How to check if the diference between several logfc differential expression results is statistically significant?

Question

[lykhenko.olexandr]

I had a gene expression matrix with placenta samples of male- and female-carrying pregnancies at four time periods of pregnancy (middle of 1st trimester, middle of 2nd trimester, preterm, term).

I found differentially expressed genes (with limma R package) between female and male samples in each time period separately, to check whether male-female difference changes over the course of pregnancy.

Genes   Pregnancy time intervals            
           1        2      3       4
DDX3Y   -3.08   -2.71   -0.52   -0.52
EIF1AY  -2.83   -2.96   -2.51   -2.55
KDM5D   -2.5    -3.14   -1.13   -1.04
KDM6A    0.5    0.54    0.74    0.58
RPS4Y1  -5.48   -5.2    -4.72   -4.59
TTTY15  -1.58   -0.9    -1.45   -1.36
TXLNGY  -0.65   -0.51   -0.7    -0.83
USP9Y   -1.92   -1.45   -0.25   -0.46
UTY     -0.57   -0.42   -0.66   -0.72
XIST     3.5    4.94    1.61    1.76

Now I have table of logfc's for genes that are differentially expressed between male and female placenta samples at all 4 time intervals. Some genes seem to have more or less constant difference between male and female samples over the course of pregnancy (like DDX3Y) while in others the male-female difference seems to diminish closer to the end of pregnancy (like XIST). Is there a way to check if it is true in a strict statistical manner?

[ATpoint]

You have to do pairwise comparisons to get statistics on logFCs between two conditions. Here that would be 2 vs 1, 3 vs 1, 4 vs 1 etc. How did you obtain this list in the first place so which kind of test did you do?

[lykhenko.olexandr]

R package limma uses generalized linear models, which use moderated t-statistics for differential expression significance tests. I took all samples for the time period 1, found difexp genes between female and male, took all samples from time period 2 etc. then took all genes which gave significant logfc for each time period.

[Papyrus]

Maybe reading about interaction models in limma will help. See the sections 9.5 and 9.6 in the limma user's guide. There you can see how to specify models, and coefficient comparisons, in which you can find out which genes change in a comparison (e.g. male vs female), differently, depending on the level another factor (e.g. being at a certain time point).