Adaptive Budgets in Clinical Trials.

We consider situations where a drug developer gets access to additional financial resources when a promising result has been observed in a pre-planned interim analysis during a clinical trial which should lead to the registration of the drug. First the option that the drug developer completely puts the additional resources into increasing the second stage sample size has been investigated. If investors invest the more the larger the observed interim effect, this may not be a reasonable strategy: Then additional sample sizes are applied when the conditional power is already very large and hardly any impact on the overall power can be expected. Nevertheless, further reducing the type II error rate in promising situations may be of interest for a drug developer. In a second step, sample size was based on a utility function including the reward of registration (which was allowed to depend on the observed effect size at the end of the trial) and sampling costs. Utility as a function of the sample size may have more than one local maximum, one of them at the lowest per group sample size. For small effects an optimal strategy could be to apply the smallest sample size accepted by regulators.