# How to correct alpha, and not p-values themselves, for visualization purposes

I have a set of differentially methylated/expressed/whatever entities with p-values attached (example below).

entity_name    p-value    magnitude
entity1        0.04459    0.68
entity2        0.02283    0.99
...
entity_n       0.78       0.025


Typically, I apply the p.adjust function in R with the "fdr" (Benjamini-Hochberg) approach to leave me with p-values adjusted to control the FDR.

adjusted <- p.adjust(mydata,"fdr")


However, I am interested in showing a volcano plot with the unadjusted p-values, and two alpha levels: 0.05 and one that corresponds to the correction. What is the best way to get this alpha? Is it appropriate to set the "corrected alpha" to the lowest original p-value that doesn't pass FDR correction?

The only way to get the alpha levels is to determine what they will be with p.adjust(), since they will depend on the distribution of your unadjusted p values. The general steps you should follow will be:

1. Add a column of adjusted p-values to your dataframe (mydata$padj = p.adjust(mydata, method="BH"), which is the same as FDR and saves a character). 2. Use which and max to determine your two alpha threshold (e.g., max(mydata$pvalue[mydata\$padj < 0.05])

Then you can adjust your plots however you like (presumably with some horizontal lines at the various alphas). Whether you take the smallest non-significant value or the largest significant value is up to you, just describe what "dots on the line" represent.

• Aren’t alpha thresholds usually exclusive? I.e. it should be < 0.05, not <= 0.05. Jun 13, 2017 at 10:20
• If it matters, you're not using p-values correctly. See the ASA position statement.
– gringer
Jun 13, 2017 at 10:23
• @KonradRudolph Yes, good catch, I've fixed that. I had >= and min() in my mind apparently. Jun 13, 2017 at 11:10

When you're doing a p-value adjustment, the same unadjusted p-value in different genes can be given different adjusted p-values depending on other factors. That means that you can't directly draw a line associated with the FDR on a plot of unadjusted p-value.

One possibility would be to take a range of values that are close to the FDR threshold (e.g. the 20 values closest to threshold), and draw a p-value greyzone within that region:

#!/usr/bin/Rscript
values <- c(rnorm(10000),rnorm(100, mean=1.5));
val.mean <- median(values);
val.diffs <- abs(values - median(values));
val.reldiffs <- (values - median(values));

val.pval <- pnorm(val.diffs, mean = mean(val.diffs),
sd=sd(val.diffs), lower.tail=FALSE);
fdr.threshold <- 0.1;

png("SE.663.png");
plot(val.reldiffs, -log10(val.pval),
col=ifelse(1:10100 <= 10000,"darkblue","darkgreen"));
abline(h=-log10(0.05), col="red");
text(0,-log10(0.05),"p=0.05", pos=1);
abline(h=range(-log10(val.pval[close.bh])), col="#00000040", lty="dashed");
rect(xleft=min(val.reldiffs)*2, xright=max(val.reldiffs)*2,
ytop=max(-log10(val.pval[close.bh])),
ybottom=min(-log10(val.pval[close.bh])), col="#00000020", border=NA);
text(0,min(-log10(val.pval[close.bh])),"FDR=0.1", pos=1);
invisible(dev.off());


• Why the dummy <- assignment? Jun 13, 2017 at 10:18
• It's my default workaround to stop reporting null device / 1 to standard out. I've changed it to invisible(dev.off()), which does the same thing (and is probably more descriptive about its purpose).
– gringer
Jun 13, 2017 at 10:21
• Ah. The writeout never bothered me here. It’s not like it would be written to the output in an actual script/document. Jun 13, 2017 at 10:22
• Sometimes I send stdout to files and parse it. I've just got into the habit of getting rid of things like this so that I don't have weird errors cropping up for unknown reasons. I also have an issue with the scan function, which I silence when I use it.
– gringer
Jun 13, 2017 at 10:27