A highly significant difference in baseline characteristics: the play of chance or evidence of a more selective game?

The previous article in this series discussed the reasons why statistical significance tests are rarely appropriate when comparing baseline characteristics in randomised clinical trials [1]. We quoted guidance from the European Agency for the Evaluation of Medicinal Products (EMEA): "Statistical testing for baseline imbalance has no role in a trial where the handling of the randomisation and blinding has been fully satisfactory." But the second part of that statement should not be ignored, and deserves further consideration. Thus, we do not suggest that one should never carry out significance tests on baseline characteristics. In this article, we will give one example in which significance testing was of major importance in revealing a problem in a trial, and provide an example of a situation in which significance testing of baseline characteristics should perhaps be recommended as routine. Many years ago, in the mid-1990s, one of us (P.F.) received a phone call from the World Health Organization: "Peter, can you visit Beijing next week? We have an ongoing randomised clinical trial of intrauterine contraceptive devices, but one of our consultants has noticed that there seems to be a very highly significant difference in ages. The women in one of the treatment arms are younger than in the other arms."