The quantro user’s guide
25 April 2023
Abstract
A test for when to use global normalization methods, such as quantile normalization.
Package
quantro 1.34.0
1 Introduction
Multi-sample normalization techniques such as quantile normalization Bolstad et al. (2003), Irizarry et al. (2003) have become a standard and essential part of analysis pipelines for high-throughput data. Although it was originally developed for gene expression microarrays, it is now used across many different high-throughput applications including genotyping arrays, DNA Methylation, RNA Sequencing (RNA-Seq) and Chromatin Immunoprecipitation Sequencing (ChIP-Seq). These techniques transform the original raw data to remove unwanted technical variation. However, quantile normalization and other global normalization methods rely on assumptions about the data generation process that are not appropriate in some context. Until now, it has been left to the researcher to check for the appropriateness of these assumptions.
Quantile normalization assumes that the statistical distribution of each sample is the same. Normalization is achieved by forcing the observed distributions to be the same and the average distribution, obtained by taking the average of each quantile across samples, is used as the reference. This method has worked very well in practice but note that when the assumptions are not met, global changes in distribution, that may be of biological interest, will be wiped out and features that are not different across samples can be artificially induced. These types of assumptions are justified in many biomedical applications, for example in gene expression studies in which only a minority of genes are expected to be differentially expressed. However, if, for example, a substantially higher percentage of genes are expected to be expressed in only one group of samples, it may not be appropriate to use global adjustment methods.
The quantro R-package can be used to test for global differences
between groups of distributions which asses whether global normalization
methods such as quantile normalization should be applied. Our method uses
the raw unprocessed high-throughput data to test for global differences in
the distributions across a set of groups. The main function quantro()
will perform two tests:
An ANOVA to test if the medians of the distributions are different across groups. Differences across groups could be attributed to unwanted technical variation (such as batch effects) or real global biological variation. This is a helpful step for the user to verify if there is any technical variation unaccounted for.
A test for global differences between the distributions across groups which returns a test statistic called
quantroStat. This test statistic is a ratio of two variances and is similar to the idea of ANOVA. The main idea is to compare the variability of distributions within groups relative to between groups. If the variability between groups is sufficiently larger than the variability within groups, then this suggests global adjustment methods may not be appropriate. As a default, we perform this test on the median normalized data, but the user may change this option.
2 Getting Started
2.1 Installation
The R-package quantro can be installed from the Bioconductor
if (!requireNamespace("BiocManager", quietly=TRUE))
install.packages("BiocManager")
BiocManager::install("quantro")2.2 Load the package in R
After installation, the package can be loaded into R.
library(quantro)3 Data
3.1 flowSorted Data Example
To explore how to use quantro(), we use the
FlowSorted.DLPFC.450k data package in Bioconductor
Jaffe and Kaminsky (2021).
The data in this package originally came from Guintivano, Aryee, and Kaminsky (2013).
This data set in FlowSorted.DLPFC.450k contains raw data objects of 58
Illumina 450K DNA methylation microarrays, formatted as RGset
objects. The samples represent two different cellular populations of brain
tissues on the same 29 individuals extracted using flow sorting. For more
information on this data set, please see the FlowSorted.DLPFC.450k User’s
Guide.For the purposes of this vignette, a MethylSet object from the
minfi Bioconductor package Aryee et al. (2014) was created which is
a subset of the rows from the original FlowSorted.DLPFC.450k data
set. This MethylSet object is found in the /data folder and the script to
create the object is found in /inst.
Here we will explore the distributions of these two cellular populations of
brain tissue (NeuN_pos and NeuN_neg) and then test if there
are global differences in the distributions across groups. First, load the
MethylSet object (flowSorted) and compute the Beta values using
the function getBeta() in the minfi Bioconductor package.
We use an offset of 100 as this is the default used by Illumina.
library(minfi)
data(flowSorted)
p <- getBeta(flowSorted, offset = 100)
pd <- pData(flowSorted)
dim(p)## [1] 10000 58head(pd)## DataFrame with 6 rows and 11 columns
## Sample_Name SampleID CellType Sentrix.Barcode Sample.Section
## <character> <character> <character> <numeric> <character>
## 813_N 813_N 813 NeuN_pos 7766130090 R02C01
## 1740_N 1740_N 1740 NeuN_pos 7766130090 R02C02
## 1740_G 1740_G 1740 NeuN_neg 7766130090 R04C01
## 1228_G 1228_G 1228 NeuN_neg 7766130090 R04C02
## 813_G 813_G 813 NeuN_neg 7766130090 R06C01
## 1228_N 1228_N 1228 NeuN_pos 7766130090 R06C02
## diag sex ethnicity age PMI
## <character> <character> <character> <integer> <integer>
## 813_N Control Female Caucasian 30 14
## 1740_N Control Female African 13 17
## 1740_G Control Female African 13 17
## 1228_G Control Male Caucasian 47 13
## 813_G Control Female Caucasian 30 14
## 1228_N Control Male Caucasian 47 13
## BasePath
## <character>
## 813_N /dcs01/lieber/ajaffe..
## 1740_N /dcs01/lieber/ajaffe..
## 1740_G /dcs01/lieber/ajaffe..
## 1228_G /dcs01/lieber/ajaffe..
## 813_G /dcs01/lieber/ajaffe..
## 1228_N /dcs01/lieber/ajaffe..3.2 Plot distributions
quantro contains two functions to view the distributions of the
samples of interest: matdensity() and matboxplot(). The function
matdensity() computes the density for each sample (columns) and
uses the matplot() function to plot all the densities.
matboxplot() orders and colors the samples by a group level variable.
These two functions use the RColorBrewer package and the brewer
palettes can be changed using the arguments brewer.n and
brewer.name.
The distributions of the two groups of cellular populations are shown here.
The NeuN_neg samples are colored in green and the NeuN_pos are
colored in red.
matdensity(p, groupFactor = pd$CellType, xlab = " ", ylab = "density",
main = "Beta Values", brewer.n = 8, brewer.name = "Dark2")
legend('top', c("NeuN_neg", "NeuN_pos"), col = c(1, 2), lty = 1, lwd = 3)
matboxplot(p, groupFactor = pd$CellType, xaxt = "n", main = "Beta Values")
4 Using the quantro() function
4.1 Input for quantro()
The quantro() function must have two objects as input:
An
objectwhich is a data frame or matrix with observations (e.g. probes or genes) on the rows and samples as the columns.A
groupFactorwhich represents the group level information about each sample. For example if the samples represent tumor and normal samples, providequantro()with a factor representing which columns in theobjectare normal and tumor samples.
4.2 Running quantro()
In this example, the groups we are interested in comparing are contained in
the CellType column in the pd dataset. To run the
quantro() function, input the data object and the object containing
the phenotypic data. Here we use the flowSorted data set as an
example.
qtest <- quantro(object = p, groupFactor = pd$CellType)
qtest## quantro: Test for global differences in distributions
## nGroups: 2
## nTotSamples: 58
## nSamplesinGroups: 29 29
## anovaPval: 0.01206
## quantroStat: 8.80735
## quantroPvalPerm: Use B > 0 for permutation testing.The details related to the experiment can be extracted using the
summary accessor function:
summary(qtest)## $nGroups
## [1] 2
##
## $nTotSamples
## [1] 58
##
## $nSamplesinGroups
## NeuN_neg NeuN_pos
## 29 29To asssess if the medians of the distributions different across groups,
we perform an ANOVA on the medians from the samples. Those results can be
found using anova:
anova(qtest)## Analysis of Variance Table
##
## Response: objectMedians
## Df Sum Sq Mean Sq F value Pr(>F)
## groupFactor 1 0.006919 0.0069194 6.7327 0.01206 *
## Residuals 56 0.057553 0.0010277
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The full output can be seen The test statistic produced from
quantro() testing for global differences between distributions
is given by quantroStat:
quantroStat(qtest)## [1] 8.8073484.3 eSets
quantro() also can accept objects that inherit eSets
such as an ExpressionSet or MethylSet. The
groupFactor must still be provided.
is(flowSorted, "MethylSet")## [1] TRUEqtest <- quantro(flowSorted, groupFactor = pData(flowSorted)$CellType)
qtest ## quantro: Test for global differences in distributions
## nGroups: 2
## nTotSamples: 58
## nSamplesinGroups: 29 29
## anovaPval: 0.01206
## quantroStat: 8.80735
## quantroPvalPerm: Use B > 0 for permutation testing.4.4 Output from quantro()
Elements in the S4 object from quantro() include:
| Element | Description |
|---|---|
summary |
A list that contains (1) number of groups (nGroups), (2) total number of samples (nTotSamples) (3) number of samples in each group (nSamplesinGroups) |
anova |
ANOVA to test if the average medians of the distributions are different across groups |
MSbetween |
mean squared error between groups |
MSwithin |
mean squared error within groups |
quantroStat |
test statistic which is a ratio of the mean squared error between groups of distributions to the mean squared error within groups of distributions |
quantroStatPerm |
If B is not equal to 0, then a permutation test was performed to assess the statistical significance of quantroStat. These are the test statistics resulting from the permuted samples |
quantroPvalPerm |
If B is not equal to 0, then this is the \(p\)-value associated with the proportion of times the test statistics (quantroStatPerm) resulting from the permuted samples were larger than quantroStat |
5 Assessing the statistical significance
To assess statistical significance of the test statistic, we use
permutation testing. We use the foreach package which distribute
the computations across multiple cross in a single machine or across
multiple machines in a cluster. The user must pick how many permutations
to perform where B is the number of permutations. At each
permutation of the samples, a test statistic is calculated. The proportion
of test statistics (quantroStatPerm) that are larger than the
quantroStat is reported as the quantroPvalPerm. To use
the foreach package, we first register a backend, in this case a
machine with 1 cores.
library(doParallel)
registerDoParallel(cores=1)
qtestPerm <- quantro(p, groupFactor = pd$CellType, B = 1000)
qtestPerm## quantro: Test for global differences in distributions
## nGroups: 2
## nTotSamples: 58
## nSamplesinGroups: 29 29
## anovaPval: 0.01206
## quantroStat: 8.80735
## quantroPvalPerm: 0.0016 Visualizing the statistical significance from permutation tests
If permutation testing was used (i.e. specifying B \(>\) 0), then
there is a second function in the package called quantroPlot()
which will plot the test statistics of the permuted samples. The plot is
a histogram of the null test statistics quantroStatPerm from
quantro() and the red line is the observed test statistic
quantroStat from quantro().
quantroPlot(qtestPerm)
Additional options in the quantroPlot() function include:
| Element | Description |
|---|---|
| xLab | the x-axis label |
| yLab | the y-axis label |
| mainLab | title of the histogram |
| binWidth | change the binwidth |
7 SessionInfo
sessionInfo()## R version 4.3.0 RC (2023-04-13 r84269)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Ubuntu 22.04.2 LTS
##
## Matrix products: default
## BLAS: /home/biocbuild/bbs-3.17-bioc/R/lib/libRblas.so
## LAPACK: /usr/lib/x86_64-linux-gnu/lapack/liblapack.so.3.10.0
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
## [3] LC_TIME=en_GB LC_COLLATE=C
## [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
## [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
## [9] LC_ADDRESS=C LC_TELEPHONE=C
## [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
##
## time zone: America/New_York
## tzcode source: system (glibc)
##
## attached base packages:
## [1] parallel stats4 stats graphics grDevices utils datasets
## [8] methods base
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## other attached packages:
## [1] doParallel_1.0.17 minfi_1.46.0
## [3] bumphunter_1.42.0 locfit_1.5-9.7
## [5] iterators_1.0.14 foreach_1.5.2
## [7] Biostrings_2.68.0 XVector_0.40.0
## [9] SummarizedExperiment_1.30.0 Biobase_2.60.0
## [11] MatrixGenerics_1.12.0 matrixStats_0.63.0
## [13] GenomicRanges_1.52.0 GenomeInfoDb_1.36.0
## [15] IRanges_2.34.0 S4Vectors_0.38.0
## [17] BiocGenerics_0.46.0 quantro_1.34.0
## [19] knitr_1.42 BiocStyle_2.28.0
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## loaded via a namespace (and not attached):
## [1] RColorBrewer_1.1-3 jsonlite_1.8.4
## [3] magrittr_2.0.3 magick_2.7.4
## [5] GenomicFeatures_1.52.0 farver_2.1.1
## [7] rmarkdown_2.21 BiocIO_1.10.0
## [9] zlibbioc_1.46.0 vctrs_0.6.2
## [11] multtest_2.56.0 memoise_2.0.1
## [13] Rsamtools_2.16.0 DelayedMatrixStats_1.22.0
## [15] RCurl_1.98-1.12 askpass_1.1
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## [25] plyr_1.8.8 cachem_1.0.7
## [27] GenomicAlignments_1.36.0 lifecycle_1.0.3
## [29] pkgconfig_2.0.3 Matrix_1.5-4
## [31] R6_2.5.1 fastmap_1.1.1
## [33] GenomeInfoDbData_1.2.10 digest_0.6.31
## [35] colorspace_2.1-0 siggenes_1.74.0
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## [53] HDF5Array_1.28.0 biomaRt_2.56.0
## [55] MASS_7.3-59 openssl_2.0.6
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## [61] glue_1.6.2 quadprog_1.5-8
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## [99] cli_3.6.1 xtable_1.8-4
## [101] munsell_0.5.0 jquerylib_0.1.4
## [103] Rcpp_1.0.10 dbplyr_2.3.2
## [105] png_0.1-8 XML_3.99-0.14
## [107] ggplot2_3.4.2 readr_2.1.4
## [109] blob_1.2.4 prettyunits_1.1.1
## [111] mclust_6.0.0 doRNG_1.8.6
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## [119] rlang_1.1.0 KEGGREST_1.40.0Aryee, Martin J, Andrew E Jaffe, Hector Corrada-Bravo, Christine Ladd-Acosta, Andrew P Feinberg, Kasper D Hansen, and Rafael A Irizarry. 2014. “Minfi: A Flexible and Comprehensive Bioconductor Package for the Analysis of Infinium Dna Methylation Microarrays.” Bioinformatics 30 (10): 1363–9. https://doi.org/10.1093/bioinformatics/btu049.
Bolstad, B M, R A Irizarry, M Astrand, and T P Speed. 2003. “A Comparison of Normalization Methods for High Density Oligonucleotide Array Data Based on Variance and Bias.” Bioinformatics 19 (2): 185–93.
Guintivano, Jerry, Martin J Aryee, and Zachary A Kaminsky. 2013. “A cell epigenotype specific model for the correction of brain cellular heterogeneity bias and its application to age, brain region and major depression.” Epigenetics 8 (3): 290–302. https://doi.org/10.4161/epi.23924.
Irizarry, Rafael A, Bridget Hobbs, Francois Collin, Yasmin D Beazer-Barclay, Kristen J Antonellis, Uwe Scherf, and Terence P Speed. 2003. “Exploration, Normalization, and Summaries of High Density Oligonucleotide Array Probe Level Data.” Biostatistics 4 (2): 249–64. https://doi.org/10.1093/biostatistics/4.2.249.
Jaffe, A J, and Z A Kaminsky. 2021. FlowSorted.DLPFC.450k: Illumina Humanmethylation Data on Sorted Frontal Cortex Cell Populations. R package version 1.29.0.