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I am looking at levels of genes in a dataset and want to identify genes that do not vary much in terms of their expression level. While I can do this using the coefficient of correlation, calculating the covariance or by looking for number of genes within the botton x percent of genes using median absolute deviation those methods appear to be arbitrary.

What I am interested in is defining a cutoff based on P.values - is there any way of finding out which genes show significantly less variability than would be expected by chance without having external controls to compare it to?

Cheers, Ankur.

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  • $\begingroup$ What data do you have access to? Do you have biological/technical replicates? Is this RNA-seq, microarray, or cytometry-based measurement of expression? $\endgroup$
    – vector07
    Apr 1 '14 at 0:15
  • $\begingroup$ It is microarray data for a few hundreds of tumour samples. I am looking to see which expression states are highly conserved and recurrent. The idea is to identify genes that are significantly less variable in terms of expression than expected by chance. $\endgroup$ Apr 9 '14 at 19:35
  • $\begingroup$ Do you have spike-in data for absolute normalization between arrays? If not, your analysis will be almost impossible. There are numerous normalization methods you can use without spike-in data, but they are often predicated on either rank or normalizing by a gene that "doesn't change much" (constitutively active). The former fails spectacularly when there are global changes to expression, and the later fails spectacularly because the choice of a (or even a cluster) of constitutively active genes is arbitrary, unverifiable, and small changes in these references distort the entire array analysis $\endgroup$
    – vector07
    Apr 10 '14 at 17:02
  • $\begingroup$ Nope - the closest I can come to between-array normalisation is to run Combat or something similar for cross-study batch/isva to estimate batch effects and eliminate batch effects as much as possible. $\endgroup$ Apr 10 '14 at 23:36
  • $\begingroup$ Think you're SOL. Things you can probably do pretty well: identify highly differentially expressed genes since their rank will change dramatically. The general assumption behind that approach is that most genes don't change much from experiment to experiment (ie, 5% of genes are up/down regulated when exposed to a certain condition). Since you're interested in genes that don't change, looking for genes whose rank doesn't change much won't be very informative. Only other idea is to pick a gene from each sample and do qPCR to get an absolute reference for each, and normalize to that gene. $\endgroup$
    – vector07
    Apr 11 '14 at 1:34
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If you're only interested in checking the variability, it sounds like an analysis of variance would be a good start.

Idea 1: Perform an F-test against the different variances for each control. The null hypothesis is that the two controls come from the same normal distribution, but potentially with different means.

Idea 2: an analysis of variance (ANOVA) on the continuous variable separated into the controls. The idea is to look at the variance of the continuous variable within each class $s_i$ and compare it to the total variance $s_t$. The correlation coefficient for one class compared to the total is then $\eta_i = \sqrt{s_i / s_t}$. The test is then an F-test. There is an assumption of a normal distribution here also.

As for the p-values, they represent the level where you can accept or reject the null hypothesis (the variances are all equal). If the p-value is low (below a 5% level, for example) you reject the null hypothesis and assume that the variables have different variances based on the control groups.

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