Survival-LCS: Rule-Based Survival Analysis without Proportional Hazard Assumptions

Survival analysis is widely utilized to model time-to-event data across biomedical, epidemiological, and engineering domains. However, traditional methods such as Cox regression impose strong assumptions, including proportional hazards, and are often inadequate for capturing complex, non-linear relationships in high-dimensional or heterogeneous data. Rule-based machine learning algorithms, such as "ExSTraCS," can interpretably model complex biomedical associations in classification tasks. This study extends ExSTraCS to the challenges of right-censored survival data to yield "Survival-LCS," the first rule-based survival analysis algorithm that additionally handles heterogeneous feature types and missing values and makes no assumptions about baseline hazard or survival time distributions. Survival-LCS is evaluated and compared across a variety of simulated genetic survival datasets covering distinct genetic architectures (additive, epistatic, heterogeneous, and univariate), censoring values, number of features, and survival distributions (random monotonic spline, Gamma, Gaussian, and Weibull) using Integrated Brier Scores and statistical significance testing. Results demonstrate that Survival-LCS reliably captures complex associations with survival outcomes, performing competitively with standard approaches, particularly in settings that challenge traditional models. This work highlights the capability of rule-based algorithms to be adapted as interpretable, assumption-free (i.e., data-driven) survival analysis methods, particularly in domains with higher-dimensional data or complex underlying associations.