Dear Community,

I’m currently analyzing an RNA-Seq gene expression dataset, downloaded from the recount project. It includes trios of paired samples of primary cancers, their liver metastases and their normal adjucent tissue samples (18 patients-54 samples). The code chunk used for downstream analysis in order to perform paired group comparisons of primary cancers versus normal samples and metastatic vs normal:

colData(rse)$title
 [1] "primary colorectal cancer AMC_2-1"  "primary colorectal cancer AMC_3-1" 
 [3] "primary colorectal cancer AMC_6-1"  "primary colorectal cancer AMC_5-1" 
 [5] "primary colorectal cancer AMC_7-1"  "primary colorectal cancer AMC_8-1" 
 [7] "primary colorectal cancer AMC_9-1"  "primary colorectal cancer AMC_10-1"
 [9] "primary colorectal cancer AMC_12-1" "primary colorectal cancer AMC_13-1"
[11] "primary colorectal cancer AMC_17-1" "primary colorectal cancer AMC_18-1"
[13] "primary colorectal cancer AMC_19-1" "primary colorectal cancer AMC_20-1"
[15] "primary colorectal cancer AMC_21-1" "primary colorectal cancer AMC_22-1"
[17] "primary colorectal cancer AMC_23-1" "primary colorectal cancer AMC_24-1"
[19] "normal colon AMC_2-2"               "normal colon AMC_3-2"              
[21] "normal colon AMC_5-2"               "normal colon AMC_6-2"              
[23] "normal colon AMC_7-2"               "normal colon AMC_8-2"              
[25] "normal colon AMC_9-2"               "normal colon AMC_10-2"             
[27] "normal colon AMC_12-2"              "normal colon AMC_13-2"             
[29] "normal colon AMC_17-2"              "normal colon AMC_18-2"             
[31] "normal colon AMC_19-2"              "normal colon AMC_20-2"             
[33] "normal colon AMC_21-2"              "normal colon AMC_22-2"             
[35] "normal colon AMC_23-2"              "normal colon AMC_24-2"             
[37] "metastasized cancer AMC_2-3"        "metastasized cancer AMC_3-3"       
[39] "metastasized cancer AMC_5-3"        "metastasized cancer AMC_6-3"       
[41] "metastasized cancer AMC_7-3"        "metastasized cancer AMC_8-3"       
[43] "metastasized cancer AMC_9-3"        "metastasized cancer AMC_10-3"      
[45] "metastasized cancer AMC_12-3"       "metastasized cancer AMC_17-3"      
[47] "metastasized cancer AMC_13-3"       "metastasized cancer AMC_18-3"      
[49] "metastasized cancer AMC_19-3"       "metastasized cancer AMC_20-3"      
[51] "metastasized cancer AMC_21-3"       "metastasized cancer AMC_22-3"      
[53] "metastasized cancer AMC_23-3"       "metastasized cancer AMC_24-3"

sampleID = colData(rse)$title
sampleID <- gsub("primary colorectal cancer AMC_","s",sampleID)
sampleID <- gsub("normal colon AMC_","s",sampleID)
sampleID <- gsub("metastasized cancer AMC_","s",sampleID)
sampleID <-gsub("-1","",sampleID)
sampleID <-gsub("-2","",sampleID)
sampleID <-gsub("-3","",sampleID)

sample_info <- data.frame(
run = colData(rse_gene)$run,
group = dx,
sampleID = as.factor(sampleID), 
sex = rse$predicted_sex,
tissue = as.factor(rse$predicted_tissue))

sample_info$sex <- droplevels(sample_info$sex)
sample_info$tissue <- droplevels(sample_info$tissue)

colData(rse)$group <- sample_info$group
colData(rse)$sampleID <- sample_info$sampleID
colData(rse)$Tissue <- sample_info$tissue
colData(rse)$sex <- sample_info$sex

pdata <- SummarizedExperiment::colData(rse)[,c("group","sampleID","Tissue","sex")]

dge <- calcNormFactors(y, method = "TMM")

dge$samples
          group lib.size norm.factors sampleID    Tissue    sex
SRR975551    PC 35844673    1.1616300       s2 Intestine   male
SRR975552    PC 35323037    1.1391519       s3 Intestine   male
SRR975554    PC 35085885    1.0716169       s6 Intestine   male
SRR975553    PC 34522671    1.0263454       s5 Intestine female
SRR975555    PC 35522336    1.0567555       s7 Intestine female
SRR975556    PC 34645824    0.9466883       s8 Intestine   male
SRR975557    PC 35819078    1.0069037       s9 Intestine   male
SRR975558    PC 35597072    1.1556164      s10 Intestine   male
SRR975559    PC 35644146    1.1339967      s12 Intestine   male
SRR975560    PC 34354387    0.9064396      s13 Intestine   male
SRR975561    PC 34984479    0.8787232      s17 Intestine   male
SRR975562    PC 35309596    0.9132710      s18 Intestine   male
SRR975563    PC 34192875    1.0469936      s19 Intestine   male
SRR975564    PC 36541848    1.0269095      s20 Intestine   male
SRR975565    PC 35054486    1.1543370      s21 Intestine   male
SRR975566    PC 34810630    1.0930002      s22 Intestine   male
SRR975567    PC 35187393    1.1480416      s23 Intestine   male
SRR975568    PC 34440602    1.0693811      s24 Intestine female
SRR975569    NC 34331252    1.1120207       s2 Intestine   male
SRR975570    NC 34791427    1.0362509       s3 Intestine   male
SRR975571    NC 34134685    1.0313145       s5 Intestine female
SRR975572    NC 33389913    1.0868100       s6 Intestine   male
SRR975573    NC 34403772    1.0498040       s7 Intestine female
SRR975574    NC 34118206    0.9927762       s8 Intestine   male
SRR975575    NC 34240628    1.0132546       s9 Intestine   male
SRR975576    NC 33537688    0.9343132      s10 Intestine   male
SRR975577    NC 33515873    0.9544540      s12 Intestine   male
SRR975578    NC 34219524    0.8533124      s13 Intestine   male
SRR975579    NC 36504080    0.8891647      s17 Intestine   male
SRR975580    NC 34796910    0.9228019      s18 Intestine   male
SRR975581    NC 34051137    1.0257172      s19 Intestine   male
SRR975582    NC 34224865    1.0302613      s20 Intestine   male
SRR975583    NC 34719272    1.0324915      s21 Intestine   male
SRR975584    NC 34440539    1.0310448      s22 Intestine   male
SRR975585    NC 34425993    1.0752771      s23 Intestine   male
SRR975586    NC 34897034    0.9417058      s24 Intestine female
SRR975587    MC 35280616    1.0106831       s2     Liver   male
SRR975588    MC 35477420    1.1044894       s3 Intestine   male
SRR975589    MC 36036263    1.0950962       s5 Intestine female
SRR975590    MC 35076617    1.1788985       s6     Liver   male
SRR975591    MC 33780190    1.1091615       s7     Liver female
SRR975592    MC 35827952    0.9863091       s8     Liver   male
SRR975593    MC 35536763    1.1022580       s9     Liver   male
SRR975594    MC 35962611    0.5544939      s10     Liver   male
SRR975595    MC 35042076    1.0685238      s12     Liver   male
SRR975597    MC 35531306    1.1121061      s17     Liver   male
SRR975596    MC 35778359    1.0032715      s13 Intestine   male
SRR975598    MC 35524218    1.0070292      s18     Liver   male
SRR975599    MC 33710189    0.4600261      s19     Liver   male
SRR975600    MC 35206322    1.1116100      s20     Liver   male
SRR975601    MC 34967028    0.9487985      s21     Liver   male
SRR975602    MC 34348262    0.8462756      s22 Intestine   male
SRR975603    MC 35301582    1.0008410      s23     Liver   male
SRR975604    MC 35778773    0.9315822      s24     Liver female


condition.group <- as.factor(dge$samples$group)
tissue.group <- as.factor(dge$samples$Tissue)
sex.group <- as.factor(dge$samples$sex)
Subject <- as.factor(dge$samples$sampleID) #  the factor indicating the pairs/trios of samples belonging to each patient
condition.group <- relevel(condition.group,ref="NC") # as the first level the normal samples



design <- model.matrix(~Subject +condition.group +tissue.group +sex.group)

head(design)
  (Intercept) Subjects12 Subjects13 Subjects17 Subjects18 Subjects19 Subjects2
1           1          0          0          0          0          0         1
2           1          0          0          0          0          0         0
3           1          0          0          0          0          0         0
4           1          0          0          0          0          0         0
5           1          0          0          0          0          0         0
6           1          0          0          0          0          0         0
  Subjects20 Subjects21 Subjects22 Subjects23 Subjects24 Subjects3 Subjects5
1          0          0          0          0          0         0         0
2          0          0          0          0          0         1         0
3          0          0          0          0          0         0         0
4          0          0          0          0          0         0         1
5          0          0          0          0          0         0         0
6          0          0          0          0          0         0         0
  Subjects6 Subjects7 Subjects8 Subjects9 condition.groupMC condition.groupPC
1         0         0         0         0                 0                 1
2         0         0         0         0                 0                 1
3         1         0         0         0                 0                 1
4         0         0         0         0                 0                 1
5         0         1         0         0                 0                 1
6         0         0         1         0                 0                 1
  tissue.groupLiver sex.groupmale
1                 0             1
2                 0             1
3                 0             1
4                 0             0
5                 0             0
6                 0             1

y3 <- estimateDisp(dge, design, robust=TRUE)
Error in glmFit.default(sely, design, offset = seloffset, dispersion = 0.05,  : 
  Design matrix not of full rank.  The following coefficients not estimable:
 sex.groupmale

Thus, my questions are the following:

1) For the above error, i should simply remove the coefficient "sex.groupmale" ? and essentially, the coefficients condition.groupMC and condition.groupPC represent the paired analysis for the comparison of primary cancer versus normal, and metastatic versus normal, adjusted for tissue and sex ?

2) If i would like additionally to perform a direct comparison between primary cancers and their metastatic counterparts, i should follow an "intersept-free comparison" ? without even including the normal samples ?

Thank you in advance,

Efstathios