  Evidence-based decision making often relies on meta-analyzing multiple
studies, which enables more precise estimation and investigation of
generalizability. Integrative analysis of multiple heterogeneous studies is,
however, highly challenging in the ultra high dimensional setting. The
challenge is even more pronounced when the individual level data cannot be
shared across studies, known as DataSHIELD constraint (Wolfson et al., 2010).
Under sparse regression models that are assumed to be similar yet not identical
across studies, we propose in this paper a novel integrative estimation
procedure for data-Shielding High-dimensional Integrative Regression (SHIR).
SHIR protects individual data through summary-statistics-based integrating
procedure, accommodates between study heterogeneity in both the covariate
distribution and model parameters, and attains consistent variable selection.
Theoretically, SHIR is statistically more efficient than the existing
distributed approaches that integrate debiased LASSO estimators from the local
sites. Furthermore, the estimation error incurred by aggregating derived data
is negligible compared to the statistical minimax rate and SHIR is shown to be
asymptotically equivalent in estimation to the ideal estimator obtained by
sharing all data. The finite-sample performance of our method is studied and
compared with existing approaches via extensive simulation settings. We further
illustrate the utility of SHIR to derive phenotyping algorithms for coronary
artery disease using electronic health records data from multiple chronic
disease cohorts.
