Differentially private hypothesis testing in survival analysis

2026-05-16

AI Summary

This study addresses the absence of differentially private hypothesis testing methods for right-censored data in survival analysis by establishing the first finite-sample theoretical framework in this domain. It proposes differentially private partial likelihood ratio and score tests for Cox regression coefficients and develops a private distributed two-sample test for the cumulative hazard function. Theoretical analysis derives minimax lower bounds that precisely characterize the impact of privacy constraints on statistical efficiency. The proposed methods maintain validity under finite-sample settings while guaranteeing differential privacy, and simulation studies empirically demonstrate the trade-off between privacy cost and testing power.

Abstract

Survival analysis is widely used in applications involving sensitive individual-level data, yet differentially private hypothesis testing for right-censored data remains largely undeveloped. We initiate a finite-sample theory of private hypothesis testing in survival analysis applications. For Cox regression coefficients, we develop private partial-likelihood-ratio and score-type tests, including a private calibration procedure for the rejection threshold. For cumulative hazard functions, we propose a private distributed two-sample test. Across these problems, we prove differential privacy and finite-sample testing guarantees, as well as minimax lower bounds. Our results identify when privacy is statistically negligible, when it dominates the testing rate, and where optimal private rates for testing in semiparametric survival models remain open. This theoretical analysis is accompanied by numerical experiments on simulated data.

Problem

• differential privacy
• survival analysis
• hypothesis testing
• right-censored data
• Cox regression

Innovation

• differential privacy
• survival analysis
• hypothesis testing
• Cox regression
• finite-sample guarantees