{"ID":2877515,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.19640","arxiv_id":"2508.19640","title":"Optimal Cox regression under federated differential privacy: coefficients and cumulative hazards","abstract":"We study two foundational problems in distributed survival analysis under federated differential privacy (FDP): estimation of the Cox regression coefficients and of the cumulative baseline hazard functions, allowing for heterogeneous per-sever sample sizes and privacy budgets. To quantify the fundamental cost of privacy, we derive minimax lower bounds together with upper bounds that match up to poly-logarithmic factors for the regression coefficients, thereby revealing server-level phase transitions between private and non-private regimes. We also consider a relaxed differential privacy framework with partially public information. Our analysis shows that the role of public covariates depends strongly on the privacy model. For cumulative hazard estimation, we propose a private tree-based version of the Breslow estimator for nonparametric integral estimation under FDP. As a by-product, this leads to a private survival function estimator that attains a nearly minimax optimal rate. Numerical experiments, including a real-data application, support the theoretical findings. The proposed methods are implemented in an accompanying R package FDPCox.","short_abstract":"We study two foundational problems in distributed survival analysis under federated differential privacy (FDP): estimation of the Cox regression coefficients and of the cumulative baseline hazard functions, allowing for heterogeneous per-sever sample sizes and privacy budgets. To quantify the fundamental cost of privac...","url_abs":"https://arxiv.org/abs/2508.19640","url_pdf":"https://arxiv.org/pdf/2508.19640v2","authors":"[\"Elly K. H. Hung\",\"Yi Yu\"]","published":"2025-08-27T07:29:19Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"stat.ME\"]","methods":"[]","has_code":false}