A clinical trial designed to show that an experimental treatment E is similar to a control treatment S in a specified direction is a one-sided equivalence or similarity trial--in the terminology of the International Conference on Harmonisation, a non-inferiority trial (ICH, 1998). We design such a study to show that E is not worse than S (often an accepted or standard treatment) by as much as a pre-specified margin theta0. The quantity theta0 can be either a difference or ratio of an appropriate outcome in individuals treated with E and S. A critical issue is whether one can conclude from a non-inferiority trial that E is effective. Closely related is an appropriate choice of theta0, which should be substantially less than the estimated effect of S if available from previous studies; theta0 should also be acceptable to clinicians, either because of advantages of E or because a difference or ratio less than theta0 is considered unimportant clinically. Another possible approach for showing that E is effective is to estimate its effect compared with placebo from historical data. If previous studies that consistently show an effect of S are not available, alternative study designs should be considered. Findings of superiority or non-inferiority of E, when the study was planned to show the other, are possible and may be supportable. A finding that E is at the same time statistically significantly worse than S and "non-inferior" to S should not be a problem, if the criterion theta0 is appropriate and this possibility was considered in the protocol. Various sorts of non-adherence may make treatments appear similar, even if they are not. In particular, random non-adherence of study participants to the assigned treatment regimen may cause an intention-to-treat analysis to give a misleading result of similarity. Thus, maintaining a high degree of adherence to protocol is especially important in an equivalence or non-inferiority trial. Interim analysis does not present statistical problems in these trials; early stopping may not be wise in many cases, however, because strong interim evidence for non-inferiority may actually be an indicator that E is superior to S.