NewmanOmics: Tools for Personalized Transcriptomics

In this vignette, we describe how to use the NewmanOmics Paired and Banked tests to analyze gene expression data from a single sample.

Getting Started

As usual, we start by loading the package:

library(NewmanOmics)

The package contains paired tumor and normal samples from patients with head and neck cancer. these came from a study that was submitted to the Gene Expression Omnibus.

data(GSE6631)
dim(GSE6631)
## [1] 2000   44
GSE6631[1:5, 1:4]
##            Normal.mucosa.1  Cancer.1 Normal.mucosa.2  Cancer.2
## 34155_s_at        26.42586  22.19725        22.13673  18.66223
## 34281_at         334.29232 382.92879       393.40014 509.30754
## 39125_at         258.62695 290.06060       268.97994 220.16837
## 37276_at          45.65556  38.86692        34.77368  33.40627
## 1519_at          423.26690 366.40731       308.62338 550.34888

As we can see, this consists of (normalized) Affymetrix microarray data. The odd numbered columns are derived from normal mucosa, and the even numbered columns are derived from paired tumor samples.

Before proceeding, we are going to log-transform the data.

HN <- log2(1 + GSE6631)
boxplot(HN, col=c("forestgreen", "dodgerblue"))
Box plot of log-transformed data.

Box plot of log-transformed data.

The figure suggests that the the data have been reasonably normalized, and that it is unlikely to be overwhelmed by artifacts.

Paired Statistic

To illustrate the Newman Paired test, we are going to use only one sample.

HN1 <- HN[, 1:2]
result1 <- pairedStat(HN1, pairing = c(-1,1))
summary(result1@nu.statistics)
##     Cancer.1        
##  Min.   :5.842e-04  
##  1st Qu.:4.158e-01  
##  Median :9.885e-01  
##  Mean   :1.417e+00  
##  3rd Qu.:1.835e+00  
##  Max.   :1.744e+01
summary(result1@p.values)
##     Cancer.1     
##  Min.   :0.0000  
##  1st Qu.:0.3004  
##  Median :0.5770  
##  Mean   :0.5463  
##  3rd Qu.:0.8144  
##  Max.   :0.9997

We can create a histogram of the per-gene (empirical) p-values

hist(result1)
Histogram of empoirical p-values.

Histogram of empoirical p-values.

We can also produce an “M-versus-A” plot of the data.

plot(result1)
Bland-Altman plot.

Bland-Altman plot.

Alternate Inputs

The pairedStat function has flexible inputs, allowing you to store the data in various ways. Here we run the algorithm for three pairs, with an explicit pairing vector.

result2 <- pairedStat(HN[, 1:6], pairing=c(-1, 1, -2, 2, -3, 3))
summary(result2@nu.statistics)
##     Cancer.1            Cancer.2            Cancer.3        
##  Min.   :5.842e-04   Min.   :9.836e-04   Min.   : 0.001682  
##  1st Qu.:4.158e-01   1st Qu.:4.591e-01   1st Qu.: 0.369775  
##  Median :9.885e-01   Median :1.021e+00   Median : 0.878206  
##  Mean   :1.417e+00   Mean   :1.417e+00   Mean   : 1.419570  
##  3rd Qu.:1.835e+00   3rd Qu.:1.780e+00   3rd Qu.: 1.765563  
##  Max.   :1.744e+01   Max.   :1.526e+01   Max.   :16.572431
summary(result2@p.values)
##     Cancer.1         Cancer.2         Cancer.3     
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.2999   1st Qu.:0.3150   1st Qu.:0.3187  
##  Median :0.5773   Median :0.5650   Median :0.6206  
##  Mean   :0.5463   Mean   :0.5375   Mean   :0.5630  
##  3rd Qu.:0.8145   3rd Qu.:0.7957   3rd Qu.:0.8346  
##  Max.   :0.9997   Max.   :0.9996   Max.   :0.9992
plot(result2)
Bland-ALtman plots.

Bland-ALtman plots.

Bland-ALtman plots.

Bland-ALtman plots.

Bland-ALtman plots.

Bland-ALtman plots. 

hist(result2)
P-value histograms.

P-value histograms.

P-value histograms.

P-value histograms.

P-value histograms.

P-value histograms.

We can also input the same data as a pair of matrices.

normals <- HN[, c(1,3,5)]
tumors <- HN[, c(2,4,6)]
result3 <- pairedStat(normals, tumors)
summary(result3@nu.statistics)
##     Cancer.1            Cancer.2            Cancer.3        
##  Min.   :5.842e-04   Min.   :9.836e-04   Min.   : 0.001682  
##  1st Qu.:4.158e-01   1st Qu.:4.591e-01   1st Qu.: 0.369775  
##  Median :9.885e-01   Median :1.021e+00   Median : 0.878206  
##  Mean   :1.417e+00   Mean   :1.417e+00   Mean   : 1.419570  
##  3rd Qu.:1.835e+00   3rd Qu.:1.780e+00   3rd Qu.: 1.765563  
##  Max.   :1.744e+01   Max.   :1.526e+01   Max.   :16.572431
summary(result3@p.values)
##     Cancer.1         Cancer.2         Cancer.3     
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.3006   1st Qu.:0.3155   1st Qu.:0.3194  
##  Median :0.5774   Median :0.5652   Median :0.6207  
##  Mean   :0.5465   Mean   :0.5377   Mean   :0.5632  
##  3rd Qu.:0.8151   3rd Qu.:0.7963   3rd Qu.:0.8355  
##  Max.   :0.9998   Max.   :0.9996   Max.   :0.9993

Or we can input the same data as a list of paired samples.

listOfPairs <- list(HN[,1:2], HN[,3:4], HN[,5:6])
result4 <- pairedStat(listOfPairs)
summary(result4@nu.statistics)
##     Cancer.1            Cancer.2            Cancer.3        
##  Min.   :5.842e-04   Min.   :9.836e-04   Min.   : 0.001682  
##  1st Qu.:4.158e-01   1st Qu.:4.591e-01   1st Qu.: 0.369775  
##  Median :9.885e-01   Median :1.021e+00   Median : 0.878206  
##  Mean   :1.417e+00   Mean   :1.417e+00   Mean   : 1.419570  
##  3rd Qu.:1.835e+00   3rd Qu.:1.780e+00   3rd Qu.: 1.765563  
##  Max.   :1.744e+01   Max.   :1.526e+01   Max.   :16.572431
summary(result4@p.values)
##     Cancer.1         Cancer.2         Cancer.3     
##  Min.   :0.0000   Min.   :0.0000   Min.   :0.0000  
##  1st Qu.:0.3008   1st Qu.:0.3157   1st Qu.:0.3194  
##  Median :0.5766   Median :0.5641   Median :0.6197  
##  Mean   :0.5461   Mean   :0.5374   Mean   :0.5628  
##  3rd Qu.:0.8141   3rd Qu.:0.7954   3rd Qu.:0.8343  
##  Max.   :0.9997   Max.   :0.9996   Max.   :0.9992

Banked Statistic

A completely different approach to personalized transcriptomics is to compare individual samples to a “bank” of known normals.

normals <- HN[, seq(1, ncol(HN), 2)] # odds are normal
tumors <- HN[, seq(2, ncol(HN), 2)] # evens are tumor
bank <- createBank(normals)
result5 <- bankStat(bank, tumors[,1,drop=FALSE])
summary(result5$nu.statistics)
##     Cancer.1      
##  Min.   :-9.6255  
##  1st Qu.:-0.5540  
##  Median : 0.2797  
##  Mean   : 0.1027  
##  3rd Qu.: 0.9911  
##  Max.   : 6.7524
summary(result5$p.values)
##     Cancer.1     
##  Min.   :0.0000  
##  1st Qu.:0.2898  
##  Median :0.6101  
##  Mean   :0.5569  
##  3rd Qu.:0.8392  
##  Max.   :1.0000
hist(result5$p.values, breaks=101)