标题： 在联邦差分隐私下的最优Cox回归：系数和累计风险 显示英文标题

标题： Optimal Cox regression under federated differential privacy: coefficients and cumulative hazards

摘要： 我们研究了分布式生存分析中的两个基础问题：在联邦差分隐私约束下估计Cox回归系数和累积危险函数，允许每个服务器的样本大小和隐私预算不同。 为了量化隐私的基本成本，我们推导了极小极大下界，并给出了匹配（至多多项对数因子）的上界。 特别是，为了估计累积危险函数，我们设计了一个私有的基于树的算法用于非参数积分估计。 我们的结果揭示了在隐私和非隐私速率之间的服务器级别相变，以及在对分布式数据子集施加隐私约束时估计精度的降低。 为了应对部分公共信息的情况，我们还考虑了一个放松的差分隐私框架，并提供了相应的极小极大分析。 据我们所知，这是生存分析中对部分公共数据的首次处理，并确立了精度无提升的现象。 最后，我们进行了广泛的数值实验，配套的R包FDPCox验证了我们的理论结果。 这些实验还包括一个完全交互的算法，具有更紧密的隐私组合，展示了改进的估计精度。 显示英文摘要

摘要： We study two foundational problems in distributed survival analysis: estimating Cox regression coefficients and cumulative hazard functions, under federated differential privacy constraints, allowing for heterogeneous per-sever sample sizes and privacy budgets. To quantify the fundamental cost of privacy, we derive minimax lower bounds along with matching (up to poly-logarithmic factors) upper bounds. In particular, to estimate the cumulative hazard function, we design a private tree-based algorithm for nonparametric integral estimation. Our results reveal server-level phase transitions between the private and non-private rates, as well as the reduced estimation accuracy from imposing privacy constraints on distributed subsets of data. To address scenarios with partially public information, we also consider a relaxed differential privacy framework and provide a corresponding minimax analysis. To our knowledge, this is the first treatment of partially public data in survival analysis, and it establishes a no-gain in accuracy phenomenon. Finally, we conduct extensive numerical experiments, with an accompanying R package FDPCox, validating our theoretical findings. These experiments also include a fully-interactive algorithm with tighter privacy composition, which demonstrates improved estimation accuracy.