  Autism Spectrum Disorder (ASD) is a neurodevelopmental condition associated
with difficulties with social interactions, communication, and restricted or
repetitive behaviors. To characterize ASD, investigators often use functional
connectivity derived from resting-state functional magnetic resonance imaging
of the brain. However, participants' head motion during the scanning session
can induce motion artifacts. Many studies remove scans with excessive motion,
which can lead to drastic reductions in sample size and introduce selection
bias. To avoid such exclusions, we propose an estimand inspired by causal
inference methods that quantifies the difference in average functional
connectivity in autistic and non-ASD children while standardizing motion
relative to the low motion distribution in scans that pass motion quality
control. We introduce a nonparametric estimator for motion control, called
MoCo, that uses all participants and flexibly models the impacts of motion and
other relevant features using an ensemble of machine learning methods. We
establish large-sample efficiency and multiple robustness of our proposed
estimator. The framework is applied to estimate the difference in functional
connectivity between 132 autistic and 245 non-ASD children, of which 34 and 126
pass motion quality control. MoCo appears to dramatically reduce motion
artifacts relative to no participant removal, while more efficiently utilizing
participant data and accounting for possible selection biases relative to the
na\"ive approach with participant removal.
