Differential Privacy Techniques for Healthcare Data

Abstract

This paper analyzes techniques to enable differential privacy by adding Laplace noise to healthcare data. First, as healthcare data contain natural constraints for data to take only integral values, we show that drawing only integral values does not provide differential privacy. In contrast, rounding randomly drawn values to the nearest integer provides differential privacy. Second, when a variable is constructed using two other variables, noise must be added to only one of them. Third, if the constructed variable is a fraction, then noise must be added to its constituent private variables, and not to the fraction directly. Fourth, the accuracy of analytics following noise addition increases with the privacy budget, $\epsilon$, and the variance of the independent variable. Finally, the accuracy of analytics following noise addition increases disproportionately with an increase in the privacy budget when the variance of the independent variable is greater. Using actual healthcare data, we provide evidence supporting the two predictions on the accuracy of data analytics. Crucially, to enable accuracy of data analytics with differential privacy, we derive a relationship to extract the slope parameter in the original dataset using the slope parameter in the noisy dataset.