  Accurate power and sample size estimation are crucial to the design and
analysis of genetic association studies. When analyzing a binary trait via
logistic regression, important covariates such as age and sex are typically
included in the model. However, their effects are rarely properly considered in
power or sample size computation during study planning. Unlike when analyzing a
continuous trait, the power of association testing between a binary trait and a
genetic variant depends, explicitly, on covariate effects, even under the
assumption of gene-environment independence. Earlier work recognizes this
hidden factor but implemented methods are not flexible. We thus propose and
implement a generalized method for estimating power and sample size for
(discovery or replication) association studies of binary traits that a)
accommodates different types of non-genetic covariates E, b) deals with
different types of G-E relationships, and c) is computationally efficient.
Extensive simulation studies show that the proposed method is accurate and
computationally efficient for both prospective and retrospective sampling
designs with various covariate structures. A proof-of-principle application
focused on the understudied African sample in the UK Biobank data. Results show
that, in contrast to studying the continuous blood pressure trait, when
analyzing the binary hypertension trait ignoring covariate effects of age and
sex leads to overestimated power and underestimated replication sample size.
