What is the probability of replicating a statistically significant association in genome-wide association studies?

The goal of genome-wide association studies (GWASs) is to discover genetic variants associated with diseases/traits. Replication is a common validation method in GWASs. We regard an association as true finding when it shows significance in both primary and replication studies. A question worth pondering is what is the probability of a primary association (i.e. a statistically significant association in the primary study) being validated in the replication study? This article systematically reviews the answers to this question from different points of view. As Bayesian methods can help us integrate out the uncertainty about the underlying effect of the primary association, we will mainly focus on the Bayesian view in this article. We refer the Bayesian replication probability as the replication rate (RR). We further describe an estimation method for RR, which makes use of the summary statistics from the primary study. We can use the estimated RR to determine the sample size of the replication study and to check the consistency between the results of the primary study and those of the replication study. We describe an R-package to estimate and apply RR in GWASs. Simulation and real data experiments show that the estimated RR has good prediction and calibration performance. We also use these data to demonstrate the usefulness of RR. The R-package is available at http://bioinformatics.ust.hk/RRate.html.