02-pairedStat: Paired Newman Statistic

In NewmanOmics: Extending the Newman Studentized Range Statistic to Transcriptomics

Paired Newman Statistic

Description

The Paired Newman Statistic is used for one-to-one comparison of paired individual samples. Commonly used to find differential expression between tumor-normal pairs or before-after treatment pairs.

Usage

pairedStat(baseData, perturbedData = NULL, pairing = NULL,
           ptype = c("empirical", "theoretical"),
           ntype = c("one-sided", "two-sided"))

Arguments

baseData	Either a list or a matrix. May contain data for just the base condition (for example, normal samples or samples before treatment) or for both the base condition and the perturbed condition (for example, tumor samples or samples after treatment). See details.
perturbedData	An optional matrix containing data for the "perturbed" samples. May be NULL if the baseData argument is a list or a matrix containing all the data.
pairing	An optional vector indicating the pairing between base and perturbed samples. Entries must be integers. Positive integers indicate perturbed samples and negative integers with the same absolute value indicate the paired base samples. See details.
ptype	Enumerated character string indicating which method to use to compute p-values.
ntype	Enumerated character string indicating where to return one-sided (all positive) or two-sided (signed) nu-statistics with corresponding p-values.

Details

In the simplest case, we have gene expression data on one "base" sample and one "perturbed" sample, and the goal is to identify genes whose expression changes between the two states. Our primary assumption is that the standard deviation (SD) of gene expression varies as a smooth function of the mean; fitting such a curve allows us to detect individual genes whose difference is large compared to the smoothed SD.

Note that this assumption is most useful on the log-transformed scale (https://pubmed.ncbi.nlm.nih.gov/25092958/). If your data is on a raw scale, then we recommend transforming it before computing the Newman paired statistic.

The input arguments to the pairedStats function are moderately complicated in order to allow users to choose a convenient method for supplying data when they have multiple paired samples. The first posssibility is to have all the base samples in one matrix and all the perturbed samples in a second matrix. In this case, we assume (without checking) that the columns in the two matrices correspond to the paired samples, and that the genes-rows are in the same order.

The second possibility is to put the data for both the base samples and the perturbed samples in the same matrix. In this case, the user must supply a pairing vector to explain how the samples should be matched. If the column order is ("base1", "perturbed1", "base2", "perturbed2", ...), then the pairiing vector should be written as c(-1, 1, -2, 2, -3, 3, ...).

The third possibility is to provide the paired samples in a list, each of whose entries is a matrix with two columns,with the first column being the base state and the second column being the perturbed state.

This flexibility means that there are three equivalent ways to input the data even if you have only one base sample (with data in the one-column matrix B) and one perturbed sample (with data in the one-column matrix P). If we let BP <- cbind(B, P) , then we can choose (1) pairedStats(B, P), or (2) pairedStats(list(BP)), or (3) pairedStats(BP, pairing = c(-1,1)).

The final two option, ptype and ntype, have been added for backwards comatibility. The default values match the performance of the original versions of the package, which returned the absolute values of the nu-statistics and computed empirical p-values using null simulations. Over time, we came to realize that the signed nu-statistics were simetimes useful. We also belatedly relaized that we could compute theoretical p-values from a particular normal distribution, N(0, sqrt(pi)), which arises becaue the smoothing step is equivalent in the null case to a transformation built from the half-normal distribution.

Value

An object of the NewmanPaired class.

Examples

data(GSE6631)
Normal <- GSE6631[, c(1,3)]
Tumor <- GSE6631[, c(2,4)]

### input two separate matrices
ps0 <- pairedStat(Normal, Tumor)
summary([e-mail])
summary([e-mail])

### use the theoreticl p-values
ps1 <- pairedStat(Normal, Tumor, ntype = "two-sided")
folded <- 1 - abs(1 - 2*[e-mail])
summary(as.vector(folded - ([e-mail])))

### input one combined matrix and a pairing vector
ps2 <- pairedStat(GSE6631, pairing=c(-1, 1, -2, 2))
summary([e-mail])
summary([e-mail])

### input a list of matrix-pairs
ps3 <- pairedStat(list(One = GSE6631[, 1:2],
                       Two = GSE6631[, 3:4]))
summary([e-mail])
summary([e-mail])

NewmanOmics documentation built on April 27, 2026, 3:05 a.m.