Enhancing Survival Analysis Model Selection through XAI(t) in Healthcare

Abstract

Artificial intelligence algorithms have become extensively utilized in survival analysis for high-dimensional, multi-source data. However, due to their complexity, these methods often yield poorly interpretable outcomes, posing challenges in the analysis of several conditions. One of these conditions is obstructive sleep apnea, a sleep disorder characterized by the simultaneous occurrence of comorbidities. Survival analysis provides a potential solution for assessing and categorizing the severity of obstructive sleep apnea, aiding personalized treatment strategies. Given the critical role of time in such scenarios and considering limitations in model interpretability, time-dependent explainable artificial intelligence algorithms have been developed in recent years for direct application to basic Machine Learning models, such as Cox regression and survival random forest. Our work aims to enhance model selection in OSA survival analysis using time-dependent XAI for Machine Learning and Deep Learning models. We developed an end-to-end pipeline, training several survival models and selecting the best performers. Our top models—Cox regression, Cox time, and logistic hazard—achieved good performance, with C-index scores of 0.81, 0.78, and 0.77, and Brier scores of 0.10, 0.12, and 0.11 on the test set. We applied SurvSHAP methods to Cox regression and logistic hazard to investigate their behavior. Although the models showed similar performance, our analysis established that the results of the log hazard model were more reliable and useful in clinical practice compared to those of Cox regression in OSA scenarios.

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 the simultaneous 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. In Section 2, we describe the clinical dataset, the survival models involved, and the XAI(t) algorithms used. Section 3 presents the obtained results. In Section 4, we compare the best ML and DL models based on SurvSHAP explanations. Finally, Section 5 reports the conclusions.

2. Materials and Methods

First, we perform pre-processing operations to clean and prepare the data. Then, we compute statistical tests and correlations for feature selection. Next, we split the data into training and test sets and train the SA models to choose the best-performing ones based on the evaluation metrics on the test set. The final step involves interpreting and comparing the selected models using SurvSHAP. Figure 1 depicts an overview of the pipeline designed for the analysis.

• Dataset

For this study, we use an internal dataset collected by the Istituti Clinici Scientifici (ICS) Maugeri, Hospital Sleep Laboratory, Bari. All patients’ data were gathered while they underwent rehabilitation. All patients involved were certified as being affected by OSA, established by in-laboratory overnight polysomnography (PSG).

The raw data are available in [28].

The original dataset is composed of 1592 samples with 45 features, including clinical data and data retrieved from polysomnography exams. In addition to the information on age, follow-up time, status, marital status, profession, and sex, our dataset contains indications of Body Mass Index (BMI), the value of the Glomerular Filtrate Rate (GFR), Ejection Fraction (EF), Oxygen Desaturation Index (ODI), minimum saturation of blood oxygen recorded (${\mathrm{SaO}}_2$ min), apnea-hypopnea index (AHI), and other information on comorbidities like heart disease and diabetes.

• Data Pre-Processing

The first operation involved dropping non-relevant features: patient I.D., the number of health records (N CC), admission date, discharge date, profession description, and follow-up date. Then, we converted the survival time from days to months without performing any aggregation operations to facilitate both the analysis and interpretation of data. Next, we checked for null values in EF, ODI, and anemia features. We dropped the EF and ODI features due to 90% null values and lack of information, while we imputed the anemia values based on hemoglobin levels, considering the patient’s sex.

Afterward, we discretized the variables wherever feasible: Age was categorized into two classes, 0 if Age $\le 65$ years old, 1 otherwise. GFR and BMI were binned according to reference values present in the medical literature [29,30]. The age cutoff value was chosen according to the relevant medical literature [31,32,33]. The adoption of unsupervised cutoffs that do not rely on data distribution (but are still relevant in medicine) allowed for better generalization of results. Finally, we included two other features: Continuous Positive Airway Pressure (CPAP) (a binary categorical feature indicating whether a subject followed CPAP treatment) and the corresponding treatment duration in years (Years_of_CPAP).

Outlier removal was not performed, as in the medical domain, removing outliers from clinical data is not always feasible due to the possibility that they may indicate pathological conditions. Finally, since our study focuses on a respiratory disease, samples with last follow-up dates after 2020 (i.e., 198 samples) were excluded due to the COVID-19 pandemic to avoid the presence of bias in our results. As a result of pre-processing, we retained 1394 samples.

• 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 $\left|PC\right|>0.6$. The correlation matrices before and after filtering are depicted in Appendix A, Figure A1 and Figure 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. Final dataset with related statistics.

Feature	Type	Description	Number	Mean ± Std	p-Value
Number of Patients = 1394
Demographics
Status	Categorical	Indicates whether the patient is dead or alive at follow-up			Reference
Dead			363	-
Alive			1031	-
Sex	Categorical	Sex of the patient			0.182
Male			997	-
Female			397	-
Age	Categorical	Indicates whether the patient is over 65			<0.001
Under 65 years			700	-
Over 65 years			694	-
Marital Status	Categorical	Marital status of the patient			0.842
Married			262	-
Not married			1132	-
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
Valvular 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
Malignancy	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
Anemia	Categorical	Presence of anemia	263	-	<0.001
Cholesterol Category	Categorical	Categorical column classifying cholesterol into 3 categories			0.030
Value ≤200 [mg/dL]			870	-
Value in 200–239 [mg/dL]			371	-
Value ≥240 [mg/dL]			153	-
Weight Categories	Categorical	Categories of weight based on BMI value			<0.001
Normal weight			75	-
Overweight			291	-
Obesity class I			397	-
Obesity class II			327	-
Morbid obesity			304	-
Polysomnographic data
AHI	Numeric	Apnea-hypopnea index	-	57.01 ± 19.16	0.002
SaO2 min $[\%]$	Numeric	Minimum oxygen saturation	-	70.94 ± 13.63	0.335
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

. For the survival analysis task, the status feature represents the event, while follow-up days (converted into months) represents the time.

• Survival models

To perform the experiments, we included the following models:

• Machine Learning—Cox proportional hazards (CPH) [34], survival random forest (SRF) [35], survival gradient boosting [36], survival support vector machine [37].
• Deep Learning—Cox time (CT) [38], DeepHit (DH) [39], DeepSurv (DS) [40], and NNet-Survival (logistic hazard (LH) and piecewise constant hazard (PCH)) [41,42].

• Time-Dependent XAI

Unlike other ad hoc explanation methods, such as SurvLIME [27] and survNAM [43], SurvSHAP [18] also takes into account time in the explanation process. This method generalizes Shapley additive explanations (SHAP) [25] to survival models, giving a global explanation of the overall behavior of the model over time. SurvSHAP can reveal the importance of comorbidities affecting the prognosis over the follow-up period, offering valuable insights into the progression of OSA and strategies for improving patient prognosis. Similarly, SurvLIME explains individual predictions, so it is helpful for analyzing single-case predictions and planning personalized treatment over the follow-up period.

Specifically, SurvSHAP describes variable contributions across the entire considered time period to detect variables with a time-dependent effect. Its aggregation approach determines the variables’ importance for a prediction better than the others. $\mathbb{D}=\left\{(X_i,y_i,t_i)\right\}$ denotes the dataset used for training, where $\mathbb{D}$ contains m unique time instants $t_m>t_{m-1}>\cdots >t_1$. $y_i$ is the status of the patient, i.e., whether a patient is dead or alive, and $t_i$ is the time point of the follow-up. Therefore, every patient is represented by n covariates, a status y, and an instant of time t. For each individual described by a variable vector X, the model returns the individual’s survival distribution $\widehat{S}(t,X)$. For the observation of interest $X_{*}$ at any selected time point t, the algorithm assigns an importance value ${\varphi }_t(X_{*},c)$ to the value of each variable $X\left(c\right)$ included in the model, where $c\in \left\{1,2,\dots ,n\right\}$ and n is the number of variables. To calculate every value of the SurvSHAP function, it is necessary to define the expected value for the survival function conditioned by the values of the features:

$$e_{t,{\mathbf{X}}_{*}}^c=\mathbb{E}\left[\widehat{S}(t,\mathbf{X})\right|{\mathbf{X}}^c={\mathbf{X}}_{*}^c]$$

(1)

By defining P(c,$\pi$) as the precedence subset of c in a permutation $\pi$, i.e., $\mathcal{P}(c,\pi )=\{x\in \mathbf{X}\mid x\mathrm{precedes}c\mathrm{in}\pi \}$, the contribution of the variable c to the model is calculated as:

$${\varphi }_t({\mathbf{X}}_{*},c)=\frac{1}{|\Pi |}\sum _{\pi \in \Pi }{e}_{{\mathbf{X}}_{*},t}^{\mathcal{P}(c,\pi )\bigcup c}-e_{{\mathbf{X}}_{*},t}^{\mathcal{P}(c,\pi )}$$

(2)

where $\Pi$ is a set of all permutations of n variables and the indices indicate which variables contribute to the estimation of the survival function. The first term in (2) refers to the contribution of the model with the subset up to variable c with c included, while the second term represents the contribution of the subset before variable c In this way, we obtain the contribution of each single variable to the prediction. For an easier comparison among different models and time points, this value can be normalized to obtain values on a common scale from −1 to 1, so the contribution becomes:

$${\varphi }_t^{*}({\mathbf{X}}_{*},c)=\frac{{\varphi }_t({\mathbf{X}}_{*},c)}{{\sum }_{j=1}^p\left|{\varphi }_t({\mathbf{X}}_{*},j)\right|}$$

(3)

To calculate the global variable importance, we aggregate the time-dependent contributions, thus achieving the following average aggregate SurvSHAP value:

$$\Psi (\mathbf{X},c)={\int }_0^{t_m}\left|{\varphi }_t^{*}({\mathbf{X}}_{*},c)\right|$$

(4)

• Experimental Pipeline

We performed experiments using R (v. 4.3.2) and Python (v. 3.8) languages. We randomly split the dataset using the holdout technique, with 70% used as the training set and the remaining 30% as the test set, stratifying by the Status feature. We also verified that the observation period in the test set did not exceed the observation period in the training set.

The experimental pipeline workflow is illustrated in Figure 2.

Appendix A, Algorithm A1, reports the pseudo-code related to the experimental pipeline workflow depicted in Figure 2.

3. Results

We evaluated the models’ performance on the test set according to the following metrics:

• Harrell’s C-Index [44]—Also known as the concordance index, it measures the proportion of all pairs of observations for which the survival order predicted by the model matches the order in the data. A higher C-index (ideally equal to 1) indicates better concordance between the model prediction and the relative ground truth, whereas a C-index equal to 0.5 indicates a random prediction.
• Integrated Cumulative-Dynamic Area Under the Curve (C/D AUC) [45]—This measures the area under the Receiver Operating Characteristic (ROC) curve at different time points during the observation.
• Brier Score [46]—This measures the difference between the model prediction and the corresponding ground truth event; a lower Brier score suggests better model precision, while a high Brier score indicates performance degradation. Ideal Brier score values should be closer to 0 since values closer to 0.5 indicate random predictions.

We placed greater emphasis on the C-index and the Brier score, as they are the most commonly used metrics in survival tasks and are generally more easily understandable than the C/D AUC.

The evaluation metrics on the test set are shown in

Table 2. Metrics of survival models computed on the test set, with best performance metrics highlighted. Cox proportional hazards (CPH); survival random forest (SRF); survival SVM (SSVM); and survival gradient boosted model (SGBM).

Family	Model	C-Index	Integrated C/D AUC	Integrated Brier Score
Machine Learning	CPH	$0.81$	$0.72$	$0.10$
	SRF	0.81	0.70	0.12
	SSVM	0.71	0.61	0.15
	SGBM	0.79	0.69	0.14
Deep Learning	Cox time	$0.78$	$0.73$	0.12
	DeepHit	0.73	0.70	0.13
	DeepSurv	0.57	0.60	0.16
	LogHazard	0.77	0.70	$0.11$
	PCHazard	$0.78$	0.71	0.13

, with graphical comparisons shown in Figure 3 and Figure 4 for the ML and DL models, respectively.

• ML Model Results As a general result, SSVM was the worst-performing model, while all other models achieved good results. The differences between Cox regression, SGBM, and SRF were minimal for the C-index and integrated C/D AUC, whereas Cox regression exhibited a lower Brier score.
  Thus, we chose CPH for the explainability step. Moreover, this model returned a hazard ratio for each feature that can be used for data explainability in addition to XAI techniques (Section 4).
  DL Model Results As shown in Figure 4, CT, PCH, and LH exhibited similar performance and were thus the best models. We selected LH for the explainability phase (see Section 4 for more details).
  The time-variant Brier scores and C/D AUC values for the CPH, CT, and LH models are depicted in Figure 5.

Moreover, to assess the stability of the outcomes, we performed model training using 10-fold cross-validation. The results obtained (on the same test set used in the holdout approach) are depicted in Appendix A,

Table A1. Performance metrics obtained on the test set in terms of the C-index and integrated Brier score using 10-fold cross-validation.

Family	Model	C-Index	Integrated Brier Score
Machine Learning	CPH	$0.82$	0.10
	SRF	0.82	0.12
	SSVM	0.72	0.32
	SGBM	0.80	0.11
Deep Learning	Cox time	0.77	0.12
	DeepHit	0.74	0.15
	DeepSurv	0.57	0.17
	LogHazard	0.76	0.12
	PCHazard	0.77	0.14

, confirming the performance trends obtained with the holdout split.

4. Discussion

4.1. Related Works

In the artificial intelligence field, results are difficult to interpret, especially when dealing with deep models that are considered “black boxes”, making it difficult to understand how the model generates predictions. XAI has recently been adapted to this context to improve the explainability, interpretability, and transparency of model results [47,48,49]. The goal of XAI algorithms is to convert unexplained ML and DL predictions into more interpretable “white-box” glass ones. Notably, in the realm of survival analysis, understanding which characteristics significantly influence predictions—essentially, understanding how such features are “weighted” for prognosis or diagnosis—is fundamental because it allows clinicians to choose the type of treatments for patients (preventive or curative). Most existing works apply XAI techniques like SHAP and LIME to AI-based frameworks addressing SA. Qi et al. [50] used SHAP to improve the explainability of an ML-based framework concerning the role of mitochondrial regulatory genes in the evolution of renal clear cell carcinoma. Zaccaria et al. [13] adopted approximated SHAP values to build an interpretable transcriptomics-based prognostic system for Diffuse Large B-Cell Lymphoma (DLBCL). Srinidhi and Bhargavi [22] embedded SHAP and LIME in ML- and DL-based frameworks to support the prediction of survival rates for patients with pancreatic cancer. Zuo et al. [51] employed both SHAP and LIME to explain the survival predictions of many ML methods fed with a radiomics feature set extracted from tomographic images. Chadaga et al. [23] used SHAP and LIME to explain ML-based estimations concerning the survival probability of children after bone marrow transplantation. Both SHAP and LIME were included in Alabi’s study [21] to better interpret the predictions of ML algorithms addressing SA on clinical data from people with nasopharyngeal carcinoma. Peng and colleagues [24] used SHAP and LIME to corroborate the outcomes of ML models concerning hepatitis diagnosis and prognosis. Even fewer works have employed either SurvSHAP or SurvLIME for performing SA within ML-based workflows. Zhu and colleagues [12] employed SurvSHAP to investigate the efficacy of adjuvant chemotherapy starting from predictions of both ML and DL models concerning the survival probability of breast cancer patients. Passera et al. [20] explained the outcomes of survival models fed by demographic and clinical features using both SurvSHAP(t) and SurvLIME. These XAI methods were oriented toward global and local explanations by analyzing data from the whole cohort or a single patient. Baniecki et al. [19] performed SA to estimate hospitalization times by training ML algorithms on a multimodal dataset and explaining the results of time-to-event models for single patients using SurvSHAP. Remarkably, as far as we know, no studies have utilized XAI(t) to elucidate the predictions generated by a Deep Learning model. In fact, such architectures often play a supporting role in SA workflows; they are used not to predict mortality risks but to determine additional metrics that are then fed into a classical survival pipeline for performing SA [2,4,14]. In addition, these works did not include XAI strategies to better interpret how the model generated survival predictions. Related works in the literature show a paucity of studies on survival analysis with either ML algorithms or DL models embedding XAI techniques, e.g., SurvSHAP and SurvLIME, to increase the interpretability of the predictions of mortality risk.

Table 3. Related works.

Author	Year	Task	Input Data	Survival Analysis Model	Explainability Model
Zaccaria et al. [13]	2023	Prognosis of DLBCL	Transcriptomic data	AutoEncoders	DeepSHAP
Alabi et al. [21]	2023	Prognosis of NPC	CT images, clinical data	Linear Regression, KNN, support vector machines, Naive Bayes, tree-based models,	SHAP, LIME
Srinidhi et al. [22]	2023	Prognosis of pancreatic cancer	CT images, clinical data	Convolutional Neural Networks, support vector machines	SHAP, LIME
Chadaga et al. [23]	2023	Prediction of BMT efficacy	Clinical data	Tree-base models, Linear Regression, KNN, AdaBoost, CartBoost	SHAP, LIME
Peng et al. [24]	2021	Prognosis of hepatitis	Clinical and demographic data	Linear Regression, CART, KNN, tree-based models, Naive Bayes	SHAP, LIME
Qi et al. [50]	2023	Prognosis of RCC	Genomic data	LASSO-Cox	SHAP, LIME
Zuo et al. [51]	2023	Identification of EGFR in lung adenocarcinoma	CT images	Light GBM, Linear Regression, tree-based models	SHAP, LIME
Zhu et al. [12]	2024	Prognosis of breast cancer	Clinical and demographic data	Cox Mixtures, DeepSurv, Cox PH, survival random forest	SurvSHAP
Baniecki et al. [19]	2023	Prediction of hospital LoS	Text data, tabular data, X-ray images	Tree-based models, CoxPH, DeepSurv, DeepHit	SurvSHAP, SurvLIME
Passera et al. [20]	2023	Test XAI on SA for BMT	Clinical and demographic data	CoxPH, survival random forest	SurvSHAP, SurvLIME

summarizes related works involving classical XAI and XAI(t) in SA.

4.2. Explanation Methods

The model explanation methods can be classified into two categories: dataset-level explanations and model-level explanations. The former category aims at analyzing the dataset characteristics to understand their impact on event predictions; the latter focuses on ranking and highlighting the features that the model considers important for predictions.

Intuitively, both methods present some limitations:

• Dataset-level explanation limitations: SHAP is designed to return a local explanation, i.e., it gives an explanation for a single sample. Consequently, SurvSHAP behaves in the same way. When used on a dataset, its resulting explanation depends on the sample distribution. In fact, if the data are unbalanced for specific features, their contribution will be minimal, but this conclusion cannot be generalized to other data. Hence, the ideal scenario could be to use a large dataset for the sake of higher generalization of the results. However, the computation of feature contributions for a single sample is computationally expensive because of model complexity and the operations involved (e.g., multiple feature permutations, predictions, and performance computations for SHAP values; local sample generation, local model training, and prediction for LIME values). In XAI(t), this is exacerbated since the feature contributions are also computed for different time instants.
• Model-level explanation limitations: Although model-level explanations are computationally less expensive than dataset-level ones, they return explanation information at the population level that cannot be used for explanations at a single prediction level. Moreover, the explanation methods based on permutation can lead to misinterpretations when the independent variables are strongly correlated [52].

To overcome the limitations of both explanation methods, they can be exploited in a complementary way: while the model-level explanation method can be used to identify the most important features affecting predictions, the dataset-level explanation method can be used to investigate how they affect predictions.

Obviously, both methods strongly depend on model performance: if a model is not reliable, then the model-level explanation method will not be able to identify some features that may be important for event predictions, while the dataset-level explanation method can lead to misinterpretations of feature behavior.

Here, we performed both dataset- and model-level time-dependent explanations on the test set (419 samples) by comparing ML and DL survival models and using SurvSHAP. Notably, all results in the following are presented in relation to the survival function.

We note that generating explanations for all test samples is computationally intensive for Deep Learning models. Also, there are minimal performance differences between the CT and LH models. For these reasons, we opted for the LH model for the explanation phase due to its computational optimizations, which enable the generation of comprehensive explanations within a reasonable time. Here, the issue related to the permutation method for model-level explanations was mitigated by filtering the features based on the correlation coefficients, as described in Section 2.

• Dataset-Level Explanations
  We computed the SurvSHAP values on the test data, retrieving and ranking the most important features.

As depicted on the left side of Figure 6, relative to CPH, age emerges as the most important feature, followed by years of CPAP, renal dysfunction, COP, BMI categories, sex, and anemia.

Similarly, in Figure 7, age remains a predominant feature, yet the LH model assigns almost the same importance (with minimum differences) to the other ones. In more detail, AHI comes in second, followed by renal dysfunction, ${\mathrm{SaO}}_2$ min, years of CPAP, COPD, and anemia. In the LH model, these features exhibit greater importance in terms of their average contributions to the predictions compared to the CPH model. The reason behind the differences in feature importance can be attributed to the non-linear relationships between features and targets discovered by the LH model, which preferred numeric features over categorical ones in some cases. The temporal trends related to the model outcomes are depicted on the right side of Figure 6 and Figure 7. Interestingly, in the CPH model, after ∼9 years (∼110 months), years of CPAP, sex, and BMI categories gained importance with respect to renal dysfunction, anemia, and COPD, respectively.

A similar behavior was seen in the LH model, where a discretization effect on predictions was observed. Although ${\mathrm{SaO}}_2$ ranked fourth in terms of feature contribution and initially did not appear to be very important, in the last part of the observation period, it gained more and more importance as the number of months increased, becoming the third most important feature in the last part of the observation period.

Finally, although in the CPH model, all features had similar contributions in the final observation period, we can observe a set of features consisting of AHI and ${\mathrm{SaO}}_2$ and another composed of renal dysfunction, COPD, and years of CPAP.

While in classical XAI approaches the variable importance is presented as a statistical measure reflecting the overall importance, the exploitation of SurvSHAP makes the variable importance change over time, thus leading to a different evaluation of the impact of predictions at time t.

This dynamic understanding enables clinicians to assign different weights to features based on their evolving importance throughout all stages of patient care, contributing to a more personalized and effective patient care approach.

Furthermore, we investigated the individual contribution of each feature for each subject by plotting a bee swarm plot, as depicted in Figure 8 and Figure 9.

Here, each data sample corresponds to several points in the plot according to its feature value. Aggregated SurvSHAP(t) values close to 0 typically indicate a minimal impact on the survival function. The above figures confirm that the models interpreted the feature values in a coherent way. High values of features considered risk factors or comorbidities in medicine contributed negatively to survival, while high values related to protective factors contributed positively. This alignment with medical understanding underscores the models’ coherent interpretation of feature values and their impact on survival outcomes.

• 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. Cox proportional hazards matrix with features sorted by hazard ratio in descending order.

Variable	Coef.	Exp. Coef.	Se. Coef.	Z	Pr$..$ z $..$
Malignancy	1.83	6.21	0.29	6.30	2.89 × ${10}^{-10}$
Idiopathic dilated cardiomyopathy	1.41	4.08	0.48	2.92	0.00
COPD	0.53	1.70	0.14	3.81	1.37 × ${10}^{-4}$
Renal dysfunction	0.56	1.75	0.15	3.81	1.37 × ${10}^{-4}$
Age	1.37	3.94	0.18	7.75	9.28 × ${10}^{-15}$
Anemia	0.40	1.49	0.15	2.73	0.01
Atrial fibrillation	0.37	1.45	0.23	1.64	0.10
Heart failure	0.35	1.41	0.28	1.24	0.22
Diabetes	0.11	1.12	0.14	0.78	0.43
Sex	0.30	1.35	0.16	1.81	0.07
Hypertension	0.02	1.02	0.13	0.15	0.88
Cardiovascular disease	−0.01	0.99	0.19	−0.06	0.95
BMI categories	−0.07	0.93	0.06	−1.12	0.26
Cholesterol categories	−0.08	0.92	0.10	−0.83	0.41
Valvular disease	−0.02	0.98	0.42	−0.05	0.96
SaO2 min	−0.01	0.99	0.01	−1.16	0.25
AHI	−0.01	0.99	0.00	−1.54	0.12
Years of CPAP	−0.13	0.87	0.03	−5.06	4.11 × ${10}^{-7}$

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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.

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 ∼150 to ∼170 months (∼12.5 to 14 years). In addition, starting from ∼125 months, the ${\mathrm{SaO}}_2$ min started to gain more and more importance until it became the most important feature. Comparing Figure 10 and Figure 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 related to OSA pathology, such as the minimum oxygenation level (${\mathrm{SaO}}_2$ min) and apnea-hypopnea index (AHI), which gained importance over the observation period. In light of this, the use of SurvSHAP may lead clinicians to assess that, for parity of performances, the results of the LH model are more reliable here. Ultimately, the results of the LH model are also more useful since the AHI and ${\mathrm{SaO}}_2$ min are directly derived from polysomnography and more relevant features compared to the presence of malignancies or dilated cardiomyopathy, which are rarer conditions in the population (thus making these data not always applicable).

A summary of the differences between the CPH and LH models from an XAI(t) perspective is depicted in

Table 5. Summary of differences between the CPH and LH models. DCM—dilated cardiomyopathy.

	Performance Metrics		Dataset-Level Explanations (419 Test Samples)			Model-Level Explanations
	C-Index	Brier Score	Relevant Features	Prevailing Features	Observations	Relevant Features	Prevailing Features	Observations
CPH	0.81	0.10	Age, years of CPAP, renal dysfunction, COPD, BMI, sex, anemia.	Age	Huge gap in age contribution with respect to other features; Feature contributions have few variations over time.	Age, years of CPAP, renal dysfunction, COPD, anemia, malignancy, DCM.	Age, followed by years of CPAP.	Age still prevails over other features; Malignancy and DCM are not strictly related to mortality, and they are not very common in the population.
LH	0.77	0.11	Age, AHI, renal dysfunction, ${\mathrm{SaO}}_2\min$, years of CPAP, COPD, anemia.	Age	Moderated gap between age contribution and other features; These ones provide the same contribution, but it varies over time.	Age, years of CPAP, renal dysfunction, COPD, anemia, AHI, ${\mathrm{SaO}}_2\min$.	All features have the same contribution.	The relevant features have almost the same contribution. AHI and ${\mathrm{SaO}}_2\min$ are more useful and accessible in the OSA context.

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5. Conclusions

In this study, we provided a full pipeline for training and comparing survival ML and DL models, and we leveraged SurvSHAP to enrich our understanding of model predictions over time.

In the context of survival analysis, this work aimed to address two crucial issues: (i) identifying the most reliable model for survival prediction among models performing equally well, and (ii) determining and analyzing the variable importance according to the observation time t.

We focused on the domain of obstructive sleep apnea, with a particular emphasis on the role of comorbidities. However, any other pathology may be considered as a use case for performing explainable survival analysis with the SurvSHAP method. In addition, we made comparisons among Machine Learning and Deep Learning survival models.

The performance and reliability of the AI survival model in the OSA context are affected by several factors, such as data quality and quantity, features relevant to OSA pathology, and AI model architecture. Here, we demonstrated how complex survival models are particularly capable of identifying the features that most accurately describe the pathology under examination.

After performing data exploration and preparation operations, we trained four survival ML models and five survival DL models. Then, we selected the best-performing models according to evaluation metrics computed on the test set. Finally, we leveraged SurvSHAP algorithms and classified the explanations into two categories—dataset- and model-level explanations—to investigate the differences among the best models based on this study’s observation time.

The achieved results illustrated the differences among the values of feature importance retrieved by ML and DL models, highlighting how the models identify the most important variables and how they affect the predictions over time. We demonstrated how time-dependent explainability, i.e., XAI(t), helps understand the model’s behavior and the interpretation of data feature contributions to the survival function. Our XAI-based analysis showed that although the CPH model exhibited slightly higher performance, the LH model proved to be more reliable and clinically useful for supporting the follow-up of patients with OSA.

Such a dynamic evaluation and understanding can enhance the clinical decision-making process during the follow-up stages of the rehabilitation process by assisting physicians in assigning different weights to the features related to patients’ conditions based on their evolving importance over time.