Survival analysis is an essential statistics and machine learning field in various critical applications like medical research and predictive maintenance. In these domains understanding models' predictions is paramount. While machine learning techniques are increasingly applied to enhance the predictive performance of survival models, they simultaneously sacrifice transparency and explainability. 

Survival models, in contrast to regular machine learning models, predict functions rather than point estimates like regression and classification models. This creates a challenge regarding explaining such models using the known off-the-shelf machine learning explanation techniques, like Shapley Values, Counterfactual examples, and others.   

Censoring is also a major issue in survival analysis where the target time variable is not fully observed for all subjects. Moreover, in predictive maintenance settings, recorded events do not always map to actual failures, where some components could be replaced because it is considered faulty or about to fail in the future based on an expert's opinion. Censoring and noisy labels create problems in terms of modeling and evaluation that require to be addressed during the development and evaluation of the survival models.

Considering the challenges in survival modeling and the differences from regular machine learning models, this thesis aims to bridge this gap by facilitating the use of machine learning explanation methods to produce plausible and actionable explanations for survival models. It also aims to enhance survival modeling and evaluation revealing a better insight into the differences among the compared survival models.

In this thesis, we propose two methods for explaining survival models which rely on discovering survival patterns in the model's predictions that group the studied subjects into significantly different survival groups. Each pattern reflects a specific survival behavior common to all the subjects in their respective group. We utilize these patterns to explain the predictions of the studied model in two ways. In the first, we employ a classification proxy model that can capture the relationship between the descriptive features of subjects and the learned survival patterns. Explaining such a proxy model using Shapley Values provides insights into the feature attribution of belonging to a specific survival pattern. In the second method, we addressed the "what if?" question by generating plausible and actionable counterfactual examples that would change the predicted pattern of the studied subject. Such counterfactual examples provide insights into actionable changes required to enhance the survivability of subjects.

We also propose a variational-inference-based generative model for estimating the time-to-event distribution. The model relies on a regression-based loss function with the ability to handle censored cases. It also relies on sampling for estimating the conditional probability of event times. Moreover, we propose a decomposition of the C-index into a weighted harmonic average of two quantities, the concordance among the observed events and the concordance between observed and censored cases. These two quantities, weighted by a factor representing the balance between the two, can reveal differences between survival models previously unseen using only the total Concordance index. This can give insight into the performances of different models and their relation to the characteristics of the studied data.

Finally, as part of enhancing survival modeling, we propose an algorithm that can correct erroneous event labels in predictive maintenance time-to-event data. we adopt an expectation-maximization-like approach utilizing a genetic algorithm to find better labels that would maximize the survival model's performance. Over iteration, the algorithm builds confidence about events' assignments which improves the search in the following iterations until convergence.

We performed experiments on real and synthetic data showing that our proposed methods enhance the performance in survival modeling and can reveal the underlying factors contributing to the explainability of survival models' behavior and performance.

Survival Analysis is a major sub-field of statistics that studies the time to an event, like a patient's death or a machine's failure. This makes survival analysis crucial in critical applications like medical studies and predictive maintenance. In such applications, safety is critical creating a demand for trustworthy models. Machine learning and deep learning techniques started to be used, spurred by the growing volume of collected data. While this direction holds promise for improving certain qualities, such as model performance, it also introduces new challenges in other areas, particularly model explainability. This challenge is general in machine learning due to the black-box nature of most machine learning models, especially deep neural networks (DNN). However, survival models usually output functions rather than point estimates like regression and classification models which makes their explainability even more challenging task. 

Other challenges also exist due to the nature of time-to-event data, such as censoring. This phenomenon happens due to several reasons, most commonly due to the limited study time, resulting in a considerable number of studied subjects not experiencing the event during the study. Moreover, in industrial settings, recorded events do not always correspond to actual failures. This is because companies tend to replace machine parts before their failure due to safety or cost considerations resulting in noisy event labels. Censoring and noisy labels create a challenge in building and evaluating survival models.    

This thesis addresses these challenges by following two tracks, one focusing on explainability and the other on improving performance. The two tracks eventually merge providing an explainable survival model while maintaining the performance of its black-box counterpart.

In the explainability track, we propose two post-hoc explanation methods based on what we define as Survival Patterns. These are patterns in the predictions of the survival model that represent distinct survival behaviors in the studied population. We propose an algorithm for discovering the survival patterns upon which the two post-hoc explanation methods rely. The first method, SurvSHAP, utilizes a proxy classification model that learns the relationship between the input space and the discovered survival patterns. The proxy model is then explained using the SHAP method resulting in per-pattern explanations. The second post-hoc method relies on finding counterfactual explanations that would change the decision of the survival model from one source survival pattern to another. The algorithm uses Particle Swarm Optimization (PSO) with a tailored objective function to guarantee certain explanation qualities in plausibility and actionability.

On the performance track, we propose a Variational Encoder-Decoder model for estimating the survival function using a sampling-based approach. The model is trained using a regression-based objective function that accounts for censored instances assisted with a differentiable lower bound of the concordance index (C-index). In the same work, we propose a decomposition of the C-index where we found out that it can be expressed as a weighted harmonic average of two quantities; one quantifies the concordance among the observed event cases and the other quantifies the concordance between observed events and censored cases. The two quantities are weighted by a factor that balances the contribution of event and censored cases to the total C-index. Such decomposition uncovers hidden differences among survival models that seem equivalent based on the C-index. We also used genetic programming to search for a regression-based loss function for survival analysis with an improved concordance ability. The search results uncovered an interesting phenomenon, upon which we propose the use of the continuously differentiable Softplus function instead of the sharp-cut Relu function for handling censored cases. Lastly in the performance track, we propose an algorithm for correcting erroneous observed event labels that can be caused by preventive maintenance activities. The algorithm adopts an iterative expectation-maximization-like approach utilizing a genetic algorithm to search for better event labels that can maximize a surrogate survival model's performance.

Finally, the two tracks merge and we propose CoxSE a Cox-based deep neural network model that provides inherent explanations while maintaining the performance of its black-box counterpart. The model relies on the Self-Explaining Neural Networks (SENN) and the Cox Proportional Hazard formulation. We also propose CoxSENAM, an enhancement to the Neural Additive Model (NAM) by adopting the NAM structure along with the SENN loss function and type of output. The CoxSENAM model demonstrated better explanations than the NAM-based model with enhanced robustness to noise.