  Randomized controlled trials (RCTs) are the gold standard for causal
inference, but they are often powered only for average effects, making
estimation of heterogeneous treatment effects (HTEs) challenging. Conversely,
large-scale observational studies (OS) offer a wealth of data but suffer from
confounding bias. Our paper presents a novel framework to leverage OS data for
enhancing the efficiency in estimating conditional average treatment effects
(CATEs) from RCTs while mitigating common biases. We propose an innovative
approach to combine RCTs and OS data, expanding the traditionally used control
arms from external sources. The framework relaxes the typical assumption of
CATE invariance across populations, acknowledging the often unaccounted
systematic differences between RCT and OS participants. We demonstrate this
through the special case of a linear outcome model, where the CATE is sparsely
different between the two populations. The core of our framework relies on
learning potential outcome means from OS data and using them as a nuisance
parameter in CATE estimation from RCT data. We further illustrate through
experiments that using OS findings reduces the variance of the estimated CATE
from RCTs and can decrease the required sample size for detecting HTEs.
