Regression Adjustment for Ratios of Treatment Effects in Randomized Experiments

We study regression adjustment for ratios of treatment effects in completely randomized experiments. The existing literature adjusts the numerator and denominator separately, but this approach misses the efficiency target, loss of which matters more when richer or high-dimensional covariate information and flexible or regularized prediction methods are used to pursue further efficiency gains. We propose a two-step estimator that directly predicts the relevant transformed outcome. Using cross-fitting, our method accommodates high-dimensional first-stage prediction while keeping the final adjustment fixed-dimensional, thereby avoiding instability from a growing number of adjustment covariates. We further develop persistence-based LASSO theory that does not require sparsity, permits more covariates than observations, and allows cross-validated penalty selection under prediction-level conditions. For additional efficiency gains, our augmented two-step estimator nests the benchmark adjustment spaces and is therefore asymptotically no less efficient than the benchmark estimators, while its feasible conservative variance estimator satisfies the same efficiency ordering. Simulation studies and a real-data analysis demonstrate that our proposed estimator performs better than existing methods.