  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.
