Robustness to misspecification when adjusting for baseline in RCTs

It is well known that adjusting for one or more baseline covariates can increase statistical power in randomized controlled trials. One reason that adjusted analyses are not used more widely may be because researchers may be concerned that results may be biased if the baseline covariate(s)' effects are not modelled correctly in the regression model for outcome. For example, a continuous baseline covariate would by default be entered linearly in a regression model, but in truth it's effect on outcome may be non-linear. In this post we'll review an important result which shows that for continuous outcomes modelled with linear regression, this does not matter in terms of bias - we obtain unbiased estimates of treatment effect even if we mis-specify a baseline covariate's effect on outcome.

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