Title: | Extending the Newman Studentized Range Statistic to Transcriptomics |
---|---|
Description: | Extends the classical Newman studentized range statistic in various ways that can be applied to genome-scale transcriptomic or other expression data. |
Authors: | Zachary Abrams, Greg Gershkowitz, Anoushka Joglekar, Chao Liu, Kevin R. Coombes |
Maintainer: | Kevin R. Coombes <[email protected]> |
License: | Apache License (== 2.0) |
Version: | 1.0.11 |
Built: | 2024-12-25 06:43:30 UTC |
Source: | CRAN |
The Newman Banked Statistic is used to compare an individual sample to a cohort of similar samples.
bankStat(bankObj, testSet, bankMatrix) createBank(bankMatrix)
bankStat(bankObj, testSet, bankMatrix) createBank(bankMatrix)
bankObj |
Compressed representation of the cohort being compared to. |
testSet |
Matrix containing data from one or more individual samples to be compared to the bank. |
bankMatrix |
Data for the bank of "normal" or "untreated" or "baseline" control samples. |
A list containing two matrices: the nu.statistics
and the p.values
.
data(GSE6631) HN <- as.matrix(log2(1 + GSE6631)) bankMatrix <- HN[,seq(1, ncol(HN), 2)] # odd columns are normal testSet <- HN[, seq(2, 6, 2)] # evn columns are tumor bs <- bankStat(testSet = testSet, bankMatrix = bankMatrix) summary(bs$nu.statistics) summary(bs$p.values)
data(GSE6631) HN <- as.matrix(log2(1 + GSE6631)) bankMatrix <- HN[,seq(1, ncol(HN), 2)] # odd columns are normal testSet <- HN[, seq(2, 6, 2)] # evn columns are tumor bs <- bankStat(testSet = testSet, bankMatrix = bankMatrix) summary(bs$nu.statistics) summary(bs$p.values)
Provides functions to fit a beta-mixture model to a set of p-values that has peaks at both zero and one, and to estimate false discovery rates.
fitMix3(datavec, forever=100, epsilon=0.001, relative = 0.001, print.level=0) computeFDR(object, alpha) computeCutoff(object, fdr)
fitMix3(datavec, forever=100, epsilon=0.001, relative = 0.001, print.level=0) computeFDR(object, alpha) computeCutoff(object, fdr)
datavec |
A numeric vector containing p-values. |
forever |
An integer; maximum number of iterations while fitting the mixture model. |
epsilon |
A real number; change in the log likelihood that should be used to terminate the model-fitting loop. |
relative |
A real number; change in the relative log likelihood that should be used to terminate the model-fitting loop. |
print.level |
An integer; how much detail should |
object |
An object of the |
alpha |
A real number between 0 and 1; the cutoff on the nominal p-value where the FDR should be computed. |
fdr |
A real number beteen 0 and 1; the targeted FDR value. |
We have observed empirically that the set of p-values obtained when computing the Newman paired test statistic often has peaks both at zero (representing genes of interest) and at one (representing "boring" genes that change much less than expected). We attribute the latter phenomenon to the fact that we use locally smoothed instead of gene-by-gene estimates of the standard deviation; genes whose SD is increased by the smoothing process contribute to the boring peak near one.
To estimate p-values in this context, we fit a three-component beta mixture model, combining (1) a right-peaked distribution Beta(L,1), (2) a left-peaked dfistribution Beta(1,M), and (3) a uniform distribution. Specfically, we look for models of the form
.
Model-fitting uses an expectation-maximization (EM) algorithm. In
addition to the parameters mle=c(L,M)
and psi=c(alpha,
beta, gamma)
, we introduce a matrix Z
of latent variables that
indicate which distribution each point is likely to arise
form. Z
has three columns (one for each mixture component) and
one row for each p-value; the entries in each row are nonegative and
sum to one. The M-step of the algorithm uses the nlm
optimization function to compute the maximum-likelihood mle
values given psi
and Z
. The E-step first updates
psi
from the Z
-matrix, and then updates the values of
Z
based on the current mle
.
We are able to use the mixture distribution to compute the relationship between a cutoff on the nominal p-values and the false discovery rate (FDR).
The model-fitting function, fitMix3
, returns an object of the
MixOf3Beta
class.
The computeFDR
function returns a real number in [0,1], the
false discovery rate assiociated with the nominal cutoff.
The computeCutoff
function returns a real number in [0,1], the
cutoff required to achieve the desired FDR.
set.seed(98765) ds <- c(rbeta(3000, 20, 1), rbeta(1000, 1, 40), runif(6000)) fit <- fitMix3(ds) computeFDR(fit, 0.01) computeCutoff(fit, 0.01) computeFDR(fit, 0.0016438) computeCutoff(fit, 0.05) computeFDR(fit, 0.00702114)
set.seed(98765) ds <- c(rbeta(3000, 20, 1), rbeta(1000, 1, 40), runif(6000)) fit <- fitMix3(ds) computeFDR(fit, 0.01) computeCutoff(fit, 0.01) computeFDR(fit, 0.0016438) computeCutoff(fit, 0.05) computeFDR(fit, 0.00702114)
Represents the results of fitting a beta-mixture model to a set of p-values that has peaks at both zero and one.
Given a set of p-values (or any data on the interval [0,1]) that has peaks at both ends of the interval, we fit a three-componet mixture model. One component is uniform, and represents the expected distribution under the null hypothesis that nothing interesting is happening anywhere. The second component has the distribution Beta(1,M); this has a peak at zero and represents the features of interest. The final component has the distribution Beta(L,1). In the context of the Newman paired statistic, this represents genes or features whose variabilirt is smaller than the locally smoothed estimate of the standard deviation; we can think of these as "extra boring".
In practice, users will use the fitMix3
function to
construct an object of the MixOf3Beta
class. Hand
construction is strongly discouraged.
input
:A numeric vector containing the input p-values.
mle
: A numeric vactor of length 2 containing the beta
parameters L
and M
(in that order).
psi
:A numeric vector of length three containing the mixing parameters, in the order (right-peak component, left-peak component, and uniform-component).
Z
:A matrix of size N (number of features) by 3. This contains the latent indicator matrix. Each row corresponds to a gene or feature, and the entries show the proabbiltiy that the feature arose from the right, left, or uniform comnponent.
Plot the decompositon of the data into thre pieces.
Plot a histogram of the p-values along with the fitted model of the distribution.
Plot a (sorted) image of the latent variable Z-matrix.
Kevin R. Coombes [email protected]
Abrams ZB, Joglekar A, Gershkowitz GR, Sinicropi-yao S, Asiaee A, Carbone DP, Coombes KR. Personalized Transcriptomics: Selecting Drugs Based on Gene Expression Profiles. Preprint.
pairedStat
, NewmanPaired-class
set.seed(98765) ds <- c(rbeta(3000, 20, 1), rbeta(1000, 1, 40), runif(6000)) fit <- fitMix3(ds) image(fit, col=topo.colors(64)) hist(fit, col="skyblue", lcol="blue") plot(fit)
set.seed(98765) ds <- c(rbeta(3000, 20, 1), rbeta(1000, 1, 40), runif(6000)) fit <- fitMix3(ds) image(fit, col=topo.colors(64)) hist(fit, col="skyblue", lcol="blue") plot(fit)
These data sets contain paired normal and tumor samples usewd to ilustrate te Newman pairted test and the Newman bank test.
data(LungPair) data(GSE6631)
data(LungPair) data(GSE6631)
LungPair
is a data matrix containing normalized second
generation sequencing data from The Cancer Genome Atlas (TCGA), with
20,531 row (genes) and 2 columns (samples). The first column contains
data for the normal sample and the second column contains data for the
tumor sample from the patient with barcode TCGA.38.4625.
GSE6631
is a data matrix containing normalized Affymetrix
microarray data from paired head-and-neck cancer samples in the Gene
Expression Omnibus set GSE6631. The matrix contains 200 rows (a rando
subset of genes) and 44 columns (samples). The odd numbered colukmns
are derived from normal mucosa; te even numbered columns are derived
from paired tumor samples from the same patient.
The full squamous cell lung cancer (LUSC) data from TCGA was downloaded from http://firebrowse.org/, and the data for this pair were separated and saved as a binary R data file. The head-and-neck cancer data were downloaded from the Gene Expression Omnibus at https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE6631. A subset of 2000 genes was randomly selected before saving the binary R data file.
Kuriakose MA, Chen WT, He ZM, Sikora AG et al. Selection and validation of differentially expressed genes in head and neck cancer. Cell Mol Life Sci 2004 Jun;61(11):1372-83.
data(LungPair) data(GSE6631)
data(LungPair) data(GSE6631)
Represents the reusults of computing the Newman Paired test statistic on one or more paired samples.
In practice, users will use the pairedStat
function to
construct an object of the NewmanPaired
class. Hand
construction is strongly discouraged.
pairedMean
:A matrix of size N (number of features) by S (number of sample pairs). The mean expression of each feature in each paired sample. Also called "A" in the M-versus-A plots of the microarray era.
difference
:A matrix of size N (number of features) by S (number of sample pairs). The difference (perturbed - base) in expression of each feature in each paired sample. Also called "M" in the M-versus-A plots of the microarray era.
smoothSD
:A matrix of size N (number of features) by S (number
of sample pairs). The results of fitting a loess smooth to the
relationship between the PairedMean
and the observed estimate
of standard deviation (i.e., abs(difference)/sqrt(2)
).
nuStatistics
:A matrix of size N (number of features) by S (number of sample pairs). The Newman paired statistics, nu.
pValues
:A matrix of size N (number of features) by S (number of sample pairs). Empirical p-values for the Newman statistics.
Select a subset of features or sample pairs.
The dimension, N by S, of the object.
Plot the results of the analysis of one sample pair.
Plot a histogram of the p-values for one sample-pair.
Kevin R. Coombes [email protected]
Abrams ZB, Joglekar A, Gershkowitz GR, Sinicropi-yao S, Asiaee A, Carbone DP, Coombes KR. Personalized Transcriptomics: Selecting Drugs Based on Gene Expression Profiles. Preprint.
showClass("NewmanPaired")
showClass("NewmanPaired")
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.
pairedStat(baseData, perturbedData = NULL, pairing = NULL)
pairedStat(baseData, perturbedData = NULL, pairing = NULL)
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 |
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. |
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://www.ncbi.nlm.nih.gov/pmc/articles/PMC4120293/). 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))
.
A list containing two marices: the nu.statistics
and the p.values
.
data(GSE6631) Normal <- GSE6631[, c(1,3)] Tumor <- GSE6631[, c(2,4)] ### input two separate matrices ps1 <- pairedStat(Normal, Tumor) summary([email protected]) summary([email protected]) ### input one combined matrix and a pairing vector ps2 <- pairedStat(GSE6631, pairing=c(-1, 1, -2, 2)) summary([email protected]) summary([email protected]) ### input a list of matrix-pairs ps3 <- pairedStat(list(One = GSE6631[, 1:2], Two = GSE6631[, 3:4])) summary([email protected]) summary([email protected])
data(GSE6631) Normal <- GSE6631[, c(1,3)] Tumor <- GSE6631[, c(2,4)] ### input two separate matrices ps1 <- pairedStat(Normal, Tumor) summary(ps1@nu.statistics) summary(ps1@p.values) ### input one combined matrix and a pairing vector ps2 <- pairedStat(GSE6631, pairing=c(-1, 1, -2, 2)) summary(ps2@nu.statistics) summary(ps2@p.values) ### input a list of matrix-pairs ps3 <- pairedStat(list(One = GSE6631[, 1:2], Two = GSE6631[, 3:4])) summary(ps3@nu.statistics) summary(ps3@p.values)