Baseline differences in RCT: Which variables (if any) should be included as covariates? I recently completed a study whereby I randomly assigned participants to one of two treatment groups.  I tested participants at baseline, immediately post-intervention, 1 months, and 4 months on a somewhat large number of outcome variables. I was planning on running several mixed ANOVAs to examine group x time interactions.  Some of the comparisons will be 2 (group) x 2 (time: baseline and post-intervention) comparisons and some will be 2 (group) x 3 (time: baseline, 1 month, 4 month) comparisons.
Before beginning my analyses, I compared the two treatment groups on all baseline variables.  I found that the groups differ on 4 baseline variables if I use an alpha level of .05  or 2 baseline variables if I use an alpha level of .01 to compare the groups.  
I have two questions about this:


*

*What alpha level should I be using to compare the groups at
baseline? I was thinking an alpha level of .01 because I am
comparing the two groups on 24 baseline characteristics and I
thought I should chose a more stringent alpha level than .05 to
reduce family-wise error rate seeing as a large number of tests are
being performed, but from my readings it seems most people use .05. 
What do you recommend?

*What do I do about these differences? I could include these
variables as covariates, but my sample size is quite small and using
4 covariates does not seem appropriate (which is also partly why I
am favouring only accepting differences if they are significant at
the .05 level)
Any help on this would be very much appreciated!
 A: As Stephen Senn has written, it is not appropriate to compare baseline distributions in a randomized study.  The way I like to talk about this is to ask the question "where do you stop?", i.e., how many other baseline covariates should you go back and try to retrieve?  You will find counter-balancing covariates if you look hard enough.
The basis for chosing a model is not post-hoc differences but rather apriori subject matter knowledge about which variables are likely to be important predictors of the response variable.  The baseline version of the response variable is certainly a dominating predictor but there are others that are likely to be important.  The goal is explaining explainable heterogeneity in the outcome to maximize precision and power.  There is almost no role for statistical significance testing in model formulation.
A pre-specified model will take care of chance differences on the variables that matter - those predicting the outcome.
A: Normally what you should care about in comparing the two groups at baseline is not so much statistical significance of differences but size of differences:  is any of these differences large enough to matter to the study? Large enough to affect the group comparisons and variable relationships that are the focus of the research? Large enough that adjusting for it (by using it as a covariate) is necessary?  
Now, your case is a little bit interesting in that, even with random assignment, you've got 4 out of 24 variables showing differences significant at the .05 level (17% instead of the expected 5%).  That may seem concerning for your randomization process or some other aspect of the study.  But theoretically, if the randomization were done flawlessly and there was no attrition in either group afterwards, a result this extreme or more so should occur 2.4% of the time, based on 24!/(4!(24-4)!) (.05^4) (.95^(24-4)).  That is not really such a rare occurrence after all.  What you have could well be a set of random differences.  I'd stick with judging based on magnitude of differences.
A: +1 to @FrankHarrell.  I might add one small point.  If you randomly assigned your participants to the groups, any 'significant' differences in covariate values prior to intervention are necessarily type I errors.  
