Last updated: 2020-09-25

Checks: 6 1

Knit directory: causal-TWAS/

This reproducible R Markdown analysis was created with workflowr (version 1.6.2). The Checks tab describes the reproducibility checks that were applied when the results were created. The Past versions tab lists the development history.


The R Markdown file has unstaged changes. To know which version of the R Markdown file created these results, you’ll want to first commit it to the Git repo. If you’re still working on the analysis, you can ignore this warning. When you’re finished, you can run wflow_publish to commit the R Markdown file and build the HTML.

Great job! The global environment was empty. Objects defined in the global environment can affect the analysis in your R Markdown file in unknown ways. For reproduciblity it’s best to always run the code in an empty environment.

The command set.seed(20191103) was run prior to running the code in the R Markdown file. Setting a seed ensures that any results that rely on randomness, e.g. subsampling or permutations, are reproducible.

Great job! Recording the operating system, R version, and package versions is critical for reproducibility.

Nice! There were no cached chunks for this analysis, so you can be confident that you successfully produced the results during this run.

Great job! Using relative paths to the files within your workflowr project makes it easier to run your code on other machines.

Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility.

The results in this page were generated with repository version f55918c. See the Past versions tab to see a history of the changes made to the R Markdown and HTML files.

Note that you need to be careful to ensure that all relevant files for the analysis have been committed to Git prior to generating the results (you can use wflow_publish or wflow_git_commit). workflowr only checks the R Markdown file, but you know if there are other scripts or data files that it depends on. Below is the status of the Git repository when the results were generated:


Ignored files:
    Ignored:    .Rhistory
    Ignored:    .Rproj.user/
    Ignored:    code/workflow/.ipynb_checkpoints/
    Ignored:    data/

Untracked files:
    Untracked:  code/susie_filter.R

Unstaged changes:
    Modified:   analysis/simulation-multi-ukbchr17to22-gtex.adipose_susieprior.Rmd
    Modified:   code/run_UKB_process.R
    Modified:   code/run_simulate_data.R
    Modified:   code/run_test_susieI_m.R
    Modified:   code/workflow/workflow-ashtest4.ipynb

Note that any generated files, e.g. HTML, png, CSS, etc., are not included in this status report because it is ok for generated content to have uncommitted changes.


These are the previous versions of the repository in which changes were made to the R Markdown (analysis/simulation-multi-ukbchr17to22-gtex.adipose_susieprior.Rmd) and HTML (docs/simulation-multi-ukbchr17to22-gtex.adipose_susieprior.html) files. If you’ve configured a remote Git repository (see ?wflow_git_remote), click on the hyperlinks in the table below to view the files as they were in that past version.

File Version Author Date Message
Rmd f55918c simingz 2020-09-22 susie prior
html f55918c simingz 2020-09-22 susie prior
Rmd e9d56aa simingz 2020-09-20 causal susie prior
html e9d56aa simingz 2020-09-20 causal susie prior
Rmd cab7999 simingz 2020-09-19 susie cali truth
html cab7999 simingz 2020-09-19 susie cali truth
Rmd 13cad06 simingz 2020-09-14 susieI plots
html 13cad06 simingz 2020-09-14 susieI plots
Rmd c1c6bcc simingz 2020-09-14 susieI plots
Rmd 4d39fd6 simingz 2020-09-14 susieI plots
html 4d39fd6 simingz 2020-09-14 susieI plots
Rmd bb0bce0 simingz 2020-09-03 susie prior
html bb0bce0 simingz 2020-09-03 susie prior
Rmd 193a8df simingz 2020-09-01 increase gene pve
html 193a8df simingz 2020-09-01 increase gene pve
Rmd 86681eb simingz 2020-08-28 susieI all regions
html 86681eb simingz 2020-08-28 susieI all regions

  • Run susie with different priors and see how much prior affects results.

  • Data: ukb chr 17 to chr 22 combined. SNPs are downsampled to 1/10, eQTLs defined by FUSION-TWAS (Adipose/GTEx) lasso effect size > 0 were kept, p= 86k, n = 20k.

  • For each simulation scenarios(1-x, 3-x), we picked two few parameter sets (priors for gene and snps) estimated by susieI and check if PIPs for genes are calibrated.

library(mr.ash.alpha)
library(data.table)
suppressMessages({library(plotly)})
library(tidyr)
library(plyr)
library(stringr)
library(kableExtra)
source("analysis/summarize_twas_plots.R")

Test true prior

Regions rPIP > 0.5, simulation 1-x

simdatadir <- "~/causalTWAS/simulations/simulation_ashtest_20200721/"
outputdir <- "~/causalTWAS/simulations/simulation_ashtest_20200721/"
susiedir <- "/home/simingz/causalTWAS/simulations/simulation_susietest_20200721/20200721-1-fixprior_rpip0.5/"

We run 50 simulations and run susie using the true parameter (gene and snp pi1) as prior. We run susie for regions with regional sum of pip from mr.ash2s for both genes and snps > 0.5. run susie with L=1.

Truth

  • The true parameters we used to simulate data:
par <- read.table(paste0(susiedir, "20200721-1-fixedprior_2.txt"), header = T)
t(par[,2, drop = F])
        gene.pi1    gene.pve     snp.pi1    snp.pve
truth 0.05021174 0.008497975 0.002498094 0.05003487

Use truth as prior

  • The prior used is:
par <- read.table(paste0(susiedir, "20200721-1-fixedprior_2.txt"), header = T)
t(par[c(1,3),1, drop = F])
            gene.pi1     snp.pi1
estimated 0.05118395 0.002274899
susiedir <- "/home/simingz/causalTWAS/simulations/simulation_susietest_20200721/20200721-1-fixprior_rpip0.5/"
  • susie results:
pipfs <- Sys.glob(paste0(susiedir,"20200721-1-*.fixedprior2.L1.susieres.expr.txt"))
res <- do.call(rbind, lapply(pipfs, read.table, header = T))
par(mfrow=c(1,3))
cp_plot(res$pip.null, res$ifcausal, main = "SUSIE.uniform PIP")
cp_plot(res$pip, res$ifcausal, main = "SUSIE.weighted PIP")
cp_plot(res$pip.w0, res$ifcausal, main = "SUSIE.weighted-w-null PIP")

Version Author Date
f55918c simingz 2020-09-22
cab7999 simingz 2020-09-19

Regions rPIP > 0.9, simulation 3-x

We run 50 simulations and run susie using the true parameter (gene and snp pi1) as prior. We run susie for regions with regional sum of pip from mr.ash2s for both genes and snps > 0.9. run susie with L= 2.

Truth

  • The true parameters we used to simulate data:
susiedir <- "/home/simingz/causalTWAS/simulations/simulation_susietest_20200721/20200721-3-fixprior_rpip0.9/"
par <- read.table(paste0(susiedir, "20200721-3-fixedprior_2.txt"), header = T)
t(par[,2, drop = F])
       gene.pi1    gene.pve     snp.pi1    snp.pve
truth 0.0199637 0.007322058 0.002498094 0.05257447

Use truth as prior

  • The prior used is:
par <- read.table(paste0(susiedir, "20200721-3-fixedprior_2.txt"), header = T)
t(par[c(1,3),1, drop = F])
          gene.pi1 snp.pi1
estimated     0.02  0.0025
  • susie results:
pipfs <- Sys.glob(paste0(susiedir,"20200721-3-*.fixedprior2.susieres.expr.txt"))
res <- do.call(rbind, lapply(pipfs, read.table, header = T))
par(mfrow=c(1,3))
cp_plot(res$pip.null, res$ifcausal, main = "SUSIE.uniform PIP")
cp_plot(res$pip, res$ifcausal, main = "SUSIE.weighted PIP")
cp_plot(res$pip.w0, res$ifcausal, main = "SUSIE.weighted-w-null PIP")

Causal regions, simulation 3-x

We run susie for regions with causal signals. run susie with L=1.

Truth

  • The true parameters we used to simulate data:
susiedir <- "/home/simingz/causalTWAS/simulations/simulation_susietest_20200721/20200721-3-fixprior_causal/"
par <- read.table(paste0(susiedir, "20200721-3-fixedprior_2.txt"), header = T)
t(par[,2, drop = F])
       gene.pi1    gene.pve     snp.pi1    snp.pve
truth 0.0199637 0.007322058 0.002498094 0.05257447

Use truth as prior

  • The prior used is:
par <- read.table(paste0(susiedir, "20200721-3-fixedprior_2.txt"), header = T)
t(par[c(1,3),1, drop = F])
          gene.pi1   snp.pi1
estimated     0.02 0.0030996
  • susie results:
pipfs <- Sys.glob(paste0(susiedir,"20200721-3-*.fixedprior2.L1.susieres.expr.txt"))
res <- do.call(rbind, lapply(pipfs, read.table, header = T))
par(mfrow=c(1,3)); 
cp_plot(res$pip.null, res$ifcausal, main = "SUSIE.uniform PIP")
cp_plot(res$pip, res$ifcausal, main = "SUSIE.weighted PIP")
cp_plot(res$pip.w0, res$ifcausal, main = "SUSIE.weighted-w-null PIP")

Version Author Date
f55918c simingz 2020-09-22
e9d56aa simingz 2020-09-20

All regions, simulation 3-x

We run susie for all regions. Run susie with L=1.

Truth

  • The true parameters we used to simulate data:
susiedir <- "/project2/mstephens/causalTWAS/simulations/simulation_susietest_20200721/20200721-3-fixprior_allregions/"
par <- read.table(paste0(susiedir, "20200721-3-fixedprior_2.txt"), header = T)
t(par[,2, drop = F])
       gene.pi1    gene.pve     snp.pi1    snp.pve
truth 0.0199637 0.007322058 0.002498094 0.05257447

Use truth as prior

  • The prior used is:
par <- read.table(paste0(susiedir, "20200721-3-fixedprior_2.txt"), header = T)
t(par[c(1,3),1, drop = F])
          gene.pi1   snp.pi1
estimated     0.02 0.0030996
  • susie results:
pipfs <- Sys.glob(paste0(susiedir,"20200721-3-*.fixedprior2.L1.susieres.expr.txt"))
res <- do.call(rbind, lapply(pipfs, read.table, header = T))
par(mfrow=c(1,3)); 
cp_plot(res$pip.null, res$ifcausal, main = "SUSIE.uniform PIP")
cp_plot(res$pip, res$ifcausal, main = "SUSIE.weighted PIP")
cp_plot(res$pip.w0, res$ifcausal, main = "SUSIE.weighted-w-null PIP")

Test over and underestimated gene pi1

We intentionally use over or underestimated gene pi1 and use the same snp pi1 (close to truth) when running SUSIE. Run susie L=1.

Causal regions, simulation 3-x

  • The true parameters we used to simulate data:
susiedir <- "/home/simingz/causalTWAS/simulations/simulation_susietest_20200721/20200721-3-fixprior_causal/"
par <- read.table(paste0(susiedir, "20200721-3-fixedprior_2.txt"), header = T)
t(par[,2, drop = F])
       gene.pi1    gene.pve     snp.pi1    snp.pve
truth 0.0199637 0.007322058 0.002498094 0.05257447

Use overestimated gene pi1

  • The prior used is:
par <- read.table(paste0(susiedir, "20200721-3-fixedprior_1.txt"), header = T)
t(par[c(1,3),1, drop = F])
           gene.pi1   snp.pi1
estimated 0.1054679 0.0030996
  • susie results:
pipfs <- Sys.glob(paste0(susiedir,"20200721-3-*.fixedprior1.L1.susieres.expr.txt"))
res <- do.call(rbind, lapply(pipfs, read.table, header = T))
par(mfrow=c(1,3))
cp_plot(res$pip.null, res$ifcausal, main = "SUSIE.uniform PIP")
cp_plot(res$pip, res$ifcausal, main = "SUSIE.weighted PIP")
cp_plot(res$pip.w0, res$ifcausal, main = "SUSIE.weighted-w-null PIP")

Version Author Date
f55918c simingz 2020-09-22

Use underrestimated gene pi1

  • The prior used is:
par <- read.table(paste0(susiedir, "20200721-3-fixedprior_3.txt"), header = T)
t(par[c(1,3),1, drop = F])
          gene.pi1   snp.pi1
estimated     0.01 0.0030996
  • susie results:
pipfs <- Sys.glob(paste0(susiedir,"20200721-3-*.fixedprior3.L1.susieres.expr.txt"))
res <- do.call(rbind, lapply(pipfs, read.table, header = T))
par(mfrow=c(1,3))
cp_plot(res$pip.null, res$ifcausal, main = "SUSIE.uniform PIP")
cp_plot(res$pip, res$ifcausal, main = "SUSIE.weighted PIP")
cp_plot(res$pip.w0, res$ifcausal, main = "SUSIE.weighted-w-null PIP")

Version Author Date
f55918c simingz 2020-09-22

Test susieI results

Simulation 1-x, setting 1

simdatadir <- "~/causalTWAS/simulations/simulation_ashtest_20200721/"
outputdir <- "~/causalTWAS/simulations/simulation_ashtest_20200721/"
susiedir <- "~/causalTWAS/simulations/simulation_susietest_20200721/20200721-1-fixprior_rpip0.3_causal/"

We run 100 simulations and run susie using priors obtained from susieI. Two examples are shown. The setting is the same as in here. Regions are rpip from mr.ash2 > 0.3 and causal. We take simulation setting 1-x.

Truth

  • The true parameters we used to simulate data:
par <- read.table(paste0(susiedir, "20200721-1-fixedprior_1.txt"), header = T)
t(par[,2, drop = F])
        gene.pi1    gene.pve     snp.pi1    snp.pve
truth 0.05021174 0.008497975 0.002498094 0.05003487

Use prior from susie estimates 1.

  • The prior used is:
par <- read.table(paste0(susiedir, "20200721-1-fixedprior_1.txt"), header = T)
t(par[c(1,3),1, drop = F])
          gene.pi1  snp.pi1
estimated  0.07617 0.004203
  • susie results:
pipfs <- Sys.glob(paste0(susiedir,"20200721-1-*.fixedprior1.susieres.expr.txt"))
res <- do.call(rbind, lapply(pipfs, read.table, header = T))
par(mfrow=c(1,3))
cp_plot(res$pip.null, res$ifcausal, main = "SUSIE.uniform PIP")
cp_plot(res$pip, res$ifcausal, main = "SUSIE.weighted PIP")
cp_plot(res$pip.w0, res$ifcausal, main = "SUSIE.weighted-w-null PIP")

Version Author Date
f55918c simingz 2020-09-22
4d39fd6 simingz 2020-09-14
bb0bce0 simingz 2020-09-03
193a8df simingz 2020-09-01
86681eb simingz 2020-08-28

Use prior from susie estimates 2.

  • The prior used is:
par <- read.table(paste0(susiedir, "20200721-1-fixedprior_2.txt"), header = T)
t(par[c(1,3),1, drop = F])
          gene.pi1 snp.pi1
estimated  0.01642 0.00577
pipfs <- Sys.glob(paste0(susiedir,"20200721-1-*.fixedprior2.susieres.expr.txt"))
res <- do.call(rbind, lapply(pipfs, read.table, header = T))
par(mfrow=c(1,3))
cp_plot(res$pip.null, res$ifcausal, main = "SUSIE.uniform PIP")
cp_plot(res$pip, res$ifcausal, main = "SUSIE.weighted PIP")
cp_plot(res$pip.w0, res$ifcausal, main = "SUSIE.weighted-w-null PIP")

Version Author Date
f55918c simingz 2020-09-22
4d39fd6 simingz 2020-09-14
bb0bce0 simingz 2020-09-03
193a8df simingz 2020-09-01
86681eb simingz 2020-08-28

simulation 1-x, setting 2

susiedir <- "~/causalTWAS/simulations/simulation_susietest_20200721/20200721-1-fixprior_rpip0.3/"

We run 100 simulations and run susie using priors obtained from susieI. Two examples are shown. The setting is the same as in here. Regions are rpip from mr.ash2 > 0.3. We take simulation setting 1-x.

Truth

  • The true parameters we used to simulate data:
par <- read.table(paste0(susiedir, "20200721-1-fixedprior_1.txt"), header = T)
t(par[,2, drop = F])
        gene.pi1    gene.pve     snp.pi1    snp.pve
truth 0.05021174 0.008497975 0.002498094 0.05003487

Use prior from susie estimates 1.

  • The prior used is:
par <- read.table(paste0(susiedir, "20200721-1-fixedprior_1.txt"), header = T)
t(par[c(1,3),1, drop = F])
          gene.pi1   snp.pi1
estimated 0.002185 0.0007039
  • susie results:
pipfs <- Sys.glob(paste0(susiedir,"20200721-1-*.fixedprior1.susieres.expr.txt"))
res <- do.call(rbind, lapply(pipfs, read.table, header = T))
par(mfrow=c(1,3))
cp_plot(res$pip.null, res$ifcausal, main = "SUSIE.uniform PIP")
cp_plot(res$pip, res$ifcausal, main = "SUSIE.weighted PIP")
cp_plot(res$pip.w0, res$ifcausal, main = "SUSIE.weighted-w-null PIP")

Version Author Date
f55918c simingz 2020-09-22
4d39fd6 simingz 2020-09-14
bb0bce0 simingz 2020-09-03

Use prior from susie estimates 2.

  • The prior used is:
par <- read.table(paste0(susiedir, "20200721-1-fixedprior_2.txt"), header = T)
t(par[c(1,3),1, drop = F])
          gene.pi1  snp.pi1
estimated  0.02611 0.008102
pipfs <- Sys.glob(paste0(susiedir,"20200721-1-*.fixedprior2.susieres.expr.txt"))
res <- do.call(rbind, lapply(pipfs, read.table, header = T))
par(mfrow=c(1,3)) 
cp_plot(res$pip.null, res$ifcausal, main = "SUSIE.uniform PIP")
cp_plot(res$pip, res$ifcausal, main = "SUSIE.weighted PIP")
cp_plot(res$pip.w0, res$ifcausal, main = "SUSIE.weighted-w-null PIP")

Version Author Date
f55918c simingz 2020-09-22
4d39fd6 simingz 2020-09-14
bb0bce0 simingz 2020-09-03

Simulation 3-x, setting 1

susiedir <- "~/causalTWAS/simulations/simulation_susietest_20200721/20200721-3-fixprior_rpip0.3_causal/"

We run 100 simulations and run susie using priors obtained from susieI. Two examples are shown. The setting is the same as in here. Regions are rpip from mr.ash2 > 0.3 and causal. We take simulation setting 3-x.

Truth

  • The true parameters we used to simulate data:
par <- read.table(paste0(susiedir, "20200721-3-fixedprior_1.txt"), header = T)
t(par[,2, drop = F])
       gene.pi1    gene.pve     snp.pi1    snp.pve
truth 0.0199637 0.007322058 0.002498094 0.05257447

Use prior from susie estimates 1.

  • The prior used is:
par <- read.table(paste0(susiedir, "20200721-3-fixedprior_1.txt"), header = T)
t(par[c(1,3),1, drop = F])
           gene.pi1   snp.pi1
estimated 0.1054679 0.0030996
  • susie results:
pipfs <- Sys.glob(paste0(susiedir,"20200721-3-*.fixedprior1.susieres.expr.txt"))
res <- do.call(rbind, lapply(pipfs, read.table, header = T))
par(mfrow=c(1,3))
cp_plot(res$pip.null, res$ifcausal, main = "SUSIE.uniform PIP")
cp_plot(res$pip, res$ifcausal, main = "SUSIE.weighted PIP")
cp_plot(res$pip.w0, res$ifcausal, main = "SUSIE.weighted-w-null PIP")

Version Author Date
f55918c simingz 2020-09-22
4d39fd6 simingz 2020-09-14
bb0bce0 simingz 2020-09-03

Use prior from susie estimates 2.

  • The prior used is:
par <- read.table(paste0(susiedir, "20200721-3-fixedprior_2.txt"), header = T)
t(par[c(1,3),1, drop = F])
          gene.pi1  snp.pi1
estimated  0.05083 0.004532
  • susie results:
pipfs <- Sys.glob(paste0(susiedir,"20200721-3-*.fixedprior2.susieres.expr.txt"))
res <- do.call(rbind, lapply(pipfs, read.table, header = T))
par(mfrow=c(1,3))
cp_plot(res$pip.null, res$ifcausal, main = "SUSIE.uniform PIP")
cp_plot(res$pip, res$ifcausal, main = "SUSIE.weighted PIP")
cp_plot(res$pip.w0, res$ifcausal, main = "SUSIE.weighted-w-null PIP")

Version Author Date
f55918c simingz 2020-09-22
4d39fd6 simingz 2020-09-14
bb0bce0 simingz 2020-09-03

Simulation 3-x, setting 2

susiedir <- "~/causalTWAS/simulations/simulation_susietest_20200721/20200721-3-fixprior_rpip0.3/"

We run 100 simulations and run susie using priors obtained from susieI. Two examples are shown. The setting is the same as in here. Regions are rpip from mr.ash2 > 0.3. We take simulation setting 1-x.

Truth

  • The true parameters we used to simulate data:
par <- read.table(paste0(susiedir, "20200721-3-fixedprior_1.txt"), header = T)
t(par[,2, drop = F])
       gene.pi1    gene.pve     snp.pi1    snp.pve
truth 0.0199637 0.007322058 0.002498094 0.05257447

Use prior from susie estimates 1.

  • The prior used is:
par <- read.table(paste0(susiedir, "20200721-3-fixedprior_1.txt"), header = T)
t(par[c(1,3),1, drop = F])
          gene.pi1  snp.pi1
estimated  0.01602 0.004202
  • susie results:
pipfs <- Sys.glob(paste0(susiedir,"20200721-3-*.fixedprior2.susieres.expr.txt"))
res <- do.call(rbind, lapply(pipfs, read.table, header = T))
par(mfrow=c(1,3))
cp_plot(res$pip.null, res$ifcausal, main = "SUSIE.uniform PIP")
cp_plot(res$pip, res$ifcausal, main = "SUSIE.weighted PIP")
cp_plot(res$pip.w0, res$ifcausal, main = "SUSIE.weighted-w-null PIP")

Version Author Date
f55918c simingz 2020-09-22
4d39fd6 simingz 2020-09-14

Use prior from susie estimates 2.

  • The prior used is:
par <- read.table(paste0(susiedir, "20200721-3-fixedprior_2.txt"), header = T)
t(par[c(1,3),1, drop = F])
          gene.pi1  snp.pi1
estimated  0.03533 0.007996
  • susie results:
pipfs <- Sys.glob(paste0(susiedir,"20200721-3-*.fixedprior2.susieres.expr.txt"))
res <- do.call(rbind, lapply(pipfs, read.table, header = T))
par(mfrow=c(1,3)) 
cp_plot(res$pip.null, res$ifcausal, main = "SUSIE.uniform PIP")
cp_plot(res$pip, res$ifcausal, main = "SUSIE.weighted PIP")
cp_plot(res$pip.w0, res$ifcausal, main = "SUSIE.weighted-w-null PIP")

Version Author Date
f55918c simingz 2020-09-22
4d39fd6 simingz 2020-09-14

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.4 (Nitrogen)

Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [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] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] kableExtra_1.2.1    stringr_1.4.0       plyr_1.8.6         
[4] tidyr_0.8.3         plotly_4.9.2.9000   ggplot2_3.3.1      
[7] data.table_1.12.7   mr.ash.alpha_0.1-34

loaded via a namespace (and not attached):
 [1] Rcpp_1.0.4.6      compiler_3.5.1    pillar_1.4.4     
 [4] later_0.7.5       git2r_0.26.1      workflowr_1.6.2  
 [7] tools_3.5.1       digest_0.6.25     viridisLite_0.3.0
[10] jsonlite_1.6.1    evaluate_0.12     tibble_3.0.1     
[13] lifecycle_0.2.0   gtable_0.2.0      lattice_0.20-38  
[16] pkgconfig_2.0.2   rlang_0.4.6       Matrix_1.2-15    
[19] rstudioapi_0.11   yaml_2.2.0        xml2_1.2.0       
[22] httr_1.4.1        withr_2.1.2       dplyr_1.0.0      
[25] knitr_1.20        htmlwidgets_1.3   generics_0.0.2   
[28] fs_1.3.1          vctrs_0.3.1       webshot_0.5.1    
[31] tidyselect_1.1.0  rprojroot_1.3-2   grid_3.5.1       
[34] glue_1.4.1        R6_2.3.0          rmarkdown_1.10   
[37] purrr_0.3.4       magrittr_1.5      whisker_0.3-2    
[40] backports_1.1.2   scales_1.0.0      promises_1.0.1   
[43] htmltools_0.3.6   ellipsis_0.3.1    rvest_0.3.2      
[46] colorspace_1.3-2  httpuv_1.4.5      stringi_1.3.1    
[49] lazyeval_0.2.1    munsell_0.5.0     crayon_1.3.4