| Title: | An Empirical Bayes Approach for Replicability Analysis Across Two Studies |
|---|---|
| Description: | A robust and powerful empirical Bayesian approach is developed for replicability analysis of two large-scale experimental studies. The method controls the false discovery rate by using the joint local false discovery rate based on the replicability null as the test statistic. An EM algorithm combined with a shape constraint nonparametric method is used to estimate unknown parameters and functions. [Li, Y. et al., (2023), <https://www.biorxiv.org/content/10.1101/2023.05.30.542607v1>]. |
| Authors: | Yan Li [aut, cre, cph], Xiang Zhou [aut], Rui Chen [aut], Xianyang Zhang [aut], Hongyuan Cao [aut, ctb] |
| Maintainer: | Yan Li <[email protected]> |
| License: | GPL-3 |
| Version: | 1.0.3 |
| Built: | 2024-12-09 06:46:21 UTC |
| Source: | CRAN |
Estimate the local false discovery rate across two studies and apply a step-up procedure to control the FDR of replicability null.
em_lfdr(pa_in, pb_in, pi0a_in, pi0b_in)em_lfdr(pa_in, pb_in, pi0a_in, pi0b_in)
pa_in |
A numeric vector of p-values from study 1. |
pb_in |
A numeric vector of p-values from study 2. |
pi0a_in |
An initial estimate of the null probability in study 1. |
pi0b_in |
An initial estimate of the null probability in study 2. |
Lfdr |
The estimated local false discovery rate for replicability null. |
fdr |
The adjusted values based on local false discovery rate for FDR control. |
xi00 |
An estimate of the prior probability for joint state (0, 0). |
xi01 |
An estimate of the prior probability for joint state (0, 1). |
xi10 |
An estimate of the prior probability for joint state (1, 0). |
xi11 |
An estimate of the prior probability for joint state (1, 1). |
f1 |
A non-parametric estimate for the non-null probability density function in study 1. |
f2 |
A non-parametric estimate for the non-null probability density function in study 2. |
An empirical Bayes approach for replicability analysis across two studies
stareg(pa, pb, init.pi0 = TRUE)stareg(pa, pb, init.pi0 = TRUE)
pa |
A numeric vector of p-values from study 1. |
pb |
A numeric vector of p-values from study 2. |
init.pi0 |
A logistic value for deciding whether to initialize the prior probabilities based on the estimates of pi0's. If true, estimate the marginal pi0's in two studies using qvalue; otherwise, specify pi0_pa = pi_pb = 0.9. |
A list:
Lfdr |
The estimated local false discovery rate for replicability null. |
fdr |
The adjusted Lfdr values based on the step-up procedure for FDR control. |
xi00 |
An estimate of the prior probability for joint state (0, 0) in two studies. |
xi01 |
An estimate of the prior probability for joint state (0, 1) in two studies. |
xi10 |
An estimate of the prior probability for joint state (1, 0) in two studies. |
xi11 |
An estimate of the prior probability for joint state (1, 1) in two studies. |
f1 |
A non-parametric estimate for the non-null probability density function in study 1. |
f2 |
A non-parametric estimate for the non-null probability density function in study 2. |
# Simulate p-values in two studies m = 10000 h = sample(0:3, m, replace = TRUE, prob = c(0.9, 0.025, 0.025, 0.05)) states1 = rep(0, m); states2 = rep(0, m) states1[which(h==2|h==3)] = 1; states2[which(h==1|h==3)] = 1 z1 = rnorm(m, states1*2, 1) z2 = rnorm(m, states2*3, 1) p1 = 1 - pnorm(z1); p2 = 1 - pnorm(z2) # Run STAREG to identify replicable signals res.stareg = stareg(p1, p2) sig.idx = which(res.stareg$fdr <= 0.05)# Simulate p-values in two studies m = 10000 h = sample(0:3, m, replace = TRUE, prob = c(0.9, 0.025, 0.025, 0.05)) states1 = rep(0, m); states2 = rep(0, m) states1[which(h==2|h==3)] = 1; states2[which(h==1|h==3)] = 1 z1 = rnorm(m, states1*2, 1) z2 = rnorm(m, states2*3, 1) p1 = 1 - pnorm(z1); p2 = 1 - pnorm(z2) # Run STAREG to identify replicable signals res.stareg = stareg(p1, p2) sig.idx = which(res.stareg$fdr <= 0.05)