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everyone, I'm new at the statistical analysis so I need some help from more experienced people. I'm working with biological data from gene expression analysis. I have 5 treatments (1 parental toxin; 3 compounds resulting from the metabolism of the parental toxin -let's calll them A, B and C), and a control, each one with 3 time points (6, 12 and 18h). I was trying to relate them somehow, although they are independent experiments, and summarize like this "the response of the toxin A after 12h is 23% similar to the parental toxin after 6h". So here's a list of what I've tried so far: 1. Pearson correlation/Cosine similarity. I created a matrix comparing each treatment. However, it didn't add much, because I can't turn the coefficient into a numerical valueor percentage. 2. Linear regression. Since Pearson does not discriminate between the axis, I used linear regression shifting the position of the treatment that I wanted to be the "dependent variable" (in this case, x=A,B or C toxins and y=parental toxin). I was planning to use the slope (a), as measure. If the angle a was between 0 and 22.5º degrees, I would have a response of y = 0.5 times toxin A; if the angle was 45 º, I would have y = toxin A; and if the angle >45º, I would have y = 2 times toxin. But I'm sure that's not a good idea. My supervisor insists on that, but I don't know if that's viable. What do I do with the euqation intercepts? 3. Multiple linear regression. I used the treatments that showed the highest correlation coefficients to build a multiple linear regression equation, and so I had "parental toxin 6h = 0.754 toxin A 12h + 0.246 toxin B 12h + 0.847 toxin C 18h". That's almost what I want, but, again, I feel that this is not the best way to analysze my data because it doesn't fulfill the necessary assumptions to use linear regression. 4. Binary analysis, percent agreement, logistic regression, matrix determinants, etc.

So, if anyone have any suggestion, publication suggestion, anything that could shed some light to my (so far) insoluble problem, I would appreciate very much.

Thanks in advance.

ADDITIONAL INFO: My data is composed of 2280 genes, which have different expression values among treatments. In some treatments they are significant (expression ratio >1.5 or <-1.5 times and p-value cutoff 0.05), in others, don't. Thus, I have a lot of positive and negative values, ranging from -8.0 to +8.0, but not linearly.

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Welcome to the site. Since you have measured things multiple times, your data is not independent and you should not use linear regression. You probably want either a multi-level model of some kind or generalized estimating equations. These are relatively advanced techniques, and you may have to consult with an expert.

You seem to be a bit confused about what a "dependent variable" is. It is hard to imagine that it should shift in the way you describe. The dependent variable is, well, the thing you thing depends on other things; "treatment" cannot be a dependent variable, the dependent variable would be what you think the treatment will affect.

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  • $\begingroup$ Yes, that's why I was so reluctant in using linear regression, because of the abscence of a "dependent variable" whatsoever. When I said that I shifted the axis (x,y) to be like parental toxin x toxin A and then toxin A x parental toxin. My advisor insisted that I could do that, but I wanted to be sure. Thanks for your response! $\endgroup$ – Terezinha Souza Aug 12 '13 at 12:03
  • $\begingroup$ This makes no sense. If you apply treatments, you must expect them to affect something. $\endgroup$ – Peter Flom Aug 12 '13 at 12:48

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