  Based on technological advances in sensing modalities, randomized trials with
primary outcomes represented as high-dimensional vectors have become
increasingly prevalent. For example, these outcomes could be week-long
time-series data from wearable devices or high-dimensional neuroimaging data,
such as from functional magnetic resonance imaging. This paper focuses on
randomized treatment studies with such high-dimensional outcomes characterized
by sparse treatment effects, where interventions may influence a small number
of dimensions, e.g., small temporal windows or specific brain regions.
Conventional practices, such as using fixed, low-dimensional summaries of the
outcomes, result in significantly reduced power for detecting treatment
effects. To address this limitation, we propose a procedure that involves
subset selection followed by inference. Specifically, given a potentially large
set of outcome summaries, we identify the subset that captures treatment
effects, which requires only one call to the Lasso, and subsequently conduct
inference on the selected subset. Via theoretical analysis as well as
simulations, we demonstrate that our method asymptotically selects the correct
subset and increases statistical power.
