## 3 Results
### Pcnn  
The results of the analysis of implementing the PCNN model are also described. The NN was composed of ten input nodes, two hidden nodes, and one output node, and Tangent is used as the activation function. The hidden node bias was 0.1, and the learning rate was 0.3. The learning algorithm used was backpropagation. The results of the feature-sensitivity analysis are presented in Table 2. The most sensitive variable for the classification of BCR was SV (9.01), followed by SM (4.75), PNI (3.79), and LNM (3.32). Age (0 years) and BMI (0.46) were the lowest. Thus, the sensitivity analysis yielded similar results to those of the Pearson correlation coefficient. In the Pearson correlation, the Gleason score and pathology T stage were effective, but in the feature sensitivity analysis, SV, SM, PNI, and LNM were effective. All variables in the ranking can be considered as useful for predicting the BCR. The parameters of the NN were as follows: learning rate = 0.1, activation function = sigmoid, learning algorithm = backpropagation, batch size = 10, and epochs = 1000. The results of the partial correlation analysis are presented in Table 3. A total of 10 variables were determined based on their mutual influence. That is, the correlated variables affected the sensitivity change owing to their mutual influence. For example, age (+\(\eta\)) affected the value of age as the candidate groups LNM and SM changed. Thus, LNM \begin{table}
\begin{tabular}{c c c c} \hline  & **BCR** & **Non-BCR** & **Pearson Correlation** \\ \hline  & 283 & 738 & \\ Age & 67.47 & 66.747 & \(-\)0.05 \\ BMI & 23.416 & 23.253 & \(-\)0.025 \\ PSA & 23.576 & 4.765 & \(-\)0.144 \\ Gleason score (sum) & & & \(-\)0.385 \\
5 & - & 8 & \\
6 & 4 & 115 & \\
7 & 154 & 536 & \\
8 & 64 & 45 & \\
9 & 57 & 33 & \\
10 & 4 & 1 & \\ Pathology T stage & & & \(-\)0.385 \\ T1 & 1 & 4 & \\ T2a & 7 & 87 & \\ T2b & 8 & 29 & \\ T2c & 67 & 445 & \\ T3a & 96 & 112 & \\ T3b & 95 & 56 & \\ T4 & 9 & 5 & \\ ECE & & & \(-\)0.421 \\ Present & 94 & 575 & \\ Absent & 189 & 163 & \\ SV & & & \(-\)0.361 \\ Present & 174 & 676 & \\ Absent & 109 & 62 & \\ PNI & & & \(-\)0.236 \\ Present & 33 & 264 & \\ Absent & 250 & 477 & \\ LNM & & & \(-\)0.295 \\ Present & 174 & 647 & \\ Absent & 109 & 91 & \\ SM & & & \(-\)0.291 \\ Present & 119 & 540 & \\ Absent & 164 & 198 & \\ \hline \end{tabular}
\end{table} 
Table 1: Characteristics of patient data. BMI, body mass index; PSA, prostate-specific antigen; ECE, extracapsular extension; SV, seminal vesicle; PNI, perineural invasion; LVM, lymph node metastasis, SM, surgical margin. and SM were amplified with age. As both LNM and SM had age in the candidate group, they had a partial correlation. There was no partial correlation in the PSA levels because SM was in the candidate group, but other variables were not in the candidate group. Partial correlations were constructed for the remaining features in the same manner. The PCNN, which connects the hidden layers based on the correlation of variables, was modeled as depicted in Figure 2. The PCNN consists of an input layer composed of ten nodes, hidden layer 1 composed of eight nodes, hidden layer 2 composed of two nodes, and an output layer composed of one node. Learning and inference are performed between variables with partial correlations in the eight layers. The PSA level is the most significant variable for PCa and may be effective for inference because it is unaffected by other factors. Hidden layer 2 was designed to solve the \"XOR problem\" of the perceptron. \begin{table}
\begin{tabular}{c c c} \hline \hline  & **Sensitivity** & **Rank** \\ \hline NN\_k (X, Age-n) & 0 & 10 \\ NN\_k (X, BMI-n) & 0.46 & 9 \\ NN\_k (X, PSA-n) & 1.89 & 7 \\ NN\_k (X, GS -n) & 0.47 & 8 \\ NN\_k (X, pT-n) & 2.83 & 5 \\ NN\_k (X, ECE-n) & 2.83 & 5 \\ NN\_k (X, SV-n) & 9.01 & 1 \\ NN\_k (X, PNI-n) & 3.79 & 3 \\ NN\_k (X, LNM-n) & 3.32 & 4 \\ NN\_k (X, SM-n) & 4.75 & 2 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of feature sensitivity analysis.