  Regression adjustment is broadly applied in randomized trials under the
premise that it usually improves the precision of a treatment effect estimator.
However, previous work has shown that this is not always true. To further
understand this phenomenon, we develop a unified comparison of the asymptotic
variance of a class of linear regression-adjusted estimators. Our analysis is
based on the classical theory for linear regression with heteroscedastic errors
and thus does not assume that the postulated linear model is correct. For a
completely randomized binary treatment, we provide sufficient conditions under
which some regression-adjusted estimators are guaranteed to be more
asymptotically efficient than others. We explore other settings such as general
treatment assignment mechanisms and generalized linear models, and find that
the variance dominance phenomenon no longer occurs.
