A Lasso approach to covariate selection and average treatment effect estimation for clustered RCTs using design-based methods

Statistical power is often a concern for clustered randomized control trials (RCTs) due to variance inflation from design effects and the high cost of adding study clusters (such as hospitals, schools, or communities). While covariate pre-specification can improve power for estimating regression-adjusted average treatment effects (ATEs), further precision gains can be achieved through covariate selection once primary outcomes have been collected. This article uses design-based methods underlying clustered RCTs to develop Lasso methods for the post-hoc selection of covariates for ATE estimation that avoids a lack of transparency and model overfitting. Our focus is on two-stage estimators: in the first stage, Lasso estimation is conducted using data on cluster-level averages or sums, and in the second stage, standard ATE estimators are adjusted for covariates using the first-stage Lasso results. We discuss l1{l}_{1} consistency of the estimated Lasso coefficients, asymptotic normality of the ATE estimators, and design-based variance estimation. The nonparametric approach applies to continuous, binary, and discrete outcomes. We present simulation results and demonstrate the method using data from a federally funded clustered RCT testing the effects of school-based programs promoting behavioral health.