Estimation Efficiency With Omitted Covariates in Generalized Linear Models

Abstract

Abstract Although omitting covariates associated with the response in generalized linear models can yield seriously biased estimates of the effects of the included covariates, in certain settings there is no bias. This article considers the effect of omitted covariates on the efficiency of the estimated effects of the included covariates in these cases. I consider the case where the omitted covariate is independent of the included covariates, as in studies with randomized treatment assignment, as well as the case where the omitted covariate is correlated with the included but not a confounder. I present expressions to show that omitting covariates associated with the response and independent of the included covariate can result in serious efficiency losses for estimates of the effects of the included covariates. I also present expressions to show that omitting nonconfounding covariates can lead to efficiency gains. These expressions also quantify the magnitude of estimation efficiency with omitted covariates. The findings suggest that to improve the efficiency of estimated covariate effects of interest, analysts of randomized clinical trial data should adjust for covariates that are strongly associated with the outcome, and that analysts of observational data should not adjust for covariates that do not confound the association of interest.