Adjust for covariables even in randomized experiments? Randomization does not guarantee balance in an experiment. Balance is the prerequisite for causality, so theres a potential for using regression adjustment in randomized experiments. This is somewhat counterintuitive, at least to me. It is described fairly well here. It appears to be relevant only for continuous outcomes.
Whats a good strategy on this matter?
Pitfalls? Situations when it is pivotal to do covariable adjustment?
I aim for a general discussion on these strategies.
 A: This has been extensively written about by several authors, e.g. Senn in his book on Statistical Issues in Drug Development. In short, ommitting covariates that are correlated for outcomes has different effects for different types of outcomes and models:


*

*for continuous outcomes, it results in more variable estimates of the
treatment effect, inflated standard errors and wider confidence
intervals,

*for categorical outcomes (binary, survival) the effect depends on the
used link function. For a logit or log link-function ommitting    the
covariates leads to regression coefficients for the treatment effect being biased towards zero (no treatment difference). Although the confidence intervals may be narrower.


If you specify the outcome covariate relationship correctly, both an analysis with and without covariates keeps the type I error for testing the null hypothesis of no treatment effect (no necessarily true for non-inferiority hypotheses for categorical outcomes). However, for both continuous or categorical outcomes ommitting important covariates typically means a loss of power.
In practice, it is standard practice for continuous outcomes to adjust at a minimum for the baseline of the outcome variable and often other covariates judged to be important predictors of outcomes. Analyses without adjustment are typically not presented, because they are widely accepted to be of close to zero value. For non-continuous outcomes, practices vary a bit more and there is often nothing as obvious to use as a covariate as a baseline of the outcome variable (e.g. in the case of analyzing time to death, when everyone is hopefully alive at baseline). However, when there are very important predictors (e.g. history of previous events known to predict previous events in a survival analysis, number - or log-number - of events in the previous year in a count data analysis etc.) it is also very wasteful to not adjust for this information.
A: It has been shown that covariate adjustment increases precision and reduces bias, eg by Lee.
However, it is not commonly performed.
In addition, what would you do in a scenario in which unadjusted analysis in not significant whilst the adjusted one is? And what, in the most extreme scenario, the unadjusted one goes significantly one way and the adjusted significantly in another?
Probably you would discard the trial and call for another (larger) one.
That's precisely why, in my opinion, covariate adjustment in randomized trials is not routinely performed.
A: One can distinguish a number of scenarios:


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If the outcome is continuous and it has also been measured at baseline then it is usually included as a covariate in order to account for individual differences.  The alternative is just to analyse change scores but that is less flexible since in effect it fixes the regression coefficient at unity


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Various design features may need to be included such as the strata if randomisation was stratified and centre if it is a multi-centre trial.
To see why strata are included consider the limiting case where each stratum has exactly two participants one randomised to each arm.
Would you carry out a paired or independent $t$-test?  If paired then you are considering that strata should be included in the model


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If there is substantial loss to follow-up any variable which predicts missingness could be included at least in a secondary sensitivity analysis.


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Any variable which is poorly balanced between arms could be included in a secondary sensitivity analysis



Of course all this should be in the protocol which you registered before you started recruitment.
