  The large-scale multiple testing inherent to high throughput biological data
necessitates very high statistical stringency and thus true effects in data are
difficult to detect unless they have high effect sizes. One solution to this
problem is to use an independent information to prioritize the most promising
features of the data and thus increase the power to detect them. Weighted
p-values provide a general framework for doing this in a statistically rigorous
fashion. However, calculating weights that incorporate the independent
information and optimize statistical power remains a challenging problem
despite recent advances in this area. Existing methods tend to perform poorly
in the common situation that true positive features are rare and of low effect
size. We introduce covariate based weighting methods for calculating optimal
weights conditioned on the effect sizes of the tests. This approach uses the
probabilistic relationship between covariate and test effect size to calculate
more informative weights that are not diluted by null effects as is common with
group-based methods. This relationship can be calculated theoretically for
normally distributed covariates or estimated empirically in other cases. We
showed via simulations and applications to data that this method outperforms
existing methods by a large margin in the rare/low effect size scenario and has
at least comparable performance in all scenarios.
