When was a "negative" clinical trial big enough? How many patients you needed depends on what you found

Abstract

"Negative" clinical trials that conclude that neither of the treatments is superior are often criticized for having enrolled too few patients. These criticisms usually are based on formal sample size calculations that compute the numbers of patients required prospectively, as if the trial had not yet been carried out. We suggest that this "prospective" sample size calculation is incorrect, for once the trial is over we have "hard" data from which to estimate the actual size of the treatment effect. We can either generate confidence limits around the observed treatment effect or retrospectively compare it with the effect hypothesized before the trial. If the observed effect is small, the risk of the false-negative conclusion (and the sample size required to draw negative or equivalency conclusions) is often much less than that generated by the "prospective" calculation.