This guide will serve as a brief overview to the pathway significance testing workflow with the pathwayPCA
package. We will discuss the four basic steps of pathway significance testing with the pathwayPCA
package. These steps are: importing data, creating an Omics
data object, testing pathways for significance, and inspecting the results. For detailed discussions of these steps, see the following appropriate vignettes:
pathwayPCA
is a package for R, so you need R first. We also strongly recommend the RStudio integrated development environment as a user-friendly graphical wrapper for R.
The stable build of our package will be available on Bioconductor in May of 2019. To access Bioconductor packages, first install BiocManager, then use BiocManager to install this package:
install.packages("BiocManager")
BiocManager::install("pathwayPCA")
Because we are currently in the development phase for version 2 of this package, you can install the package from GitHub. In order to install a package from GitHub, you will need the devtools::
package (https://github.com/r-lib/devtools) and either Rtools (for Windows) or Xcode (for Mac). Then you can install the development version of the pathwayPCA
package from GitHub:
devtools::install_github("gabrielodom/pathwayPCA")
Also, if you want your analysis to be performed with parallel computing, you will need a package to help you. We recommend the parallel
package (it comes with R
automatically). We also recommend the tidyverse
package to help you run some of the examples in these vignettes (while the tidyverse
package suite is required for many of the examples in the vignettes, it is not required for any of the functions in this package).
install.packages("tidyverse")
This section is a quick overview of the material covered in the Import and Tidy Data vignette. Here we show how to import pathway information, assay and phenotype data, and how to join the assay and phenotype data into one data frame.
.gmt
FilesThe .gmt
format is a commonly used file format for storing pathway information. Lists of pathways in the Molecular Signatures Database (MSigDB) can be downloaded from the MSigDB Collections page, and you can use the read_gmt
function to import such a .gmt
file into R. All .gmt
files have a “description” field, which contains additional information on the pathway. However, this field can be left empty. In this example, we use description = FALSE
to skip importing the “description” field.
gmt_path <- system.file("extdata", "c2.cp.v6.0.symbols.gmt",
package = "pathwayPCA", mustWork = TRUE)
cp_pathwayCollection <- read_gmt(gmt_path, description = FALSE)
cp_pathwayCollection
#> Object with Class(es) 'pathwayCollection', 'list' [package 'pathwayPCA'] with 2 elements:
#> $ pathways:List of 1329
#> $ TERMS : chr [1:1329] "KEGG_GLYCOLYSIS_GLUCONEOGENESIS" ...
The imported .gmt
file is stored as a pathwayCollection
list object. This list contains:
pathways
),TERMS
), anddescription
). For Canonical Pathways files, if you specify description = TRUE
, this is the hyperlink to the pathway description card on the GSEA website.We assume that the assay data (e.g. transcriptomic data) is either in an Excel file or flat text file. For example, your data may look like this:
In this example data set, the columns are individual samples. The values in each row are the gene expression measurements for that gene. Use the read_csv
function from the readr
package to import .csv
files into R
as tibble (table and data frame) objects. The read_csv
function prints messages to the screen informing you of the assumptions it makes when importing your data. Specifically, this message tells us that all the imported data is numeric (col_double()
) except for the gene name column (X1 = col_character()
).
assay_path <- system.file("extdata", "ex_assay_subset.csv",
package = "pathwayPCA", mustWork = TRUE)
assay_df <- read_csv(assay_path)
#> Warning: Missing column names filled in: 'X1' [1]
#>
#> ── Column specification ────────────────────────────────────────────────────────
#> cols(
#> .default = col_double(),
#> X1 = col_character()
#> )
#> ℹ Use `spec()` for the full column specifications.
Incidentally, we consider gene symbols to adhere to the following conditions:
Furthermore, if your data has samples in the columns and -omic feature measurements in the rows (like the data set above), you’ll need to “tidy” the imported assay with the TransposeAssay
function. The transposed data set will appear similar to the following:
assayT_df <- TransposeAssay(assay_df)
assayT_df
#> # A tibble: 36 x 18
#> Sample SOAT1 LSS SQLE EBP CYP51A1 DHCR7 CYP27B1 DHCR24 HSD17B7 MSMO1
#> <chr> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 T21101311 5.37 9.77 7.74 4.68 8.27 8.32 6.78 4.70 7.63 7.60
#> 2 T21101312 5.52 9.78 8.06 5.12 8.21 8.33 6.47 5.06 7.63 7.33
#> 3 T21101313 5.89 8.11 7.00 5.78 8.20 8.39 6.57 4.89 8.15 7.61
#> 4 T21101314 5.62 8.67 8.59 5.64 8.07 8.64 6.47 4.98 8.13 5.56
#> 5 T21101315 5.49 9.83 8.13 5.73 9.38 8.15 6.43 5.03 7.70 6.30
#> 6 T21101316 5.58 9.85 8.55 5.13 9.40 8.71 6.56 4.87 7.75 7.77
#> 7 T21101317 5.32 10.0 6.99 5.86 8.08 9.25 6.86 4.72 7.88 6.97
#> 8 T21101318 5.49 9.72 7.47 5.16 6.67 7.37 6.70 4.92 7.50 5.48
#> 9 T21101319 5.57 9.88 7.97 5.40 7.91 8.06 6.58 5.06 8.16 7.06
#> 10 T21101320 5.16 9.87 7.42 5.50 7.43 8.68 6.55 4.85 8.20 6.15
#> # … with 26 more rows, and 7 more variables: FDFT1 <dbl>, SC5DL <dbl>,
#> # LIPA <dbl>, CEL <dbl>, TM7SF2 <dbl>, NSDHL <dbl>, SOAT2 <dbl>
Use the read_csv
function to import the phenotype data. Once again, the read_csv
function displays a message informing us of the types of data in each column. The following phenotype dataset for subject survival information contains the subject ID (Sample
), survival time after disease onset in months (eventTime
), and a logical (or binary) variable indicating if the subject died (TRUE
or 1) or was lost to follow up (eventObserved
; 0 or FALSE
).
pInfo_path <- system.file("extdata", "ex_pInfo_subset.csv",
package = "pathwayPCA", mustWork = TRUE)
pInfo_df <- read_csv(pInfo_path)
#>
#> ── Column specification ────────────────────────────────────────────────────────
#> cols(
#> Sample = col_character(),
#> eventTime = col_double(),
#> eventObserved = col_logical()
#> )
pInfo_df
#> # A tibble: 36 x 3
#> Sample eventTime eventObserved
#> <chr> <dbl> <lgl>
#> 1 T21101311 14.2 TRUE
#> 2 T21101312 1 TRUE
#> 3 T21101313 6.75 FALSE
#> 4 T21101314 8.5 TRUE
#> 5 T21101315 7.25 FALSE
#> 6 T21101316 5 TRUE
#> 7 T21101317 20 TRUE
#> 8 T21101318 13.2 FALSE
#> 9 T21101319 7.75 FALSE
#> 10 T21101320 9 FALSE
#> # … with 26 more rows
Now that you have the assay data in tidy form (assayT_df
) and the phenotype data (pInfo_df
), you can use the inner_join
function from the dplyr
package to match the assay measurements to phenotype information by subject identifier.
exSurv_df <- inner_join(pInfo_df, assayT_df, by = "Sample")
exSurv_df
#> # A tibble: 36 x 20
#> Sample eventTime eventObserved SOAT1 LSS SQLE EBP CYP51A1 DHCR7 CYP27B1
#> <chr> <dbl> <lgl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 T21101… 14.2 TRUE 5.37 9.77 7.74 4.68 8.27 8.32 6.78
#> 2 T21101… 1 TRUE 5.52 9.78 8.06 5.12 8.21 8.33 6.47
#> 3 T21101… 6.75 FALSE 5.89 8.11 7.00 5.78 8.20 8.39 6.57
#> 4 T21101… 8.5 TRUE 5.62 8.67 8.59 5.64 8.07 8.64 6.47
#> 5 T21101… 7.25 FALSE 5.49 9.83 8.13 5.73 9.38 8.15 6.43
#> 6 T21101… 5 TRUE 5.58 9.85 8.55 5.13 9.40 8.71 6.56
#> 7 T21101… 20 TRUE 5.32 10.0 6.99 5.86 8.08 9.25 6.86
#> 8 T21101… 13.2 FALSE 5.49 9.72 7.47 5.16 6.67 7.37 6.70
#> 9 T21101… 7.75 FALSE 5.57 9.88 7.97 5.40 7.91 8.06 6.58
#> 10 T21101… 9 FALSE 5.16 9.87 7.42 5.50 7.43 8.68 6.55
#> # … with 26 more rows, and 10 more variables: DHCR24 <dbl>, HSD17B7 <dbl>,
#> # MSMO1 <dbl>, FDFT1 <dbl>, SC5DL <dbl>, LIPA <dbl>, CEL <dbl>, TM7SF2 <dbl>,
#> # NSDHL <dbl>, SOAT2 <dbl>
Omics
Data ObjectThis section is a quick overview of the material covered in the Creating Data Objects vignette.
Using the data you just imported, create a data object specific to survival, regression, or categorical responses. For our example dataset, we will create a survival Omics
object to hold our assay, pathways, and survival responses. If your indicator is a binary variable, the CreateOmics
function will attempt to coerce it to a logical variable. Therefore, death indicators should be coded as 0-1, not 1-2.
This package includes a subject-matched colon cancer survival assay subset (colonSurv_df
) and a toy pathway collection with 15 pathways (colon_pathwayCollection
). When we create this OmicsSurv
object, the pathwayPCA
package checks the overlap between the -omes recorded in the assay data and the gene symbols in the supplied pathway collection. The CreateOmics()
function also prints some diagnostic messages to inform you of how well your pathway collection overlaps your data.
data("colonSurv_df")
data("colon_pathwayCollection")
colon_OmicsSurv <- CreateOmics(
assayData_df = colonSurv_df[, -(2:3)],
pathwayCollection_ls = colon_pathwayCollection,
response = colonSurv_df[, 1:3],
respType = "survival"
)
#>
#> ====== Creating object of class OmicsSurv =======
#> The input pathway database included 676 unique features.
#> The input assay dataset included 656 features.
#> Only pathways with at least 3 or more features included in the assay dataset are
#> tested (specified by minPathSize parameter). There are 15 pathways which meet
#> this criterion.
#> Because pathwayPCA is a self-contained test (PMID: 17303618), only features in
#> both assay data and pathway database are considered for analysis. There are 615
#> such features shared by the input assay and pathway database.
After you create an Omics
object, print the object to the screen to view a summary of the data contained therein.
colon_OmicsSurv
#> Formal class 'OmicsSurv' [package "pathwayPCA"] with 6 slots
#> ..@ eventTime : num [1:250] 64.9 59.8 62.4 54.5 46.3 ...
#> ..@ eventObserved : logi [1:250] FALSE FALSE FALSE FALSE TRUE FALSE ...
#> ..@ assayData_df : tibble [250 × 656] (S3: tbl_df/tbl/data.frame)
#> ..@ sampleIDs_char : chr [1:250] "subj1" "subj2" "subj3" "subj4" ...
#> ..@ pathwayCollection :List of 3
#> .. ..- attr(*, "class")= chr [1:2] "pathwayCollection" "list"
#> ..@ trimPathwayCollection:List of 4
#> .. ..- attr(*, "class")= chr [1:2] "pathwayCollection" "list"
Because the printing procedure for Omics
objects is to show a summary of the contents, you need to use the get*()
functions to view the individual components of the colon_OmicsSurv
object we just created. Overall, you can use accessor functions to extract, edit, or replace data contained in the object. The accessor functions are listed in more detail in the Table of Accessors subsection of Chapter 3. Use these functions to confirm that the data object you created accurately reflects the data you intend to analyze.
getAssay(colon_OmicsSurv)
#> # A tibble: 250 x 656
#> JUN SOS2 PAK3 RAF1 PRKCB BTC SHC1 PRKCA ELK1 NRG1
#> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 -0.880 0.367 1.30 0.480 -0.867 -0.790 -0.284 0.0104 1.04 0.670
#> 2 -1.11 2.15 1.62 0.165 0.547 -0.261 -0.000491 1.18 1.49 1.30
#> 3 -0.752 0.764 0.330 -0.541 0.164 0.452 0.691 -0.950 0.667 0.128
#> 4 1.03 -0.751 2.75 -0.878 -1.09 -0.481 -1.34 1.52 2.23 3.65
#> 5 -1.73 0.613 2.66 0.550 0.197 -1.02 0.156 -1.29 1.68 -2.15
#> 6 -0.162 0.126 -0.324 0.627 -0.106 -1.17 1.11 -1.27 0.964 1.79
#> 7 -0.980 -0.520 1.28 -0.343 -0.762 -0.489 -0.257 0.0518 1.21 -0.312
#> 8 0.616 0.0633 0.343 -0.0195 0.578 -1.37 0.638 1.37 1.05 -0.703
#> 9 1.35 -0.467 -0.149 -0.718 -0.898 0.527 -0.0604 1.32 -1.00 -0.266
#> 10 -0.538 0.413 -0.503 -1.27 -0.466 0.178 0.345 -1.40 -0.378 0.0623
#> # … with 240 more rows, and 646 more variables: PAK2 <dbl>, MTOR <dbl>,
#> # PAK4 <dbl>, MAP2K4 <dbl>, EIF4EBP1 <dbl>, BAD <dbl>, PRKCG <dbl>,
#> # NRG3 <dbl>, MAPK9 <dbl>, ERBB4 <dbl>, MAPK10 <dbl>, PTK2 <dbl>,
#> # ERBB2 <dbl>, ERBB3 <dbl>, MAP2K2 <dbl>, TGFA <dbl>, BRAF <dbl>,
#> # MAP2K1 <dbl>, MAP2K7 <dbl>, ABL1 <dbl>, NRG2 <dbl>, AKT1 <dbl>, ABL2 <dbl>,
#> # AKT2 <dbl>, SHC4 <dbl>, RPS6KB1 <dbl>, RPS6KB2 <dbl>, AKT3 <dbl>,
#> # NRAS <dbl>, GRB2 <dbl>, AREG <dbl>, STAT5B <dbl>, MAPK3 <dbl>,
#> # STAT5A <dbl>, PAK6 <dbl>, SOS1 <dbl>, MYC <dbl>, MAPK1 <dbl>, NCK1 <dbl>,
#> # PIK3R5 <dbl>, NRG4 <dbl>, HRAS <dbl>, MAPK8 <dbl>, EGFR <dbl>, GSK3B <dbl>,
#> # CBLB <dbl>, KRAS <dbl>, CBL <dbl>, SHC3 <dbl>, CDKN1B <dbl>, CDKN1A <dbl>,
#> # EGF <dbl>, EREG <dbl>, ARAF <dbl>, NCK2 <dbl>, SRC <dbl>, PIK3R3 <dbl>,
#> # CAMK2A <dbl>, CAMK2B <dbl>, CAMK2D <dbl>, CAMK2G <dbl>, PAK1 <dbl>,
#> # CBLC <dbl>, CRK <dbl>, PIK3CA <dbl>, PIK3CB <dbl>, CRKL <dbl>,
#> # PIK3CD <dbl>, GAB1 <dbl>, PLCG1 <dbl>, PLCG2 <dbl>, SHC2 <dbl>,
#> # HBEGF <dbl>, PIK3CG <dbl>, PIK3R1 <dbl>, PIK3R2 <dbl>, EPHB2 <dbl>,
#> # EPHB4 <dbl>, EFNA5 <dbl>, PXN <dbl>, CDC42 <dbl>, EFNB3 <dbl>, RRAS <dbl>,
#> # GRB7 <dbl>, SYNJ1 <dbl>, EPHB3 <dbl>, EFNB1 <dbl>, DNM1 <dbl>,
#> # MAP4K4 <dbl>, GRIA1 <dbl>, EPHB1 <dbl>, ROCK1 <dbl>, ITSN1 <dbl>,
#> # RAP1A <dbl>, RAC1 <dbl>, RAP1B <dbl>, EFNB2 <dbl>, WASL <dbl>, TF <dbl>,
#> # KALRN <dbl>, …
pathwayCollection
ListWe can use the vector subsetting mechanic in R (vector[]
) to view only the first ten event times.
After you have confirmed that the CreateOmics
function created the Omics
object you wanted, you can analyze the object with adaptive, elastic-net, sparse (AES) PCA or supervised PCA. This section is a quick overview of the material covered in the Test Pathway Significance vignette. For details of these methods functions, please see their respective sections in Chapter 4.
The function arguments are as follows. Both the AESPCA_pVals
and SuperPCA_pVals
functions take in an Omics
object as the value to the object
argument. AES-PCA can use permutation-based \(p\)-values, so the numReps
argument controls how many permutations to take. If we set the number of permutations to 0, then the \(p\)-values will be calculated parametrically. The numPCs
argument specifies how many principal components will be extracted from each pathway. The parallel
and numCores
arguments are used to control if and how the functions make use of parallel computing. Finally, the adjustment
argument allows you to specify a family-wise error rate (FWER) or false discovery rate (FDR) adjustment for the pathway \(p\)-values. These options are documented in the adjustRaw_pVals
function (see the help documentation for details).
Perform AES-PCA pathway significance testing on the Omics
object with the AESPCA_pVals
function. For more details on this function, see the AES-PCA section of Chapter 4. We will adjust the pathway \(p\)-values by the estimated FDR calculated with the "BH"
procedure (Benjamini and Hochberg, 1995).
colon_aespcOut <- AESPCA_pVals(
object = colon_OmicsSurv,
numReps = 0,
numPCs = 2,
parallel = TRUE,
numCores = 2,
adjustpValues = TRUE,
adjustment = "BH"
)
#> Part 1: Calculate Pathway AES-PCs
#> Initializing Computing Cluster: DONE
#> Extracting Pathway PCs in Parallel: DONE
#>
#> Part 2: Calculate Pathway p-Values
#> Initializing Computing Cluster: DONE
#> Extracting Pathway p-Values in Parallel: DONE
#>
#> Part 3: Adjusting p-Values and Sorting Pathway p-Value Data Frame
#> DONE
Perform Supervised PCA pathway significance testing on the Omics
object with the SuperPCA_pVals
function. For more details on this function, see the Supervised PCA section of Chapter 4.
colon_superpcOut <- SuperPCA_pVals(
object = colon_OmicsSurv,
numPCs = 2,
parallel = TRUE,
numCores = 2,
adjustpValues = TRUE,
adjustment = "BH"
)
#> Initializing Computing Cluster: DONE
#> Calculating Pathway Test Statistics in Parallel: DONE
#> Calculating Pathway Critical Values in Parallel: DONE
#> Calculating Pathway p-Values: DONE
#> Adjusting p-Values and Sorting Pathway p-Value Data Frame: DONE
This section is a quick overview of the material covered in the Visualizing the Results vignette. The output of AESPCA_pVals()
is list object with class aespcOut
. The output of SuperPCA_pVals()
is a list object with class superpcOut
. Both of these objects have the following three elements:
pVals_df
: a data frame with \(p\)-values and their details each pathwayPCs_ls
: a list of the data frames of the first selected principal component(s) extracted from the assay data subset corresponding to each pathway.loadings_ls
: a list of the matrices of the loading vectors that correspond to the principal components in PCs_ls
.For a quick and easy view of the pathway significance testing results, we can use the getPathpVals()
function to access and subset the output data frame. If you are not using the tidyverse
package suite, your results will print differently.
getPathpVals(colon_superpcOut)
#> # A tibble: 15 x 3
#> terms rawp FDR_BH
#> <chr> <dbl> <dbl>
#> 1 KEGG_ERBB_SIGNALING_PATHWAY 0.000655 0.00581
#> 2 REACTOME_INSULIN_RECEPTOR_SIGNALLING_CASCADE 0.00151 0.00581
#> 3 PID_EPHB_FWD_PATHWAY 0.00153 0.00581
#> 4 REACTOME_SIGNALING_BY_INSULIN_RECEPTOR 0.00155 0.00581
#> 5 PID_TNF_PATHWAY 0.00205 0.00614
#> 6 KEGG_NON_SMALL_CELL_LUNG_CANCER 0.00308 0.00769
#> 7 REACTOME_PHOSPHOLIPID_METABOLISM 0.00414 0.00886
#> 8 BIOCARTA_TNFR1_PATHWAY 0.0116 0.0217
#> 9 KEGG_ASTHMA 0.0162 0.0269
#> 10 ST_GA12_PATHWAY 0.0278 0.0417
#> 11 KEGG_RETINOL_METABOLISM 0.0341 0.0464
#> 12 KEGG_PENTOSE_PHOSPHATE_PATHWAY 0.0371 0.0464
#> 13 BIOCARTA_RELA_PATHWAY 0.0903 0.104
#> 14 KEGG_ANTIGEN_PROCESSING_AND_PRESENTATION 0.112 0.120
#> 15 BIOCARTA_SET_PATHWAY 0.403 0.403
This function has the following modifying arguments:
score = FALSE
: . Return the raw \(p\)-values. Return the \(p\)-value score, \(-\log(p)\), instead of the unadjusted (raw) \(p\)-values with score = FALSE
.numPaths = 20
: Return the top 20 pathways by \(p\)-value score.alpha = NULL
: Return all pathways with raw \(p\)-values less than alpha
. If you specify alpha
, then do not specify numPaths
.To visualize the significance of the pathways based on FDR or uncorrected \(p\)-values, we can use the ggplot2
package to create summary graphics of the analysis results.
In order to take advantage of the publication-quality graphics created with the ggplot2
package, we first need to tidy the data frames returned by the AESPCA_pVals
and SuperPCA_pVals
functions. The following code takes in the \(p\)-values data frame from the Supervised PCA method, modifies it to be compatible with the ggplot
function, and saves the new data frame (colonOutGather_df
).
colonOutGather_df <-
getPathpVals(colon_superpcOut) %>%
gather(variable, value, -terms) %>%
mutate(score = -log(value)) %>%
mutate(variable = factor(variable)) %>%
mutate(variable = recode_factor(variable,
rawp = "None",
FDR_BH = "FDR"))
graphMax <- ceiling(max(colonOutGather_df$score))
colonOutGather_df
#> # A tibble: 30 x 4
#> terms variable value score
#> <chr> <fct> <dbl> <dbl>
#> 1 KEGG_ERBB_SIGNALING_PATHWAY None 0.000655 7.33
#> 2 REACTOME_INSULIN_RECEPTOR_SIGNALLING_CASCADE None 0.00151 6.49
#> 3 PID_EPHB_FWD_PATHWAY None 0.00153 6.48
#> 4 REACTOME_SIGNALING_BY_INSULIN_RECEPTOR None 0.00155 6.47
#> 5 PID_TNF_PATHWAY None 0.00205 6.19
#> 6 KEGG_NON_SMALL_CELL_LUNG_CANCER None 0.00308 5.78
#> 7 REACTOME_PHOSPHOLIPID_METABOLISM None 0.00414 5.49
#> 8 BIOCARTA_TNFR1_PATHWAY None 0.0116 4.46
#> 9 KEGG_ASTHMA None 0.0162 4.12
#> 10 ST_GA12_PATHWAY None 0.0278 3.58
#> # … with 20 more rows
Now that our output is tidy, we can make a bar chart of the pathway significance based on the unadjusted \(p\)-values.
raw_df <- colonOutGather_df %>%
filter(variable == "None") %>%
select(-variable, -value)
ggplot(raw_df) +
theme_bw() +
aes(x = reorder(terms, score), y = score) +
geom_bar(stat = "identity", position = "dodge", fill = "#005030") +
scale_fill_discrete(guide = FALSE) +
ggtitle("Supervised PCA Significant Colon Pathways") +
xlab("Pathways") +
scale_y_continuous("Negative Log p-Value", limits = c(0, graphMax)) +
geom_hline(yintercept = -log(0.01), size = 2) +
coord_flip()
Now that you have an idea of how to use this package, please see each of our vignettes for detailed and thorough commentary and guiding information on each of the three topics discussed herein. The vignettes are:
Omics
Data ObjectsHere is the R session information for this vignette:
sessionInfo()
#> R version 4.1.0 (2021-05-18)
#> Platform: x86_64-pc-linux-gnu (64-bit)
#> Running under: Ubuntu 20.04.2 LTS
#>
#> Matrix products: default
#> BLAS: /home/biocbuild/bbs-3.13-bioc/R/lib/libRblas.so
#> LAPACK: /home/biocbuild/bbs-3.13-bioc/R/lib/libRlapack.so
#>
#> locale:
#> [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C
#> [3] LC_TIME=en_GB LC_COLLATE=C
#> [5] LC_MONETARY=en_US.UTF-8 LC_MESSAGES=en_US.UTF-8
#> [7] LC_PAPER=en_US.UTF-8 LC_NAME=C
#> [9] LC_ADDRESS=C LC_TELEPHONE=C
#> [11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C
#>
#> attached base packages:
#> [1] parallel stats graphics grDevices utils datasets methods
#> [8] base
#>
#> other attached packages:
#> [1] survminer_0.4.9 ggpubr_0.4.0 survival_3.2-11 pathwayPCA_1.8.0
#> [5] forcats_0.5.1 stringr_1.4.0 dplyr_1.0.6 purrr_0.3.4
#> [9] readr_1.4.0 tidyr_1.1.3 tibble_3.1.2 ggplot2_3.3.3
#> [13] tidyverse_1.3.1
#>
#> loaded via a namespace (and not attached):
#> [1] nlme_3.1-152 fs_1.5.0 lubridate_1.7.10 httr_1.4.2
#> [5] tools_4.1.0 backports_1.2.1 bslib_0.2.5.1 utf8_1.2.1
#> [9] R6_2.5.0 DBI_1.1.1 mgcv_1.8-35 colorspace_2.0-1
#> [13] withr_2.4.2 tidyselect_1.1.1 gridExtra_2.3 curl_4.3.1
#> [17] compiler_4.1.0 cli_2.5.0 rvest_1.0.0 xml2_1.3.2
#> [21] labeling_0.4.2 sass_0.4.0 scales_1.1.1 survMisc_0.5.5
#> [25] digest_0.6.27 foreign_0.8-81 rmarkdown_2.8 rio_0.5.26
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