Table 2 Description of the methods evaluated

BH

The classic procedure. p values for m hypotheses are ordered from the smallest to the largest. Given a target FDR level α, the ith hypothesis is rejected if the p value is less than the threshold α\(\frac{i}{m}\).

stats (p.adjust)

[28]

ST

The global proportion of null hypotheses is estimated and used to adjust the threshold in the BH procedure. Less conservative than BH when the signal is not sparse.

qvalue

(qvalue)

[29]

FDRreg

Covariates are allowed to influence the prior probability of null. The rejection rule is based on local false discovery rate (lFDR) under the two-component mixture model.

FDRreg

(FDRreg)

[39]

IHW

Tests are divided into groups based on the covariate. Each group is associated with a weight, and the weight is used to adjust the threshold in the BH procedure. Only one covariate is allowed.

ihw

(ihw)

[40]

BL

A regression framework is used to estimate the proportion of null hypotheses conditional on observed covariates. The estimates are used to adjust the threshold in the BH procedure.

swfdr

(lm_pi0)

[42]

AdaPT

Covariates are allowed to influence both the null probability and the p value distribution under the alternative. The rejection rule is based on lFDR and an adaptive approach is implemented to control FDR in finite sample.

adaptMT

(adapt_glm)

[43]

CAMT

Covariates are allowed to influence both the null probability and the p value distribution under the alternative. A new rejection rule is designed to be robust to model mis-specification.

CAMT

(camt.fdr)

[51]