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I believe that for ANOVA unbalanced means unequal groups. But for randomised controlled trials unbalanced seems to mean something like groups of different characteristics despite randomisation. So in case of RCTs does unbalanced simply mean unlucky randomisation? Nothing to do with group sizes? What's the definition of an unbalanced RCT?

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  • $\begingroup$ The cheeky one liner: Unbalanced = hard maths. Balanced = easy maths. :) $\endgroup$ – probabilityislogic Jun 18 '11 at 3:44
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I have always seen "balance" for a clinical trial described as you suggested - that there is some difference in the covariate patterns between the treatment and control arm. Note however, that there are ways this can arise beyond just misfortune during randomization. Two that come to mind quickly are:

  1. Time-varying confounders. If confounding arises after randomization, randomization does not protect against it.

  2. Informative censoring. If one set of people are more likely due to treatment to drop out - say a particular subgroup tends to have trouble complying with trial protocol when in the treatment arm - the treatment and control arms will be unbalanced even under situations of perfect randomization.

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Balanced designs have really just one goal, orthogonal treatment effects. Orthogonal design lowers the risk of unobservables sneaking into your effect estimates in an uneven way. See: http://www1.umn.edu/statsoft/doc/statnotes/stat06.txt for an excellent discussion of this topic.

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