transfer learning process, which allows for a pretrained network with weights from another dataset to quickly and more accurately build new models, was used with initial weights created from the 14-million-image \"ImageNet\" dataset [26]. The top layer of the ImageNet model network was removed, and additional dense and dropout layers were added to yield a total of 269,224,449 trainable parameters out of 292,812,161 parameters. Model layers were activated using the Rectified Linear Unit (ReLU) activation function. A learning rate, which controls how much each model weight can be changed during each training epoch, of \(2\times 10^{-5}\) was applied. The algorithm was trained for 50 epochs (one epoch is one pass through all of the data.) The ResNet algorithm architecture and parameters are summarized in Figure 1 and Tables S1 and S2. All equations used for training and validation are detailed in Table S3. tested on (a) ProstateX-2; (b) local institutional; and (c) combined ProstateX-2 and local institutional image data using (i) T2, (ii) ADC, and (iii) combined T2 and ADC map images. The combination of algorithm training and testing sets are summarized in Figure 2. The total numbers of patients included in each model are listed in Table 2. Mean accuracy and areas under the receiver operating characteristic curve (AUCs) were calculated across five (cross-validated) runs. Algorithm parameters and performance are reported in accordance with the CLAIM checklist criteria [27]. The statistical significance of the results of the trained models were also evaluated. \"Randomization\" or \"shuffle\" testing was performed, where the labels on the training data are shuffled and passed through the modeling process 100 times to determine if any randomly shuffled dataset could achieve the same results as the final model. A \(p<0.01\) \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**ResNet Algorithm** & **Training Image Source** & **Testing Image Source** & **Total Training Images** & **Total Testing Images** \\ \hline \multirow{3}{*}{Model\({}^{\text{PX2}}\)} & \multirow{3}{*}{PX2} & PX2 & 89 (80\%) & 23 (20\%) \\  & & Local & 89 (80\%) & 13 (20\% of 63 initial) \\  & & PXL & 89 (80\%) & 36 (20\%) \\ \hline \multirow{3}{*}{Model\({}^{\text{Loc}}\)} & \multirow{3}{*}{Local} & Local & 50 (80\%) & 13 (20\%) \\  & & PX2 & 50 (80\%) & 23 (20\%) \\ \hline \multirow{3}{*}{Model\({}^{\text{PXL}}\)} & \multirow{3}{*}{PXL} & PXL & 139 (80\%) & 36 (20\%) \\  & & PX2 & 139 (80\%) & 23 (20\%) \\ \cline{1-1}  & & Local & 139 (80\%) & 13 (20\%) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Total patients included in each of the initial datasets trained and tested. The total included images for each imaging type (T2, ADC, or T2 + ADC) where the same imaging types were used for each training/testing combination for the model. Figure 2: Schematic summarizing image datasets, algorithm training and testing. was considered significant, indicating that no shuffled runs achieved the same accuracy and AUC as the final reported result. The statistical significance of the differences in the performance of the models was also tested using a 2-tailed \(t\)-test.