Differentially Private Regression for Discrete-Time Survival Analysis

TL;DR

This paper introduces differentially private methods for discrete-time survival regression, extending existing techniques and proposing a new MCMC-based sampling approach to ensure privacy with high accuracy.

Contribution

It develops novel differentially private regression algorithms for survival analysis, including extensions of Output and Objective Perturbation and a new MCMC sampling method.

Findings

Achieves comparable accuracy to non-private models.

Provides formal differential privacy guarantees.

Outperforms existing privacy-preserving methods in survival analysis.

Abstract

In survival analysis, regression models are used to understand the effects of explanatory variables (e.g., age, sex, weight, etc.) to the survival probability. However, for sensitive survival data such as medical data, there are serious concerns about the privacy of individuals in the data set when medical data is used to fit the regression models. The closest work addressing such privacy concerns is the work on Cox regression which linearly projects the original data to a lower dimensional space. However, the weakness of this approach is that there is no formal privacy guarantee for such projection. In this work, we aim to propose solutions for the regression problem in survival analysis with the protection of differential privacy which is a golden standard of privacy protection in data privacy research. To this end, we extend the Output Perturbation and Objective Perturbation approaches which are originally proposed to protect differential privacy for the Empirical Risk Minimization (ERM) problems. In addition, we also propose a novel sampling approach based on the Markov Chain Monte Carlo (MCMC) method to practically guarantee differential privacy with better accuracy. We show that our proposed approaches achieve good accuracy as compared to the non-private results while guaranteeing differential privacy for individuals in the private data set.