Researchers often include covariates when they analyze the results of randomized controlled trials (RCTs), valuing the increased precision of the estimates over the potential of inducing small-sample bias when doing so. In this paper, we develop a sufficient condition which ensures that the inclusion of covariates does not induce small-sample bias in the effect estimates. Using this result as a building block, we develop a novel approach that uses machine learning techniques to reduce the variance of the average treatment effect estimates while guaranteeing that the effect estimates remain unbiased. The framework also highlights how researchers can use data from outside the study sample to improve the precision of the treatment effect estimate by using the auxiliary data to better model the relationship between the covariates and the outcomes. We conclude with a simulation, which highlights the value of using the proposed approach.
Opper, Isaac M., Using Machine Learning Techniques to Improving Average Treatment Effect Estimates in Small-Scale Randomized Controlled Trials. Santa Monica, CA: RAND Corporation, 2020. https://www.rand.org/pubs/working_papers/WRA1004-1.html.
Opper, Isaac M., Using Machine Learning Techniques to Improving Average Treatment Effect Estimates in Small-Scale Randomized Controlled Trials, Santa Monica, Calif.: RAND Corporation, WR-A1004-1, 2020. As of October 06, 2021: https://www.rand.org/pubs/working_papers/WRA1004-1.html