Deciding whether follow-up studies have replicated findings in a preliminary large-scale omics study

Significance The use of big data is becoming a central way of discovering knowledge in modern science. Large amounts of potential findings are screened to discover the few real ones. To verify these discoveries a follow-up study is often conducted, wherein only the promising discoveries are followed up. Such follow-up studies are common in genomics, in proteomics, and in other areas where high-throughput methods are used. We show how to decide whether promising findings from the preliminary study are replicated by the follow-up study, keeping in mind that the preliminary study involved an extensive search for rare true signal in a vast amount of noise. The proposal computes a number, the r value, to quantify the strength of replication.