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I would like to make an adjustment on a baseline variable (which has a small imbalance).This is a post hoc adjustment (I recognize, however, the limits of this adjustment which has not been pre-specified). It is a randomized clinical trial. I am wondering if analysis of variance is more appropriate here than linear regression. What factor should be taken into account to decide which type of analysis to use?

However I have some missing value for the baseline variable that I shoud adjust for. I hypothesize missing data randomly.The variable to be adjusted for is a continuous variable. Is it a good idea to categorize the variable and transform into a non-responding category, the individuals for whom we have NA ? or should we do an imputation by the mean and leave the variable in numeric?

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It is not permissible to adjust for observed imbalances. This causes a bias and inflates the standard error for treatment. Covariate adjustment needs to be pre-specified. Failure to pre-specify covariate adjustment as the primary analysis is a failure to understand how to maximize statistical power for an RCT. Details are here.

NEVER categorize a continuous variable.

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