Mentorship

Daniel E. Weeks November 21, 2020, 14:11

1 Load Libraries

library(tidyverse)
# library(tidylog)
library(ggExtra)
library(arsenal)

2 Input directory and files

# Print the working directory
getwd()

## [1] "/Users/dweeks/data/Mentorship"

3 The AlShebli et al (2020) mentorship paper

Here I examine the data provided by the authors of this paper:

AlShebli B, Makovi K, Rahwan T. The association between early career informal mentorship in academic collaborations and junior author performance. Nat Commun. 2020 Nov 17;11(1):5855. doi: 10.1038/s41467-020-19723-8. PMID: 33203848. https://pubmed.ncbi.nlm.nih.gov/33203848/

4 The data

4.1 The input data

The input data are from the ‘bedoor/Mentorship’ GitHub repository at

https://github.com/bedoor/Mentorship

Their repository is described as:

‘This repository includes all data used in “The Association between Early Career Informal Mentorship in Academic Collaborations and Junior Author Performance”.’

LinesRead <- 1e+05
inFile <- "Mentorship/Repository_Data/Data_7yearcutoff.csv"
a <- read_csv(file = inFile, n_max = LinesRead)

## Parsed with column specification:
## cols(
##   .default = col_double(),
##   Pr0tegeGender = col_character(),
##   AffiliationRank = col_character()
## )

## See spec(...) for full column specifications.

names(a)

##  [1] "Disambiguated_ProtegeID"   "AvgBigShot"               
##  [3] "AvgBigShotBin"             "AvgHub"                   
##  [5] "AvgHubBin"                 "Avg_c5"                   
##  [7] "numMentors"                "numMentorsBin"            
##  [9] "ProtegeFirstPubYear"       "ProtegeFirstPubYearBin"   
## [11] "Pr0tegeGender"             "ProtegeGenderBin"         
## [13] "AffiliationRank"           "AffiliationRankBin"       
## [15] "AvgMentorsAcAges"          "AvgMentorsAcAgesBin"      
## [17] "NumYearsPostMentorship"    "NumYearsPostMentorshipBin"
## [19] "ProtegeDisciplineID"       "Avg_c10"                  
## [21] "MaxBigShot"                "MaxBigShotBin"            
## [23] "MedianBigShot"             "MedianBigShotBin"         
## [25] "MaxHub"                    "MaxHubBin"                
## [27] "MedianHub"                 "MedianHubBin"

total_records <- as.integer(system2("wc", args = c("-l", inFile, " | awk '{print $1}'"), 
    stdout = TRUE))
total_records

## [1] 1055213

4.2 Disclaimer: For speed, only read in the first 10^{5} lines

To speed up the analyses, we read only the first 10^{5} lines of the input file, instead of reading all 1055213 lines.

4.3 Problem: No gender information for mentors

There does not appear to be any information in the provided file about the mentor’s gender, so the provided data do not appear to be ‘all the data’.

There is no data dictionary, so we are left to infer what is in each column of the data file from the column names and content.

5 ProtegeFirstPubYear

6 Distribution of ProtegeFirstPubYear

“Year of the protege’s first publication: The year in which the protege published their first mentored paper.”

summary(a$ProtegeFirstPubYear)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1897    1992    2000    1997    2006    2013

ggplot(data = a, mapping = aes(x = ProtegeFirstPubYear)) + geom_histogram() + ggtitle("Distribution of ProtegeFirstPubYear")

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


table(a$Pr0tegeGender)

## 
## female   male 
##  34257  65743

ggplot(data = a, mapping = aes(x = ProtegeFirstPubYear)) + geom_histogram() + ggtitle("Distribution of ProtegeFirstPubYear") + 
    facet_grid(~Pr0tegeGender)

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


a$MaleProtegeFirstPubYear <- a$ProtegeFirstPubYear
a$MaleProtegeFirstPubYear[a$Pr0tegeGender == "female"] <- NA

a$FemaleProtegeFirstPubYear <- a$ProtegeFirstPubYear
a$FemaleProtegeFirstPubYear[a$Pr0tegeGender == "male"] <- NA

summary(a$MaleProtegeFirstPubYear)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##    1897    1990    1999    1996    2005    2013   34257

summary(a$FemaleProtegeFirstPubYear)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max.    NA's 
##    1901    1995    2002    2000    2007    2013   65743

p <- ggplot(data = a, aes(x = x)) + geom_histogram(aes(x = MaleProtegeFirstPubYear, 
    y = ..density..), fill = "#69b3a2") + annotate("text", x = 1950, y = 0.03, label = "MaleProtegeFirstPubYear", 
    color = "#69b3a2") + geom_histogram(aes(x = FemaleProtegeFirstPubYear, y = -..density..), 
    fill = "#404080") + annotate("text", x = 1950, y = -0.03, label = "FemaleProtegeFirstPubYear", 
    color = "#404080") + xlab("ProtegeFirstPubYear") + ggtitle("Distributions of ProtegeFirstPubYear by gender")
p

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Warning: Removed 34257 rows containing non-finite values (stat_bin).

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

## Warning: Removed 65743 rows containing non-finite values (stat_bin).


p <- ggplot(data = a, aes(x = x)) + geom_density(aes(x = MaleProtegeFirstPubYear, 
    y = ..density..), fill = "#69b3a2") + annotate("text", x = 1950, y = 0.03, label = "MaleProtegeFirstPubYear", 
    color = "#69b3a2") + geom_density(aes(x = FemaleProtegeFirstPubYear, y = -..density..), 
    fill = "#404080") + annotate("text", x = 1950, y = -0.03, label = "FemaleProtegeFirstPubYear", 
    color = "#404080") + xlab("ProtegeFirstPubYear") + ggtitle("Distributions of ProtegeFirstPubYear by gender")
p

## Warning: Removed 34257 rows containing non-finite values
## (stat_density).

## Warning: Removed 65743 rows containing non-finite values
## (stat_density).

6.1 Problem: ProtegeFirstPubYear time range is very large

in the first 10^{5} lines of this data set, the ProtegeFirstPubYear ranges from 1897 to 2013. It seems that it would be very difficult to properly compare the impact factors of papers published in rmin(a$ProtegeFirstPubYear)`, well before the advent of team science and the current deluge of scientific publications, to those published as recently 2013.

7 NumYearsPostMentorship

“The number of years post mentorship: Since our dataset is up to Dec 31st 2019, we are only able to calculate c5—the number of citations accumulated five years post publication—for papers published before

  1. Thus, given a protege whose first paper was published in year x, the number of years post mentorship is 2015 - (x + 6), bearing in mind that the mentorship period is 7 years and we do not include proteges with a gap of 5 years of more in their career history.”

7.1 Problem: Error in the equation for NumYearsPostMentorship

Note that the stated equation of 2015 - (x + 6) for computing the number of years post mentorship is not what was used, as instead 2015 - (x + 2), where x is the year the protege’s paper was first published, as we see here in the first 10^{5} lines of the input file:

all.equal(a$NumYearsPostMentorship, 2015 - (a$ProtegeFirstPubYear + 2))

## [1] TRUE

7.2 Distribution of NumYearsPostMentorship

summary(a$NumYearsPostMentorship)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    0.00    7.00   13.00   15.68   21.00  116.00

ggplot(data = a, mapping = aes(x = NumYearsPostMentorship)) + geom_histogram() + 
    ggtitle("Distribution of NumYearsPostMentorship")

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


a$ProtegeGender <- as.factor(a$Pr0tegeGender)
p <- ggplot(data = a, mapping = aes(x = ProtegeFirstPubYear, y = NumYearsPostMentorship)) + 
    geom_point() + ggtitle("NumYearsPostMentorship vs. ProtegeFirstPubYear")
ggMarginal(p, type = "histogram")

7.3 Problem: some values of NumYearsPostMentorship are unrealistically large

In the first 10^{5} lines of the input file of this data set, there are values of NumYearsPostMentorship as large as 116. These values are unrealistically large.

8 AvgMentorsAcAges

8.1 Distribution of AvgMentorsAcAges

“Average academic age of mentors: This is computed for any given protege by first computing the academic age of each mentor in the year of their first publication with the protege, and then averaging these numbers over all the mentors.”

“Given a scientist whose first paper was published in year x, the academic age of this scientist in year y is y-x.”

summary(a$AvgMentorsAcAges)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    7.00   13.00   16.67   18.18   21.00  213.00

ggplot(data = a, mapping = aes(x = AvgMentorsAcAges)) + geom_histogram() + ggtitle("Distribution of AvgMentorsAcAges")

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


ggplot(data = a, mapping = aes(x = ProtegeFirstPubYear, y = AvgMentorsAcAges, col = ProtegeGender)) + 
    geom_point() + ggtitle("ProtegeFirstPubYear vs. AvgMentorsAcAges")


ggplot(data = a, mapping = aes(x = ProtegeFirstPubYear, y = AvgMentorsAcAges)) + 
    geom_point() + facet_grid(~ProtegeGender) + ggtitle("ProtegeFirstPubYear vs. AvgMentorsAcAges by ProtegeGender")

8.2 Problem: some AvgMentorsAcAges are unrealistically large

There are AvgMentorsAcAges as large as 213 in the first 10^{5} lines of this data set. This is unrealistically large.

Among proteges who published their first paper after 2000, there are AvgMentorsAcAges as large as 213 in this data set. Should we be evaluating the mentorship effects of mentors who were born than 200 years ago?

9 Avg_c5

9.1 Distribution of Avg_c5

summary(a$Avg_c5)

##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
##    0.000    2.068    6.692   11.557   14.254 1126.429

ggplot(data = a, mapping = aes(x = Avg_c5)) + geom_histogram() + ggtitle("Distribution of Avg_c5")

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


ggplot(data = a, mapping = aes(x = ProtegeFirstPubYear, y = Avg_c5, col = ProtegeGender)) + 
    geom_point() + ggtitle("ProtegeFirstPubYear vs. Avg_c5")


ggplot(data = a, mapping = aes(x = ProtegeFirstPubYear, y = Avg_c5)) + geom_point() + 
    facet_grid(~ProtegeGender) + ggtitle("ProtegeFirstPubYear vs. Avg_c5")

9.2 Joint distribution of Avg_c5 and AvgMentorsAcAges

ggplot(data = a, mapping = aes(y = Avg_c5, x = AvgMentorsAcAges, col = ProtegeGender)) + 
    geom_point() + ggtitle("Avg_c5 vs. AvgMentorsAcAges")


ggplot(data = a, mapping = aes(y = Avg_c5, x = AvgMentorsAcAges, col = ProtegeFirstPubYear)) + 
    geom_point() + scale_color_gradient(low = "red", high = "blue") + facet_grid(~ProtegeGender) + 
    ggtitle("Avg_c5 vs. AvgMentorsAcAges")

10 Avg_c10

10.1 Distribution of Avg_c10

summary(a$Avg_c10)

##     Min.  1st Qu.   Median     Mean  3rd Qu.     Max. 
##    0.000    2.694    9.093   16.945   20.857 3057.000

ggplot(data = a, mapping = aes(x = Avg_c10)) + geom_histogram() + ggtitle("Distribution of Avg_c10")

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


ggplot(data = a, mapping = aes(x = ProtegeFirstPubYear, y = Avg_c10, col = ProtegeGender)) + 
    geom_point() + ggtitle("ProtegeFirstPubYear vs. Avg_c10")


ggplot(data = a, mapping = aes(x = ProtegeFirstPubYear, y = Avg_c10)) + geom_point() + 
    facet_grid(~ProtegeGender) + ggtitle("ProtegeFirstPubYear vs. Avg_c10")

10.2 Problem with Avg_c10: Cannot compute a value Avg_c10 for recent publications

As the dataset is up to Dec 31st 2019, how can one compute a valid Avg_c10 for someone whose first publication year was 2012 or 2013?

a %>% filter(ProtegeFirstPubYear == max(ProtegeFirstPubYear) - 1) %>% select(ProtegeFirstPubYear, 
    Avg_c5, Avg_c10) %>% head(20)

## # A tibble: 20 x 3
##    ProtegeFirstPubYear Avg_c5 Avg_c10
##                  <dbl>  <dbl>   <dbl>
##  1                2012  0       0    
##  2                2012  0       0    
##  3                2012  0       0    
##  4                2012  0.5     0.5  
##  5                2012  0.5     0.5  
##  6                2012  0       0    
##  7                2012  0.5     0.5  
##  8                2012  0.5     0.5  
##  9                2012  0       0    
## 10                2012  0.182   0.182
## 11                2012  0.182   0.182
## 12                2012  0.182   0.182
## 13                2012  0.2     0.2  
## 14                2012  0       0    
## 15                2012  0       0    
## 16                2012  0       0    
## 17                2012  0       0    
## 18                2012  0       0    
## 19                2012  0       0    
## 20                2012  0       0

11 Avg_c5 vs Avg_c10

11.1 Tables of Avg_c5 and Avg_c10

my_controls <- tableby.control(test = T, total = T, numeric.stats = c("meansd", "medianq1q3", 
    "range", "Nmiss2"), cat.stats = c("countpct", "Nmiss2"), stats.labels = list(meansd = "Mean (SD)", 
    medianq1q3 = "Median (Q1, Q3)", range = "Min - Max", Nmiss2 = "Missing"))

my_controls2 <- tableby.control(numeric.stats = c("medianq1q3"), stats.labels = list(medianq1q3 = "Median (Q1, Q3)"))

t.test(Avg_c5 ~ ProtegeGender, data = a)

## 
##  Welch Two Sample t-test
## 
## data:  Avg_c5 by ProtegeGender
## t = 4.0045, df = 69256, p-value = 6.22e-05
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.3010699 0.8783127
## sample estimates:
## mean in group female   mean in group male 
##             11.94469             11.35500

t.test(Avg_c10 ~ ProtegeGender, data = a)

## 
##  Welch Two Sample t-test
## 
## data:  Avg_c10 by ProtegeGender
## t = 2.6735, df = 69586, p-value = 0.007508
## alternative hypothesis: true difference in means is not equal to 0
## 95 percent confidence interval:
##  0.1643062 1.0669714
## sample estimates:
## mean in group female   mean in group male 
##             17.34958             16.73394

t1 <- tableby(ProtegeGender ~ ., data = a %>% select(ProtegeGender, Avg_c5, Avg_c10))

summary(t1, title = "Table of Avg_c5 and Avg_c10 by ProtegeGender")
  female (N=34257) male (N=65743) Total (N=100000) p value
Avg_c5       < 0.001
   Mean (SD) 11.945 (22.121) 11.355 (22.056) 11.557 (22.080)  
   Range 0.000 - 1076.000 0.000 - 1126.429 0.000 - 1126.429  
Avg_c10       0.008
   Mean (SD) 17.350 (34.528) 16.734 (34.614) 16.945 (34.586)  
   Range 0.000 - 2128.000 0.000 - 3057.000 0.000 - 3057.000  

Table of Avg_c5 and Avg_c10 by ProtegeGender

t1 <- tableby(ProtegeGender ~ ., data = a %>% select(ProtegeGender, Avg_c5, Avg_c10), 
    control = my_controls2)

summary(t1, title = "Table of Avg_c5 and Avg_c10 by ProtegeGender")
  female (N=34257) male (N=65743) Total (N=100000) p value
Avg_c5       < 0.001
   Median (Q1, Q3) 7.000 (2.000, 15.000) 6.565 (2.182, 13.969) 6.692 (2.068, 14.254)  
Avg_c10       0.008
   Median (Q1, Q3) 9.000 (2.286, 21.510) 9.111 (2.935, 20.425) 9.093 (2.694, 20.857)  

Table of Avg_c5 and Avg_c10 by ProtegeGender

t1 <- tableby(ProtegeGender ~ ., data = a %>% select(ProtegeGender, Avg_c5, Avg_c10), 
    control = my_controls)

summary(t1, title = "Table of Avg_c5 and Avg_c10 by ProtegeGender")
  female (N=34257) male (N=65743) Total (N=100000) p value
Avg_c5       < 0.001
   Mean (SD) 11.945 (22.121) 11.355 (22.056) 11.557 (22.080)  
   Median (Q1, Q3) 7.000 (2.000, 15.000) 6.565 (2.182, 13.969) 6.692 (2.068, 14.254)  
   Min - Max 0.000 - 1076.000 0.000 - 1126.429 0.000 - 1126.429  
   Missing 0 0 0  
Avg_c10       0.008
   Mean (SD) 17.350 (34.528) 16.734 (34.614) 16.945 (34.586)  
   Median (Q1, Q3) 9.000 (2.286, 21.510) 9.111 (2.935, 20.425) 9.093 (2.694, 20.857)  
   Min - Max 0.000 - 2128.000 0.000 - 3057.000 0.000 - 3057.000  
   Missing 0 0 0  

Table of Avg_c5 and Avg_c10 by ProtegeGender

11.2 Joint distribution of Avg_c5 and Avg_c10

ggplot(data = a, mapping = aes(x = Avg_c5, y = Avg_c10, col = ProtegeGender)) + geom_point() + 
    geom_abline(intercept = 0, slope = 1, col = "red") + ggtitle("Avg_c5 vs. Avg_c10")


ggplot(data = a, mapping = aes(x = Avg_c5, y = Avg_c10, col = ProtegeFirstPubYear)) + 
    geom_point() + scale_color_gradient(low = "red", high = "blue") + geom_abline(intercept = 0, 
    slope = 1, col = "red") + facet_grid(~ProtegeGender) + ggtitle("Avg_c5 vs. Avg_c10")

12 numMentors

12.1 Distribution of numMentors

summary(a$numMentors)

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   1.000   1.000   3.000   4.514   6.000  91.000

ggplot(data = a, mapping = aes(x = numMentors)) + geom_histogram() + ggtitle("Distribution of numMentors")

## `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


ggplot(data = a, mapping = aes(x = ProtegeFirstPubYear, y = numMentors, col = ProtegeGender)) + 
    geom_point() + ggtitle("ProtegeFirstPubYear vs. numMentors")


ggplot(data = a, mapping = aes(x = ProtegeFirstPubYear, y = numMentors)) + geom_point() + 
    facet_grid(~ProtegeGender) + ggtitle("ProtegeFirstPubYear vs. numMentors")

12.2 Problem: some numMentors values are too large

How could someone possibly really have more than a handful of mentors?

In the first 10^{5} lines of this data set, there are individuals with 91 mentors!

The Supplement states that:

“Whenever a junior scientist publishes a paper with a senior scientist, we consider the former to be a protege, and the latter to be a mentor, as long as they authored at least one paper with 20 or less co-authors and share the same discipline and US-based affiliation.”

Oh, but we are really measuring co-authorship at the same US-based affiliation on joint papers with 20 or less co-authors.

13 Summary

Here I examine the data provided by the authors of this paper:

AlShebli B, Makovi K, Rahwan T. The association between early career informal mentorship in academic collaborations and junior author performance. Nat Commun. 2020 Nov 17;11(1):5855. doi: 10.1038/s41467-020-19723-8. PMID: 33203848. https://pubmed.ncbi.nlm.nih.gov/33203848/

For speed, I examined only the first 10^{5} lines of the data file Mentorship/Repository_Data/Data_7yearcutoff.csv from the ‘bedoor/Mentorship’ GitHub repository at

https://github.com/bedoor/Mentorship

Their repository is described by the authors as:

‘This repository includes all data used in “The Association between Early Career Informal Mentorship in Academic Collaborations and Junior Author Performance”.’

13.1 Problem: No gender information for mentors

There does not appear to be any information in the provided file about the mentor’s gender, so the provided data do not appear to be ‘all the data’.

13.2 Problem: ProtegeFirstPubYear time range is very large

In the first 10^{5} lines of this data set, the ProtegeFirstPubYear ranges from 1897 to 2013. It seems that it would be very difficult to properly compare the impact factors of papers published in 1897, well before the advent of team science and the current deluge of scientific publications, to those published as recently 2013.

13.3 Problem: Error in the equation for NumYearsPostMentorship

Note that the stated equation of 2015 - (x + 6) for computing the number of years post mentorship is not what was used, as instead 2015 - (x + 2), where x is the year the protege’s paper was first published.

13.4 Problem: some values of NumYearsPostMentorship are unrealistically large

In the first 10^{5} lines of the input file of this data set, there are values of NumYearsPostMentorship as large as 116. These values are unrealistically large.

13.5 Problem: some AvgMentorsAcAges are unrealistically large

There are AvgMentorsAcAges as large as 213 in the first 10^{5} lines of this data set. This is unrealistically large.

Among proteges who published their first paper after 2000, there are AvgMentorsAcAges as large as 213 in this data set. Should we be evaluating the mentorship effects of mentors who were born than 200 years ago?

13.6 Problem with Avg_c10: Cannot compute a value Avg_c10 for recent publications

As the dataset is up to Dec 31st 2019, how can one compute a valid Avg_c10 for someone whose first publication year was 2012 or 2013?

13.7 Problem: some numMentors values are too large

How could someone possibly really have more than a handful of mentors?

In the first 10^{5} lines of this data set, there are individuals with 91 mentors!

The Supplement states that:

“Whenever a junior scientist publishes a paper with a senior scientist, we consider the former to be a protege, and the latter to be a mentor, as long as they authored at least one paper with 20 or less co-authors and share the same discipline and US-based affiliation.”

Oh, but we are really measuring co-authorship at the same US-based affiliation on joint papers with 20 or less co-authors.

14 Generating GitHub Markdown

library(rmarkdown)
library(here)
finalize <- function() {
    rmd <- here("mentorship.Rmd")
    rmarkdown::render(rmd, "github_document")
}

15 Session Information

sessionInfo()

## R version 4.0.2 (2020-06-22)
## Platform: x86_64-apple-darwin17.0 (64-bit)
## Running under: macOS High Sierra 10.13.6
## 
## Matrix products: default
## BLAS:   /System/Library/Frameworks/Accelerate.framework/Versions/A/Frameworks/vecLib.framework/Versions/A/libBLAS.dylib
## LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib
## 
## locale:
## [1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
## 
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods  
## [7] base     
## 
## other attached packages:
##  [1] here_0.1        rmarkdown_2.5   arsenal_3.4.0   ggExtra_0.9    
##  [5] forcats_0.5.0   stringr_1.4.0   dplyr_1.0.0     purrr_0.3.4    
##  [9] readr_1.3.1     tidyr_1.1.2     tibble_3.0.1    ggplot2_3.3.0  
## [13] tidyverse_1.3.0 knitr_1.30     
## 
## loaded via a namespace (and not attached):
##  [1] Rcpp_1.0.4.6     lubridate_1.7.8  lattice_0.20-41 
##  [4] utf8_1.1.4       rprojroot_1.3-2  assertthat_0.2.1
##  [7] digest_0.6.25    mime_0.9         R6_2.4.1        
## [10] cellranger_1.1.0 backports_1.1.7  reprex_0.3.0    
## [13] evaluate_0.14    highr_0.8        httr_1.4.2      
## [16] pillar_1.4.4     rlang_0.4.6      readxl_1.3.1    
## [19] rstudioapi_0.11  miniUI_0.1.1.1   Matrix_1.2-18   
## [22] splines_4.0.2    labeling_0.3     munsell_0.5.0   
## [25] shiny_1.5.0      broom_0.5.6      compiler_4.0.2  
## [28] httpuv_1.5.4     modelr_0.1.7     xfun_0.17       
## [31] pkgconfig_2.0.3  htmltools_0.5.0  tidyselect_1.1.0
## [34] fansi_0.4.1      crayon_1.3.4     dbplyr_1.4.3    
## [37] withr_2.2.0      later_1.0.0      grid_4.0.2      
## [40] nlme_3.1-148     jsonlite_1.6.1   xtable_1.8-4    
## [43] gtable_0.3.0     lifecycle_0.2.0  DBI_1.1.0       
## [46] formatR_1.7      magrittr_1.5     scales_1.1.1    
## [49] cli_2.0.2        stringi_1.4.6    farver_2.0.3    
## [52] fs_1.4.1         promises_1.1.0   xml2_1.3.2      
## [55] ellipsis_0.3.1   generics_0.0.2   vctrs_0.3.1     
## [58] tools_4.0.2      glue_1.4.1       hms_0.5.3       
## [61] survival_3.1-12  fastmap_1.0.1    yaml_2.2.1      
## [64] colorspace_1.4-1 rvest_0.3.5      haven_2.2.0