A High Performance Cox Proportional Hazards Model for Large Scale Survival Analysis

The Cox proportional hazards (CPH) model remains the preeminent methodological framework for survival analysis. However, evaluating the partial likelihood function and resolving tied event times on massive big health data presents a severe computational bottleneck. These algorithmic inefficiencies often prohibit the analysis of massive cohorts and restrict the deployment of dynamic, real-time predictive models on low power edge devices.

To overcome these computational limitations, we developed c-cox, a high performance, open source implementation written natively in C. The architecture leverages OpenMP for the multi-threaded parallelization of complex risk set evaluations and integrates the GNU Scientific Library (GSL) to ensure highly efficient, numerically stable matrix operations during Newton-Raphson optimization. The package provides a comprehensive statistical framework supporting standard and time-varying multivariable covariates, robust variance estimation for clustered data, and cumulative incidence functions (CIF).

Rigorous empirical validations were conducted utilizing clinical datasets, specifically the United Kingdom Biobank (UK Biobank) and China Health and Retirement Longitudinal Study (CHARLS) cohorts, alongside massive synthetic stress tests comprising up to one million observations. Across all computational experiments, c-cox maintained strict statistical concordance with industry standard Python (lifelines) and R (survival ) packages, generating mathematically identical regression coefficients, hazard ratios, and robust standard errors. Crucially, c-cox achieved exponential reductions in runtime by processing a one million row cohort in a mere 2.72 seconds, compared to 8.64 seconds in R and over 268 minutes in Python.

The c-cox framework consistently delivers uncompromising statistical reliability while affording orders of magnitude improvements in computational speed and energy 1 efficiency, aligning directly with Green AI principles. Its self-contained, dependency free architecture guarantees reproducible numerics for stringent regulatory audit trails. Ultimately, this profound efficiency leap democratizes large scale survival analysis and enables decentralized, privacy preserving execution directly on severely resource-constrained embedded systems.