| Summary: | We develop statistical methods for tackling two important problems in genetic association studies. First, we propose
a Bayesian approach to overcome the winner's curse in genetic studies. Second, we consider a Bayesian latent variable
model for analyzing longitudinal family data with pleiotropic phenotypes.
Winner's curse in genetic association studies refers to the estimation bias of the reported odds ratios (OR) for an associated
genetic variant from the initial discovery samples. It 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 the low power studies.
We investigate the performance of the method with simulations
and applications to four real data examples.
Pleiotropy occurs when a single genetic factor influences multiple quantitative or qualitative phenotypes, and it is present in
many genetic studies of complex human traits. The longitudinal family studies combine the features of longitudinal studies
in individuals and cross-sectional studies in families. Therefore, they provide more information about the genetic and environmental factors associated with the trait of interest. We propose a Bayesian latent variable modeling approach to model multiple
phenotypes simultaneously in order to detect the pleiotropic effect and allow for longitudinal and/or family data. An efficient MCMC
algorithm is developed to obtain the posterior samples by using hierarchical centering and parameter expansion techniques.
We apply spike and slab prior methods to test whether the phenotypes are significantly associated with the latent disease status. We compute
Bayes factors using path sampling and discuss their application in testing the significance of factor loadings and the indirect fixed effects. We examine the performance of our methods via extensive simulations and
apply them to the blood pressure data from a genetic study of type 1 diabetes (T1D) complications.
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