Privacy Protection for Flexible Parametric Survival Models

Data privacy is a major concern in modern society. In this work, we propose two solutions to the privacy-preserving problem of regression models on medical data. We focus on flexible parametric models which are powerful alternatives to the well-known Cox regression model. For the first approach, we propose a sampling mechanism which guarantees differential privacy for flexible parametric survival models. We first transform the likelihood function of the models to guarantee that likelihood values are bounded. We then use a Hamiltonian Monte-Carlo sampler to sample a random parameter vector from the posterior distribution. As a result, this random vector satisfies the requirement for differential privacy. For the second approach, as predictions with high accuracy and high confidence are very important for medical applications, we propose a mechanism which protects privacy by randomly perturbing the posterior distribution. We can then use the sampler to draw multiple random samples of the perturbed posterior to estimate the credible intervals of the parameters. The proposed mechanism does not guarantee differential privacy for the perturbed posterior. However, it allows controlling the contribution of each individual data record to the posterior. In the worst case scenario, when all data records are revealed except the target data record, the random noise added to the posterior would make it extremely difficult to obtain the target data record. The experiments conducted on two real datasets show that our proposed approaches outperform state-of-the-art methods in predicting the survival rate of individuals.