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 sample9
gene1      86     376       6     132       2     196      73      16       1
gene2      91     343      10     140     366     123       2     232       1
gene3       1       7      20      51       1      13      92       1       2
gene4      22      76      15      19       4     165      36       1      34
gene5     303      21      11       2       4       9      21      19       2
gene6     171      43      70      10       1     646      60       5     179
      sample10 sample11 sample12 sample13 sample14 sample15 sample16 sample17
gene1      120       70       30        1        4      434       14        9
gene2       13       10        3        1        2        3        1        1
gene3       29      100      156        6       47       51        1       90
gene4        4       11       42       33        4      143       45        1
gene5       23      164       35       68      371        8       36        4
gene6       75       48        4        1        1        2        5        1
      sample18 sample19 sample20
gene1       33        1      771
gene2      270       16      201
gene3        1       48        5
gene4        1      171      259
gene5       14        7       45
gene6      390       71      253

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 63.29676 -0.8041195 -0.42622390 -0.5262095    0
sample2 55.69575  0.7617944 -1.67210790 -0.2016715    2
sample3 70.10650  2.2472788  0.11908446 -0.9896059    1
sample4 70.63567 -0.6641999  0.04521703  2.2840708    2
sample5 77.96669 -1.3180549  1.02961283  0.5713979    2
sample6 38.88339  0.9885427 -0.40173411 -1.2102923    1

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 7 columns
              baseMean              edf                 stat             pvalue
             <numeric>        <numeric>            <numeric>          <numeric>
gene1 81.4253796400377 1.00007419295041    0.572934259894597  0.449120409510763
gene2 64.2089409567406  1.0001805798025   0.0060870922093718  0.937812323068874
gene3 25.4176877255583 1.00016353565239   0.0360828830129869  0.849293862751811
gene4  49.414986734078 1.00009983657056     1.58905492703792  0.207502782756702
gene5 52.6868952663877  1.0000903343974 0.000201044287467747  0.988808979717613
gene6 101.964447252056 1.00012758158107     4.43364325483717 0.0352504020178051
                   padj              AIC              BIC
              <numeric>        <numeric>        <numeric>
gene1  0.76740404962448 221.237092511362 228.207292302555
gene2  0.98315823005564 210.027976254288 216.998281978303
gene3  0.98315823005564 186.150599623867 193.120888376472
gene4 0.518756956891755 212.087923725399 219.058149050772
gene5 0.988808979717613 208.985693252506 215.955909116259
gene6 0.220315012611282 213.205039928405  220.17529288038

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 8 columns
              baseMean               coef                SE               stat
             <numeric>          <numeric>         <numeric>          <numeric>
gene1 81.4253796400377 0.0349902301863601 0.353519641254002 0.0989767642393025
gene2 64.2089409567406  -1.10324626082546 0.382295850906086  -2.88584419164015
gene3 25.4176877255583  0.986836362736786 0.335410495603989    2.9421749637254
gene4  49.414986734078 0.0728591057203441 0.366217723435414  0.198950244780257
gene5 52.6868952663877  0.191059797207517 0.346928651164302  0.550717839435618
gene6 101.964447252056 -0.419486934543395 0.356564642620362  -1.17646811938677
                   pvalue               padj              AIC              BIC
                <numeric>          <numeric>        <numeric>        <numeric>
gene1   0.921156718950734   0.99197975902208 221.237092511362 228.207292302555
gene2  0.0039036535851509 0.0650608930858484 210.027976254288 216.998281978303
gene3 0.00325915727736301 0.0650608930858484 186.150599623867 193.120888376472
gene4   0.842301665380016   0.99197975902208 212.087923725399 219.058149050772
gene5   0.581827113553702   0.80809321326903 208.985693252506 215.955909116259
gene6   0.239407864815875  0.492632321705494 213.205039928405  220.17529288038

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 8 columns
              baseMean               coef                SE               stat
             <numeric>          <numeric>         <numeric>          <numeric>
gene1 81.4253796400377   -2.7131639288422  1.05078662267793  -2.58203128045891
gene2 64.2089409567406   1.16127575308661   1.1236278425628   1.03350567607682
gene3 25.4176877255583 0.0467667599049966 0.972884479289927 0.0480702086429933
gene4  49.414986734078 -0.504745493271176  1.08044349495277 -0.467165099914122
gene5 52.6868952663877 -0.728095802725808  1.01311664517777 -0.718669272873364
gene6 101.964447252056 -0.384564998847924  1.05291218612657 -0.365239384551768
                   pvalue              padj              AIC              BIC
                <numeric>         <numeric>        <numeric>        <numeric>
gene1 0.00982206819568156  0.13767978454464 221.237092511362 228.207292302555
gene2   0.301367315625772 0.717256325091551 210.027976254288 216.998281978303
gene3   0.961660288806558 0.976095822927323 186.150599623867 193.120888376472
gene4   0.640381760981334 0.878857924247414 212.087923725399 219.058149050772
gene5   0.472344719999109 0.878857924247414 208.985693252506 215.955909116259
gene6   0.714932721383029 0.893665901728786 213.205039928405  220.17529288038

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 7 columns
               baseMean              edf             stat               pvalue
              <numeric>        <numeric>        <numeric>            <numeric>
gene40 88.2535569044162 1.00013418959521 19.9134522390307 8.11913321784354e-06
gene16 63.7942069042264 1.00005861188695 10.1529904506291  0.00144128421239361
gene50 27.9997131432142 1.00003850939091 8.24635950147757  0.00408436534757521
gene21 56.8866459752251 1.00007860425559 8.19655243786665  0.00419853838989665
gene49 91.1287231731843 1.00004624043672 5.58321538643428   0.0181379955833232
gene36 71.2859287192644 1.00005179073371 5.54907912291258   0.0184957946586043
                       padj              AIC              BIC
                  <numeric>        <numeric>        <numeric>
gene40 0.000405956660892177 205.261742169082 212.232001700871
gene16   0.0360321053098403 194.405860677708 201.376044954333
gene50   0.0524817298737081 178.954856401689  185.92502066161
gene21   0.0524817298737081 190.606598193669 197.576802377341
gene49    0.154131622155036 227.980918816647  234.95109077462
gene36    0.154131622155036 221.544745003359 228.514922487942

Session info

R version 3.6.2 (2019-12-12)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows Server 2012 R2 x64 (build 9600)

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] parallel  stats4    stats     graphics  grDevices utils     datasets 
[8] methods   base     

other attached packages:
 [1] ggplot2_3.2.1               NBAMSeq_1.2.1              
 [3] SummarizedExperiment_1.16.1 DelayedArray_0.12.2        
 [5] BiocParallel_1.20.1         matrixStats_0.55.0         
 [7] Biobase_2.46.0              GenomicRanges_1.38.0       
 [9] GenomeInfoDb_1.22.0         IRanges_2.20.2             
[11] S4Vectors_0.24.3            BiocGenerics_0.32.0        

loaded via a namespace (and not attached):
 [1] bit64_0.9-7            splines_3.6.2          Formula_1.2-3         
 [4] assertthat_0.2.1       latticeExtra_0.6-29    blob_1.2.1            
 [7] GenomeInfoDbData_1.2.2 yaml_2.2.1             RSQLite_2.2.0         
[10] pillar_1.4.3           backports_1.1.5        lattice_0.20-38       
[13] glue_1.3.1             digest_0.6.24          RColorBrewer_1.1-2    
[16] XVector_0.26.0         checkmate_2.0.0        colorspace_1.4-1      
[19] htmltools_0.4.0        Matrix_1.2-18          DESeq2_1.26.0         
[22] XML_3.99-0.3           pkgconfig_2.0.3        genefilter_1.68.0     
[25] zlibbioc_1.32.0        purrr_0.3.3            xtable_1.8-4          
[28] snow_0.4-3             scales_1.1.0           jpeg_0.1-8.1          
[31] htmlTable_1.13.3       tibble_2.1.3           annotate_1.64.0       
[34] mgcv_1.8-31            farver_2.0.3           withr_2.1.2           
[37] nnet_7.3-12            lazyeval_0.2.2         survival_3.1-8        
[40] magrittr_1.5           crayon_1.3.4           memoise_1.1.0         
[43] evaluate_0.14          nlme_3.1-144           foreign_0.8-75        
[46] tools_3.6.2            data.table_1.12.8      lifecycle_0.1.0       
[49] stringr_1.4.0          locfit_1.5-9.1         munsell_0.5.0         
[52] cluster_2.1.0          AnnotationDbi_1.48.0   compiler_3.6.2        
[55] rlang_0.4.4            grid_3.6.2             RCurl_1.98-1.1        
[58] rstudioapi_0.11        htmlwidgets_1.5.1      labeling_0.3          
[61] bitops_1.0-6           base64enc_0.1-3        rmarkdown_2.1         
[64] gtable_0.3.0           DBI_1.1.0              R6_2.4.1              
[67] gridExtra_2.3          knitr_1.28             dplyr_0.8.4           
[70] bit_1.1-15.2           Hmisc_4.3-1            stringi_1.4.6         
[73] Rcpp_1.0.3             geneplotter_1.64.0     vctrs_0.2.2           
[76] rpart_4.1-15           acepack_1.4.1          png_0.1-7             
[79] tidyselect_1.0.0       xfun_0.12             

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). BioMed Central: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). Oxford University Press: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). Oxford University Press:2672–8.