How does Cuffdiff assign p-value when it detects differentially splicing?

[zhixingfeng]

Hi,
The document of cufflink said that cuffdiff measured "distance" between relative abundances of a group of transcripts in two difference conditions by JS divergence, and assigned a p-value the observed changes based on the JS divergence. However, how did it get distribution or variance of test statistics under of null hypothesis? Thanks in advance.

The original document is at

http://cufflinks.cbcb.umd.edu/howitworks.html

Best.

Zhixing

[Gangcai]

Does anybody know how cuffdiff assign p value?

[jb2]

I'm also very interested in getting information as to how p-values are calculated from the square root of the Jensen–Shannon divergence. Based on my basic understanding, the larger the JS divergence, the more extreme the changes in the abundance percentages of the transcripts (grouped together via tss_groups or within a tss) being examined between case and control samples. I don't understand how this value is then converted into a p-value however, especially since it looks like (at least in my data) you can have high JS divergences and yet not be significant and vice versa.

[jb2]

Just a note, it looks like the math for deriving the significance is found on pages 26-28 of the Cufflinks paper supplemental pdf. It is still a bit bewildering, but maybe others can get a better understanding of it by reviewing that section of the paper?

[sterding]

Here is the related text in the supplementary pdf:

We define "overloading" to be a signicant change in relative abundances for a set
of transcripts (as determined by the Jensen-Shannon metric, see below). The term is
intended to generalize the simple notion of "isoform switching" that is well-defined in
the case of two transcripts, to multiple transcripts. It is complementary to absolute
differential changes in expression: the overall expression of a gene may remain constant
while individual transcripts change drastically in relative abundances resulting in over-
loading. The term is borrowed from computer science, where in some statically-typed
programming languages, a function may be used in multiple, specialized instances via
"method overloading".
We tested for overloaded genes by performing a one-sided t-test based on the asymp-
totics of the Jensen-Shannon metric under the null hypothesis of no change in relative
abundnaces of isoforms (either grouped by shared TSS for for post-transcriptional over-
loading, or by comparison of groups of isoforms with shared TSS for transcriptional
overloading). Type I errors were controlled with the Benjamini-Hochberg [2] correction
for multiple testing. A selection of overloaded genes are displayed in Supplemental Figs.
10 and 11.

But still, I am not clear how the p-value is calculated.

[sterding]

Anyone got clue to the question?

[sdriscoll]

It sounds like the trick is they are using the delta method (http://en.wikipedia.org/wiki/Delta_method) to estimate the distribution of the JS metric they calculate at any pairwise comparison. keep in mind the JS metric gives you a single value for any pairwise comparison of two probability distributions. at any pairwise comparison they wish to know if the JS metric computed is significantly different from 0, the null hypothesis.

when you do a t-test you usually have two sets of numbers. you get a mean and variance for each set and those go into a formula for the t-statisitc form which you can calculate a p-value. so at a pairwise comparison they've got a JS metric and 0, the value of the JS metric for two equal distributions. Thanks to the delta method they are able to estimate the distribution of the JS metric which leads them to being able to find the variance associated with the JS metric. now those values can be plugged into the equation for a t-statisitc and the p-value follows.

[xiangq]

It sounds like the trick is they are using the delta method (http://en.wikipedia.org/wiki/Delta_method) to estimate the distribution of the JS metric they calculate at any pairwise comparison. keep in mind the JS metric gives you a single value for any pairwise comparison of two probability distributions. at any pairwise comparison they wish to know if the JS metric computed is significantly different from 0, the null hypothesis.

when you do a t-test you usually have two sets of numbers. you get a mean and variance for each set and those go into a formula for the t-statisitc form which you can calculate a p-value. so at a pairwise comparison they've got a JS metric and 0, the value of the JS metric for two equal distributions. Thanks to the delta method they are able to estimate the distribution of the JS metric which leads them to being able to find the variance associated with the JS metric. now those values can be plugged into the equation for a t-statisitc and the p-value follows.

Hi, sdriscoll

I read their papers and supplementary to calculate the JS metric and pvalue and find that it seems not easy to estimate the distribution of the JS metric.
1. First, based on the delta method, the variance of the JS metric is calculated based on the partial derivatives of the JS(P1,P2) evaluated on the mean of the P1 and P2. However, how to calculate the mean of P1 and P2? Using the sample mean?
2. second, the variance of JS metric also relate to the variance of P1 and P2, covariance of P1 and P2, how to get such kind of information?
Could u give me some hints?

Thanks a lot.