  Genome-wide association studies (GWAS) are widely used to discover genetic
variants associated with diseases. To control false positives, all findings
from GWAS need to be verified with additional evidences, even for associations
discovered from a high power study. Replication study is a common verification
method by using independent samples. An association is regarded as true
positive with a high confidence when it can be identified in both primary study
and replication study. Currently, there is no systematic study on the behavior
of positives in the replication study when the positive results of primary
study are considered as the prior information.
  In this paper, two probabilistic measures named Reproducibility Rate (RR) and
False Irreproducibility Rate (FIR) are proposed to quantitatively describe the
behavior of primary positive associations (i.e. positive associations
identified in the primary study) in the replication study. RR is a conditional
probability measuring how likely a primary positive association will also be
positive in the replication study. This can be used to guide the design of
replication study, and to check the consistency between the results of primary
study and those of replication study. FIR, on the contrary, measures how likely
a primary positive association may still be a true positive even when it is
negative in the replication study. This can be used to generate a list of
potentially true associations in the irreproducible findings for further
scrutiny. The estimation methods of these two measures are given. Simulation
results and real experiments show that our estimation methods have high
accuracy and good prediction performance.
