  There are a number of well-established methods such as principal components
analysis (PCA) for automatically capturing systematic variation due to latent
variables in large-scale genomic data. PCA and related methods may directly
provide a quantitative characterization of a complex biological variable that
is otherwise difficult to precisely define or model. An unsolved problem in
this context is how to systematically identify the genomic variables that are
drivers of systematic variation captured by PCA. Principal components (and
other estimates of systematic variation) are directly constructed from the
genomic variables themselves, making measures of statistical significance
artificially inflated when using conventional methods due to over-fitting. We
introduce a new approach called the jackstraw that allows one to accurately
identify genomic variables that are statistically significantly associated with
any subset or linear combination of principal components (PCs). The proposed
method can greatly simplify complex significance testing problems encountered
in genomics and can be utilized to identify the genomic variables significantly
associated with latent variables. Using simulation, we demonstrate that our
method attains accurate measures of statistical significance over a range of
relevant scenarios. We consider yeast cell-cycle gene expression data, and show
that the proposed method can be used to straightforwardly identify
statistically significant genes that are cell-cycle regulated. We also analyze
gene expression data from post-trauma patients, allowing the gene expression
data to provide a molecularly-driven phenotype. We find a greater enrichment
for inflammatory-related gene sets compared to using a clinically defined
phenotype. The proposed method provides a useful bridge between large-scale
quantifications of systematic variation and gene-level significance analyses.
