Change from baseline and analysis of covariance revisited

The case for preferring analysis of covariance (ANCOVA) to the simple analysis of change scores (SACS) has often been made. Nevertheless, claims continue to be made that analysis of covariance is biased if the groups are not equal at baseline. If the required equality were in expectation only, this would permit the use of ANCOVA in randomized clinical trials but not in observational studies. The discussion is related to Lord's paradox. In this note, it is shown, however that it is not a necessary condition for groups to be equal at baseline, not even in expectation, for ANCOVA to provide unbiased estimates of treatment effects. It is also shown that although many situations can be envisaged where ANCOVA is biased it is very difficult to imagine circumstances under which SACS would then be unbiased and a causal interpretation could be made.