On Identifying Minimum Efficacious Doses in Combination Drug Trials.

To determine that a combination drug is effective, the FDA requires demonstration that the combination itself is effective and that each component makes a contribution to the claimed effect. In a study with at least one component known to be effective at the considered doses, these regulatory requirements can be satisfied by showing that the combination is superior to each component. We term such a combination an efficacious combination. In a dose-response study involving combination drugs, one of which is known to be effective, we are interested in detecting those combinations which are efficacious, and for which no lower dose combination is also efficacious. We term these combinations the minimum efficacious dose set and our goal is to estimate this set. Our procedure requires first identifying all possible minimum efficacious dose sets and the corresponding hypotheses for a given design. Next, the proper testing order based on a graph representation is established and the hypotheses are tested using the "average" test under the closed testing principle. This procedure is shown to have strong control of overall error rate. The power of this procedure is studied by simulation.