Bayesian Inference for Survival Analysis in Private Setting

Abstract

Survival analysis is particularly important for modeling the survival probability of patients in clinical research. In this paper, we propose a novel framework for the data privacy problem of estimating the survival function and hazard function using parametric models and flexible parametric models. Our proposed Sampling-A-Posterior (SAP) framework publishes a noisy posterior distribution which is guaranteed to be differentially private. This is different from traditional private approaches which publish a point estimate of the model. In the proposed SAP framework, we represent the likelihood function as a linear combination of basis functions and use the K-norm mechanism to publish the coordinate vector of the total likelihood function. The proposed framework can be applied to design differentially private mechanisms for parametric models and flexible parametric models in survival analysis. The experimental results have shown the effectiveness of the proposed framework on real survival datasets.