  In this work, we propose a semi-supervised triply robust inductive transfer
learning (STRIFLE) approach, which integrates heterogeneous data from label
rich source population and label scarce target population to improve the
learning accuracy in the target population. Specifically, we consider a high
dimensional covariate shift setting and employ two nuisance models, a density
ratio model and an imputation model, to combine transfer learning and
surrogate-assisted semi-supervised learning strategies organically and achieve
triple robustness. While the STRIFLE approach requires the target and source
populations to share the same conditional distribution of outcome Y given both
the surrogate features S and predictors X, it allows the true underlying model
of Y|X to differ between the two populations due to the potential covariate
shift in S and X. Different from double robustness, even if both nuisance
models are misspecified or the distribution of Y|S,X is not the same between
the two populations, when the transferred source population and the target
population share enough similarities, the triply robust STRIFLE estimator can
still partially utilize the source population, and it is guaranteed to be no
worse than the target-only surrogate-assisted semi-supervised estimator with
negligible errors. These desirable properties of our estimator are established
theoretically and verified in finite-sample via extensive simulation studies.
We utilize the STRIFLE estimator to train a Type II diabetes polygenic risk
prediction model for the African American target population by transferring
knowledge from electronic health records linked genomic data observed in a
larger European source population.
