  In high throughput settings we inspect a great many candidate variables
(e.g., genes) searching for associations with a primary variable (e.g., a
phenotype). High throughput hypothesis testing can be made difficult by the
presence of systemic effects and other latent variables. It is well known that
those variables alter the level of tests and induce correlations between tests.
They also change the relative ordering of significance levels among hypotheses.
Poor rankings lead to wasteful and ineffective follow-up studies. The problem
becomes acute for latent variables that are correlated with the primary
variable. We propose a two-stage analysis to counter the effects of latent
variables on the ranking of hypotheses. Our method, called LEAPP, statistically
isolates the latent variables from the primary one. In simulations, it gives
better ordering of hypotheses than competing methods such as SVA and
EIGENSTRAT. For an illustration, we turn to data from the AGEMAP study relating
gene expression to age for 16 tissues in the mouse. LEAPP generates rankings
with greater consistency across tissues than the rankings attained by the other
methods.
