Benjamini-Hochberg Procedure with the Simulator
Jacob Bien
2016-07-12
Suppose we wish to test \(n\) hypotheses, \(H_1,\ldots, H_n\), and we have a p-value \(\hat p_i\) for each hypothesis \(H_i\). That is,
\[
\mathbb{P}_{H_i}(\hat p_i\le \alpha) = \alpha.
\]
Benjamini and Hochberg (1995) design a procedure (for when these p-values are independent) that controls what they call the false discovery rate (FDR), which is the expected proportion of the rejected tests that should not have been rejected:
\[
\mathbb{E}_{\{H_i:i\in S\}}\left[\frac{\sum_{i\in S}1\{H_i\text{ rejected}\}}{\max[1,\sum_{i=1}^n1\{H_i\text{ rejected}\}]}\right].
\]
Given a desired FDR \(q\), the BH procedure finds a data-adaptive threshold level \(\hat p(q)\) and rejects all \(H_i\) for which \(\hat p_i\le \hat p(q)\). The threshold level is given by comparing the sorted p-values \(\hat p_{(1)}\le \cdots \le \hat p_{(n)}\) to a line of slope \(q/n\) and identifying the largest p-value that is below this line. That is, \(\hat p(q)=\hat p_{(\hat i)}\) where \[
\hat i = \max\{i: \hat p_i \le q i / n\}.
\]
In this simulation, we verify that the BH procedure works, and we investigate the effect that correlation has on the FDR control.
Main simulation
In the Models section below, we show the code for make_correlated_pvalues
, a function that generates a model object given parameters \(n\) (the number of hypotheses), \(\pi_0\) (the fraction of hypotheses that are null), and \(\rho\) (the correlation between any pair of test statistics). In the simulation below, we fix \(n=20\) and vary \(\pi_0\) and \(\rho\).
name_of_simulation <- "fdr"
sim <- new_simulation(name = name_of_simulation,
label = "False Discovery Rate") %>%
generate_model(make_correlated_pvalues, seed = 123,
n = 20,
pi0 = list(0.8, 1),
rho = list(-0.01, 0, 0.1, 0.9),
vary_along = c("pi0", "rho")) %>%
simulate_from_model(nsim = 25, index = 1:4) %>%
run_method(bh_methods, parallel = list(socket_names = 2)) %>%
evaluate(list(fdp, nd))
The variable bh_methods
is defined in the Methods section below and corresponds to the BH procedure for four different values of \(q\).
We begin by looking at the results when \(\rho=0\) (i.e., independent tests).
sim %>%
subset_simulation(rho == 0) %>%
tabulate_eval(metric_name = "fdp", output_type = "html",
format_args = list(digits = 0, nsmall = 2))
A comparison of Mean false discovery proportion (averaged over 100 replicates).
|
BH (q = 0.05)
|
BH (q = 0.1)
|
BH (q = 0.2)
|
pi0 = 0.8, rho = 0
|
0.04 (0.01)
|
0.08 (0.02)
|
0.17 (0.02)
|
pi0 = 1, rho = 0
|
0.04 (0.02)
|
0.08 (0.03)
|
0.25 (0.04)
|
It appears that the BH procedure does control the FDR at each stated \(q\) value. However, we also see that when \(\pi_0\) is less than 1, it tends to be more conservative. Indeed, Benjamini and Hochberg show that the FDR of BH does not exceed \(\pi_0q\).
Adding to a simulation
We might like to increase the number of simulations.
Suppose we return to this simulation several days later and wish to double the number of random draws used. In the above code, we had 100 draws, which were simulated in 4 chunks of 25 draws each. The simulator allows us to add to a simulation without requiring us to re-run parts of the simulation that have already been run.
If we had closed the R session without saving the image[^]: for the sake of reproducibility, I like to always start with a fresh workspace, so I can be sure that my functions aren’t calling a global variable that I have forgotten about), we can open a new one in the directory that has the files
directory in it. We start by loading sim
, which is the Simulation object (containing all the necessary pointers to saved files). Loading sim
is fast because it only loads the file locations, not the files themselves.
sim <- load_simulation("fdr")
We do so by simply adding 4 more chunks, with index=5:8
. Each distinct value of index
corresponds to a separate random number generator stream. This is convenient because it means that we do not have to rely on the state of the RNG after completing one chunk to start the next one.
sim <- sim %>%
simulate_from_model(nsim = 25, index = 5:8) %>%
run_method(bh_methods, parallel = list(socket_names = 2)) %>%
evaluate(list(fdp, nd))
We can look again at the table.
sim %>%
subset_simulation(rho == 0) %>%
tabulate_eval(metric_name = "fdp", output_type = "html",
format_args = list(digits = 0, nsmall = 2))
A comparison of Mean false discovery proportion (averaged over 200 replicates).
|
BH (q = 0.05)
|
BH (q = 0.1)
|
BH (q = 0.2)
|
pi0 = 0.8, rho = 0
|
0.03 (0.01)
|
0.07 (0.01)
|
0.15 (0.01)
|
pi0 = 1, rho = 0
|
0.04 (0.01)
|
0.07 (0.02)
|
0.20 (0.03)
|
Some plots
The FDR is the average of the false discovery proportion (FDP). We can look at these raw values (200 for each method-model pair).
sim %>%
subset_simulation(rho == 0) %>%
plot_eval(metric_name = "fdp")
![](data:image/png;base64,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)
When \(\pi_0=1\), we see that the FDP is either 0 or 1. This is because if we make any number of discoveries, then they will all be false (but if we do not make any discoveries, we have FDP=0).
We now investigate the effect of \(\rho\), the correlation between the test statistics. We now fix \(\pi_0=0.8\) and look at how the plots vary with \(\rho\).
sim %>%
subset_simulation(pi0 == 0.8) %>%
plot_eval(metric_name = "fdp", varying = "rho")
![](data:image/png;base64,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)
Since \(\rho\) is numeric, it might be more informative to look at the FDR as a function of \(\rho\).
sim %>%
subset_simulation(pi0 == 0.8) %>%
plot_eval_by(metric_name = "fdp", varying = "rho")
![](data:image/png;base64,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)
We see that the procedure becomes more conservative as the dependence increases, but still does control FDR (which was shown for positive dependence in Benjamini and Yekutieli, 2001). Looking at \(\pi_0=1\), we would like to check whether for negative \(\rho\) the procedure is anti-conservative.
sim %>%
subset_simulation(pi0 == 1) %>%
plot_eval_by(metric_name = "fdp", varying = "rho")
![](data:image/png;base64,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)
Creating a simulation based on a preexisting one
To investigate this particular question in greater depth, we might create a new simulation object based on the previous one. We’d like to increase the number of random draws for this particular setting, but don’t care about doing so for the others.
sim2 <- subset_simulation(sim, pi0 == 1 & rho == -0.01) %>%
rename("fdr-negdep") %>%
relabel("BH Procedure under negative dependence") %>%
simulate_from_model(nsim = 25, index = 9:20) %>%
run_method(bh_methods, parallel = list(socket_names = 2)) %>%
evaluate(list(fdp, nd))
We remake the table (on the basis of 500 random draws) to check for anti-conservativeness.
tabulate_eval(sim2, metric_name = "fdp", output_type = "html",
format_args = list(digits = 0, nsmall = 2))
A comparison of Mean false discovery proportion (averaged over 500 replicates).
|
BH (q = 0.05)
|
BH (q = 0.1)
|
BH (q = 0.2)
|
pi0 = 1, rho = -0.01
|
0.04 (0.01)
|
0.08 (0.01)
|
0.21 (0.02)
|
Observe that at this point, sim
and sim2
are two separate simulation objects that refer to some common simulation results. For example, their Model
and Draws
objects are the same.
m <- model(sim, pi0 == 1 & rho == -0.01)
m2 <- model(sim2)
all.equal(m, m2)
## [1] TRUE
d <- draws(sim, pi0 == 1 & rho == -0.01)
d2 <- draws(sim2, index = 1:8)
all.equal(d, d2)
## [1] TRUE
When model
and draws
(and likewise output
and evals
) are called on a simulation object, they load the appropriate files referenced by the Simulation
object. The models m
and m2
are identical (and likewise for d
and d2
) because both Simulation
objects refer to the same saved files. Thus, having multiple simulation objects does not lead to copies of the (potentially large) results files being made. Instead, only the references themselves are duplicated.
Components
Models
library(mvtnorm)
make_correlated_pvalues <- function(n, pi0, rho) {
# Gaussian copula model...
#
# n pvalues, the first n*pi0 of which are null, coming from a multivariate
# normal with all correlations rho.
sigma <- matrix(rho, n, n)
diag(sigma) <- 1
n0 <- round(n * pi0)
delta <- 2 # size of signal
mu <- rep(c(0, delta), c(n0, n - n0)) # n0 are null
new_model(name = "correlated-pvalues",
label = sprintf("pi0 = %s, rho = %s", pi0, rho),
params = list(n = n, rho = rho, sigma = sigma,
pi0 = pi0, mu = mu, delta = delta,
nonnull = which(mu != 0)),
simulate = function(n, mu, sigma, nsim) {
# this function must return a list of length nsim
x <- rmvnorm(nsim, mean = mu, sigma = sigma)
pvals <- 1 - pnorm(x)
return(split(pvals, row(pvals))) # make each row its own list element
})
}
Methods
make_bh <- function(q) {
# q is the desired level of control for the FDR
new_method(name = paste0("bh", q),
label = sprintf("BH (q = %s)", q),
settings = list(q = q),
method = function(model, draw, q) {
p <- sort(draw)
cutline <- seq(model$n) * q / model$n
threshold <- max(p[p <= cutline], 0)
list(rejected = which(draw <= threshold))
})
}
qvalues <- c(0.05, 0.1, 0.2)
bh_methods <- sapply(qvalues, make_bh)
Metrics
fdp <- new_metric(name = "fdp",
label = "false discovery proportion",
metric = function(model, out) {
fp <- setdiff(out$rejected, model$nonnull)
nd <- max(length(out$rejected), 1)
return(length(fp) / nd)
})
nd <- new_metric(name = "nd",
label = "number of discoveries",
metric = function(model, out) length(out$rejected))