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Statistical power is often a concern for clustered RCTs due to varianceinflation from design effects and the high cost of adding study clusters (suchas hospitals, schools, or communities). While covariate pre-specification isthe preferred approach for improving power to estimate regression-adjustedaverage treatment effects (ATEs), further precision gains can be achievedthrough covariate selection once primary outcomes have been collected. Thisarticle uses design-based methods underlying clustered RCTs to develop aLasso-OLS hybrid procedure for the post-hoc selection of covariates and ATEestimation that avoids model overfitting and lack of transparency. In the firststage, lasso estimation is conducted using cluster-level averages, whereasymptotic normality is proved using a new central limit theorem for finitepopulation regression estimators. In the second stage, ATEs and design-basedstandard errors are estimated using weighted least squares with the first stagelasso covariates. This nonparametric approach applies to continuous, binary,and discrete outcomes. Simulation results indicate that Type 1 errors of thesecond stage ATE estimates are near nominal values and standard errors are neartrue ones, although somewhat conservative with small samples. The method isdemonstrated using data from a large, federally funded clustered RCT testingthe effects of school-based programs promoting behavioral health.

A Lasso-OLS Hybrid Approach to Covariate Selection and Average Treatment Effect Estimation for Clustered RCTs Using Design-Based Methods