  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 promising approach
for reducing the multiple testing burden is to use independent information to
prioritize the features most likely to be true effects. However, using the
independent data effectively is challenging and often does not lead to
substantial gains in power. Current state-of-the-art methods sort features into
groups by the independent information and calculate weights for each group.
However, when true effects are weak and rare (the typical situation for high
throughput biological studies), all groups will contain many null tests and
thus their weights are diluted, and performance suffers. We introduce Covariate
Rank Weighting (CRW), a method for calculating approximate optimal weights
conditioned on the ranking of tests by an external covariate. This approach
uses the probabilistic relationship between covariate ranking and test effect
size to calculate individual weights for each test that are more informative
than group weights and are not diluted by null effects. We show how this
relationship can be calculated theoretically for normally distributed
covariates. It can be estimated empirically in other cases. We show via
simulations and applications to data that this method outperforms existing
methods by as much as 10-fold in the rare/low effect size scenario common to
biological data and has at least comparable performance in all scenarios.
