Computing exact one-sided confidence limits for treatment effect in clinical trials

Abstract

One standard summary of a clinical trial is a confidence limit for the effect of the treatment. Unfortunately, standard approximate limits may have poor frequentist properties, even for quite large sample sizes. It has been known since Buehler (1957) that an imperfect confidence limit can be adjusted to have exact coverage. These “tight” limits are the gold standard frequentist confidence limit. Computing tight limits requires exact calculation of certain tail probabilities and optimisation of potentially erratic functions of the nuisance parameter. Naive implementation is both computationally unreliable and highly burdensome, and perhaps explains why they are not in common use. For clinical..