# Enhancing Survival Analysis Model Selection through XAI(t) in Healthcare
## 1 Introduction  
Obstructive Sleep Apnea (OSA) is a sleep disorder caused by the recurrence of either partial (hypopnea) or complete (apnea) collapse of the pharyngeal airway, which leads to reduced or ceased airflow during sleep [1, 2, 3]. Such a disease compromises sleep health by discontinuous episodes of hypoxia [4, 5], and its symptoms may be treated through respiratory rehabilitation [3]. Furthermore, effective follow-up during rehabilitation is crucial for monitoring the patient's progress, adjusting treatment as necessary, and ensuring long-term management of OSA symptoms. The prognosis of OSA is complicated by thesimultaneous occurrence of other comorbidities, mostly metabolic and cardiovascular [6], as well as renal [1]. Survival Analysis (SA) of patients with OSA could help clinicians better assess and categorize disease severity, thus more easily identifying higher-risk individuals, especially during the rehabilitation and follow-up phases. Therefore, treatment can be tailored to the subject's condition, considering both the comorbidities and symptoms typical of OSA, thus increasing survival probability. Survival analysis has been traditionally performed using statistical methods, such as Kaplan-Meier curves (KMCs) and Cox regression, but such methods are less effective in the case of datasets with high dimensionality [7]. On the other hand, artificial intelligence (AI) has been widely applied to overcome this limitation of traditional SA methods by exploiting either Machine Learning (ML) [6; 8; 9; 10; 11; 12] or Deep Learning (DL) models [2; 4; 12; 13; 14; 15; 16]. Notwithstanding, AI algorithms addressing survival analysis are known to be characterized by the poor interpretability of their results, since determining which feature impacts model prediction is not a simple task. Moreover, the role of comorbidities and risk factors is often evaluated only according to hazard and odds ratios [17]. This limits their applicability in decision support systems for clinical purposes [18]. Explainable Artificial Intelligence (XAI) can be integrated into SA pipelines to provide clinicians with more interpretable model predictions [13; 19; 20; 21; 22; 23; 24]. Shapley additive explanations (SHAP) [25] and local interpretable model-agnostic explanations (LIME) [26] are then utilized to clarify the relationship between the input and output of the model. Both SHAP and LIME have been extended to address survival tasks by including time and event variables in the computation. These versions are called SurvSHAP [18] and SurvLIME [27]. Specifically, SurvSHAP calculates the contribution of each feature to survival predictions at different time points, thus dynamically providing an overview of feature importance. The latter factor is crucial in healthcare to understand how a survival model made its predictions since the significance of clinical variables can evolve over time. A gap has been found in the existing literature on XAI methods for SA tasks. To the best of our knowledge, no prior works have applied time-dependent XAI-XAI(t) methods to survival DL models while offering a model comparison in terms of dataset- and model-level explanations. Most existing XAI-oriented research focuses on standard XAI methodology applied to classification tasks, possibly considering survival analysis as a separate task. Such a gap can be attributed to the novelty of XAI(t) approaches, as well as the challenges in producing a simple and reliable explanation when time is involved. Focusing on the OSA clinical scenario, this work proposes a survival analysis pipeline focused on the following:  
* Training and validating different Machine Learning and Deep Learning survival models, selecting the best-performing ones according to the metrics used in survival tasks;
* Investigating the role of comorbidities in OSA from an XAI(t) perspective;
* Performing a model comparison, selecting the most reliable models according to the explanations retrieved by XAI(t) algorithms. The rest of this work is structured as follows.