  Development of comprehensive prediction models are often of great interest in
many disciplines of science, but datasets with information on all desired
features typically have small sample sizes. In this article, we describe a
transfer learning approach for building high-dimensional generalized linear
models using data from a main study that has detailed information on all
predictors, and from one or more external studies that have ascertained a more
limited set of predictors. We propose using the external dataset(s) to build
reduced model(s) and then transfer the information on underlying parameters for
the analysis of the main study through a set of calibration equations, while
accounting for the study-specific effects of certain design variables. We then
use a generalized method of moment (GMM) with penalization for parameter
estimation and develop highly scalable algorithms for fitting models taking
advantage of the popular glmnet package. We further show that the use of
adaptive-Lasso penalty leads to the oracle property of underlying parameter
estimates and thus leads to convenient post-selection inference procedures. We
conduct extensive simulation studies to investigate both predictive performance
and post-selection inference properties of the proposed method. Finally, we
illustrate a timely application of the proposed method for the development of
risk prediction models for five common diseases using the UK Biobank study,
combining baseline information from all study participants (500K) and recently
released high-throughout proteomic data (# protein = 1500) on a subset (50K) of
the participants.
