# Enhancing Survival Analysis Model Selection through XAI(t) in Healthcare
## 4 Discussion
### Dataset-Level Explanations
#### Model-Level Explanations  
The second main evaluation step consisted of investigating the feature importance from the models' perspectives. This was accomplished by computing the difference between the loss function of the trained model and the loss function of the model with permutations. Specifically, the loss function (i.e., Brier score) was computed multiple times by changing the value of each single feature one at a time while keeping the others unchanged. Features that led to greater fluctuations in the difference were considered more influential according to the models' perspectives. The results are depicted in Figure 10 for the CPH model and Figure 11 for the LH model. The relationships between OSA and the most important features retrieved by the SA models align with the medical literature [53; 54; 55; 56; 57]. Such comorbidities were revealed to be predictors of a lower survival probability for people with OSA in a previous work [1]. The most important features identified for the CPH model aligned with the features highlighted by computing the SurvSHAP values on the test set. Remarkably, additional features such as malignancy and dilated heart disease were not reported in the dataset-level explanations. This suggests that while certain features may not stand out prominently in individual data instances (i.e., they are underrepresented in the data), they still hold significant weight when considered from a CPH model-level perspective. This conclusion can also be confirmed by looking at the related hazard ratios in Table 4.  
However, although the presence of malignancy and dilated cardiomyopathy has a strong influence on individual survival, such features are not always available since they are not common in the population and cannot be used in clinical practice (also in our cohort, see Figure A3). In addition, unlike the dataset-level explanations, where the contribution of the CPAP treatment period increased over time, in the general model, it lost its importance in the final part of the observation period, thus lessening the contributions related to renal dysfunction and COPD. Figure 10: Time-dependent feature importance for the Cox regression model, obtained by subtracting the full model Brier score from the Brier score after single feature permutations. Concerning the LH model (Figure 11), the features identified were the same as those retrieved by applying SurvSHAP to the test set. Unlike the CPH model, the contribution of age was almost equal to the other features. Surprisingly, AHI had the greatest contribution from \(\sim\)150 to \(\sim\)170 months (\(\sim\)12.5 to 14 years). In addition, starting from \(\sim\)125 months, the SaO\({}_{2}\) min started to gain more and more importance until it became the most important feature. Comparing Figures 10 and 11, the LH model computed the feature contributions in a more balanced way with respect to the CPH model. Notably, while exhibiting similar performance, the selected models focused on different feature sets. Specifically, the CPH model identified several features related to mortality in a general way, such as dilated heart disease and the presence of malignancies, while assigning greater importance to age. On the other hand, the LH model focused on features