Systemic lupus erythematosus whole blood compendium PLIER training
J. Taroni 2018
In this notebook, we’ll train a PLIER model on the systemic lupus erythematosis (SLE) whole blood (WB) compendium we processed in greenelab/rheum-plier-data/sle-wb and do some exploratory data analysis.
Functions and directory set up
library(AnnotationDbi)Loading required package: stats4
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, cbind, colMeans, colnames, colSums, do.call, duplicated, eval, evalq,
Filter, Find, get, grep, grepl, intersect, is.unsorted, lapply, lengths, Map, mapply, match, mget, order,
paste, pmax, pmax.int, pmin, pmin.int, Position, rank, rbind, Reduce, rowMeans, rownames, rowSums, sapply,
setdiff, sort, table, tapply, union, unique, unsplit, which, which.max, which.min
Loading required package: Biobase
Welcome to Bioconductor
Vignettes contain introductory material; view with 'browseVignettes()'. To cite Bioconductor, see
'citation("Biobase")', and for packages 'citation("pkgname")'.
Loading required package: IRanges
Loading required package: S4Vectors
Attaching package: ‘S4Vectors’
The following object is masked from ‘package:base’:
expand.grid`%>%` <- dplyr::`%>%`
# custom functions
source(file.path("util", "plier_util.R"))# plot and result directory setup for this notebook
plot.dir <- file.path("plots", "05")
dir.create(plot.dir, recursive = TRUE, showWarnings = FALSE)
results.dir <- file.path("results", "05")
dir.create(results.dir, recursive = TRUE, showWarnings = FALSE)Load SLE WB data
exprs.file <- file.path("data", "expression_data",
"SLE_WB_all_microarray_QN_zto_before.pcl")
exprs.df <- readr::read_tsv(exprs.file)Parsed with column specification:
cols(
.default = col_double(),
Gene = col_integer()
)
See spec(...) for full column specifications.
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symbol.obj <- org.Hs.eg.db::org.Hs.egSYMBOLmapped.genes <- AnnotationDbi::mappedkeys(symbol.obj)
symbol.list <- as.list(symbol.obj[mapped.genes])
symbol.df <- as.data.frame(cbind(names(symbol.list), unlist(symbol.list)))
colnames(symbol.df) <- c("EntrezID", "GeneSymbol")
# get gene column name to match to facilitate use with dplyr
colnames(exprs.df)[1] <- "EntrezID"
# matching types
symbol.df$EntrezID <- as.integer(as.character(symbol.df$EntrezID))
# inner join
annot.exprs.df <- dplyr::inner_join(symbol.df, exprs.df, by = "EntrezID")
symbol.file <-
file.path("data", "expression_data",
"SLE_WB_all_microarray_QN_zto_before_with_GeneSymbol.pcl")
readr::write_delim(annot.exprs.df, path = symbol.file, delim = "\t")
# matrix with gene symbol as rownames
exprs.mat <- dplyr::select(annot.exprs.df, -EntrezID)
rownames(exprs.mat) <- exprs.mat$GeneSymbol
exprs.mat <- as.matrix(dplyr::select(exprs.mat, -GeneSymbol))exprs.mat[1:5, 1:5] GSM955680_DNA10204-001.CEL GSM955681_DNA10204-003.CEL GSM955682_DNA10204-005.CEL GSM955683_DNA10204-007.CEL
NAT2 0.2872200 0.6788542 0.0000000 0.4627302
ADA 0.7331941 0.6073631 0.5483356 0.4294504
CDH2 0.2431701 0.3168936 0.3041239 0.6799173
AKT3 0.6418411 0.3147596 0.3863309 0.5632609
ZBTB11-AS1 0.2541135 0.5831909 0.3406465 0.4724936
GSM955684_DNA10204-011.CEL
NAT2 0.4656660
ADA 0.5349434
CDH2 0.1800279
AKT3 0.4955665
ZBTB11-AS1 0.3203299PLIER model training
plier.result <- PLIERNewData(exprs.mat = exprs.mat)Loading required package: PLIER
Loading required package: RColorBrewer
Loading required package: gplots
Attaching package: ‘gplots’
The following object is masked from ‘package:IRanges’:
space
The following object is masked from ‘package:S4Vectors’:
space
The following object is masked from ‘package:stats’:
lowess
Loading required package: pheatmap
Loading required package: glmnet
Loading required package: Matrix
Attaching package: ‘Matrix’
The following object is masked from ‘package:S4Vectors’:
expand
Loading required package: foreach
Loaded glmnet 2.0-13
Loading required package: knitr
Loading required package: rsvd
Loading required package: qvalue
Using rsvd: set seed for consistent results
Removing 1 pathways with too few genesComputing SVD
Using rsvd: set seed for consistent results
Done[1] 72.91089
[1] "L2 is set to 72.9108889298683"
[1] "L1 is set to 36.4554444649342"errorY (SVD based:best possible) = 0.2405
iter1 errorY= 0.961, Bdiff= 3205, Bkappa=63.2
iter2 errorY= 0.454, Bdiff= 0.7178, Bkappa=61.17
iter3 errorY= 0.3879, Bdiff= 0.09693, Bkappa=52.66
iter4 errorY= 0.3847, Bdiff= 0.03377, Bkappa=58.67
iter5 errorY= 0.3901, Bdiff= 0.01669, Bkappa=57.99
iter6 errorY= 0.3925, Bdiff= 0.01051, Bkappa=58.98
iter7 errorY= 0.3918, Bdiff= 0.007653, Bkappa=62.9
iter8 errorY= 0.39, Bdiff= 0.005949, Bkappa=69.28
iter9 errorY= 0.3881, Bdiff= 0.004802, Bkappa=72.59
iter10 errorY= 0.3865, Bdiff= 0.003974, Bkappa=78.22
iter11 errorY= 0.3851, Bdiff= 0.003345, Bkappa=84.16
iter12 errorY= 0.384, Bdiff= 0.00286, Bkappa=93.51
iter13 errorY= 0.383, Bdiff= 0.00248, Bkappa=95.31
iter14 errorY= 0.3821, Bdiff= 0.002183, Bkappa=102.1
iter15 errorY= 0.3813, Bdiff= 0.00195, Bkappa=105.2
iter16 errorY= 0.3806, Bdiff= 0.001764, Bkappa=109
iter17 errorY= 0.3799, Bdiff= 0.001615, Bkappa=103
iter18 errorY= 0.3792, Bdiff= 0.001492, Bkappa=112.6
iter19 errorY= 0.3786, Bdiff= 0.001391, Bkappa=116.6
Updating L3, current fraction= 0, target=0.7
L3 is set to 0.005372 in 11 iterations
iter20 errorY= 0.3764, prior information ratio= 0.01, Bdiff= 0.001516, Bkappa=127.5;pos. col. U=99
iter21 errorY= 0.3753, prior information ratio= 0.02, Bdiff= 0.001364, Bkappa=114.6;pos. col. U=99
iter22 errorY= 0.3745, prior information ratio= 0.02, Bdiff= 0.001246, Bkappa=120.1;pos. col. U=99
iter23 errorY= 0.3738, prior information ratio= 0.02, Bdiff= 0.001156, Bkappa=126.3;pos. col. U=98
iter24 errorY= 0.3732, prior information ratio= 0.02, Bdiff= 0.001085, Bkappa=130.5;pos. col. U=97
iter25 errorY= 0.3726, prior information ratio= 0.02, Bdiff= 0.001021, Bkappa=125.2;pos. col. U=97
iter26 errorY= 0.3721, prior information ratio= 0.02, Bdiff= 0.0009625, Bkappa=132.6;pos. col. U=97
iter27 errorY= 0.3717, prior information ratio= 0.02, Bdiff= 0.0009073, Bkappa=150;pos. col. U=95
iter28 errorY= 0.3713, prior information ratio= 0.02, Bdiff= 0.0008571, Bkappa=163.9;pos. col. U=93
iter29 errorY= 0.3709, prior information ratio= 0.02, Bdiff= 0.00081, Bkappa=145.9;pos. col. U=94
iter30 errorY= 0.3706, prior information ratio= 0.02, Bdiff= 0.000769, Bkappa=205.3;pos. col. U=95
iter31 errorY= 0.3703, prior information ratio= 0.02, Bdiff= 0.0007313, Bkappa=233.3;pos. col. U=95
iter32 errorY= 0.37, prior information ratio= 0.02, Bdiff= 0.0006994, Bkappa=290.4;pos. col. U=93
iter33 errorY= 0.3698, prior information ratio= 0.02, Bdiff= 0.00067, Bkappa=351.6;pos. col. U=92
iter34 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 0.0006404, Bkappa=436.2;pos. col. U=93
iter35 errorY= 0.3694, prior information ratio= 0.02, Bdiff= 0.0006086, Bkappa=565.3;pos. col. U=92
iter36 errorY= 0.3692, prior information ratio= 0.02, Bdiff= 0.0005764, Bkappa=738;pos. col. U=93
iter37 errorY= 0.369, prior information ratio= 0.02, Bdiff= 0.000542, Bkappa=977.9;pos. col. U=92
iter38 errorY= 0.3689, prior information ratio= 0.02, Bdiff= 0.000505, Bkappa=1302;pos. col. U=91
iter39 errorY= 0.3687, prior information ratio= 0.02, Bdiff= 0.000469, Bkappa=1740;pos. col. U=92
Updating L3, current fraction= 0.6479, target=0.7
L3 is set to 0.004375 in 4 iterations
iter40 errorY= 0.3685, prior information ratio= 0.02, Bdiff= 0.0004343, Bkappa=2309;pos. col. U=100
iter41 errorY= 0.3683, prior information ratio= 0.02, Bdiff= 0.0004026, Bkappa=3050;pos. col. U=99
iter42 errorY= 0.3681, prior information ratio= 0.02, Bdiff= 0.0003759, Bkappa=4010;pos. col. U=98
iter43 errorY= 0.368, prior information ratio= 0.02, Bdiff= 0.0003547, Bkappa=5257;pos. col. U=99
iter44 errorY= 0.3679, prior information ratio= 0.02, Bdiff= 0.0003367, Bkappa=6843;pos. col. U=99
iter45 errorY= 0.3678, prior information ratio= 0.02, Bdiff= 0.0003224, Bkappa=8754;pos. col. U=100
iter46 errorY= 0.3677, prior information ratio= 0.02, Bdiff= 0.0003107, Bkappa=11010;pos. col. U=100
iter47 errorY= 0.3676, prior information ratio= 0.02, Bdiff= 0.0003027, Bkappa=13570;pos. col. U=99
iter48 errorY= 0.3676, prior information ratio= 0.02, Bdiff= 0.0002956, Bkappa=16610;pos. col. U=100
iter49 errorY= 0.3675, prior information ratio= 0.02, Bdiff= 0.0002891, Bkappa=20120;pos. col. U=102
iter50 errorY= 0.3675, prior information ratio= 0.02, Bdiff= 0.0002837, Bkappa=24060;pos. col. U=102
iter51 errorY= 0.3674, prior information ratio= 0.02, Bdiff= 0.0002766, Bkappa=28260;pos. col. U=101
iter52 errorY= 0.3674, prior information ratio= 0.02, Bdiff= 0.0002703, Bkappa=33270;pos. col. U=101
iter53 errorY= 0.3673, prior information ratio= 0.02, Bdiff= 0.0002672, Bkappa=39490;pos. col. U=101
iter54 errorY= 0.3673, prior information ratio= 0.02, Bdiff= 0.0002619, Bkappa=47290;pos. col. U=102
iter55 errorY= 0.3673, prior information ratio= 0.02, Bdiff= 0.0002575, Bkappa=90640;pos. col. U=102
iter56 errorY= 0.3673, prior information ratio= 0.02, Bdiff= 0.0002522, Bkappa=114800;pos. col. U=103
iter57 errorY= 0.3672, prior information ratio= 0.02, Bdiff= 0.0002477, Bkappa=143100;pos. col. U=103
iter58 errorY= 0.3672, prior information ratio= 0.02, Bdiff= 0.0002437, Bkappa=176200;pos. col. U=102
iter59 errorY= 0.3672, prior information ratio= 0.02, Bdiff= 0.0002402, Bkappa=215700;pos. col. U=102
Updating L3, current fraction= 0.7183, target=0.7
L3 is set to 0.004586 in 11 iterations
iter60 errorY= 0.3673, prior information ratio= 0.02, Bdiff= 0.0002407, Bkappa=266400;pos. col. U=100
iter61 errorY= 0.3673, prior information ratio= 0.02, Bdiff= 0.0002373, Bkappa=329900;pos. col. U=99
iter62 errorY= 0.3673, prior information ratio= 0.02, Bdiff= 0.0002353, Bkappa=403300;pos. col. U=97
iter63 errorY= 0.3673, prior information ratio= 0.02, Bdiff= 0.0002334, Bkappa=480300;pos. col. U=96
iter64 errorY= 0.3673, prior information ratio= 0.02, Bdiff= 0.0002313, Bkappa=563200;pos. col. U=96
iter65 errorY= 0.3672, prior information ratio= 0.02, Bdiff= 0.0002303, Bkappa=682700;pos. col. U=96
iter66 errorY= 0.3672, prior information ratio= 0.02, Bdiff= 0.0002304, Bkappa=832400;pos. col. U=97
iter67 errorY= 0.3672, prior information ratio= 0.02, Bdiff= 0.0002356, Bkappa=1030000;pos. col. U=97
iter68 errorY= 0.3672, prior information ratio= 0.02, Bdiff= 0.0002416, Bkappa=1293000;pos. col. U=97
iter69 errorY= 0.3672, prior information ratio= 0.02, Bdiff= 0.0002485, Bkappa=1642000;pos. col. U=97
iter70 errorY= 0.3672, prior information ratio= 0.02, Bdiff= 0.0002544, Bkappa=2079000;pos. col. U=96
iter71 errorY= 0.3672, prior information ratio= 0.02, Bdiff= 0.0002608, Bkappa=2653000;pos. col. U=96
iter72 errorY= 0.3671, prior information ratio= 0.02, Bdiff= 0.0002674, Bkappa=3369000;pos. col. U=96
iter73 errorY= 0.3671, prior information ratio= 0.02, Bdiff= 0.0002753, Bkappa=4038000;pos. col. U=97
iter74 errorY= 0.3671, prior information ratio= 0.02, Bdiff= 0.0002864, Bkappa=4872000;pos. col. U=97
iter75 errorY= 0.3671, prior information ratio= 0.02, Bdiff= 0.0002905, Bkappa=5928000;pos. col. U=97
iter76 errorY= 0.367, prior information ratio= 0.02, Bdiff= 0.0002914, Bkappa=7248000;pos. col. U=96
iter77 errorY= 0.367, prior information ratio= 0.02, Bdiff= 0.0002883, Bkappa=8962000;pos. col. U=97
iter78 errorY= 0.367, prior information ratio= 0.02, Bdiff= 0.0002774, Bkappa=11420000;pos. col. U=97
iter79 errorY= 0.367, prior information ratio= 0.02, Bdiff= 0.000257, Bkappa=14720000;pos. col. U=97
Updating L3, current fraction= 0.6831, target=0.7
L3 is set to 0.004019 in 3 iterations
iter80 errorY= 0.3669, prior information ratio= 0.02, Bdiff= 0.0002324, Bkappa=18970000;pos. col. U=99
iter81 errorY= 0.3668, prior information ratio= 0.02, Bdiff= 0.000211, Bkappa=20850000;pos. col. U=99
iter82 errorY= 0.3668, prior information ratio= 0.02, Bdiff= 0.0001963, Bkappa=23650000;pos. col. U=99
iter83 errorY= 0.3668, prior information ratio= 0.02, Bdiff= 0.000181, Bkappa=28690000;pos. col. U=99
iter84 errorY= 0.3668, prior information ratio= 0.02, Bdiff= 0.0001708, Bkappa=32330000;pos. col. U=100
iter85 errorY= 0.3668, prior information ratio= 0.02, Bdiff= 0.0001627, Bkappa=40910000;pos. col. U=100
iter86 errorY= 0.3668, prior information ratio= 0.02, Bdiff= 0.0001568, Bkappa=53120000;pos. col. U=101
iter87 errorY= 0.3669, prior information ratio= 0.02, Bdiff= 0.0001521, Bkappa=65790000;pos. col. U=100
iter88 errorY= 0.3669, prior information ratio= 0.02, Bdiff= 0.0001492, Bkappa=85800000;pos. col. U=101
iter89 errorY= 0.3669, prior information ratio= 0.02, Bdiff= 0.0001471, Bkappa=107700000;pos. col. U=102
iter90 errorY= 0.3669, prior information ratio= 0.02, Bdiff= 0.0001454, Bkappa=142500000;pos. col. U=104
iter91 errorY= 0.367, prior information ratio= 0.02, Bdiff= 0.0001442, Bkappa=1.71e+08;pos. col. U=104
iter92 errorY= 0.367, prior information ratio= 0.02, Bdiff= 0.0001434, Bkappa=242600000;pos. col. U=104
iter93 errorY= 0.3671, prior information ratio= 0.02, Bdiff= 0.0001429, Bkappa=327200000;pos. col. U=104
iter94 errorY= 0.3671, prior information ratio= 0.02, Bdiff= 0.000142, Bkappa=478900000;pos. col. U=104
iter95 errorY= 0.3671, prior information ratio= 0.02, Bdiff= 0.0001412, Bkappa=617800000;pos. col. U=104
iter96 errorY= 0.3672, prior information ratio= 0.02, Bdiff= 0.0001401, Bkappa=803900000;pos. col. U=104
iter97 errorY= 0.3672, prior information ratio= 0.02, Bdiff= 0.000139, Bkappa=956500000;pos. col. U=104
iter98 errorY= 0.3673, prior information ratio= 0.02, Bdiff= 0.0001376, Bkappa=1.463e+09;pos. col. U=104
iter99 errorY= 0.3673, prior information ratio= 0.02, Bdiff= 0.0001364, Bkappa=1.485e+09;pos. col. U=104
Updating L3, current fraction= 0.7324, target=0.7
L3 is set to 0.004796 in 9 iterations
iter100 errorY= 0.3675, prior information ratio= 0.02, Bdiff= 0.0001386, Bkappa=1.963e+09;pos. col. U=99
iter101 errorY= 0.3676, prior information ratio= 0.02, Bdiff= 0.0001387, Bkappa=3.018e+09;pos. col. U=98
iter102 errorY= 0.3676, prior information ratio= 0.02, Bdiff= 0.000137, Bkappa=2.604e+09;pos. col. U=97
iter103 errorY= 0.3677, prior information ratio= 0.02, Bdiff= 0.0001356, Bkappa=4.261e+09;pos. col. U=97
iter104 errorY= 0.3678, prior information ratio= 0.02, Bdiff= 0.0001348, Bkappa=6.781e+09;pos. col. U=97
iter105 errorY= 0.3678, prior information ratio= 0.02, Bdiff= 0.0001336, Bkappa=8.941e+09;pos. col. U=98
iter106 errorY= 0.3679, prior information ratio= 0.02, Bdiff= 0.0001321, Bkappa=1.334e+10;pos. col. U=96
iter107 errorY= 0.3679, prior information ratio= 0.02, Bdiff= 0.0001312, Bkappa=1.806e+10;pos. col. U=96
iter108 errorY= 0.368, prior information ratio= 0.02, Bdiff= 0.0001321, Bkappa=1.498e+10;pos. col. U=96
iter109 errorY= 0.368, prior information ratio= 0.02, Bdiff= 0.0001342, Bkappa=2.626e+10;pos. col. U=97
iter110 errorY= 0.3681, prior information ratio= 0.02, Bdiff= 0.0001373, Bkappa=3.927e+10;pos. col. U=97
iter111 errorY= 0.3682, prior information ratio= 0.02, Bdiff= 0.0001413, Bkappa=5.418e+10;pos. col. U=97
iter112 errorY= 0.3682, prior information ratio= 0.02, Bdiff= 0.0001467, Bkappa=7.593e+10;pos. col. U=97
iter113 errorY= 0.3683, prior information ratio= 0.02, Bdiff= 0.000153, Bkappa=3.567e+10;pos. col. U=97
iter114 errorY= 0.3684, prior information ratio= 0.02, Bdiff= 0.0001604, Bkappa=9.284e+10;pos. col. U=96
iter115 errorY= 0.3685, prior information ratio= 0.02, Bdiff= 0.0001689, Bkappa=1.577e+11;pos. col. U=96
iter116 errorY= 0.3686, prior information ratio= 0.02, Bdiff= 0.0001786, Bkappa=2.661e+11;pos. col. U=95
iter117 errorY= 0.3686, prior information ratio= 0.02, Bdiff= 0.000188, Bkappa=2.905e+11;pos. col. U=95
iter118 errorY= 0.3687, prior information ratio= 0.02, Bdiff= 0.0001975, Bkappa=3.663e+11;pos. col. U=95
iter119 errorY= 0.3688, prior information ratio= 0.02, Bdiff= 0.0002096, Bkappa=6.886e+11;pos. col. U=94
Updating L3, current fraction= 0.662, target=0.7
L3 is set to 0.004351 in 5 iterations
iter120 errorY= 0.3688, prior information ratio= 0.02, Bdiff= 0.0002184, Bkappa=9.782e+11;pos. col. U=99
iter121 errorY= 0.3688, prior information ratio= 0.02, Bdiff= 0.0002269, Bkappa=1.339e+12;pos. col. U=98
iter122 errorY= 0.3689, prior information ratio= 0.02, Bdiff= 0.0002338, Bkappa=1.989e+12;pos. col. U=97
iter123 errorY= 0.3689, prior information ratio= 0.02, Bdiff= 0.0002368, Bkappa=1.569e+12;pos. col. U=98
iter124 errorY= 0.3689, prior information ratio= 0.02, Bdiff= 0.0002355, Bkappa=1.638e+12;pos. col. U=97
iter125 errorY= 0.369, prior information ratio= 0.02, Bdiff= 0.0002306, Bkappa=1.642e+12;pos. col. U=98
iter126 errorY= 0.369, prior information ratio= 0.02, Bdiff= 0.000221, Bkappa=2.305e+12;pos. col. U=98
iter127 errorY= 0.3691, prior information ratio= 0.02, Bdiff= 0.00021, Bkappa=2.832e+12;pos. col. U=98
iter128 errorY= 0.3691, prior information ratio= 0.02, Bdiff= 0.0001974, Bkappa=4.12e+12;pos. col. U=98
iter129 errorY= 0.3691, prior information ratio= 0.02, Bdiff= 0.000185, Bkappa=2.291e+12;pos. col. U=99
iter130 errorY= 0.3691, prior information ratio= 0.02, Bdiff= 0.0001719, Bkappa=6.462e+12;pos. col. U=98
iter131 errorY= 0.3691, prior information ratio= 0.02, Bdiff= 0.0001613, Bkappa=3.322e+12;pos. col. U=98
iter132 errorY= 0.3692, prior information ratio= 0.02, Bdiff= 0.0001534, Bkappa=2.686e+12;pos. col. U=97
iter133 errorY= 0.3692, prior information ratio= 0.02, Bdiff= 0.0001467, Bkappa=2.91e+12;pos. col. U=97
iter134 errorY= 0.3692, prior information ratio= 0.02, Bdiff= 0.0001416, Bkappa=9.082e+12;pos. col. U=97
iter135 errorY= 0.3692, prior information ratio= 0.02, Bdiff= 0.0001373, Bkappa=2.176e+13;pos. col. U=98
iter136 errorY= 0.3692, prior information ratio= 0.02, Bdiff= 0.000134, Bkappa=1.222e+13;pos. col. U=98
iter137 errorY= 0.3692, prior information ratio= 0.02, Bdiff= 0.0001331, Bkappa=2.596e+13;pos. col. U=98
iter138 errorY= 0.3692, prior information ratio= 0.02, Bdiff= 0.0001302, Bkappa=1.257e+13;pos. col. U=98
iter139 errorY= 0.3693, prior information ratio= 0.02, Bdiff= 0.0001264, Bkappa=2.389e+13;pos. col. U=99
Updating L3, current fraction= 0.6972, target=0.7
L3 not changed
iter140 errorY= 0.3693, prior information ratio= 0.02, Bdiff= 0.0001224, Bkappa=5.942e+13;pos. col. U=99
iter141 errorY= 0.3693, prior information ratio= 0.02, Bdiff= 0.0001175, Bkappa=1.501e+14;pos. col. U=99
iter142 errorY= 0.3694, prior information ratio= 0.02, Bdiff= 0.000112, Bkappa=1.597e+14;pos. col. U=98
iter143 errorY= 0.3694, prior information ratio= 0.02, Bdiff= 0.0001061, Bkappa=1.223e+14;pos. col. U=98
iter144 errorY= 0.3694, prior information ratio= 0.02, Bdiff= 1e-04, Bkappa=2.385e+13;pos. col. U=96
iter145 errorY= 0.3695, prior information ratio= 0.02, Bdiff= 9.465e-05, Bkappa=1.243e+14;pos. col. U=97
iter146 errorY= 0.3695, prior information ratio= 0.02, Bdiff= 8.981e-05, Bkappa=2.467e+14;pos. col. U=97
iter147 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 8.577e-05, Bkappa=2.606e+14;pos. col. U=97
iter148 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 8.266e-05, Bkappa=2.207e+14;pos. col. U=97
iter149 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 7.997e-05, Bkappa=6.04e+14;pos. col. U=98
iter150 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 7.788e-05, Bkappa=9.149e+14;pos. col. U=99
iter151 errorY= 0.3697, prior information ratio= 0.02, Bdiff= 7.639e-05, Bkappa=1.348e+15;pos. col. U=99
iter152 errorY= 0.3697, prior information ratio= 0.02, Bdiff= 7.533e-05, Bkappa=1.832e+15;pos. col. U=99
iter153 errorY= 0.3697, prior information ratio= 0.02, Bdiff= 7.472e-05, Bkappa=2.635e+15;pos. col. U=99
iter154 errorY= 0.3697, prior information ratio= 0.02, Bdiff= 7.433e-05, Bkappa=3.666e+15;pos. col. U=99
iter155 errorY= 0.3697, prior information ratio= 0.02, Bdiff= 7.421e-05, Bkappa=5.216e+15;pos. col. U=99
iter156 errorY= 0.3697, prior information ratio= 0.02, Bdiff= 7.433e-05, Bkappa=6.737e+15;pos. col. U=99
iter157 errorY= 0.3697, prior information ratio= 0.02, Bdiff= 7.46e-05, Bkappa=9.642e+15;pos. col. U=98
iter158 errorY= 0.3697, prior information ratio= 0.02, Bdiff= 7.504e-05, Bkappa=1.286e+16;pos. col. U=97
iter159 errorY= 0.3697, prior information ratio= 0.02, Bdiff= 7.568e-05, Bkappa=1.725e+16;pos. col. U=97
Updating L3, current fraction= 0.6831, target=0.7
L3 is set to 0.003947 in 5 iterations
iter160 errorY= 0.3697, prior information ratio= 0.02, Bdiff= 7.635e-05, Bkappa=2.332e+16;pos. col. U=99
iter161 errorY= 0.3697, prior information ratio= 0.02, Bdiff= 7.727e-05, Bkappa=3.203e+16;pos. col. U=99
iter162 errorY= 0.3697, prior information ratio= 0.02, Bdiff= 7.856e-05, Bkappa=4.252e+16;pos. col. U=99
iter163 errorY= 0.3697, prior information ratio= 0.02, Bdiff= 8.06e-05, Bkappa=5.515e+16;pos. col. U=99
iter164 errorY= 0.3697, prior information ratio= 0.02, Bdiff= 8.346e-05, Bkappa=8.465e+16;pos. col. U=98
iter165 errorY= 0.3697, prior information ratio= 0.02, Bdiff= 8.722e-05, Bkappa=9.738e+16;pos. col. U=98
iter166 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.21e-05, Bkappa=1.288e+17;pos. col. U=98
iter167 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.617e-05, Bkappa=1.72e+17;pos. col. U=98
iter168 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.789e-05, Bkappa=2.282e+17;pos. col. U=98
iter169 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.776e-05, Bkappa=3.229e+17;pos. col. U=97
iter170 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.678e-05, Bkappa=4.368e+17;pos. col. U=97
iter171 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.596e-05, Bkappa=5.161e+17;pos. col. U=97
iter172 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.573e-05, Bkappa=7.383e+17;pos. col. U=97
iter173 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.614e-05, Bkappa=9.916e+17;pos. col. U=96
iter174 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.718e-05, Bkappa=1.588e+18;pos. col. U=96
iter175 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.824e-05, Bkappa=2.074e+18;pos. col. U=97
iter176 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.958e-05, Bkappa=3.025e+18;pos. col. U=97
iter177 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 0.0001009, Bkappa=4.031e+18;pos. col. U=97
iter178 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 0.0001018, Bkappa=5.129e+18;pos. col. U=97
iter179 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 0.0001021, Bkappa=7.265e+18;pos. col. U=97
Updating L3, current fraction= 0.6831, target=0.7
L3 is set to 0.003825 in 5 iterations
iter180 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 0.0001018, Bkappa=9.302e+18;pos. col. U=99
iter181 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 0.0001016, Bkappa=1.232e+19;pos. col. U=100
iter182 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 0.0001012, Bkappa=1.631e+19;pos. col. U=100
iter183 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 0.0001002, Bkappa=1.947e+19;pos. col. U=100
iter184 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.996e-05, Bkappa=2.52e+19;pos. col. U=100
iter185 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.928e-05, Bkappa=3.277e+19;pos. col. U=100
iter186 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.854e-05, Bkappa=4.797e+19;pos. col. U=100
iter187 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.777e-05, Bkappa=5.799e+19;pos. col. U=99
iter188 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.714e-05, Bkappa=7.414e+19;pos. col. U=99
iter189 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.634e-05, Bkappa=1.086e+20;pos. col. U=100
iter190 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.599e-05, Bkappa=1.208e+20;pos. col. U=100
iter191 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.54e-05, Bkappa=1.565e+20;pos. col. U=100
iter192 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.526e-05, Bkappa=2.3e+20;pos. col. U=101
iter193 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.52e-05, Bkappa=3.256e+20;pos. col. U=101
iter194 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.564e-05, Bkappa=4.936e+20;pos. col. U=101
iter195 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.602e-05, Bkappa=6.396e+20;pos. col. U=101
Bdiff is not decreasing
iter196 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.601e-05, Bkappa=7.342e+20;pos. col. U=101
Bdiff is not decreasing
iter197 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.62e-05, Bkappa=1.131e+21;pos. col. U=101
Bdiff is not decreasing
iter198 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.671e-05, Bkappa=1.466e+21;pos. col. U=101
Bdiff is not decreasing
iter199 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 9.696e-05, Bkappa=2.004e+21;pos. col. U=101
Bdiff is not decreasing
Updating L3, current fraction= 0.7113, target=0.7
L3 is set to 0.004195 in 10 iterations
iter200 errorY= 0.3696, prior information ratio= 0.02, Bdiff= 0.0001001, Bkappa=2.482e+21;pos. col. U=99
Bdiff is not decreasing
converged at iteration 200 Bdiff is not decreasing
There are 57 LVs with AUC>0.70model.file <- file.path(results.dir, "SLE-WB_PLIER_model.RDS")
saveRDS(plier.result, file = model.file)Explore SLE WB PLIER model
U matrix
We can get an overview of what pathways are captured with the LVs by plotting U with PLIER::plotU. U is the prior information coefficient matrix; it tells us how the prior information in the form of pathways/gene sets relates to LVs.
pdf(file.path(plot.dir, "SLE-WB_PLIER_Uplot_auc0.75.pdf"))
PLIER::plotU(plier.result, auc.cutoff = 0.75, fontsize_row = 4,
fontsize_col = 7)
dev.off()null device
1 All LVs
What proportion of entries in U are non-zero (column-wise)? As a reminder, the fewer pathways that are associated with an LV (column), the easier interpretation will be. (Sparsity of U is a constraint in PLIER.)
num.lvs <- ncol(plier.result$Z)
u.sparsity.all <- CalculateUSparsity(plier.results = plier.result,
significant.only = FALSE)
ggplot2::ggplot(as.data.frame(u.sparsity.all),
ggplot2::aes(x = u.sparsity.all)) +
ggplot2::geom_density(fill = "blue", alpha = 0.5) +
ggplot2::theme_bw() +
ggplot2::labs(x = "proportion of positive entries in U",
title = paste("All LVs, n =", num.lvs))
plot.file <- file.path(plot.dir,
"SLE-WB_model_U_sparsity_all_density.png")
ggplot2::ggsave(plot.file, plot = ggplot2::last_plot(),
height = 5, width = 7)summary(u.sparsity.all) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000000 0.000000 0.005573 0.006033 0.011146 0.015924 Pathway-associated LVs
Now, only with significant associations (FDR < 0.05).
plier.summary <- plier.result$summary
sig.summary <- plier.summary %>%
dplyr::filter(FDR < 0.05)
num.sig.lvs <- length(unique(sig.summary$`LV index`))u.sparsity.sig <- CalculateUSparsity(plier.results = plier.result,
significant.only = TRUE,
fdr.cutoff = 0.05)
ggplot2::ggplot(as.data.frame(u.sparsity.sig),
ggplot2::aes(x = u.sparsity.sig)) +
ggplot2::geom_density(fill = "blue", alpha = 0.5) +
ggplot2::theme_bw() +
ggplot2::labs(x = "proportion of positive entries in U",
title = paste("Pathway-associated LVs, n =", num.sig.lvs))
plot.file <- file.path(plot.dir,
"SLE-WB_model_U_sparsity_sig_density.png")
ggplot2::ggsave(plot.file, plot = ggplot2::last_plot(),
height = 5, width = 7)summary(u.sparsity.sig) Min. 1st Qu. Median Mean 3rd Qu. Max.
0.000000 0.000000 0.000000 0.001929 0.003185 0.012739 Pathway coverage
What proportion of the pathways input into the model are significantly associated (FDR < 0.05) with an LV?
sle.coverage <- GetPathwayCoverage(plier.results = plier.result)
# Pathway coverage
sle.coverage$pathway[1] 0.1942675Less pathways are “covered” with this model than the recount2 model, where coverage was 0.419.
PCA of lower-dimensional (LV) space
We’ll perform PCA on the B matrix from the SLE WB PLIER model. This is mainly for visualization purposes.
The B matrix contains the samples values for each LV (from the model under consideration – here, the SLE WB PLIER model), where rows are LVs and samples are columns.
As noted when we prepped the data in greenelab/rheum-plier-data/sle-wb, there are still differences between datasets in the final compendium.
If the LVs that are not associated with any pathway (all AUC < 0.75) in fact capture nuisance variables, we expect that dropping them from the B matrix may reduce the dataset effect.
The AUC (and p-values) are calculated by holding out 1/5th of genes in a pathway (in the prior information matrix C), running PLIER, and testing how well the loadings in Z capture the held-out genes. For more information, check out the PLIER preprint (Mao, et al. 2017.).
# Which LVs have pathways with AUC > 0.75?
lv.auc <-
as.integer(unique(plier.summary$`LV index`[which(plier.summary$AUC > 0.75)]))
# B matrix
b.matrix <- as.matrix(plier.result$B)
# B matrix -- only LV AUC > 0.75 (any pathway)
sig.b.mat <- b.matrix[lv.auc, ]
# B matrix all other LV
oth.b.mat <- b.matrix[-lv.auc, ]# color palette for PCA plots
plot.color.pal <- c("#54FF9F", "#43CD80", "#2E8B57", "#006400", "#FF8C00",
"#8B4500", "#000080")
# read sample dataset mapping file
sd.file <- file.path("data", "sample_info", "sle-wb_sample_dataset_mapping.tsv")
sd.df <- readr::read_tsv(sd.file)Parsed with column specification:
cols(
SampleID = col_character(),
Dataset = col_character()
)All latent variables
# PCA
all.lv.pc <- prcomp(t(b.matrix))
cum.var.exp <- cumsum(all.lv.pc$sdev^2 / sum(all.lv.pc$sdev^2))
# PC1-2 in form suitable for ggplot2
all.lv.df <- as.data.frame(cbind(rownames(all.lv.pc$x),
all.lv.pc$x[, 1:2]))
colnames(all.lv.df)[1] <- "SampleID"
# add dataset of origin info
all.lv.df <- dplyr::full_join(all.lv.df, sd.df, by = "SampleID") %>%
dplyr::mutate(PC1 = as.numeric(as.character(PC1)),
PC2 = as.numeric(as.character(PC2)),
Dataset = factor(Dataset,
levels = c("E-GEOD-39088",
"E-GEOD-61635",
"E-GEOD-72747",
"E-GEOD-11907",
"E-GEOD-49454",
"E-GEOD-65391",
"E-GEOD-78193")))Column `SampleID` joining factor and character vector, coercing into character vector# plotting
all.plot <-
ggplot2::ggplot(all.lv.df, ggplot2::aes(x = PC1, y = PC2, colour = Dataset)) +
ggplot2::geom_point(alpha = 0.5) +
ggplot2::scale_color_manual(values = plot.color.pal) +
ggplot2::theme_bw() +
ggplot2::labs(x = paste0("PC1 (cum var exp = ",
round(cum.var.exp[1], 3), ")"),
y = paste0("PC2 (cum var exp = ",
round(cum.var.exp[2], 3), ")"),
title = "All Latent Variables") +
ggplot2::theme(plot.title = ggplot2::element_text(hjust = 0.5,
face = "bold"))
all.plot
Pathway-associated latent variables
# PCA
path.lv.pc <- prcomp(t(sig.b.mat))
cum.var.exp <- cumsum(path.lv.pc$sdev^2 / sum(path.lv.pc$sdev^2))
# PC1-2 in form suitable for ggplot2
path.lv.df <- as.data.frame(cbind(rownames(path.lv.pc$x),
path.lv.pc$x[, 1:2]))
colnames(path.lv.df)[1] <- "SampleID"
# add dataset of origin info
path.lv.df <- dplyr::full_join(path.lv.df, sd.df, by = "SampleID") %>%
dplyr::mutate(PC1 = as.numeric(as.character(PC1)),
PC2 = as.numeric(as.character(PC2)),
Dataset = factor(Dataset,
levels = c("E-GEOD-39088",
"E-GEOD-61635",
"E-GEOD-72747",
"E-GEOD-11907",
"E-GEOD-49454",
"E-GEOD-65391",
"E-GEOD-78193")))Column `SampleID` joining factor and character vector, coercing into character vector# plotting
path.plot <-
ggplot2::ggplot(path.lv.df, ggplot2::aes(x = PC1, y = PC2,
colour = Dataset)) +
ggplot2::geom_point(alpha = 0.5) +
ggplot2::scale_color_manual(values = plot.color.pal) +
ggplot2::theme_bw() +
ggplot2::labs(x = paste0("PC1 (cum var exp = ",
round(cum.var.exp[1], 3), ")"),
y = paste0("PC2 (cum var exp = ",
round(cum.var.exp[2], 3), ")"),
title = "Pathway-associated Latent Variables (AUC > 0.75)") +
ggplot2::theme(plot.title = ggplot2::element_text(hjust = 0.5,
face = "bold"))
path.plot
Other latent variables (AUC <= 0.75)
# PCA
oth.lv.pc <- prcomp(t(oth.b.mat))
cum.var.exp <- cumsum(oth.lv.pc$sdev^2 / sum(oth.lv.pc$sdev^2))
# PC1-2 in form suitable for ggplot2
oth.lv.df <- as.data.frame(cbind(rownames(oth.lv.pc$x),
oth.lv.pc$x[, 1:2]))
colnames(oth.lv.df)[1] <- "SampleID"
# add dataset of origin info
oth.lv.df <- dplyr::full_join(oth.lv.df, sd.df, by = "SampleID") %>%
dplyr::mutate(PC1 = as.numeric(as.character(PC1)),
PC2 = as.numeric(as.character(PC2)),
Dataset = factor(Dataset,
levels = c("E-GEOD-39088",
"E-GEOD-61635",
"E-GEOD-72747",
"E-GEOD-11907",
"E-GEOD-49454",
"E-GEOD-65391",
"E-GEOD-78193")))Column `SampleID` joining factor and character vector, coercing into character vector# plotting
oth.plot <-
ggplot2::ggplot(oth.lv.df, ggplot2::aes(x = PC1, y = PC2, colour = Dataset)) +
ggplot2::geom_point(alpha = 0.5) +
ggplot2::scale_color_manual(values = plot.color.pal) +
ggplot2::theme_bw() +
ggplot2::labs(x = paste0("PC1 (cum var exp = ",
round(cum.var.exp[1], 3), ")"),
y = paste0("PC2 (cum var exp = ",
round(cum.var.exp[2], 3), ")"),
title = "Latent Variables AUC <= 0.75") +
ggplot2::theme(plot.title = ggplot2::element_text(hjust = 0.5,
face = "bold"))
oth.plot
# Save to PDF
pdf(file.path(plot.dir, "SLE-WB_PLIER_LV_PCA_plots.pdf"), height = 14,
width = 7)
gridExtra::grid.arrange(all.plot, path.plot, oth.plot, ncol = 1)
dev.off()null device
1 ---
title: "Systemic lupus erythematosus whole blood compendium PLIER training"
output:   
  html_notebook: 
    toc: true
    toc_float: true
---

**J. Taroni 2018**

In this notebook, we'll train a PLIER model on the systemic lupus erythematosis 
(SLE) whole blood (WB) compendium we processed in 
[`greenelab/rheum-plier-data/sle-wb`](https://github.com/greenelab/rheum-plier-data/tree/4be547553f24fecac9e2f5c2b469a17f9df253f0/sle-wb)
and do some exploratory data analysis.

## Functions and directory set up

```{r}
library(AnnotationDbi)

`%>%` <- dplyr::`%>%`
# custom functions
source(file.path("util", "plier_util.R"))
```

```{r}
# plot and result directory setup for this notebook
plot.dir <- file.path("plots", "05")
dir.create(plot.dir, recursive = TRUE, showWarnings = FALSE)
results.dir <- file.path("results", "05")
dir.create(results.dir, recursive = TRUE, showWarnings = FALSE)
```

## Load SLE WB data
```{r}
exprs.file <- file.path("data", "expression_data", 
                        "SLE_WB_all_microarray_QN_zto_before.pcl")
exprs.df <- readr::read_tsv(exprs.file)
```
### Annotation
```{r}
symbol.obj <- org.Hs.eg.db::org.Hs.egSYMBOL
mapped.genes <- AnnotationDbi::mappedkeys(symbol.obj)
symbol.list <- as.list(symbol.obj[mapped.genes])
symbol.df <- as.data.frame(cbind(names(symbol.list), unlist(symbol.list)))
colnames(symbol.df) <- c("EntrezID", "GeneSymbol")

# get gene column name to match to facilitate use with dplyr
colnames(exprs.df)[1] <- "EntrezID"

# matching types
symbol.df$EntrezID <- as.integer(as.character(symbol.df$EntrezID))

# inner join
annot.exprs.df <- dplyr::inner_join(symbol.df, exprs.df, by = "EntrezID")

symbol.file <- 
  file.path("data", "expression_data", 
            "SLE_WB_all_microarray_QN_zto_before_with_GeneSymbol.pcl")

readr::write_delim(annot.exprs.df, path = symbol.file, delim = "\t")

# matrix with gene symbol as rownames
exprs.mat <- dplyr::select(annot.exprs.df, -EntrezID)
rownames(exprs.mat) <- exprs.mat$GeneSymbol
exprs.mat <- as.matrix(dplyr::select(exprs.mat, -GeneSymbol))
```
```{r}
exprs.mat[1:5, 1:5]
```

## PLIER model training

```{r}
plier.result <- PLIERNewData(exprs.mat = exprs.mat)
```
```{r}
model.file <- file.path(results.dir, "SLE-WB_PLIER_model.RDS")
saveRDS(plier.result, file = model.file)
```

## Explore SLE WB PLIER model

### U matrix

We can get an overview of what pathways are captured with the LVs by plotting 
`U` with `PLIER::plotU`.
`U` is the prior information coefficient matrix; it tells us how 
the prior information in the form of pathways/gene sets relates to LVs.

```{r}
pdf(file.path(plot.dir, "SLE-WB_PLIER_Uplot_auc0.75.pdf"))
PLIER::plotU(plier.result, auc.cutoff = 0.75, fontsize_row = 4,
             fontsize_col = 7)
dev.off()
```
#### All LVs

What proportion of entries in `U` are non-zero (column-wise)? 
As a reminder, the fewer pathways that are associated with an LV (column), the
easier interpretation will be. 
(Sparsity of `U` is a constraint in PLIER.)

```{r}
num.lvs <- ncol(plier.result$Z)
u.sparsity.all <- CalculateUSparsity(plier.results = plier.result,
                                     significant.only = FALSE)

ggplot2::ggplot(as.data.frame(u.sparsity.all),
                ggplot2::aes(x = u.sparsity.all)) +
  ggplot2::geom_density(fill = "blue", alpha = 0.5) +
  ggplot2::theme_bw() +
  ggplot2::labs(x = "proportion of positive entries in U",
                title = paste("All LVs, n =", num.lvs))
```

```{r}
plot.file <- file.path(plot.dir,
                       "SLE-WB_model_U_sparsity_all_density.png")
ggplot2::ggsave(plot.file, plot = ggplot2::last_plot(),
                height = 5, width = 7)
```
```{r}
summary(u.sparsity.all)
```

#### Pathway-associated LVs

Now, only with _significant_ associations (`FDR < 0.05`).

```{r}
plier.summary <- plier.result$summary
sig.summary <- plier.summary %>%
  dplyr::filter(FDR < 0.05)
num.sig.lvs <- length(unique(sig.summary$`LV index`))
```

```{r}
u.sparsity.sig <- CalculateUSparsity(plier.results = plier.result,
                                     significant.only = TRUE,
                                     fdr.cutoff = 0.05)

ggplot2::ggplot(as.data.frame(u.sparsity.sig),
                ggplot2::aes(x = u.sparsity.sig)) +
  ggplot2::geom_density(fill = "blue", alpha = 0.5) +
  ggplot2::theme_bw() +
  ggplot2::labs(x = "proportion of positive entries in U",
                title = paste("Pathway-associated LVs, n =", num.sig.lvs))
```
```{r}
plot.file <- file.path(plot.dir,
                       "SLE-WB_model_U_sparsity_sig_density.png")
ggplot2::ggsave(plot.file, plot = ggplot2::last_plot(),
                height = 5, width = 7)
```

```{r}
summary(u.sparsity.sig)
```

### Pathway coverage

What proportion of the pathways input into the model are significantly 
associated (`FDR < 0.05`) with an LV? 

```{r}
sle.coverage <- GetPathwayCoverage(plier.results = plier.result)

# Pathway coverage
sle.coverage$pathway
```

Less pathways are "covered" with this model than the recount2 model, where 
coverage was `0.419`.

### PCA of lower-dimensional (LV) space

We'll perform PCA on the `B` matrix from the SLE WB PLIER model. 
This is mainly for visualization purposes. 

The `B` matrix contains the samples values for each LV (from the model under 
consideration -- here, the SLE WB PLIER model), where rows are LVs and samples
are columns.

As noted when we prepped the data in [`greenelab/rheum-plier-data/sle-wb`](https://github.com/greenelab/rheum-plier-data/tree/4be547553f24fecac9e2f5c2b469a17f9df253f0/sle-wb), [there are still differences](https://github.com/greenelab/rheum-plier-data/blob/4be547553f24fecac9e2f5c2b469a17f9df253f0/sle-wb/plots/PCA/SLE_WB_all_microarray_QN_PC1-5_zto.before.png) between datasets in the final compendium.

If the LVs that are not associated with any pathway (all `AUC < 0.75`) 
in fact capture nuisance variables, we expect that dropping them from 
the `B` matrix may reduce the dataset effect.

The AUC (and p-values) are calculated by holding out 1/5th of genes in a pathway
(in the prior information matrix `C`), running PLIER, and testing how well the 
loadings in `Z` capture the held-out genes.
For more information, check out the [PLIER preprint (Mao, et al. 2017.)](http://dx.doi.org/10.1101/116061).

```{r}
# Which LVs have pathways with AUC > 0.75?
lv.auc <- 
  as.integer(unique(plier.summary$`LV index`[which(plier.summary$AUC > 0.75)]))

# B matrix
b.matrix <- as.matrix(plier.result$B)

# B matrix -- only LV AUC > 0.75 (any pathway)
sig.b.mat <- b.matrix[lv.auc, ]

# B matrix all other LV 
oth.b.mat <- b.matrix[-lv.auc, ]
```

```{r}
# color palette for PCA plots
plot.color.pal <- c("#54FF9F", "#43CD80", "#2E8B57", "#006400", "#FF8C00",
                    "#8B4500", "#000080")
# read sample dataset mapping file
sd.file <- file.path("data", "sample_info", "sle-wb_sample_dataset_mapping.tsv")
sd.df <- readr::read_tsv(sd.file)
```

#### All latent variables
```{r}
# PCA
all.lv.pc <- prcomp(t(b.matrix))
cum.var.exp <- cumsum(all.lv.pc$sdev^2 / sum(all.lv.pc$sdev^2))

# PC1-2 in form suitable for ggplot2
all.lv.df <- as.data.frame(cbind(rownames(all.lv.pc$x),
                                 all.lv.pc$x[, 1:2]))
colnames(all.lv.df)[1] <- "SampleID"
# add dataset of origin info
all.lv.df <- dplyr::full_join(all.lv.df, sd.df, by = "SampleID") %>%
  dplyr::mutate(PC1 = as.numeric(as.character(PC1)),
                PC2 = as.numeric(as.character(PC2)),
                Dataset = factor(Dataset, 
                                 levels = c("E-GEOD-39088",
                                            "E-GEOD-61635",
                                            "E-GEOD-72747",
                                            "E-GEOD-11907",
                                            "E-GEOD-49454",
                                            "E-GEOD-65391",
                                            "E-GEOD-78193")))

# plotting
all.plot <- 
  ggplot2::ggplot(all.lv.df, ggplot2::aes(x = PC1, y = PC2, colour = Dataset)) +
    ggplot2::geom_point(alpha = 0.5) +
    ggplot2::scale_color_manual(values = plot.color.pal) +
    ggplot2::theme_bw() +
    ggplot2::labs(x = paste0("PC1 (cum var exp = ", 
                             round(cum.var.exp[1], 3), ")"),
                  y = paste0("PC2 (cum var exp = ", 
                             round(cum.var.exp[2], 3), ")"), 
                  title = "All Latent Variables") +
    ggplot2::theme(plot.title = ggplot2::element_text(hjust = 0.5, 
                                                      face = "bold"))
all.plot
```

#### Pathway-associated latent variables
```{r}
# PCA
path.lv.pc <- prcomp(t(sig.b.mat))
cum.var.exp <- cumsum(path.lv.pc$sdev^2 / sum(path.lv.pc$sdev^2))
# PC1-2 in form suitable for ggplot2
path.lv.df <- as.data.frame(cbind(rownames(path.lv.pc$x),
                                 path.lv.pc$x[, 1:2]))
colnames(path.lv.df)[1] <- "SampleID"
# add dataset of origin info
path.lv.df <- dplyr::full_join(path.lv.df, sd.df, by = "SampleID") %>%
  dplyr::mutate(PC1 = as.numeric(as.character(PC1)),
                PC2 = as.numeric(as.character(PC2)),
                Dataset = factor(Dataset, 
                                 levels = c("E-GEOD-39088",
                                            "E-GEOD-61635",
                                            "E-GEOD-72747",
                                            "E-GEOD-11907",
                                            "E-GEOD-49454",
                                            "E-GEOD-65391",
                                            "E-GEOD-78193")))

# plotting
path.plot <- 
  ggplot2::ggplot(path.lv.df, ggplot2::aes(x = PC1, y = PC2, 
                                           colour = Dataset)) +
  ggplot2::geom_point(alpha = 0.5) +
  ggplot2::scale_color_manual(values = plot.color.pal) +
  ggplot2::theme_bw() +
  ggplot2::labs(x = paste0("PC1 (cum var exp = ", 
                           round(cum.var.exp[1], 3), ")"),
                y = paste0("PC2 (cum var exp = ", 
                           round(cum.var.exp[2], 3), ")"),
                title = "Pathway-associated Latent Variables (AUC > 0.75)") +
  ggplot2::theme(plot.title = ggplot2::element_text(hjust = 0.5, 
                                                    face = "bold"))
path.plot
```

#### Other latent variables (AUC <= 0.75)
```{r}
# PCA
oth.lv.pc <- prcomp(t(oth.b.mat))
cum.var.exp <- cumsum(oth.lv.pc$sdev^2 / sum(oth.lv.pc$sdev^2))
# PC1-2 in form suitable for ggplot2
oth.lv.df <- as.data.frame(cbind(rownames(oth.lv.pc$x),
                                 oth.lv.pc$x[, 1:2]))
colnames(oth.lv.df)[1] <- "SampleID"
# add dataset of origin info
oth.lv.df <- dplyr::full_join(oth.lv.df, sd.df, by = "SampleID") %>%
  dplyr::mutate(PC1 = as.numeric(as.character(PC1)),
                PC2 = as.numeric(as.character(PC2)),
                Dataset = factor(Dataset, 
                                 levels = c("E-GEOD-39088",
                                            "E-GEOD-61635",
                                            "E-GEOD-72747",
                                            "E-GEOD-11907",
                                            "E-GEOD-49454",
                                            "E-GEOD-65391",
                                            "E-GEOD-78193")))

# plotting
oth.plot <- 
  ggplot2::ggplot(oth.lv.df, ggplot2::aes(x = PC1, y = PC2, colour = Dataset)) +
    ggplot2::geom_point(alpha = 0.5) +
    ggplot2::scale_color_manual(values = plot.color.pal) +
    ggplot2::theme_bw() +
    ggplot2::labs(x = paste0("PC1 (cum var exp = ", 
                           round(cum.var.exp[1], 3), ")"),
                  y = paste0("PC2 (cum var exp = ", 
                           round(cum.var.exp[2], 3), ")"),
                  title = "Latent Variables AUC <= 0.75") +
    ggplot2::theme(plot.title = ggplot2::element_text(hjust = 0.5, 
                                                      face = "bold"))
oth.plot
```

```{r}
# Save to PDF
pdf(file.path(plot.dir, "SLE-WB_PLIER_LV_PCA_plots.pdf"), height = 14, 
              width = 7)
gridExtra::grid.arrange(all.plot, path.plot, oth.plot, ncol = 1)
dev.off()
```