  The introduction of data analytics into medicine has changed the nature of
patient treatment. In this, patients are asked to disclose personal information
such as genetic markers, lifestyle habits, and clinical history. This data is
then used by statistical models to predict personalized treatments. However,
due to privacy concerns, patients often desire to withhold sensitive
information. This self-censorship can impede proper diagnosis and treatment,
which may lead to serious health complications and even death over time. In
this paper, we present privacy distillation, a mechanism which allows patients
to control the type and amount of information they wish to disclose to the
healthcare providers for use in statistical models. Meanwhile, it retains the
accuracy of models that have access to all patient data under a sufficient but
not full set of privacy-relevant information. We validate privacy distillation
using a corpus of patients prescribed to warfarin for a personalized dosage. We
use a deep neural network to implement privacy distillation for training and
making dose predictions. We find that privacy distillation with sufficient
privacy-relevant information i) retains accuracy almost as good as having all
patient data (only 3\% worse), and ii) is effective at preventing errors that
introduce health-related risks (only 3.9\% worse under- or over-prescriptions).
