Optimal Cox regression under federated differential privacy: coefficients and cumulative hazards
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| Format: | Preprint |
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2025
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| _version_ | 1866914444034965504 |
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| author | Hung, Elly K. H. Yu, Yi |
| author_facet | Hung, Elly K. H. Yu, Yi |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_19640 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal Cox regression under federated differential privacy: coefficients and cumulative hazards Hung, Elly K. H. Yu, Yi Statistics Theory Methodology 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. |
| title | Optimal Cox regression under federated differential privacy: coefficients and cumulative hazards |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2508.19640 |