Improved Precision in Estimating Average Treatment Effects

The Average Treatment Effect (ATE) is a global measure of the effectiveness of an experimental treatment intervention. Classical methods of its estimation either ignore relevant covariates or do not fully exploit them. Moreover, past work has considered covariates as fixed. We present a method for improving the precision of the ATE estimate: the treatment and control responses are estimated via a regression, and information is pooled between the groups to produce an asymptotically unbiased estimate; we subsequently justify the random X paradigm underlying the result. Standard errors are derived, and the estimator's performance is compared to the traditional estimator. Conditions under which the regression-based estimator is preferable are detailed, and a demonstration on real data is presented.

[1]  William G. Cochran,et al.  Sampling Techniques, 3rd Edition , 1963 .

[2]  D. Freedman.  Bootstrapping Regression Models , 1981 .

[3]  R. Lalonde.  Evaluating the Econometric Evaluations of Training Programs with Experimental Data , 1984 .

[4]  T. Speed,et al.  On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9 , 1990 .

[5]  A. Tsiatis,et al.  Efficiency Study of Estimators for a Treatment Effect in a Pretest–Posttest Trial , 2001 .

[6]  J. Fox.  Bootstrapping Regression Models , 2002 .

[7]  V. Gebski,et al.  Inclusion of patients in clinical trial analysis: the intention‐to‐treat principle , 2003, The Medical journal of Australia.

[8]  Donald B. Rubin,et al.  Comment : Neyman ( 1923 ) and Causal Inference in Experiments and Observational Studies , 2007 .

[9]  D. Freedman.  Statistical Models and Causal Inference: On Regression Adjustments in Experiments with Several Treatments , 2008, 0803.3757.

[10]  D. Freedman,et al.  Weighting Regressions by Propensity Scores , 2008, Evaluation review.

[11]  M. Davidian,et al.  Covariate adjustment for two‐sample treatment comparisons in randomized clinical trials: A principled yet flexible approach , 2008, Statistics in medicine.

[12]  David A. Freedman,et al.  On regression adjustments to experimental data , 2008, Adv. Appl. Math..

[13]  Gary King,et al.  Misunderstandings between experimentalists and observationalists about causal inference , 2008 .

[14]  W. Lin,et al.  Agnostic notes on regression adjustments to experimental data: Reexamining Freedman's critique , 2012, 1208.2301.

[15]  Luke W. Miratrix,et al.  Adjusting treatment effect estimates by post‐stratification in randomized experiments , 2013 .

[16]  A. Buja,et al.  A Conspiracy of Random X and Model Violation against Classical Inference in Linear Regression , 2013 .

[17]  Too Kya Lau,et al.  Statistics 3rd Edition , 2015 .