  A major task in genetic studies is to identify genes related to human
diseases and traits to understand functional characteristics of genetic
mutations and enhance patient diagnosis. Besides marginal analyses of
individual genes, identification of gene pathways, i.e., a set of genes with
known interactions that collectively contribute to specific biological
functions, can provide more biologically meaningful results. Such gene pathway
analysis can be formulated into a high-dimensional two-sample testing problem.
Due to the typically limited sample size of gene expression datasets, most
existing two-sample tests may have compromised powers because they ignore or
only inefficiently incorporate the auxiliary pathway information on gene
interactions. We propose T2-DAG, a Hotelling's $T^2$-type test for detecting
differentially expressed gene pathways, which efficiently leverages the
auxiliary pathway information on gene interactions through a linear structural
equation model. We establish the asymptotic distribution of the test statistic
under pertinent assumptions. Simulation studies under various scenarios show
that T2-DAG outperforms several representative existing methods with
well-controlled type-I error rates and substantially improved powers, even with
incomplete or inaccurate pathway information or unadjusted confounding effects.
We also illustrate the performance of T2-DAG in an application to detect
differentially expressed KEGG pathways between different stages of lung cancer.
