Meta-analysis of significant (or selected) features in multivariate data Using multiple univariate tests (with multiple comparison correction), I have identified a number of molecular lipids increased in my cases compared to controls. I would like to perform a statistical analysis to gain insight into whether the significant lipids are so because of aspects of their structure.
In addition to the p-value or classification of significant/non-significant, each lipid has other "meta" data.
These lipids can be classified by:
1. Lipid class (2 levels)
2. Number of carbons (between 14 and 26)
3. Number of double bonds (0, 1, or 2)
4. Between-class connectivity (derived from network analysis on an adjacency matrix).
I am interested in determining if there is any statistical evidence that the significant lipids tend to have 1) more or fewer carbons, 2) more or fewer double bonds, and 3) have higher between-class connectivity.
Is it valid to perform a regression analysis (with a Poisson distribution for cases 1 and 2, and as linear regression for case 3) to test if significant lipids are more likely/have higher levels of these meta data?
Any thoughts or advice are welcome. I work in R, so any computational assistance in this language would be especially appreciated. 
 A: If you have already distributed the set of lipids into significant/non-significant classes, then what you presumably want to do is to compare the number of carbons, the number of double bonds, and the connectivity between the 2 classes. So you're really looking at between-group comparisons rather than regression per se (although between-group comparisons can be structured as regressions).
For the number of double bonds, a chi-square or Fisher exact test on the 2 x 3 contingency table (significance class x number of double bonds) would be most direct. You could also do that for the 2 x 7 contingency table of carbon numbers (assuming only even numbers of carbons from 14 to 26 inclusive), although a simple comparison of average lengths might work. For connectivity, it seems that a t-test comparison between the 2 significance classes would do, although you might have to transform the measure of connectivity depending on its distribution among the lipids.
This approach, however, has 2 difficulties. For one, it treats all the lipids equally, regardless of their prevalence or biologic significance. Second, it has already made a distinction into "significant" and "insignificant" classes that does not take advantage of the continuous nature of the underlying data on lipid concentrations.
You might consider instead developing a true regression model with, say, the concentration difference between the cases and controls as the dependent variable. If baseline concentrations differ among the lipids, you might start with log-transformed concentrations so that differences in the log scale represent case/control ratios in the original concentration scale. Then you could use carbon number, double-bond number, and connectivity as independent variables to relate case/control differences or ratios to these lipid characteristics directly, without having to make prior distinctions between "significant" and "insignificant" classes of lipids. This would also allow you to weight the individual lipids in the regression based on prevalence, etc., if desired.
