# The P-LOOP Estimator: Covariate Adjustment for Paired Experiments

## TL;DR

The paper introduces the P-LOOP estimator, a flexible covariate adjustment method for paired experiments that improves treatment effect estimation by automatically deciding whether to incorporate pairing information during imputation.

## Contribution

It proposes a novel covariate adjustment estimator for paired experiments that adaptively accounts for pairing, enhancing precision over existing methods.

## Key findings

- P-LOOP improves estimation precision in paired experiments.
- The method automatically decides to include pairing in covariate adjustment.
- Flexible use of prediction algorithms like lasso or random forests.

## Abstract

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.