Package Tutorial - Using LR Correction

Melike Donertas

2019-12-31

Download data and prepare for the analysis

Data is downloaded from GEO using getGEO function in GEOquery library. Expression matrix with probeset IDs, age of the samples and covarietes to be included in the analysis are extracted from geo object. Please note that this tutorial is just to demonstrate the functionality of this package and is not a proper gene expression analysis tutorial. Thus we skip many potential QC steps and probeset -> gene ID mapping.

library(GEOquery)
#> Loading required package: Biobase
#> Loading required package: BiocGenerics
#> Loading required package: parallel
#> 
#> Attaching package: 'BiocGenerics'
#> The following objects are masked from 'package:parallel':
#> 
#>     clusterApply, clusterApplyLB, clusterCall, clusterEvalQ,
#>     clusterExport, clusterMap, parApply, parCapply, parLapply,
#>     parLapplyLB, parRapply, parSapply, parSapplyLB
#> The following objects are masked from 'package:stats':
#> 
#>     IQR, mad, sd, var, xtabs
#> The following objects are masked from 'package:base':
#> 
#>     anyDuplicated, append, as.data.frame, basename, cbind,
#>     colnames, dirname, do.call, duplicated, eval, evalq, Filter,
#>     Find, get, grep, grepl, intersect, is.unsorted, lapply, Map,
#>     mapply, match, mget, order, paste, pmax, pmax.int, pmin,
#>     pmin.int, Position, rank, rbind, Reduce, rownames, sapply,
#>     setdiff, sort, table, tapply, union, unique, unsplit, which,
#>     which.max, which.min
#> Welcome to Bioconductor
#> 
#>     Vignettes contain introductory material; view with
#>     'browseVignettes()'. To cite Bioconductor, see
#>     'citation("Biobase")', and for packages 'citation("pkgname")'.
#> Setting options('download.file.method.GEOquery'='auto')
#> Setting options('GEOquery.inmemory.gpl'=FALSE)
geo <- getGEO('GSE30272',destdir = '~/temp/')[[1]]
#> Found 1 file(s)
#> GSE30272_series_matrix.txt.gz
#> Using locally cached version: ~/temp//GSE30272_series_matrix.txt.gz
#> Parsed with column specification:
#> cols(
#>   .default = col_double(),
#>   ID_REF = col_character()
#> )
#> See spec(...) for full column specifications.
#> Using locally cached version of GPL4611 found here:
#> ~/temp//GPL4611.soft
pd <- Biobase::pData(geo)
expmat <- Biobase::exprs(geo)
ages <- setNames(as.numeric(pd$`age:ch1`), pd$geo_accession)
covs <- list(array = as.factor(setNames(pd$`array batch:ch1`, pd$geo_accession)),
bbs = as.factor(setNames(pd$`brain bank source:ch1`, pd$geo_accession)),
sex = as.factor(setNames(pd$`Sex:ch1`, pd$geo_accession)),
race = as.factor(setNames(pd$`race:ch1`, pd$geo_accession)))
ages <- ages[ages >= 20]
expmat <- expmat[, names(ages)]
covs <- lapply(covs, function(x)x[names(ages)])

Calculating the age-related changes in expression level and heterogeneity

We can simply use calc.het function in our package to have all relevant results:

• Here we supply ages in years (‘age_in’ parameter) but we want the model to be constructed on the fourt root scale of age (‘age_to’ parameter).
• We want to apply first linear regression and then Quantile Normalisation (‘batch_corr’ parameter) to correct for the confounding factors.
• The list of covariates are provided to regerss out their effect
• The age-related change in gene expression will be modelled using a linear model (‘modex’ parameter).
• Data will not be log2 transformed (‘tr_log2’ parameter).
• Features (probesets), will be scaled before the analysis (‘sc_features’ parameter).
• We will use spearman correlation coefficient between absolute values of residuals from the model for age-related change in expression level and ages to assess age-related change in expression heterogeneity (‘het_change_met’ parameter).
• All p-values calculated within this function will be corrected for multiple testing using ‘FDR’ (‘padj_met’ parameter).

library(hetAge)
resx <- calc.het(exprmat = expmat[sample(rownames(expmat),1000),], # expression matrix
  age = ages, # age vector
  age_in = 'years',  # scale of the age vector
  age_to = 'pw-0.25', # scale of ages to be used
  batch_corr = 'LR+QN',  # batch correction method
  modex = 'linear', # model for the change in expression level
  tr_log2 = F, # log2 transform input matrix
  sc_features = T, # scale genes / probesets
  covariates = covs, # covariates
  het_change_met = 'spearman', # method to measure change in heterogeneity
  padj_met = 'fdr') # multiple test correction method

Result object

The resulting object is a list with several fields.

The list of samples used in the analysis:

head(resx$sampleID)
#> [1] "GSM750020" "GSM750021" "GSM750022" "GSM750023" "GSM750024" "GSM750025"

The expression matrix inputted in the first place, only including the samples used in the analysis.

resx$input_expr[1:5,1:5]
#>                       GSM750020  GSM750021  GSM750022   GSM750023
#> HEEBO-080-HCC80N4    0.05536094  0.1507817  0.3152427  0.19768144
#> HEEBO-032-HCC32G15  -0.46212516 -0.1785417 -0.6524142  0.01314049
#> HEEBO-007-HCC7J15    0.10798765  0.6721227  0.2210720  0.44720241
#> HEEBO-067-HCC67B11   0.03375834  0.1425688  0.2642302  0.15855233
#> HEEBO-102-HCA102M19  0.08739160 -0.2273785 -0.1434752 -0.08734097
#>                       GSM750024
#> HEEBO-080-HCC80N4   -0.04424940
#> HEEBO-032-HCC32G15   0.26296393
#> HEEBO-007-HCC7J15    0.09596992
#> HEEBO-067-HCC67B11  -0.78331225
#> HEEBO-102-HCA102M19  0.25483009

The ages in the original format, including only the samples used in the analysis

head(resx$input_age)
#> GSM750020 GSM750021 GSM750022 GSM750023 GSM750024 GSM750025 
#>  20.22192  20.78630  20.86301  20.94521  21.01918  21.47397

The ages after re-formetted into desired format

Here we wanted the ages to be in fourth root scale.

head(resx$usedAge)
#> GSM750020 GSM750021 GSM750022 GSM750023 GSM750024 GSM750025 
#>  9.268913  9.332920  9.341518  9.350705  9.358950  9.409170

library(tidyverse)
#> ── Attaching packages ───────────────────────────────────────────────────────────────── tidyverse 1.2.1 ──
#> ✔ ggplot2 3.2.1     ✔ purrr   0.3.2
#> ✔ tibble  2.1.3     ✔ dplyr   0.8.3
#> ✔ tidyr   0.8.3     ✔ stringr 1.4.0
#> ✔ readr   1.3.1     ✔ forcats 0.4.0
#> ── Conflicts ──────────────────────────────────────────────────────────────────── tidyverse_conflicts() ──
#> ✖ dplyr::combine()    masks Biobase::combine(), BiocGenerics::combine()
#> ✖ dplyr::filter()     masks stats::filter()
#> ✖ dplyr::lag()        masks stats::lag()
#> ✖ ggplot2::Position() masks BiocGenerics::Position(), base::Position()
data.frame(age = resx$input_age, age0.25 = resx$usedAge) %>%
  ggplot(aes(x = age, y = age0.25)) +
  geom_point() +
  geom_smooth( method = 'loess') +
  theme_bw()

Expression matrix after correcting for confounding factors

These are the expression values for the probesets after accounting for the given covariates.

resx$LR_res$correctedExp[1:5,1:5]
#>                       GSM750020   GSM750021    GSM750022   GSM750023
#> HEEBO-080-HCC80N4   -0.16396197 -0.22149804 -0.197600600  0.03081186
#> HEEBO-032-HCC32G15   0.04219525 -0.12226046 -0.003262855 -0.55147667
#> HEEBO-007-HCC7J15   -0.45231902  0.10675979 -0.335327583  0.46635458
#> HEEBO-067-HCC67B11   0.11334242  0.07164012  0.068038034  0.75231582
#> HEEBO-102-HCA102M19  0.09371474 -0.09236562 -0.038308330 -0.68887942
#>                       GSM750024
#> HEEBO-080-HCC80N4   -0.09264594
#> HEEBO-032-HCC32G15   0.52260190
#> HEEBO-007-HCC7J15   -0.21492878
#> HEEBO-067-HCC67B11  -0.83223074
#> HEEBO-102-HCA102M19  0.13335169

Covariate coefficients for each feature

head(resx$LR_res$cov_coef)
#>                      (Intercept)  covarray.1 covarray.10 covarray.11
#> HEEBO-080-HCC80N4    0.219322907  0.08750003  -0.1305402  -0.1201039
#> HEEBO-032-HCC32G15  -0.504320419  0.40085120   0.2974034   0.7171240
#> HEEBO-007-HCC7J15    0.560306672  0.26045137   0.2454188  -0.1642902
#> HEEBO-067-HCC67B11  -0.079584084  0.02868392  -0.1608617  -0.2697832
#> HEEBO-102-HCA102M19 -0.006323141 -0.11559981   0.0969940   0.2872104
#> HEEBO-022-HCC22L5   -0.271284067  0.22426268   0.1500722  -0.1117165
#>                     covarray.12 covarray.13 covarray.14 covarray.15
#> HEEBO-080-HCC80N4   -0.12963752  -0.1179102 -0.36487842          NA
#> HEEBO-032-HCC32G15   0.21191424   1.0217497  0.39830074          NA
#> HEEBO-007-HCC7J15    0.05489805  -0.3240637 -0.12649879          NA
#> HEEBO-067-HCC67B11   0.05139789  -0.6360082 -0.34283061          NA
#> HEEBO-102-HCA102M19 -0.09345170   0.6209515  0.40434827          NA
#> HEEBO-022-HCC22L5    0.11412377  -0.3845804 -0.05879186          NA
#>                      covarray.16 covarray.17 covarray.18  covarray.19
#> HEEBO-080-HCC80N4   -0.236383209 -0.01256814 -0.21471822 -0.345928155
#> HEEBO-032-HCC32G15   0.197494525  0.16805447 -0.28884289 -0.602445451
#> HEEBO-007-HCC7J15    0.005987180  0.20146058  0.72478135 -0.052421433
#> HEEBO-067-HCC67B11   0.006673755 -0.12182664  0.22822666  0.299817410
#> HEEBO-102-HCA102M19  0.140891492  0.31722961  0.10286216  0.271018330
#> HEEBO-022-HCC22L5    0.113905883 -0.01687372 -0.02721613 -0.005352384
#>                      covarray.2  covarray.3  covarray.4  covarray.5
#> HEEBO-080-HCC80N4   -0.08483412  0.32088264  0.24378589 -0.07236595
#> HEEBO-032-HCC32G15   0.10447104 -0.08272082 -0.04727094  0.08729463
#> HEEBO-007-HCC7J15    0.11950811  0.37420799  0.07832349  0.14720948
#> HEEBO-067-HCC67B11   0.32186303  0.12626691  0.19028974 -0.12329526
#> HEEBO-102-HCA102M19  0.05549022 -0.25664401  0.01754580  0.02362881
#> HEEBO-022-HCC22L5    0.03997974  0.08424111  0.03023635  0.07037596
#>                      covarray.6  covarray.7   covarray.8 covarray.9
#> HEEBO-080-HCC80N4    0.04599456  0.21514419  0.100014241         NA
#> HEEBO-032-HCC32G15   0.09855558  0.25140655  0.002797911         NA
#> HEEBO-007-HCC7J15    0.39454630  0.31502784 -0.175826731         NA
#> HEEBO-067-HCC67B11   0.10896767 -0.07666651 -0.060366446         NA
#> HEEBO-102-HCA102M19 -0.10134975 -0.11307130  0.084767005         NA
#> HEEBO-022-HCC22L5   -0.08067107 -0.06376785  0.076040328         NA
#>                     covbbs.BTB covbbs.NIMH    covsex.5    covsex.F
#> HEEBO-080-HCC80N4           NA          NA -0.20495141 -0.09298862
#> HEEBO-032-HCC32G15          NA          NA  0.03406164  0.15553867
#> HEEBO-007-HCC7J15           NA          NA -0.01774561 -0.23516077
#> HEEBO-067-HCC67B11          NA          NA  0.59727070 -0.27384718
#> HEEBO-102-HCA102M19         NA          NA -0.19375831  0.14192097
#> HEEBO-022-HCC22L5           NA          NA  0.35810534 -0.17395426
#>                     covsex.M  covrace.AA  covrace.AS covrace.CAUC
#> HEEBO-080-HCC80N4         NA  0.06545684  0.11984152  -0.02736221
#> HEEBO-032-HCC32G15        NA  0.04718792  0.33596865  -0.06211015
#> HEEBO-007-HCC7J15         NA -0.25539515 -0.32161556  -0.37811509
#> HEEBO-067-HCC67B11        NA  0.12182882 -0.04381846   0.14950935
#> HEEBO-102-HCA102M19       NA -0.01308995  0.19807991   0.15780033
#> HEEBO-022-HCC22L5         NA -0.07992426 -0.17728326  -0.15957304
#>                     covrace.HISP
#> HEEBO-080-HCC80N4             NA
#> HEEBO-032-HCC32G15            NA
#> HEEBO-007-HCC7J15             NA
#> HEEBO-067-HCC67B11            NA
#> HEEBO-102-HCA102M19           NA
#> HEEBO-022-HCC22L5             NA

P values for the covariate coefficients for each feature based on linear regression

head(resx$LR_res$cov_p)
#>                     (Intercept) covarray.1 covarray.10  covarray.11
#> HEEBO-080-HCC80N4    0.29198469 0.62988389   0.4725447 0.5178972370
#> HEEBO-032-HCC32G15   0.01780076 0.03082354   0.1077441 0.0002084299
#> HEEBO-007-HCC7J15    0.04386085 0.28093221   0.3096206 0.5053696906
#> HEEBO-067-HCC67B11   0.71553021 0.88050523   0.3999591 0.1683725902
#> HEEBO-102-HCA102M19  0.96026606 0.29838433   0.3827267 0.0124067332
#> HEEBO-022-HCC22L5    0.15459778 0.17797060   0.3665244 0.5105269422
#>                     covarray.12  covarray.13 covarray.14 covarray.16
#> HEEBO-080-HCC80N4     0.5465101 5.232629e-01 0.143065416   0.2263659
#> HEEBO-032-HCC32G15    0.3312232 2.305996e-07 0.114890647   0.3180659
#> HEEBO-007-HCC7J15     0.8474022 1.876049e-01 0.701052952   0.9815353
#> HEEBO-067-HCC67B11    0.8199935 1.325977e-03 0.190199738   0.9740057
#> HEEBO-102-HCA102M19   0.4770681 1.908464e-07 0.008540665   0.2380117
#> HEEBO-022-HCC22L5     0.5613585 2.403765e-02 0.795439984   0.5227135
#>                     covarray.17 covarray.18 covarray.19 covarray.2
#> HEEBO-080-HCC80N4   0.948344590  0.25996072  0.22574852  0.6818626
#> HEEBO-032-HCC32G15  0.393278135  0.13553380  0.03843014  0.6184027
#> HEEBO-007-HCC7J15   0.434723766  0.00472668  0.88972586  0.6636521
#> HEEBO-067-HCC67B11  0.550553075  0.25475218  0.31748642  0.1406300
#> HEEBO-102-HCA102M19 0.008331661  0.37678167  0.12115619  0.6608818
#> HEEBO-022-HCC22L5   0.924183965  0.87554951  0.98359058  0.8325618
#>                     covarray.3 covarray.4 covarray.5 covarray.6 covarray.7
#> HEEBO-080-HCC80N4   0.08014095  0.2372337  0.6965723  0.8000927  0.2594620
#> HEEBO-032-HCC32G15  0.65432612  0.8205873  0.6425228  0.5924712  0.1938148
#> HEEBO-007-HCC7J15   0.12380799  0.7743169  0.5504018  0.1036470  0.2139261
#> HEEBO-067-HCC67B11  0.51024613  0.3795815  0.5276041  0.5684285  0.7016419
#> HEEBO-102-HCA102M19 0.02260143  0.8889990  0.8349345  0.3619898  0.3318732
#> HEEBO-022-HCC22L5   0.61322847  0.8722266  0.6782144  0.6271285  0.7139725
#>                     covarray.8  covsex.5     covsex.F covrace.AA
#> HEEBO-080-HCC80N4    0.6231264 0.5561418 0.1586798357  0.7170437
#> HEEBO-032-HCC32G15   0.9891698 0.9230422 0.0208280436  0.7965039
#> HEEBO-007-HCC7J15    0.5154375 0.9693637 0.0078805728  0.2878791
#> HEEBO-067-HCC67B11   0.7777626 0.1043588 0.0001194952  0.5213527
#> HEEBO-102-HCA102M19  0.4957549 0.3630518 0.0005608039  0.9055834
#> HEEBO-022-HCC22L5    0.6826493 0.2613828 0.0043796825  0.6283440
#>                     covrace.AS covrace.CAUC
#> HEEBO-080-HCC80N4    0.6282635    0.8831436
#> HEEBO-032-HCC32G15   0.1817446    0.7419918
#> HEEBO-007-HCC7J15    0.3284997    0.1278487
#> HEEBO-067-HCC67B11   0.8662173    0.4454020
#> HEEBO-102-HCA102M19  0.1917118    0.1670572
#> HEEBO-022-HCC22L5    0.4335958    0.3491379

The expression level matrix used for modeling

This is the matrix used to model age-related expression change - the reason it is different from corrected matrix is because we may further scale the expression level for the features (‘sc_features’ parameter.)

resx$usedMat[1:5,1:5]
#>                      GSM750020  GSM750021   GSM750022  GSM750023
#> HEEBO-080-HCC80N4   -0.8561896 -0.8197030 -0.83069764  0.1116702
#> HEEBO-032-HCC32G15   0.3066547 -0.4431166  0.02467863 -1.2227296
#> HEEBO-007-HCC7J15   -1.7727068  0.3473931 -1.12815860  0.7394777
#> HEEBO-067-HCC67B11   0.5754085  0.2808906  0.27640807  1.4018269
#> HEEBO-102-HCA102M19  0.7698637 -0.5266402 -0.27153411 -2.6147143
#>                      GSM750024
#> HEEBO-080-HCC80N4   -0.2864501
#> HEEBO-032-HCC32G15   1.8812654
#> HEEBO-007-HCC7J15   -0.4967503
#> HEEBO-067-HCC67B11  -2.1817360
#> HEEBO-102-HCA102M19  0.5652887

Residuals from the model between expression level and age

Absolute values of this matrix can be considered as the level of heterogeneity for each gene, each sample.

resx$residMat[1:5,1:5]
#>                      GSM750020   GSM750021   GSM750022  GSM750023
#> HEEBO-080-HCC80N4   -0.2138064 -0.19876831 -0.21264444  0.7266449
#> HEEBO-032-HCC32G15   0.2158614 -0.53087838 -0.06267592 -1.3096490
#> HEEBO-007-HCC7J15   -1.4016385  0.70607171 -0.77114444  1.0947136
#> HEEBO-067-HCC67B11   0.2323631 -0.05070092 -0.05364464  1.0734182
#> HEEBO-102-HCA102M19  0.7199227 -0.57491368 -0.31958361 -2.6625245
#>                      GSM750024
#> HEEBO-080-HCC80N4    0.3257617
#> HEEBO-032-HCC32G15   1.7947365
#> HEEBO-007-HCC7J15   -0.1431104
#> HEEBO-067-HCC67B11  -2.5086693
#> HEEBO-102-HCA102M19  0.5176933

Data frame with the summaries of age-related changes in expression level and heterogeneity

colnames(resx$feature_result)
#> [1] "feature"                    "level_change"              
#> [3] "level_change.p"             "heterogeneity_change"      
#> [5] "heterogeneity_change.p"     "level_change.p.adj"        
#> [7] "heterogeneity_change.p.adj"
head(resx$feature_result) 
#> # A tibble: 6 x 7
#>   feature level_change level_change.p heterogeneity_c… heterogeneity_c…
#>   <chr>          <dbl>          <dbl>            <dbl>            <dbl>
#> 1 HEEBO-…       0.335       0.0000748          -0.0986           0.233 
#> 2 HEEBO-…      -0.0474      0.586               0.210            0.0104
#> 3 HEEBO-…       0.194       0.0247              0.0886           0.284 
#> 4 HEEBO-…      -0.179       0.0380              0.141            0.0875
#> 5 HEEBO-…      -0.0261      0.764              -0.110            0.182 
#> 6 HEEBO-…      -0.297       0.000485            0.119            0.151 
#> # … with 2 more variables: level_change.p.adj <dbl>,
#> #   heterogeneity_change.p.adj <dbl>

Session Info

options(width = 100)
sessioninfo::session_info()
#> ─ Session info ───────────────────────────────────────────────────────────────────────────────────
#>  setting  value                       
#>  version  R version 3.6.1 (2019-07-05)
#>  os       macOS Catalina 10.15.2      
#>  system   x86_64, darwin15.6.0        
#>  ui       X11                         
#>  language (EN)                        
#>  collate  en_GB.UTF-8                 
#>  ctype    en_GB.UTF-8                 
#>  tz       Europe/Istanbul             
#>  date     2019-12-31                  
#> 
#> ─ Packages ───────────────────────────────────────────────────────────────────────────────────────
#>  package        * version   date       lib source        
#>  annotate         1.62.0    2019-05-02 [2] Bioconductor  
#>  AnnotationDbi    1.46.0    2019-05-02 [2] Bioconductor  
#>  assertthat       0.2.1     2019-03-21 [2] CRAN (R 3.6.0)
#>  backports        1.1.5     2019-10-02 [2] CRAN (R 3.6.0)
#>  Biobase        * 2.44.0    2019-05-02 [2] Bioconductor  
#>  BiocGenerics   * 0.30.0    2019-05-02 [2] Bioconductor  
#>  BiocParallel     1.18.1    2019-08-06 [2] Bioconductor  
#>  bit              1.1-14    2018-05-29 [2] CRAN (R 3.6.0)
#>  bit64            0.9-7     2017-05-08 [2] CRAN (R 3.6.0)
#>  bitops           1.0-6     2013-08-17 [2] CRAN (R 3.6.0)
#>  blob             1.2.0     2019-07-09 [2] CRAN (R 3.6.0)
#>  broom            0.5.2     2019-04-07 [2] CRAN (R 3.6.0)
#>  cellranger       1.1.0     2016-07-27 [2] CRAN (R 3.6.0)
#>  cli              1.1.0     2019-03-19 [2] CRAN (R 3.6.0)
#>  colorspace       1.4-1     2019-03-18 [2] CRAN (R 3.6.0)
#>  crayon           1.3.4     2017-09-16 [2] CRAN (R 3.6.0)
#>  curl             4.0       2019-07-22 [2] CRAN (R 3.6.0)
#>  DBI              1.0.0     2018-05-02 [2] CRAN (R 3.6.0)
#>  desc             1.2.0     2018-05-01 [2] CRAN (R 3.6.0)
#>  digest           0.6.21    2019-09-20 [2] CRAN (R 3.6.0)
#>  dplyr          * 0.8.3     2019-07-04 [2] CRAN (R 3.6.0)
#>  evaluate         0.14      2019-05-28 [2] CRAN (R 3.6.0)
#>  fansi            0.4.0     2018-10-05 [2] CRAN (R 3.6.0)
#>  forcats        * 0.4.0     2019-02-17 [2] CRAN (R 3.6.0)
#>  fs               1.3.1     2019-05-06 [2] CRAN (R 3.6.0)
#>  genefilter       1.66.0    2019-05-02 [2] Bioconductor  
#>  generics         0.0.2     2018-11-29 [2] CRAN (R 3.6.0)
#>  GEOquery       * 2.52.0    2019-05-02 [2] Bioconductor  
#>  ggplot2        * 3.2.1     2019-08-10 [2] CRAN (R 3.6.0)
#>  glue             1.3.1     2019-03-12 [2] CRAN (R 3.6.0)
#>  gtable           0.3.0     2019-03-25 [2] CRAN (R 3.6.0)
#>  haven            2.1.1     2019-07-04 [2] CRAN (R 3.6.0)
#>  hetAge         * 0.1.0     2019-12-30 [1] local         
#>  hms              0.5.0     2019-07-09 [2] CRAN (R 3.6.0)
#>  htmltools        0.3.6     2017-04-28 [2] CRAN (R 3.6.0)
#>  httr             1.4.1     2019-08-05 [2] CRAN (R 3.6.0)
#>  IRanges          2.18.1    2019-05-31 [2] Bioconductor  
#>  jsonlite         1.6       2018-12-07 [2] CRAN (R 3.6.0)
#>  knitr            1.24      2019-08-08 [2] CRAN (R 3.6.0)
#>  labeling         0.3       2014-08-23 [2] CRAN (R 3.6.0)
#>  lattice          0.20-38   2018-11-04 [2] CRAN (R 3.6.1)
#>  lazyeval         0.2.2     2019-03-15 [2] CRAN (R 3.6.0)
#>  limma            3.40.6    2019-07-26 [2] Bioconductor  
#>  lubridate        1.7.4     2018-04-11 [2] CRAN (R 3.6.0)
#>  magrittr         1.5       2014-11-22 [2] CRAN (R 3.6.0)
#>  MASS             7.3-51.4  2019-03-31 [2] CRAN (R 3.6.1)
#>  Matrix           1.2-17    2019-03-22 [2] CRAN (R 3.6.1)
#>  matrixStats      0.54.0    2018-07-23 [2] CRAN (R 3.6.0)
#>  memoise          1.1.0     2017-04-21 [2] CRAN (R 3.6.0)
#>  mgcv             1.8-28    2019-03-21 [2] CRAN (R 3.6.1)
#>  modelr           0.1.5     2019-08-08 [2] CRAN (R 3.6.0)
#>  munsell          0.5.0     2018-06-12 [2] CRAN (R 3.6.0)
#>  nlme             3.1-140   2019-05-12 [2] CRAN (R 3.6.1)
#>  pillar           1.4.2     2019-06-29 [2] CRAN (R 3.6.0)
#>  pkgconfig        2.0.3     2019-09-22 [2] CRAN (R 3.6.0)
#>  pkgdown          1.4.1     2019-09-15 [2] CRAN (R 3.6.0)
#>  plyr             1.8.4     2016-06-08 [2] CRAN (R 3.6.0)
#>  preprocessCore   1.46.0    2019-05-02 [2] Bioconductor  
#>  purrr          * 0.3.2     2019-03-15 [2] CRAN (R 3.6.0)
#>  R6               2.4.0     2019-02-14 [2] CRAN (R 3.6.0)
#>  Rcpp             1.0.2     2019-07-25 [2] CRAN (R 3.6.0)
#>  RCurl            1.95-4.12 2019-03-04 [2] CRAN (R 3.6.0)
#>  readr          * 1.3.1     2018-12-21 [2] CRAN (R 3.6.0)
#>  readxl           1.3.1     2019-03-13 [2] CRAN (R 3.6.0)
#>  reshape2         1.4.3     2017-12-11 [2] CRAN (R 3.6.0)
#>  rlang            0.4.0     2019-06-25 [2] CRAN (R 3.6.0)
#>  rmarkdown        1.14      2019-07-12 [2] CRAN (R 3.6.0)
#>  rprojroot        1.3-2     2018-01-03 [2] CRAN (R 3.6.0)
#>  RSQLite          2.1.2     2019-07-24 [2] CRAN (R 3.6.0)
#>  rstudioapi       0.10      2019-03-19 [2] CRAN (R 3.6.0)
#>  rvest            0.3.4     2019-05-15 [2] CRAN (R 3.6.0)
#>  S4Vectors        0.22.0    2019-05-02 [2] Bioconductor  
#>  scales           1.0.0     2018-08-09 [2] CRAN (R 3.6.0)
#>  sessioninfo      1.1.1     2018-11-05 [2] CRAN (R 3.6.0)
#>  stringi          1.4.3     2019-03-12 [2] CRAN (R 3.6.0)
#>  stringr        * 1.4.0     2019-02-10 [2] CRAN (R 3.6.0)
#>  survival         2.44-1.1  2019-04-01 [2] CRAN (R 3.6.1)
#>  sva              3.32.1    2019-05-22 [2] Bioconductor  
#>  tibble         * 2.1.3     2019-06-06 [2] CRAN (R 3.6.0)
#>  tidyr          * 0.8.3     2019-03-01 [2] CRAN (R 3.6.0)
#>  tidyselect       0.2.5     2018-10-11 [2] CRAN (R 3.6.0)
#>  tidyverse      * 1.2.1     2017-11-14 [2] CRAN (R 3.6.0)
#>  utf8             1.1.4     2018-05-24 [2] CRAN (R 3.6.0)
#>  vctrs            0.2.0     2019-07-05 [2] CRAN (R 3.6.0)
#>  withr            2.1.2     2018-03-15 [2] CRAN (R 3.6.0)
#>  xfun             0.8       2019-06-25 [2] CRAN (R 3.6.0)
#>  XML              3.98-1.20 2019-06-06 [2] CRAN (R 3.6.0)
#>  xml2             1.2.2     2019-08-09 [2] CRAN (R 3.6.0)
#>  xtable           1.8-4     2019-04-21 [2] CRAN (R 3.6.0)
#>  yaml             2.2.0     2018-07-25 [2] CRAN (R 3.6.0)
#>  zeallot          0.1.0     2018-01-28 [2] CRAN (R 3.6.0)
#> 
#> [1] /private/var/folders/z1/nv26gvmx4_11_968lfd0n5rh0000gn/T/RtmpAH4Avp/temp_libpath729350b707e8
#> [2] /Library/Frameworks/R.framework/Versions/3.6/Resources/library