Covariate adjustment and prediction of mean response in randomised trials

Analyses of randomised trials are often based on regression models which adjust for baseline covariates, in addition to randomised group. Based on such models, one can obtain estimates of the marginal mean outcome for the population under assignment to each treatment, by averaging the model based predictions across the empirical distribution of the baseline covariates in the trial. We identify under what conditions such estimates are consistent, and in particular show that for canonical generalised linear models, the resulting estimates are always consistent. We show that a recently proposed variance estimator underestimates the true variance when the baseline covariates are not fixed in repeated sampling, and provide a simple adjustment to remedy this. We also describe an alternative semiparametric estimator which is consistent even when the outcome regression model used is misspecified. The different estimators are compared through simulations and application to a recently conducted trial in asthma.