## 2 Materials and Methods
### Dataset Description
Again, in a random way, we generated either an increase or a decrease in a previous PSA measurement (which we obtained from the lognormal distribution generator) to show that PSAV, according to studies performed over the years, is a great indicator and that having the appropriate threshold values of PSAD can provide important and reliable information for further monitoring of the patient [47]. The thresholds that we utilized were, as listed in Table 2, 0.25 ng/mL/year for the range of 35-59 years and 0.50 ng/mL/year for the age range of 60-70 years old. The minimum value was \(-\)0.85 ng/mL/year, which can be justified by the fact that a patient could have an inflammation of the prostate at the initial measurement and, at the final measurement, the patient might be free of inflammation. On the other hand, the maximum value was 4.54 (or 454%), which could be due to inflammation but could also be a sign of cancer. The mean value for PSAV was 0.141 ng/mL/year, and the standard deviation was 0.332 ng/mL/year. The prostatic antigen (PSA) is bound to other proteins [51]. PSA detected in the blood is usually bound to the protein a1-chymotrypsin (a proteolytic enzyme); however, more than 23% of serum PSA is in free form (free PSA). Prostate hyperplasia is more associated with an increase in free PSA, whereas PCa is more associated with a decrease in the free form of PSA [51]. The reason why this situation occurs is not clear, but one theory is that prostate cancer not only produces more PSA but also the proteins that PSA is attached to, resulting in a decrease in free PSA [51]. Thus, a very valuable indicator is a feature variable of our system known as the PSA ratio, which is the ratio of free PSA to total serum PSA. The PSA ratio is naturally derived without units and is used either as a decimal number or as a percentage. The threshold value of 0.24 (or 24%) is an important prognostic indicator. Especially for PSA values > 4-10 ng/mL, a free PSA value > 0.24 is probably an indication of benignity (of course, the gland should be evaluated as a whole). On the other hand, when the PSA ratio is <0.19 (quite a strict limit, in other studies, this limit may be lower than 0.15), there is a significant chance of prostate cancer [50]. Typically, values from 0.19 to 0.24 are reported as a gray zone, which increases the necessity for active monitoring of the patient. We also referred to a related table showing the probability of prostate cancer depending on age and free PSA value [44]. The minimum value in our dataset was 0.09, \begin{table}
\begin{tabular}{c c c} \hline \hline
**Age** & **40–59 Years** & **60–69 Years** \\ \hline PSAV & 0.25 ng/mL/year & 0.50 ng/mL/year \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Justified increase in the PSAV according to age [50]. the maximum value was 0.39, the mean value was 0.266, and the standard deviation was 0.050. These values are summarized in Table 3.  
Our last feature variable was the Digital Rectal Exam (DRE), which is carried out always by a qualified Urologist when an acute bacterial inflammation of the prostate is absent because of the risk of sepsis [52]. In our surrogate data, we chose to give the DRE variable a value of 0 or 1, where 0 denotes negative findings, whereas 1 denotes a suspicious lump. Again, in a random way, we produced the binary values of the DRE. In our dataset, we had 624 cases of 0 and 36 cases of 1, meaning that in 36 cases out of 660 (5.45%), the DRE showed a suspicious lump, whereas in 624 (94.5%), the DRE showed no findings, though we should note that no findings in the DRE do not necessarily mean the absence of PCa. Since we dealt with a binary classification problem, related to whether a patient should or should not proceed to prostate biopsy, our target variable was also in binary form, such as \"yes\" or \"no\", which can also be codified as 1 or 0. So, we used two different target variables (that represent the same result), and we called them \"Target\" and \"Class\" according to the model we used to predict the target variable.