# The marr user’s guide

Tusharkanti Ghosh1, Max McGrath1, Daisy Philtron2, Katerina Kechris1 and Debashis Ghosh1

1Colorado School of Public Health
2Penn State University

#### 19 May 2021

#### Abstract

marr (Maximum Rank Reproducibility) is a nonparametric approach that detects reproducible signals using a maximal rank statistic for high-dimensional biological data.

#### Package

marr 1.2.0

# 1 Introduction

Reproducibility is an on-going challenge with high-throughput technologies that have been developed in the last two decades for quantifying a wide range of biological processes. One of the main difficulties faced by researchers is the variability of output across replicate experiments (Li et al. (2011)). Several authors have addressed the issue of reproducibility among high-throughput experiments (Porazinska et al. (2010), Marioni et al. (2008), AC’t Hoen et al. (2013)). In each high-throughput experiment (e.g., arrays, sequencing, mass spectrometry), a large number of features are measured simultaneously, and candidates are often subjected for follow-up statistical analysis. We use the term features to refer to biological features (e.g., metabolites, genes) resulting from a high-throughput experiment in the rest of this article. When measurements show consistency across replicate experiments, we define that measurement to be reproducible. Similarly, measurements that are not consistent across replicates may be problematic and should be identified. In this vignette, features that show consistency across high-dimensional replicate experiments are termed reproducible and the ones that are not consistent are termed irreproducible. The reproducibility of a high-throughput experiment primarily depends on the technical variables, such as run time, technical replicates, laboratory operators and biological variables, such as healthy and diseased subjects. A critical step toward making optimal design choices is to assess how these biological and technical variables affect reproducibility across replicate experiments (Talloen et al. (2010), Arvidsson et al. (2008)).

In this vignette, we introduce the marr procedure Philtron et al. (2018), referred to as maximum rank reproducibility (marr) to identify reproducible features in high-throughput replicate experiments. In this vignette, we demonstrate with an example data set that the (ma)ximum (r)ank (r)eproducibility (marr) procedure can be adapted to high-throughput MS-Metabolomics experiments across (biological or technical) replicate samples (Ghosh et al, 2020, in preparation).

The marr procedure was originally proposed to assess reproducibility of gene ranks in replicate experiments. The `marr` R-package contains the `Marr()` function, which calculates a matrix of signals (\(\text{irreproducible}=0\), \(\text{reproducible}=1\)) with \(M\) rows (total number of features) and \(J\) columns (\(J={I \choose 2}\)) (replicate sample pairs \({I \choose 2}\)), where \(J\) is the total possible number of sample pairs of replicate experiments. We assign feature \(m\) to be reproducible if a certain percentage signals (\(100c_s\%\)) are reproducible for pairwise combinations of replicate experiments, i.e., if \[ \frac{{\sum_{i<i'}{{{r_{m,{(i,i')}}}}}}}{J} >c_s, \]

such that, \(c_s \in (0,1)\).

Similarly, we assign a sample pair \((i,~i')\) to be reproducible if a certain percentage signals (\(100c_m\%\)) are reproducible across all features, i.e., if \[ \frac{\sum_{m}{{r{_{m,(i,i')}}}}}{M}>c_m, \] such that, \(c_m \in (0,1)\).

The reproducible signal matrix is shown in Figure 1 below.

Figure 1: Reproducible Signal matrix

# 2 Getting Started

Load the package in R

    library(marr)

# 3 msprepCOPD Data

The marr package contains a pre-processed data `SummarizedExperiment` assay object of 645 metabolites (features) measured in plasma and 20 biological replicates from the multi-center Genetic Epidemiology of COPD (COPDGene) study which was designed to study the underlying genetic factors of COPD, (Regan et al. (2011)). We only used a subset of the original raw COPD data in this vignette.

## 3.1 msprepCOPD data pre-processing

The msprepCOPD data in the marr package was pre-processed using the MSPrep software (Hughes et al. (2013)). The data pre-processing include \(3\) steps and they are as follows: 1. `Filtering`: Metabolites are removed if they are missing more than \(80\%\) of the samples, (Bijlsma et al. (2006), Chong et al. (2018)). Originally, there were 662 metabolites in the raw data. After filtering, 645 metabolites remain. 2. `Missing value imputation technique`: We apply Bayesian Principal Component Analysis (BPCA) to impute missing values (Hastie et al. (1999)). 3. `Normalization`: Median normalization are performed.

    data("msprepCOPD")
    msprepCOPD

    ## class: SummarizedExperiment
    ## dim: 645 20
    ## metadata(0):
    ## assays(1): abundance
    ## rownames: NULL
    ## rowData names(3): Mass Retention.Time Compound.Name
    ## colnames(20): 10062C 10071D ... 10473 10544U
    ## colData names(1): subject_id

# 4 Using the `Marr()` function

## 4.1 Input for `Marr()`

The `Marr()` function must have one object as input: 1. `object`: a data frame or a matrix or a SummarizedExperiment object with abundance measurements of metabolites (features) on the rows and replicates (samples) as the columns. `Marr()` accepts objects which are a data frame or matrix with observations (e.g. metabolites) on the rows and replicates as the columns. 2. `pSamplepairs`: optional We assign a metabolite (feature) for a replicate sample pair to be reproducible using a threshold value of `pSamplepairs` (\(c_s=0.75\)). 3. `pFeatures`: optional We assign a sample pair for a metabolite (feature) to be reproducible using a threshold value of `pFeatures` (\(c_m=0.75\)). 4. `alpha`: optional level of significance to control the False Discovery rate (FDR). Default is \(0.05\) (i.e., \(\alpha=0.05\)).

## 4.2 Running `Marr()`

### 4.2.1 msprepCOPD SummarizedExperiment example - Evaluating reproducibility

We apply the Marr procedure to assess the reproducibility of replicates in the msprepCOPD data. The distribution of reproducible pairs and metabolites (features) are illustrated in Figures 2 and 3, respectively. To run the `Marr()` function, we only input the data object. We obtain 4 outputs after running the `Marr()` function. They are shown below:

    library(marr)
    Marr_output<- Marr(msprepCOPD, pSamplepairs =
                       0.75, pFeatures = 0.75, alpha=0.05)
    Marr_output

    ## Marr: Maximum Rank Reproducibility
    ## MarrSamplepairs (length = 190 ):
    ##   sampleOne sampleTwo reproducibility
    ## 1    10062C    10071D          60.000
    ## 2    10062C    10087S          64.651
    ## 3    10062C    10097V          60.620
    ## ...
    ## MarrFeatures (length = 645 ):
    ##     Mass Retention.Time              Compound.Name reproducibility
    ## 1 58.054          0.511          Aminoacetaldehyde             100
    ## 2 71.074          3.216            3-Buten-1-amine             100
    ## 3 85.089          2.119 2-Amino-3-methyl-1-butanol             100
    ## ...

    ## Head of reproducible sample pairs per metabolite (feature)
    head(MarrFeatures(Marr_output))

    ##       Mass Retention.Time              Compound.Name reproducibility
    ## 1  58.0537      0.5107867          Aminoacetaldehyde       100.00000
    ## 2  71.0741      3.2161212            3-Buten-1-amine       100.00000
    ## 3  85.0893      2.1190255 2-Amino-3-methyl-1-butanol       100.00000
    ## 4  87.0687      0.5137375       4-Aminobutyraldehyde        16.31579
    ## 5 102.0782      0.6029379      N-Nitrosodiethylamine        20.52632
    ## 6 103.1000      3.8783060                    Neurine       100.00000

    ## Head of reproducible metabolites (features) per sample pair
    head(MarrSamplepairs(Marr_output))

    ##   sampleOne sampleTwo reproducibility
    ## 1    10062C    10071D        60.00000
    ## 2    10062C    10087S        64.65116
    ## 3    10062C    10097V        60.62016
    ## 4    10062C    101020        51.78295
    ## 5    10062C    10104S        53.33333
    ## 6    10062C    10136F        55.50388

    ## Percent of reproducible sample pairs per metabolite (feature)
    ##greater than 75%
    MarrFeaturesfiltered(Marr_output)

    ## [1] 49.45736

    ## Percent of reproducible metabolites (features) per sample pair
    ## greater than 75%
    MarrSamplepairsfiltered(Marr_output)

    ## [1] 7.368421

The distribution of reproducible metabolites/features (sample pairs) per sample pair (metabolite) can be extracted using the`MarrSamplepairs()` (`MarrFeatures()`) function (see above). The distribution of reproducible metabolites/features and sample pairs can plotted using the `MarrPlotSamplepairs()` and `MarrPlotFeatures()` functions, respectively (see below).

    MarrPlotSamplepairs(Marr_output)

Figure 2: Distribution of reproducible metabolites

    MarrPlotFeatures(Marr_output)

Figure 3: Distribution of reproducible sample pairs

Figure 2 illustrates percentage of reproducible metabolites (features) per sample pair in the \(x\)-axis. In Figure 2, the higher percentage of reproducible metabolites (features) per sample pair in the \(x\)-axis would indicate stronger reproducibility between the sample pairs.

Figure 3 illustrates percentage of reproducible sample pairs per metabolite (feature) in the \(x\)-axis. In Figure 3, the higher percentage of reproducible sample pairs per metabolite (feature) in the \(x\)-axis would indicate stronger reproducibility of a metabolite (feature) across all sample pairs.

## 4.3 Filtering the data by reproducible features and/or sample pairs

    ## Filtering the data by reproducible features
    MarrFilterData(Marr_output, by = "features")

    ## class: SummarizedExperiment
    ## dim: 319 20
    ## metadata(1): removedFeatures
    ## assays(1): abundance
    ## rownames: NULL
    ## rowData names(3): Mass Retention.Time Compound.Name
    ## colnames(20): 10062C 10071D ... 10473 10544U
    ## colData names(1): subject_id

    ## Filtering the data by reproducible sample pairs
    MarrFilterData(Marr_output, by = "samplePairs")

    ## class: SummarizedExperiment
    ## dim: 645 16
    ## metadata(1): removedSamples
    ## assays(1): abundance
    ## rownames: NULL
    ## rowData names(3): Mass Retention.Time Compound.Name
    ## colnames(16): 10062C 10071D ... 10465Y 10473
    ## colData names(1): subject_id

    ## Filtering the data by both features and sample pairs
    MarrFilterData(Marr_output, by = "both")

    ## class: SummarizedExperiment
    ## dim: 319 16
    ## metadata(2): removedSamples removedFeatures
    ## assays(1): abundance
    ## rownames: NULL
    ## rowData names(3): Mass Retention.Time Compound.Name
    ## colnames(16): 10062C 10071D ... 10465Y 10473
    ## colData names(1): subject_id

# 5 Session Info

    sessionInfo()

    ## R version 4.1.0 RC (2021-05-10 r80283)
    ## Platform: x86_64-w64-mingw32/x64 (64-bit)
    ## Running under: Windows Server x64 (build 17763)
    ##
    ## Matrix products: default
    ##
    ## locale:
    ## [1] LC_COLLATE=C
    ## [2] LC_CTYPE=English_United States.1252
    ## [3] LC_MONETARY=English_United States.1252
    ## [4] LC_NUMERIC=C
    ## [5] LC_TIME=English_United States.1252
    ##
    ## attached base packages:
    ## [1] stats     graphics  grDevices utils     datasets  methods   base
    ##
    ## other attached packages:
    ## [1] marr_1.2.0       knitr_1.33       BiocStyle_2.20.0
    ##
    ## loaded via a namespace (and not attached):
    ##  [1] SummarizedExperiment_1.22.0 tidyselect_1.1.1
    ##  [3] xfun_0.23                   bslib_0.2.5.1
    ##  [5] purrr_0.3.4                 lattice_0.20-44
    ##  [7] colorspace_2.0-1            vctrs_0.3.8
    ##  [9] generics_0.1.0              htmltools_0.5.1.1
    ## [11] stats4_4.1.0                yaml_2.2.1
    ## [13] utf8_1.2.1                  rlang_0.4.11
    ## [15] jquerylib_0.1.4             pillar_1.6.1
    ## [17] glue_1.4.2                  DBI_1.1.1
    ## [19] BiocGenerics_0.38.0         matrixStats_0.58.0
    ## [21] GenomeInfoDbData_1.2.6      lifecycle_1.0.0
    ## [23] stringr_1.4.0               zlibbioc_1.38.0
    ## [25] MatrixGenerics_1.4.0        munsell_0.5.0
    ## [27] gtable_0.3.0                evaluate_0.14
    ## [29] labeling_0.4.2              Biobase_2.52.0
    ## [31] IRanges_2.26.0              GenomeInfoDb_1.28.0
    ## [33] parallel_4.1.0              fansi_0.4.2
    ## [35] highr_0.9                   Rcpp_1.0.6
    ## [37] scales_1.1.1                BiocManager_1.30.15
    ## [39] DelayedArray_0.18.0         S4Vectors_0.30.0
    ## [41] magick_2.7.2                jsonlite_1.7.2
    ## [43] XVector_0.32.0              farver_2.1.0
    ## [45] ggplot2_3.3.3               digest_0.6.27
    ## [47] stringi_1.6.2               bookdown_0.22
    ## [49] dplyr_1.0.6                 GenomicRanges_1.44.0
    ## [51] grid_4.1.0                  tools_4.1.0
    ## [53] bitops_1.0-7                magrittr_2.0.1
    ## [55] sass_0.4.0                  RCurl_1.98-1.3
    ## [57] tibble_3.1.2                crayon_1.4.1
    ## [59] pkgconfig_2.0.3             ellipsis_0.3.2
    ## [61] Matrix_1.3-3                assertthat_0.2.1
    ## [63] rmarkdown_2.8               R6_2.5.0
    ## [65] compiler_4.1.0

# References

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Li, Qunhua, James B Brown, Haiyan Huang, Peter J Bickel, and others. 2011. “Measuring Reproducibility of High-Throughput Experiments.” The Annals of Applied Statistics 5 (3): 1752–79.

Marioni, John C, Christopher E Mason, Shrikant M Mane, Matthew Stephens, and Yoav Gilad. 2008. “RNA-Seq: An Assessment of Technical Reproducibility and Comparison with Gene Expression Arrays.” Genome Research 18 (9): 1509–17.

Philtron, Daisy, Yafei Lyu, Qunhua Li, and Debashis Ghosh. 2018. “Maximum Rank Reproducibility: A Nonparametric Approach to Assessing Reproducibility in Replicate Experiments.” Journal of the American Statistical Association 113 (523): 1028–39.

Porazinska, Dorota L, WAY Sung, ROBIN M GIBLIN-DAVIS, and W Kelley Thomas. 2010. “Reproducibility of Read Numbers in High-Throughput Sequencing Analysis of Nematode Community Composition and Structure.” Molecular Ecology Resources 10 (4): 666–76.

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