# Enhancing Survival Analysis Model Selection through XAI(t) in Healthcare
## 2 Materials and Methods
### Statistical Analysis and Feature Selection  
Before training the SA models, we performed feature selection, considering only the training set. For each feature, we calculated Pearson's correlation (PC) coefficients to visualize and remove the most correlated ones through filtering \(|PC|>0.6\). The correlation matrices before and after filtering are depicted in Appendix A, Figures A1 and A2. In cases of numerical-categorical high-correlation feature pairs, we retained the numerical ones. After all pre-processing operations, we retained 1394 records with 23 features. A summary of the data is reported in Table 1. For the survival analysis task, the _status_ feature represents the event, while _follow-up days_ (converted into months) represents the time. \begin{table}
\begin{tabular}{l c c c c} \hline \hline
**Feature** & **Type** & **Description** & **Number** & **Mean \(\pm\) Std** & \(p\)**-Value** \\ \hline \multicolumn{5}{c}{**Demographics**} \\ \multicolumn{5}{c}{**Status**} \\ Dead & Categorical & Indicates whether the patient is dead or alive at follow-up & 363 & - & Reference \\ \multicolumn{5}{c}{**Sex**} \\ Male & Categorical & Sex of the patient & 997 & - & 0.182 \\ Female & Categorical & 397 & - & \\ Age & & & & \\ \multicolumn{5}{c}{Under 65 years} & Categorical & Indicates whether the patient is over 65 & 700 & - & \(<\)0.001 \\ \multicolumn{5}{c}{**Over 65 years**} \\ \multicolumn{5}{c}{**Martial Status**} \\ Married & Categorical & Marital status of the patient & 262 & - & 0.842 \\ Not married & & 1132 & - & \\ \multicolumn{5}{c}{**Comorbidities**} \\ Hypertension & Categorical & Presence of hypertension & 752 & - & 0.652 \\ Diabetes & Categorical & Presence of diabetes & 413 & - & 0.033 \\ Heart failure & Categorical & Indicates whether patients have a history of heart failure & 79 & - & \(<\)0.001 \\ Dilated cardiomyopathy & Categorical & Presence of dilated cardiomyopathy & 17 & - & \(<\)0.001 \\ Atrial fibrillation & Categorical & Indicates whether patients have a history of atrial fibrillation & 135 & - & \(<\)0.001 \\ Previous cardiovascular events & Categorical & Indicates whether patients have a history of previous CV events & 32 & - & 0.089 \\ Valuvular heart disease & Categorical & Presence of valvular heart disease & 33 & - & 0.006 \\ Cardiovascular disease & Categorical & Presence of cardiovascular disease & 339 & - & 0.001 \\ Chronic obstructive pulmonary disease (COPD) & Categorical & Presence of COPD & 288 & - & \(<\)0.001 \\ Asthma & Categorical & Presence of asthma & 70 & - & 0.297 \\ Malignanty & Categorical & Indicates whether patients have a history or presence of malignancy & 26 & - & \(<\)0.001 \\ Renal dysfunction & Categorical & Presence of renal dysfunction in patient & 308 & - & \(<\)0.001 \\ Arenemia & Categorical & Presence of anemia & 263 & - & \(<\)0.001 \\ \multicolumn{5}{c}{**Cholesterol Category**} \\ Value \(\leq\)200 (mg/dL) & Categorical & Categorical & Categorical column classifying cholesterol into 3 categories & 371 & - & 0.030 \\ Value \(\geq\)240 (mg/dL) & & 153 & - & \\ \multicolumn{5}{c}{**Weight Categories**} \\ Normal weight & & 75 & - & \\ Overview weight & 291 & - & \\ Obesity class I & Categorical & Categories of weight based on BMI value & 397 & - & \(<\)0.001 \\ Obesity class II & & 327 & - & \\ \multicolumn{5}{c}{**Polyosmographic data**} \\ AHI & & Apnea-hypopnea index & - & 57.01 + 19.16 & 0.002 \\ SaO\({}_{2}\) min [\%] & Numeric & Minimum oxygen saturation & - & 70.94 + 13.63 & 0.335 \\ \multicolumn{5}{c}{**Treatment Info**} \\ CPAP & Categorical & Received CPAP treatment & 555 & - & 0.006 \\ Years of CPAP & Numeric & Duration of CPAP usage (years) & - & 4.44 + 3.25 & \(<\)0.001 \\ Follow-up days & Numeric & Days from admission to follow-up (months) & - & 98.62 + 49.76 & \(<\)0.086 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Final dataset with related statistics.