  High-throughput screening (HTS) is a large-scale hierarchical process in
which a large number of chemicals are tested in multiple stages. Conventional
statistical analyses of HTS studies often suffer from high testing error rates
and soaring costs in large-scale settings. This article develops new
methodologies for false discovery rate control and optimal design in HTS
studies. We propose a two-stage procedure that determines the optimal numbers
of replicates at different screening stages while simultaneously controlling
the false discovery rate in the confirmatory stage subject to a constraint on
the total budget. The merits of the proposed methods are illustrated using both
simulated and real data. We show that the proposed screening procedure
effectively controls the error rate and the design leads to improved detection
power. This is achieved at the expense of a limited budget.
