StATS: Information theory and microarrays (June 1, 2005)
I have been toying with the idea of using information theory in a microarray experiment to allow incorporation of the proportion of "absent: genes in the calculation of variance reduction. An "absent" gene in an Affymetrix array is a gene where the mismatch probes light up as brightly or more brightly as the perfect match probes. As I understand it, the signal associated with these genes is probably noted related to that gene itself but to some cross hybridizing genes.
The basic concept would be that the reduction of uncertainty associated with a phenotypic variable would be the log of the ratio of standard deviations for the signal among those arrays where a signal was present plus the change in entropy in the probability of a gene being absent. So for example, if a gene is absent in 6 out of 12 arrays, that represents a high entropy. If the 6 absent genes all happen to be in the control group, that represents an enormous change in entropy. Similarly, if there is a large standard deviation in the signals of the 12 arrays, but the standard deviations in the control group and treatment group are much smaller, then there is a similar large change in entropy. Somehow, there ought to be a simple way to combine the two concepts together.
Right now, most statistical models for microarrays (at least the ones I am familiar with) do not incorporate the present or absent information in the analysis.
It's not quite the same thing, but an article in BMC Bioinformatics talks about using B-spline functions for estimating mutual information. This approach adjusts for the errors associated with binning by allowing a signal to be split into several adjacent bins.
When I have time, I'll see if there are any similar references out there.
Another interesting microarray article I ran across is
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