Interval estimates of the probability of toxicity at the maximum tolerated dose for small samples

Following on from the work of O'Quigley et al., we investigate the performance of interval estimates of the probability of toxicity following completion of a phase I clinical trial. Our particular focus is on very small sample sizes, not uncommon in phase I studies. Specifically, we study the situations for which the sample sizes are 12 or 16. Simulations are used to show that the coverage of the confidence intervals, even for very modest sample sizes, are close to nominal in most cases. Averaged over the range of situations considered, coverage rates are accurate for both sample sizes of 12 and 16. As for the larger sample size of 20, studied previously, it is possible to obtain further, albeit modest, improvements via the use of the Cornish-Fisher inversion.