Installation

To install and load NBAMSeq

Introduction

High-throughput sequencing experiments followed by differential expression analysis is a widely used approach to detect genomic biomarkers. A fundamental step in differential expression analysis is to model the association between gene counts and covariates of interest. NBAMSeq is a flexible statistical model based on the generalized additive model and allows for information sharing across genes in variance estimation. Specifically, we model the logarithm of mean gene counts as sums of smooth functions with the smoothing parameters and coefficients estimated simultaneously by a nested iteration. The variance is estimated by the Bayesian shrinkage approach to fully exploit the information across all genes.

The workflow of NBAMSeq contains three main steps:

Here we illustrate each of these steps respectively.

Data input

Users are expected to provide three parts of input, i.e. countData, colData, and design.

countData is a matrix of gene counts generated by RNASeq experiments.

      sample1 sample2 sample3 sample4 sample5 sample6 sample7 sample8
gene1       1      68      10       6       1      40       1      97
gene2      41      95     143      32     143      57      40       1
gene3       5     582       9      25     169     534     201       4
gene4      13       7       3      98       2       9     128      21
gene5     865      86     194      20      15      12      79      48
gene6     435       9      68       4      58      55     123       8
      sample9 sample10 sample11 sample12 sample13 sample14 sample15
gene1      60        1      499       13      368       28        3
gene2       1       35        1       10      151       80      574
gene3      26      367      129       13        1      192       46
gene4      10      179       12        4        2       12        1
gene5       1       22       52      553       38      416        2
gene6     134      115      247       43       30      103      501
      sample16 sample17 sample18 sample19 sample20
gene1        6      487        1       14       14
gene2        9        1        9       76      112
gene3        4        7        8        8       13
gene4      141        2        1       11      390
gene5      234      403       44      252       67
gene6       79       31       14       40      143

colData is a data frame which contains the covariates of samples. The sample order in colData should match the sample order in countData.

           pheno       var1        var2       var3 var4
sample1 55.65481  1.0657264 -0.62217573  1.3619716    1
sample2 63.89513 -1.3758422 -0.52953989 -0.7037095    2
sample3 63.83531  0.5011832 -1.81016743 -1.0769374    1
sample4 73.20474  1.0981266 -0.11230582 -0.8525421    2
sample5 24.72809 -2.8186670  0.09918202  0.4876742    1
sample6 65.51147  0.6251068 -0.39760542  1.7556906    0

design is a formula which specifies how to model the samples. Compared with other packages performing DE analysis including DESeq2 (Love, Huber, and Anders 2014), edgeR (Robinson, McCarthy, and Smyth 2010), NBPSeq (Di et al. 2015) and BBSeq (Zhou, Xia, and Wright 2011), NBAMSeq supports the nonlinear model of covariates via mgcv (Wood and Wood 2015). To indicate the nonlinear covariate in the model, users are expected to use s(variable_name) in the design formula. In our example, if we would like to model pheno as a nonlinear covariate, the design formula should be:

Several notes should be made regarding the design formula:

We then construct the NBAMSeqDataSet using countData, colData, and design:

class: NBAMSeqDataSet 
dim: 50 20 
metadata(1): fitted
assays(1): counts
rownames(50): gene1 gene2 ... gene49 gene50
rowData names(0):
colnames(20): sample1 sample2 ... sample19 sample20
colData names(5): pheno var1 var2 var3 var4

Differential expression analysis

Differential expression analysis can be performed by NBAMSeq function:

Several other arguments in NBAMSeq function are available for users to customize the analysis.

Pulling out DE results

Results of DE analysis can be pulled out by results function. For continuous covariates, the name argument should be specified indicating the covariate of interest. For nonlinear continuous covariates, base mean, effective degrees of freedom (edf), test statistics, p-value, and adjusted p-value will be returned.

DataFrame with 6 rows and 5 columns
              baseMean              edf                stat
             <numeric>        <numeric>           <numeric>
gene1 100.937580266488 1.00004934026771 0.00739771817458906
gene2 64.1566733017586 1.00013024983567    20.6606039556142
gene3 98.5440762816742 1.00011596573921    8.41353707770038
gene4 42.8141813606958 1.00003510580841    1.36409888427823
gene5 175.611056201745 1.00016073385872    2.29502462179236
gene6 94.4200060200211 1.00003675221347     1.1392203146464
                    pvalue                 padj
                 <numeric>            <numeric>
gene1    0.931496982211732    0.931496982211732
gene2 5.49086104824696e-06 0.000274543052412348
gene3  0.00372833308506262   0.0266309506075901
gene4    0.242853541081588    0.510846422256105
gene5    0.129855187879848    0.381927023176022
gene6    0.285836478487016    0.510846422256105

For linear continuous covariates, base mean, estimated coefficient, standard error, test statistics, p-value, and adjusted p-value will be returned.

DataFrame with 6 rows and 6 columns
              baseMean               coef                SE
             <numeric>          <numeric>         <numeric>
gene1 100.937580266488  0.691131557509217 0.415793265615062
gene2 64.1566733017586 -0.796355771776422 0.345981106392014
gene3 98.5440762816742  -1.24207843429552 0.382782346954202
gene4 42.8141813606958 -0.215753187480105 0.399518956600663
gene5 175.611056201745  0.626248618609277 0.434026691631932
gene6 94.4200060200211  0.381498101589746 0.340468204185752
                    stat              pvalue               padj
               <numeric>           <numeric>          <numeric>
gene1   1.66219997932593  0.0964726841805165  0.299659193166566
gene2  -2.30173196473368  0.0213502924093895 0.0996898699906995
gene3  -3.24486864187634 0.00117504814221757 0.0184090875614086
gene4 -0.540032416273454   0.589174677197809   0.74331882603971
gene5   1.44288042805523   0.149054157443745  0.368712915781896
gene6   1.12051021769307   0.262496400908593   0.46471975757829

For discrete covariates, the contrast argument should be specified. e.g.  contrast = c("var4", "2", "0") means comparing level 2 vs. level 0 in var4.

DataFrame with 6 rows and 6 columns
              baseMean               coef                SE
             <numeric>          <numeric>         <numeric>
gene1 100.937580266488   1.78966020892694 0.982971186883701
gene2 64.1566733017586  -1.75408035097624 0.888800424973438
gene3 98.5440762816742 0.0348497330412195 0.926950514479007
gene4 42.8141813606958 -0.572222219450487 0.984081448797224
gene5 175.611056201745   1.01270598805079  1.05472301348336
gene6 94.4200060200211  0.178773027907122 0.828194557609955
                    stat             pvalue              padj
               <numeric>          <numeric>         <numeric>
gene1   1.82066395516706  0.068657954526038 0.264069055869377
gene2  -1.97353680499046 0.0484344355945416 0.264069055869377
gene3 0.0375961094976109  0.970009709901786 0.987761021554848
gene4 -0.581478514964259   0.56091799435778 0.846718160930295
gene5  0.960162976539396  0.336973197102616 0.707658431242869
gene6  0.215858733028908   0.82909786500273 0.948147521787377

Visualization

We suggest two approaches to visualize the nonlinear associations. The first approach is to plot the smooth components of a fitted negative binomial additive model by plot.gam function in mgcv (Wood and Wood 2015). This can be done by calling makeplot function and passing in NBAMSeqDataSet object. Users are expected to provide the phenotype of interest in phenoname argument and gene of interest in genename argument.

In addition, to explore the nonlinear association of covariates, it is also instructive to look at log normalized counts vs. variable scatter plot. Below we show how to produce such plot.

DataFrame with 6 rows and 5 columns
               baseMean              edf             stat
              <numeric>        <numeric>        <numeric>
gene2  64.1566733017586 1.00013024983567 20.6606039556142
gene10 84.8465952698202 1.00008243290987 13.6902855589529
gene8  55.9271170671289 1.00026287520925 13.3033984048181
gene30 15.7090102460532  1.0000651518018 9.82340324781178
gene22 151.701858867258 1.00006573042838 9.60046395262862
gene34 164.578239460982 1.00005879526844  9.4297628600664
                     pvalue                 padj
                  <numeric>            <numeric>
gene2  5.49086104824696e-06 0.000274543052412348
gene10 0.000215712061941596  0.00443108302025615
gene8  0.000265864981215369  0.00443108302025615
gene30  0.00172418018146628   0.0177973244103175
gene22  0.00194666870785135   0.0177973244103175
gene34  0.00213567892923811   0.0177973244103175

Session info

R Under development (unstable) (2019-11-03 r77362)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: OS X El Capitan 10.11.6

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib

locale:
[1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] parallel  stats4    stats     graphics  grDevices utils     datasets 
[8] methods   base     

other attached packages:
 [1] ggplot2_3.2.1               NBAMSeq_1.3.0              
 [3] SummarizedExperiment_1.17.0 DelayedArray_0.13.0        
 [5] BiocParallel_1.21.0         matrixStats_0.55.0         
 [7] Biobase_2.47.0              GenomicRanges_1.39.1       
 [9] GenomeInfoDb_1.23.0         IRanges_2.21.1             
[11] S4Vectors_0.25.0            BiocGenerics_0.33.0        

loaded via a namespace (and not attached):
 [1] bit64_0.9-7            splines_4.0.0          Formula_1.2-3         
 [4] assertthat_0.2.1       latticeExtra_0.6-28    blob_1.2.0            
 [7] GenomeInfoDbData_1.2.2 yaml_2.2.0             pillar_1.4.2          
[10] RSQLite_2.1.2          backports_1.1.5        lattice_0.20-38       
[13] glue_1.3.1             digest_0.6.22          RColorBrewer_1.1-2    
[16] XVector_0.27.0         checkmate_1.9.4        colorspace_1.4-1      
[19] htmltools_0.4.0        Matrix_1.2-17          DESeq2_1.27.2         
[22] XML_3.98-1.20          pkgconfig_2.0.3        genefilter_1.69.0     
[25] zlibbioc_1.33.0        purrr_0.3.3            xtable_1.8-4          
[28] scales_1.0.0           htmlTable_1.13.2       tibble_2.1.3          
[31] annotate_1.65.0        mgcv_1.8-30            withr_2.1.2           
[34] nnet_7.3-12            lazyeval_0.2.2         survival_3.1-6        
[37] magrittr_1.5           crayon_1.3.4           memoise_1.1.0         
[40] evaluate_0.14          nlme_3.1-141           foreign_0.8-72        
[43] tools_4.0.0            data.table_1.12.6      stringr_1.4.0         
[46] locfit_1.5-9.1         munsell_0.5.0          cluster_2.1.0         
[49] AnnotationDbi_1.49.0   compiler_4.0.0         rlang_0.4.1           
[52] grid_4.0.0             RCurl_1.95-4.12        rstudioapi_0.10       
[55] htmlwidgets_1.5.1      labeling_0.3           bitops_1.0-6          
[58] base64enc_0.1-3        rmarkdown_1.16         gtable_0.3.0          
[61] DBI_1.0.0              R6_2.4.0               gridExtra_2.3         
[64] knitr_1.25             dplyr_0.8.3            zeallot_0.1.0         
[67] bit_1.1-14             Hmisc_4.2-0            stringi_1.4.3         
[70] Rcpp_1.0.2             geneplotter_1.65.0     vctrs_0.2.0           
[73] rpart_4.1-15           acepack_1.4.1          tidyselect_0.2.5      
[76] xfun_0.10             

References

Di, Y, DW Schafer, JS Cumbie, and JH Chang. 2015. “NBPSeq: Negative Binomial Models for Rna-Sequencing Data.” R Package Version 0.3. 0, URL Http://CRAN. R-Project. Org/Package= NBPSeq.

Love, Michael I, Wolfgang Huber, and Simon Anders. 2014. “Moderated Estimation of Fold Change and Dispersion for Rna-Seq Data with Deseq2.” Genome Biology 15 (12): 550.

Robinson, Mark D, Davis J McCarthy, and Gordon K Smyth. 2010. “EdgeR: A Bioconductor Package for Differential Expression Analysis of Digital Gene Expression Data.” Bioinformatics 26 (1): 139–40.

Wood, Simon, and Maintainer Simon Wood. 2015. “Package ’Mgcv’.” R Package Version 1: 29.

Zhou, Yi-Hui, Kai Xia, and Fred A Wright. 2011. “A Powerful and Flexible Approach to the Analysis of Rna Sequence Count Data.” Bioinformatics 27 (19): 2672–8.