  We present a Transfer Causal Learning (TCL) framework when target and source
domains share the same covariate/feature spaces, aiming to improve causal
effect estimation accuracy in limited data. Limited data is very common in
medical applications, where some rare medical conditions, such as sepsis, are
of interest. Our proposed method, named \texttt{$\ell_1$-TCL}, incorporates
$\ell_1$ regularized TL for nuisance models (e.g., propensity score model); the
TL estimator of the nuisance parameters is plugged into downstream average
causal/treatment effect estimators (e.g., inverse probability weighted
estimator). We establish non-asymptotic recovery guarantees for the
\texttt{$\ell_1$-TCL} with generalized linear model (GLM) under the sparsity
assumption in the high-dimensional setting, and demonstrate the empirical
benefits of \texttt{$\ell_1$-TCL} through extensive numerical simulation for
GLM and recent neural network nuisance models. Our method is subsequently
extended to real data and generates meaningful insights consistent with medical
literature, a case where all baseline methods fail.
