Beta matrix

There exists a transformation between M value (analyzed here, and first introduced in this paper) and the Beta value (formula for transformation is also described here):

beta=2^M/(2^M+1); M=log2(M/U); beta=M/(M+U+offset)

Data distribution based on the expression used for measuring DNA methylation (beta vs M value):

I used the matrix of M values and transformed them into beta values. Here are the plots of the first eigengene, first eigenarray (colored by the probe dye) and the outliers identified in the first eigengene:

Density plots by the color of the dye of the first 3 eigenarrays:

Consultation with Brig and Justin: don't split the data, keep all probes together.

Correlation with adjustment and biological variables:

PC	Batch	Center	Amount	Concentr.	Day	Month	Column	Row	Year	Grade	Stage	Age
1	0.1404	0.1263	0.004464	0.559545	0.120663	0.966426	0.423536	0.258863	0.036442	0.06361	0.35619	0.006236
2	2.2e-16	2.2e-16	2.447e-18	6.019e-03	2.198e-51	3.374e-32	1.389e-01	1.027e-01	2.397e-26	0.06419	0.12857	0.3884
3	8.057e-05	0.001862	0.0030439	0.5574784	0.0001560	0.0002149	0.7666292	0.5092963	0.0012852	0.6350	0.8488	0.1439
4	0.9221	0.2629	0.5526	0.3857	0.9925	0.7725	0.3971	0.8410	0.7211	0.0750	0.6507	0.0003187

since we already know from the analyses of the M value that batch, center, plate row and plate column have effect on the data, I will skip the preliminary steps and remove these factors. Also, the dataset will exclude batch number 0652.

> X<-model.matrix(~factor(batch[mask]) + adj$plate_row[mask] + adj$plate_column[mask] + factor(center[mask]))
> Xmod<-solve(t(X) %*% X) %*% t(X) %*% t(beta[,mask])
> betaRes<- beta[,mask] - t(X %*% Xmod)

Correlation with adjustment and biological variables:

PC	Batch	Center	Amount	Concentr.	Day	Month	Column	Row	Year	Grade	Stage	Age
1	1	1	0.9830	0.6760	0.9999	1.0000	0.4995	0.9871	0.9133	0.3422	0.2915	0.01044
2	1	1	0.9750	0.7878	1.0000	1.0000	0.8328	1.0000	0.8487	0.5115	0.6704	0.4074
3	0.99	1	0.9402	0.7498	0.9994	1.0000	0.8415	0.9993	0.9304	0.11282	0.02903	0.0001028
4	1	1	0.9521	0.1648	1.0000	0.9998	0.5466	1.0000	0.9786	0.4573	0.6384	0.8565

It seems that with beta value I see a stronger correlation with age. First eigengene, first and second eigenarrays and the outliers:

We can proceed with building a comethylation network although the outliers look terrible.