  Electronic health records (EHRs) offer great promises for advancing precision
medicine and, at the same time, present significant analytical challenges.
Particularly, it is often the case that patient-level data in EHRs cannot be
shared across institutions (data sources) due to government regulations and/or
institutional policies. As a result, there are growing interests about
distributed learning over multiple EHRs databases without sharing patient-level
data. To tackle such challenges, we propose a novel communication efficient
method that aggregates the local optimal estimates, by turning the problem into
a missing data problem. In addition, we propose incorporating posterior samples
of remote sites, which can provide partial information on the missing
quantities and improve efficiency of parameter estimates while having the
differential privacy property and thus reducing the risk of information
leaking. The proposed approach, without sharing the raw patient level data,
allows for proper statistical inference and can accommodate sparse regressions.
We provide theoretical investigation for the asymptotic properties of the
proposed method for statistical inference as well as differential privacy, and
evaluate its performance in simulations and real data analyses in comparison
with several recently developed methods.
