HDSI Causal Seminar: Fan Li, Duke University

September 7, 2023 Covariate Adjustment in Randomized Experiments with Missing Data Covariate adjustment is often conducted in randomized experiments to increase precision of the treatment effect estimate. However, a main barrier for implementing covariate adjustment is the ubiquitous presence of missing data. This paper focuses on the theory of covariate adjustment with missing outcomes with or without missing covariates. We begin with the case with missingness in only outcome data, and establish the theoretical properties of regression adjustment and estimated-propensity-score weighting, as two commonly used covariate-adjustment techniques, under correctly specified outcome missingness model. The main findings are twofold. First, covariate adjustment by estimated-propensity-score weighting ensures efficiency gain over unadjusted inference, and including more covariates in adjustment never harms asymptotic efficiency. Second, deviating from the theory when all data are observed, regression adjustment by fully interacted specification no longer ensures efficiency gain when the true outcome model is not linear in covariates, such that the asymptotic equivalence between regression adjustment and estimated-propensity-score weighting breaks down. We then extend to the case with missingness in both outcomes and covariates, and establish the value of partially observed covariates for securing additional efficiency. Based on these findings, we recommend a simple algorithm for covariate adjustment with incomplete outcome and/or covariate data that ensures asymptotic efficiency gain over unadjusted inference as long as the outcome missingness model is correctly specified. This is a joint work with Anqi Zhao and Peng Ding. Speaker: Fan Li, Professor, Department of Statistical Science and Department of Biostatistics and Bioinformatics, Duke University