  Distributed health data networks that use information from multiple sources
have drawn substantial interest in recent years. However, missing data are
prevalent in such networks and present significant analytical challenges. The
current state-of-the-art methods for handling missing data require pooling data
into a central repository before analysis, which may not be possible in a
distributed health data network. In this paper, we propose a privacy-preserving
distributed analysis framework for handling missing data when data are
vertically partitioned. In this framework, each institution with a particular
data source utilizes the local private data to calculate necessary intermediate
aggregated statistics, which are then shared to build a global model for
handling missing data. To evaluate our proposed methods, we conduct simulation
studies that clearly demonstrate that the proposed privacy-preserving methods
perform as well as the methods using the pooled data and outperform several
na\"ive methods. We further illustrate the proposed methods through the
analysis of a real dataset. The proposed framework for handling vertically
partitioned incomplete data is substantially more privacy-preserving than
methods that require pooling of the data, since no individual-level data are
shared, which can lower hurdles for collaboration across multiple institutions
and build stronger public trust.
