EdgeR GLM linear regression of time series

[bsuac6]

Hi All,

I am using RNA-seq data. I have 3 time points in my data 6 months (young), 12 months (middle) and 28 months (old). I want to do a differential expression analysis across the 3 time points. I have used EdgeR GLM to do this though the design isnt allowing me to look at linear changes with increasing age whilst taking into account the expression at middle age. So after looking on lots of forums I have come up with a work round (see below). Though not being experienced in R or statistics I am not sure it is doing what I want it to. Could someone please look it over and see if I am actually getting linear changes with increasing age whilst taking in account the expression at middle age?
Many thanks

> library(edgeR)
> library(limma)
> targets<-read.delim (file="coding_targets.txt")
> targets$age<-C(targets$age,poly,1)
> attr(targets$age,"contrasts")
.L
a-young -7.071068e-01
b-middle -7.850462e-17
c-old 7.071068e-01
> targets$sample<-factor(targets$sample)
> targets
X files age sample
1 p1 p1_coding_counts.txt a-young 1
2 p2 p2_coding_counts.txt a-young 2
3 p3 p3_coding_counts.txt a-young 3
4 p7 p7_coding_counts.txt b-middle 7
5 p8 p8_coding_counts.txt b-middle 8
6 p9 p9_coding_counts.txt b-middle 9
7 p4 p4_coding_counts.txt c-old 4
8 p5 p5_coding_counts.txt c-old 5
9 p6 p6_coding_counts.txt c-old 6
> d<-readDGE(targets, skip=1, comment.char='#')
> colnames(d)<-row.names(targets)
> d<- calcNormFactors(d)
> d
An object of class "DGEList"
$samples
X files age sample lib.size norm.factors
1 p1 p1_coding_counts.txt a-young 1 3445622 0.9655724
2 p2 p2_coding_counts.txt a-young 2 2696547 0.9902573
3 p3 p3_coding_counts.txt a-young 3 3308099 0.9787044
4 p7 p7_coding_counts.txt b-middle 7 2503479 1.0584660
5 p8 p8_coding_counts.txt b-middle 8 2639127 1.0477893
6 p9 p9_coding_counts.txt b-middle 9 2696547 0.9902573
7 p4 p4_coding_counts.txt c-old 4 3037440 0.9778553
8 p5 p5_coding_counts.txt c-old 5 2647915 1.0144109
9 p6 p6_coding_counts.txt c-old 6 2475370 0.9809077

$counts
1 2 3 4 5 6 7 8 9
ENSRNOG0000000xxxx 1287 1285 1041 788 968 1285 1092 1009 960
ENSRNOG0000000xxxx 0 0 0 0 1 0 0 1 0
ENSRNOG0000000xxxx 0 0 0 3 0 0 1 0 0
ENSRNOG0000000xxxx 38 405 50 18 105 405 372 42 282
ENSRNOG0000000xxxx 0 0 0 0 0 0 0 0 0
22932 more rows ...
> d<-d[rowSums(d$counts)>9,]
> design<- model.matrix(~ age, data = targets)
> design
(Intercept) age.L
1 1 -7.071068e-01
2 1 -7.071068e-01
3 1 -7.071068e-01
4 1 -7.850462e-17
5 1 -7.850462e-17
6 1 -7.850462e-17
7 1 7.071068e-01
8 1 7.071068e-01
9 1 7.071068e-01
attr(,"assign")
[1] 0 1
attr(,"contrasts")
attr(,"contrasts")$age
.L
a-young -7.071068e-01
b-middle -7.850462e-17
c-old 7.071068e-01
> d<-estimateGLMCommonDisp(d, design)
> glmfit<- glmFit(d, design, dispersion=d$common.dispersion)
> results<- glmLRT(d, glmfit, coef=c(2))
> topTags(results)
Coefficient: age.L
logConc logFC LR P.Value FDR
ENSRNOG000000xxxxx -11.271529 -1.9336775 55.45465 9.564007e-14 1.453825e-09
ENSRNOG000000xxxxx -10.359443 1.2661223 49.11802 2.410161e-12 1.831843e-08
ENSRNOG000000xxxxx -11.317494 -1.5480925 47.35359 5.926938e-12 3.003180e-08

[Gordon Smyth]

Dear bsuac6,

edgeR easily allows you to estimate a linear trend with age. Just put age as a column in the design matrix.

If you're still having trouble with it, could you post your question to the Bioconductor mailing list? See the section "how to get help" in the edgeR User's Guide.

Best wishes
Gordon

[David Robinson]

Gordon Smyth: Given the link function for negative binomial regression, wouldn't this estimate an exponential trend rather than a linear one? (After all, wouldn't a linear trend be impossible since it could lead to a negative expected value?)

[Gordon Smyth]

Yes. It is a linear trend on the scale of the model formula and linear predictor, and this corresponds to an exponential trend on the scale of the predicted counts.