  Genomic data are subject to various sources of confounding, such as
demographic variables, biological heterogeneity, and batch effects. To identify
genomic features associated with a variable of interest in the presence of
confounders, the traditional approach involves fitting a confounder-adjusted
regression model to each genomic feature, followed by multiplicity correction.
This study shows that the traditional approach was sub-optimal and proposes a
new two-dimensional false discovery rate control framework (2dFDR+) that
provides significant power improvement over the conventional method and applies
to a wide range of settings. 2dFDR+ uses marginal independence test statistics
as auxiliary information to filter out less promising features, and FDR control
is performed based on conditional independence test statistics in the remaining
features. 2dFDR+ provides (asymptotically) valid inference from samples in
settings where the conditional distribution of the genomic variables given the
covariate of interest and the confounders is arbitrary and completely unknown.
To achieve this goal, our method requires the conditional distribution of the
covariate given the confounders to be known or can be estimated from the data.
We develop a new procedure to simultaneously select the two cutoff values for
the marginal and conditional independence test statistics. 2dFDR+ is proved to
offer asymptotic FDR control and dominate the power of the traditional
procedure. Promising finite sample performance is demonstrated via extensive
simulations and real data applications.
