Efficient two-stage sequential arrays of proof of concept studies for pharmaceutical portfolios.

Previous work has shown that individual randomized "proof-of-concept" (PoC) studies may be designed to maximize cost-effectiveness, subject to an overall PoC budget constraint. Maximizing cost-effectiveness has also been considered for arrays of simultaneously executed PoC studies. Defining Type III error as the opportunity cost of not performing a PoC study, we evaluate the common pharmaceutical practice of allocating PoC study funds in two stages. Stage 1, or the first wave of PoC studies, screens drugs to identify those to be permitted additional PoC studies in Stage 2. We investigate if this strategy significantly improves efficiency, despite slowing development. We quantify the benefit, cost, benefit-cost ratio, and Type III error given the number of Stage 1 PoC studies. Relative to a single stage PoC strategy, significant cost-effective gains are seen when at least one of the drugs has a low probability of success (10%) and especially when there are either few drugs (2) with a large number of indications allowed per drug (10) or a large portfolio of drugs (4). In these cases, the recommended number of Stage 1 PoC studies ranges from 2 to 4, tracking approximately with an inflection point in the minimization curve of Type III error.