Multiple hypothesis testing, adjusting for latent variables

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. It is less well known that dependencies can change the relative ordering of significance levels among hypotheses. Poor rankings lead to wasteful and ineffective followup 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.