Non-inferiority trials: the 'at least as good as' criterion with dichotomous data.

The 'at least as good as' criterion, introduced by Laster and Johnson for a continuous response variate, is developed here for applications with dichotomous data. This approach is adaptive in nature, as the margin of non-inferiority is not taken as a fixed difference; it varies as a function of the positive control response. When the non-inferiority margin is referenced as a high fraction of the positive control response, the procedure is seen to be uniformly more efficient than the fixed margin approach, yielding smaller sample sizes when sizing non-inferiority trials under identically specified conditions. Extending this method to proportions is straightforward, but highlights special considerations in the design of non-inferiority trials versus superiority trials, including potential trade-offs in statistical efficiency and interpretability.