SurvReLU: Inherently Interpretable Survival Analysis via Deep ReLU Networks

TL;DR

SurvReLU tackles the interpretability gap in survival analysis by introducing a deliberately structured deep ReLU network that partitions the input space into tree-like regions while preserving neural expressiveness. It models the hazard rate with a learnable function over activation patterns, $h_{\boldsymbol{x}}(t)=g_{\theta}(\boldsymbol{x},t)$, and integrates covariates at every layer to enable non-axis-aligned splits. A statistically-driven topology optimization using log-rank tests prunes the network to a compact, interpretable tree, and the model can be trained end-to-end with either continuous-time or discrete-time survival losses. Empirical results on simulated and real datasets show competitive performance with state-of-the-art deep models and superior interpretability, offering a practical path for deployable survival analysis that blends interpretability and predictive power.

Abstract

Survival analysis models time-to-event distributions with censorship. Recently, deep survival models using neural networks have dominated due to their representational power and state-of-the-art performance. However, their "black-box" nature hinders interpretability, which is crucial in real-world applications. In contrast, "white-box" tree-based survival models offer better interpretability but struggle to converge to global optima due to greedy expansion. In this paper, we bridge the gap between previous deep survival models and traditional tree-based survival models through deep rectified linear unit (ReLU) networks. We show that a deliberately constructed deep ReLU network (SurvReLU) can harness the interpretability of tree-based structures with the representational power of deep survival models. Empirical studies on both simulated and real survival benchmark datasets show the effectiveness of the proposed SurvReLU in terms of performance and interoperability. The code is available at \href{https://github.com/xs018/SurvReLU}{\color{magenta}{ https://github.com/xs018/SurvReLU}}.

Figures (4)

• Figure 1: Illustrative example to approximate a linear hazard function: $h(\boldsymbol{x})=x_0 + 2 x_1$: (a) the network structure of the proposed SurvReLU network, (b) the decision boundary at each partitioning/layer, and (c) the resulting tree structures, respectively.
• Figure 2: The change of rank ratio of matrix $\boldsymbol{O}$ over epochs.
• Figure 3: (a) The predicted risk function versus the true Gaussian risk function on the simulated Gaussian dataset. (b) and (c): The resulting tree structures of SurvReLU w/ and w/o the proposed topology optimization in Sec. \ref{['sec:2.2']} on METABRIC dataset.
• Figure 4: Ablations on number of layers $L$ (Left) and sparsity of $\boldsymbol{W}$ (Right) using the simulated Gaussian dataset.