  In paired experiments, participants are grouped into pairs with similar
characteristics, and one observation from each pair is randomly assigned to
treatment. Because of both the pairing and the randomization, the treatment and
control groups should be well balanced; however, there may still be small
chance imbalances. It may be possible to improve the precision of the treatment
effect estimate by adjusting for these imbalances. Building on related work for
completely randomized experiments, we propose the P-LOOP (paired leave-one-out
potential outcomes) estimator for paired experiments. We leave out each pair
and then impute its potential outcomes using any prediction algorithm. The
imputation method is flexible; for example, we could use lasso or random
forests. While similar methods exist for completely randomized experiments,
covariate adjustment methods in paired experiments are relatively understudied.
A unique trade-off exists for paired experiments, where it can be unclear
whether to factor in pair assignments when making adjustments. We address this
issue in the P-LOOP estimator by automatically deciding whether to account for
the pairing when imputing the potential outcomes. By addressing this trade-off,
the method has the potential to improve precision over existing methods.
