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:
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
## 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"))
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.:0.3008
## Median :0.5772
## Mean :0.5464
## 3rd Qu.:0.8153
## Max. :1.0000
We can create a histogram of the per-gene (empirical) p-values
We can also produce an
“M-versus-A” plot of the data.
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.:0.3008 1st Qu.:0.3151 1st Qu.:0.3197
## Median :0.5777 Median :0.5646 Median :0.6213
## Mean :0.5464 Mean :0.5376 Mean :0.5632
## 3rd Qu.:0.8157 3rd Qu.:0.7958 3rd Qu.:0.8354
## Max. :0.9995 Max. :0.9989 Max. :0.9999
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.:0.3007 1st Qu.:0.3153 1st Qu.:0.3191
## Median :0.5767 Median :0.5650 Median :0.6193
## Mean :0.5463 Mean :0.5376 Mean :0.5629
## 3rd Qu.:0.8148 3rd Qu.:0.7959 3rd Qu.:0.8346
## Max. :0.9988 Max. :0.9998 Max. :1.0000
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.:0.3007 1st Qu.:0.3150 1st Qu.:0.3195
## Median :0.5775 Median :0.5649 Median :0.6213
## Mean :0.5464 Mean :0.5376 Mean :0.5632
## 3rd Qu.:0.8153 3rd Qu.:0.7959 3rd Qu.:0.8351
## Max. :0.9999 Max. :0.9999 Max. :0.9996
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)
