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h4. Batch vs clinical traits, data collection

Correlation of batch with clinical traits (READ: can be found here, COAD: can be found here). READ, number of batches: 11, COAD, number of batches: 15

Additional technical variables to be considered in normalization: batch (6th field in the patient's barcode), center (2nd field in the patients' barcode), amount, barcode bottom \(?), concentration, day, month, year (to be concatenated and considered as a single variable), plate row, plate column. This information is available from clinical_aliquot_public_CANCERTYPE.txt  files.

DNA methylation: 27k, level1 downloaded on December 19th, 2011.  

Total number of COAD patients (tumor/matched normal/unmatched normal) = 212

Total number of READ patients (tumor/matched normal/unmatched normal) = 81

Place them in the same directory and combine in a single matrix of *M values (log2(methylated/unmethylated))*

Total number of tumor samples: 237

Extracted batch and center information, relationship between them:
{code}> table(center,batch)
      batch
center 0820 0825 0904 1020 1110 1116 A004 A00B A081
    A6    4    2    0    4    0    0    0    0    0
    AA   26    5   31   44    4    0   15   17   13
    AF    4    0    0    0    0    1    0    0    0
    AG   12   10    8    0    0   17    9    9    0
    AY    0    0    0    0    2    0    0    0    0
{code}

For the combined DNA methylation dataset (237 patients) batch vs clinical traits significant correlations (P value = 0.05) are listed. Note: traits 1 and 2 should be used for the calculation of the survival and then Cox model should be used to show that batch is predictive of survival.

{csv}"COLON_clinical traits","DataType","NumberOfNAs","Test","Pvalue"
"days_to_last_followup","integer",0,"Kruskal-Wallis rank sum test",1.19E-23
"days_to_last_known_alive","integer",0,"Kruskal-Wallis rank sum test",2.63E-19
"days_to_form_completion","integer",0,"Kruskal-Wallis rank sum test",1.32E-14
"tumor_tissue_site","factor",2,"Pearson's Chi-squared test",3.41E-14
"histological_type","factor",7,"Pearson's Chi-squared test",9.69E-11
"year_of_initial_pathologic_diagnosis","integer",0,"Kruskal-Wallis rank sum test",3.77E-09
"anatomic_organ_subdivision","factor",2,"Pearson's Chi-squared test",8.00E-07
"vascular_invasion_present","factor",27,"Pearson's Chi-squared test",8.85E-06
"vital_status","factor",1,"Pearson's Chi-squared test",3.20E-05
"lymphatic_invasion_present","factor",12,"Pearson's Chi-squared test",3.53E-05
"residual_tumor","factor",6,"Pearson's Chi-squared test",5.04E-04
"number_of_lymphnodes_examined","integer",2,"Kruskal-Wallis rank sum test",1.48E-03
"kras_gene_analysis_performed","factor",1,"Pearson's Chi-squared test",5.44E-02
"gender","factor",0,"Pearson's Chi-squared test",6.25E-02
"person_neoplasm_cancer_status","factor",0,"Pearson's Chi-squared test",8.27E-02
"tumor_stage","factor",27,"Pearson's Chi-squared test",8.89E-02
{csv}

h4. Data normalization

For the normalization I didn't split the probes into "red" and "green". Approach: perform SVD, identify tech variables that are highly correlated with the first PCs and remove the variables. Use M value to express methylation status of each probes. The M value was calculated in the following way (the code was take from Bioconductor lumi package, functions for the analysis of Illumina Human Methylation 27k data):

SVD on the whole matrix, relative variance before normalization:
!Colon_RelativeVarianceNoNorm.png|thumbnail!

Created a file with technical variables, merged day, month and year into a single variable. Tech file, head:
{code}> head(k)
  row.names bcr_sample_barcode          bcr_aliquot_barcode  amount biospecimen_barcode_bottom
1        63   TCGA-A6-2674-01A TCGA-A6-2674-01A-02D-0820-05 26.7 uL                 0096500431
2       150   TCGA-A6-2677-01A TCGA-A6-2677-01A-01D-0820-05 26.7 uL                 0096500430
3       182   TCGA-A6-2678-01A TCGA-A6-2678-01A-01D-0820-05 26.7 uL                 0096500407
4       334   TCGA-A6-2683-01A TCGA-A6-2683-01A-01D-0820-05 26.7 uL                 0096500406
5      1186   TCGA-AA-3514-01A TCGA-AA-3514-01A-02D-0820-05 26.7 uL                 0096500383
6      1254   TCGA-AA-3517-01A TCGA-AA-3517-01A-01D-0820-05 26.7 uL                 0096500382
  concentration  shipment plate_column plate_row batch      shortID
1    0.14 ug/uL 22-2-2010            1         B  0820 TCGA-A6-2674
2    0.15 ug/uL 22-2-2010            1         C  0820 TCGA-A6-2677
3    0.15 ug/uL 22-2-2010            1         D  0820 TCGA-A6-2678
4    0.16 ug/uL 22-2-2010            1         E  0820 TCGA-A6-2683
5    0.15 ug/uL 22-2-2010            1         F  0820 TCGA-AA-3514
6    0.13 ug/uL 22-2-2010            1         G  0820 TCGA-AA-3517{code}
Ignore bcr_sample_barcode, bcr_aliquot_barcode, these are not tech variables.
Here are the correlation of the tech variables with the first 4 PCs. 
{code}> k
   bcr_sample_barcode bcr_aliquot_barcode     amount biospecimen_barcode_bottom concentration     shipment
V1          0.4700026           0.4877315 0.04672452                  0.3017151  1.601134e-07 8.334984e-34
V2          0.4510048           0.4877315 0.48950693                  0.5316963  3.392774e-01 5.699460e-03
V3          0.4510048           0.4877315 0.18777379                  0.6925323  1.141026e-01 7.733551e-02
V4          0.4513158           0.4877315 0.58958142                  0.6705972  6.211816e-01 6.664406e-02
   plate_column   plate_row        batch   shortID
V1 3.009061e-05 0.001491552 2.491659e-33 0.4702436
V2 1.947964e-01 0.989450736 1.349671e-04 0.4511082
V3 9.369050e-01 0.463424193 1.437189e-01 0.4511082
V4 3.395272e-01 0.688070623 1.012497e-01 0.4514159
{code}

Outliers of the first principal component:
!Colon_Mval_noNorm_PC1outliers.png|thumbnail!
Seems that the batch has the biggest effect on the data. Remove the batch, relative variance after that:

!Colon_RelativeVariance_noBatch.png|thumbnail!
Calculate correlation with the clinical variables after removing the batch effect:

{code}> k
   bcr_sample_barcode bcr_aliquot_barcode    amount biospecimen_barcode_bottom concentration  shipment
V1          0.4691690           0.4877315 0.6106733                  0.5489680     0.4263794 0.9956323
V2          0.4534001           0.4877315 0.8880134                  0.7069529     0.4187061 0.9950998
V3          0.4536645           0.4877315 0.8589996                  0.7271536     0.4000974 0.9856611
V4          0.4543147           0.4877315 0.8880134                  0.6459688     0.9405449 0.9999056
   plate_column plate_row     batch   shortID
V1   0.04191285 0.5627797 0.9981536 0.4690814
V2   0.97317059 0.6821160 0.9999954 0.4536160
V3   0.55783761 0.0703874 0.9992998 0.4537400
V4   0.52248494 0.8718225 0.9999849 0.4543834{code}
Seems that this took care of all the problems, there is still a borderline significant correlation of the PC1 with the plate column  , not going to worry about it. 

Look at the outliers of the first principal component after removing the batch: 

!Colon_batchRemoved_PC1outliers.png|thumbnail!

Conclusion: consider the data to be normalized.