  Survival analysis studies the statistical properties of the time until an
event of interest occurs. It has been commonly used to study the effectiveness
of medical treatments or the lifespan of a population. However, survival
analysis can potentially leak confidential information of individuals in the
dataset. The state-of-the-art techniques apply ad-hoc privacy-preserving
mechanisms on publishing results to protect the privacy. These techniques
usually publish sanitized and randomized answers which promise to protect the
privacy of individuals in the dataset but without providing any formal
mechanism on privacy protection. In this paper, we propose private mechanisms
for parametric survival analysis with Weibull distribution. We prove that our
proposed mechanisms achieve differential privacy, a robust and rigorous
definition of privacy-preservation. Our mechanisms exploit the property of
local sensitivity to carefully design a utility function which enables us to
publish parameters of Weibull distribution with high precision. Our
experimental studies show that our mechanisms can publish useful answers and
outperform other differentially private techniques on real datasets.
