Survival Analysis models usually output functions (survival or hazard functions) rather than point predictions like regression and classification models. This makes the explanations of such models a challenging task, especially using the Shapley values. We propose SurvSHAP, a new model-agnostic algorithm to explain survival models that predict survival curves. The algorithm is based on discovering patterns in the predicted survival curves, the output of the survival model, that would identify significantly different survival behaviors, and utilizing a proxy model and SHAP method to explain these distinct survival behaviors. Experiments on synthetic and real datasets demonstrate that the SurvSHAP is able to capture the underlying factors of the survival patterns. Moreover, SurvSHAP results on the Cox Proportional Hazard model are compared with the weights of the model to show that we provide faithful overall explanations, with more fine-grained explanations of the sub-populations. We also illustrate the wrong model and explanations learned by a Cox model when applied to heterogeneous sub-populations. We show that a non-linear machine learning survival model with SurvSHAP can better model the data and provide better explanations than linear models.

The development of black-box survival models has created a need for methods that explain their outputs, just as in the case of traditional machine learning methods. Survival models usually predict functions rather than point estimates. This special nature of their output makes it more difficult to explain their operation. We propose a method to generate plausible counterfactual explanations for survival models. The method supports two options that handle the special nature of survival models' output. One option relies on the Survival Scores, which are based on the area under the survival function, which is more suitable for proportional hazard models. The other one relies on Survival Patterns in the predictions of the survival model, which represent groups that are significantly different from the survival perspective. This guarantees an intuitive well-defined change from one risk group (Survival Pattern) to another and can handle more realistic cases where the proportional hazard assumption does not hold. The method uses a Particle Swarm Optimization algorithm to optimize a loss function to achieve four objectives: the desired change in the target, proximity to the explained example, likelihood, and the actionability of the counterfactual example. Two predictive maintenance datasets and one medical dataset are used to illustrate the results in different settings. The results show that our method produces plausible counterfactuals, which increase the understanding of black-box survival models. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2024.

The Concordance Index (C-index) is a commonly used metric in Survival Analysis for evaluating the performance of a prediction model. This paper proposes a decomposition of the C-index into a weighted harmonic mean of two quantities: one for ranking observed events versus other observed events, and the other for ranking observed events versus censored cases. This decomposition enables a more fine-grained analysis of the strengths and weaknesses of survival prediction methods. The usefulness of this decomposition is demonstrated through benchmark comparisons against state-of-the-art and classical models, together with a new variational generative neural-network-based method (SurVED), which is also proposed in this paper. Performance is assessed using four publicly available datasets with varying levels of censoring. The analysis using the C-index decomposition and synthetic censoring shows that deep learning models utilize the observed events more effectively than other models, allowing them to keep a stable C-index in different censoring levels. In contrast, classical machine learning models deteriorate when the censoring level decreases due to their inability to improve on ranking the events versus other events. © 2024 The Author(s)

In this work, we use an Evolutionary Algorithm (EA) to discover a novel Neural Network (NN) regression-based survival loss function with the aim of improving the C-index performance. Our contribution is threefold; firstly, we propose an evolutionary meta-learning algorithm SAGA$_{loss}$ for optimizing a neural-network regression-based loss function that maximizes the C-index; our algorithm consistently discovers specialized loss functions that outperform MSCE. Secondly, based on our analysis of the evolutionary search results, we highlight a non-intuitive insight that signifies the importance of the non-zero gradient for the censored cases part of the loss function, a property that is shown to be useful in improving concordance. Finally, based on this insight, we propose MSCE$_{Sp}$, a novel survival regression loss function that can be used off-the-shelf and generally performs better than the Mean Squared Error for censored cases. We performed extensive experiments on 19 benchmark datasets to validate our findings. © 2024 is held by the owner/author(s).

Time-To-Event (TTE) modeling using survival analysis in industrial settings faces the challenge of premature replacements of machine components, which leads to bias and errors in survival prediction. Typically, TTE survival data contains information about components and if they had failed or not up to a certain time. For failed components, the time is noted, and a failure is referred to as an event. A component that has not failed is denoted as censored. In industrial settings, in contrast to medical settings, there can be considerable uncertainty in an event; a component can be replaced before it fails to prevent operation stops or because maintenance staff believe that the component is faulty. This shows up as “no fault found” in warranty studies, where a significant proportion of replaced components may appear fault-free when tested or inspected after replacement.

In this work, we propose an expectation-maximization-like method for discovering such premature replacements in survival data. The method is a two-phase iterative algorithm employing a genetic algorithm in the maximization phase to learn better event assignments on a validation set. The learned labels through iterations are accumulated and averaged to be used to initialize the following expectation phase. The assumption is that the more often the event is selected, the more likely it is to be an actual failure and not a “no fault found”.

Experiments on synthesized and simulated data show that the proposed method can correctly detect a significant percentage of premature replacement cases.

The Cox Proportional Hazards (CPH) model has long been the preferred survival model for its explainability. However, to increase its predictive power beyond its linear log-risk, it was extended to utilize deep neural networks, sacrificing its explainability. In this work, we explore the potential of self-explaining neural networks (SENN) for survival analysis. We propose a new locally explainable Cox proportional hazards model, named CoxSE, by estimating a locally-linear log-hazard function using the SENN. We also propose a modification to the Neural additive (NAM) models hybrid with SENN, named CoxSENAM, which enables the control of the stability and consistency of the generated explanations. 

Several experiments using synthetic and real datasets are presented, benchmarking CoxSE and CoxSENAM against a NAM-based model, a DeepSurv model explained with SHAP, and a linear CPH model. The results show that, unlike the NAM-based model, the SENN-based model can provide more stable and consistent explanations while maintaining the predictive power of the black-box model. The results also show that, due to their structural design, NAM-based models demonstrate better robustness to non-informative features. Among the models, the hybrid model exhibits the best robustness.