In genetic association analyses, it is often desired to analyze data from
multiple potentially-heterogeneous subgroups. The amount of expected
heterogeneity can vary from modest (as might typically be expected in a
meta-analysis of multiple studies of the same phenotype, for example), to large
(e.g. a strong gene-environment interaction, where the environmental exposure
defines discrete subgroups). Here, we consider a flexible set of Bayesian
models and priors that can capture these different levels of heterogeneity.
Recently-developed genotype imputation methods are a powerful tool for
detecting untyped genetic variants that affect disease susceptibility in
genetic association studies. However, existing imputation methods require
individual-level genotype data, whereas, in practice, it is often the case that
only summary data are available. For example, this may occur because, for
reasons of privacy or politics, only summary data are made available to the
research community at large; or because only summary data are collected, as in
DNA pooling experiments.