  Parameter estimates for associated genetic variants, report ed in the initial
discovery samples, are often grossly inflated compared to the values observed
in the follow-up replication samples. This type of bias is a consequence of the
sequential procedure in which the estimated effect of an associated genetic
marker must first pass a stringent significance threshold. We propose a
hierarchical Bayes method in which a spike-and-slab prior is used to account
for the possibility that the significant test result may be due to chance. We
examine the robustness of the method using different priors corresponding to
different degrees of confidence in the testing results and propose a Bayesian
model averaging procedure to combine estimates produced by different models.
The Bayesian estimators yield smaller variance compared to the conditional
likelihood estimator and outperform the latter in studies with low power. We
investigate the performance of the method with simulations and applications to
four real data examples.
