Hi,
I made several simulation using a gene list of interest and different publicly available cancer gene list to see if a there is an enrichment.
So I have a matrix of p-values like this
param1 param2 param3 list1 pval_a pval_b pval_c list2 pval_d pval_e pval_f list3 pval_g pval_h pval_i
I know it's difficult to compare p-values because each cancer gene list has a different size so the statistcal power will be different. But do you have advice to represent these results in a easily readable plot ?
Thanks
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Nicolas Rosewick
Yes, ditch the p-values and show the effect size instead. (or at least both.) As you say, it is meaningless to compare P-values across comparisons, since the underlying data for the test will be different. Also remember that p-value is NOT proportional to effect size.
You can easily make a plot with lists over Y-axis and parameters over X-axis in ggplot2, and colour/size it according to effect size/p-value, respectively.
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written
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David Westergaard
Thanks. How do you introduce the effect size in the plot?
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written
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Nicolas Rosewick
require(ggplot2); require(plyr)
df <- data.frame(samples = c(rep('L1',3), rep('L2', 3), rep('L3', 3)), params=c('param1', 'param2', 'param3'), pval=runif(9), effect_size=rnorm(9, mean=10))
# Normalize within sample to make comparable across samples
df$effect_norm <- ddply(df, .(samples), function(x) {return(x[4]/max(x[4]))})$effect_size
# Plot stuff.
p <- ggplot(df) + geom_point(aes(x=samples, y=params, size=effect_norm)) + aes(colour=-log10(pval))
Not quite sure what you mean, but I attached some code showing the general idea of the plot.
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David Westergaard
Thanks. Pretty interesting. For me here list size are stable ( so L1 will have the same value for each of the param used ). So the point size will be the same for the same list independent of the param.
with "effect size" David meant effect size, not the length of your lists.
also, why don't you try to perform some kind of meta-analysis, to get a single p-value at the end?
or if you simply want to plot the p-values, I would suggest you to log-transform them and produce a dotplot
Adding to David Westergaard's excellent answer, the typical way to visualise these sorts of results in epidemiology and other disciplines that do a lot of among-studies comparisons is the Forest Plot. Basically, you'd plot the effect size and 95% CI for each parameter-estimate. The effect size, and the method of getting the CI from the p-value will depend on exactly what the studies are measuering. But you'd end up with something like this (using the data-frame from David Westergaard's answer):
df$ci <- abs(rnorm(9, 0, df$effect_size))/2
forest_p <- ggplot(df, aes(samples, effect_size))
forest_p + geom_point(size=3) +
geom_pointrange(aes(ymin=effect_size - ci, ymax=effect_size + ci)) +
geom_hline(x=0) +
facet_wrap(~params) +
coord_flip()
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