Session 01 - Exercises Key
Last updated: 2023-06-29
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Case-Control Association Testing
Before you begin:
- Make sure that R is installed on your computer
- For this lab, we will use the
data.tableanddplyrlibrary
library(data.table)
library(dplyr)
library(tidyr)
library(ggplot2)Introduction
We will be using the LHON dataset covered in the lecture notes for this portion of the exercises. The LHON dataset is from a case-control study and includes both phenotype and genotype data for a candidate gene.
Let’s first load the LHON data file into the R session. You can read the file directly from the web (if you are connected to the web) using the following command:
LHON.df <- fread("https://raw.githubusercontent.com/joellembatchou/SISG2023_Association_Mapping/master/data/LHON.txt", header=TRUE)Alternatively, you can save the file to your computer and read it into R from the directory where the file is located:
LHON.df <- fread("LHON.txt", header=TRUE)Exercises
Here are some things to look at:
- Examine the variables in the dataset:
# Each row is a sample
LHON.df %>%
head IID GENO PHENO
1: ID1 TT CONTROL
2: ID2 CT CONTROL
3: ID3 TT CASE
4: ID4 CT CONTROL
5: ID5 TT CONTROL
6: ID6 TT CONTROL# Character variables
LHON.df %>%
strClasses 'data.table' and 'data.frame': 328 obs. of 3 variables:
$ IID : chr "ID1" "ID2" "ID3" "ID4" ...
$ GENO : chr "TT" "CT" "TT" "CT" ...
$ PHENO: chr "CONTROL" "CONTROL" "CASE" "CONTROL" ...
- attr(*, ".internal.selfref")=<externalptr> - How many observations?
LHON.df %>%
nrow[1] 328- How many cases/controls?
LHON.df %>% select(PHENO) %>% tablePHENO
CASE CONTROL
89 239 - What is the distribution of the genotypes across cases/controls?
LHON.df %>%
select(PHENO, GENO) %>%
table GENO
PHENO CC CT TT
CASE 6 8 75
CONTROL 10 66 163- What about for allele types?
LHON.df %>%
group_by(PHENO) %>%
summarize(
n.C = 2 * sum(GENO == "CC") + 1 * sum(GENO == "CT"),
n.T = 2 * sum(GENO == "TT") + 1 * sum(GENO == "CT")
)# A tibble: 2 × 3
PHENO n.C n.T
<chr> <dbl> <dbl>
1 CASE 20 158
2 CONTROL 86 392- Perform a logistic regression analysis for this data with
CCas the reference genotype using theglm()function. (Hint: make sure to convert the phenotype to a binary 0/1 variable)
LHON.df <- LHON.df %>%
mutate(
PHENO.bin = as.numeric(PHENO == "CASE"),
GENO.factor = factor(GENO, levels = c("CC", "CT", "TT"))
)
log.model <- glm(PHENO.bin ~ GENO.factor, data = LHON.df, family = binomial(link = "logit")) View summary information from the fitted model, including coefficient estimates, standard errors and p-values.
log.model %>% summary
Call:
glm(formula = PHENO.bin ~ GENO.factor, family = binomial(link = "logit"),
data = LHON.df)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.5108 0.5164 -0.989 0.3226
GENO.factorCT -1.5994 0.6378 -2.508 0.0122 *
GENO.factorTT -0.2654 0.5349 -0.496 0.6197
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 383.49 on 327 degrees of freedom
Residual deviance: 368.48 on 325 degrees of freedom
AIC: 374.48
Number of Fisher Scoring iterations: 4- Obtain odds ratios and confidence intervals for the
CTandTTgenotypes relative to theCCreference genotype. Interpret.
- By hand
# OR for CT and TT
log.model %>% coef %>% exp (Intercept) GENO.factorCT GENO.factorTT
0.6000000 0.2020202 0.7668712 # CI for CT
exp( -1.5994 + c(-1,1) * 1.96 * 0.6378)[1] 0.05787394 0.70517308# CI for TT
exp( -0.2654 + c(-1,1) * 1.96 * 0.5349)[1] 0.2687956 2.1880353- Using R function
confint.default()
confint.default(log.model) %>% exp 2.5 % 97.5 %
(Intercept) 0.21806837 1.650858
GENO.factorCT 0.05787424 0.705187
GENO.factorTT 0.26878265 2.187981- Is there evidence of differences in odds of being a case for the
CTandTTgenotypes (compared toCC)?
Check the p-values.
Extra: 5. Perform the logistic regression analysis with the additive genotype coding. Obtain odds ratios and confidence intervals. Is there evidence of an association? How does it compare with the 2-parameter model?
LHON.df <- LHON.df %>%
mutate(
GENO.num = 0 + 1 * (GENO == "CT") + 2 * (GENO == "TT")
)
log.model.add <- glm(PHENO.bin ~ GENO.num, data = LHON.df, family = binomial(link = "logit"))
log.model.add %>% summary
Call:
glm(formula = PHENO.bin ~ GENO.num, family = binomial(link = "logit"),
data = LHON.df)
Coefficients:
Estimate Std. Error z value Pr(>|z|)
(Intercept) -1.8077 0.4554 -3.970 7.2e-05 ***
GENO.num 0.4787 0.2505 1.911 0.0559 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
(Dispersion parameter for binomial family taken to be 1)
Null deviance: 383.49 on 327 degrees of freedom
Residual deviance: 379.47 on 326 degrees of freedom
AIC: 383.47
Number of Fisher Scoring iterations: 4log.model.add %>% coef %>% exp(Intercept) GENO.num
0.1640322 1.6140439 confint.default(log.model.add) %>% exp 2.5 % 97.5 %
(Intercept) 0.06718883 0.4004616
GENO.num 0.98792490 2.6369796Association Testing with Quantitative Traits
Introduction
We will be using the Blood Pressure dataset for this portion of the exercises. This dataset contains diastolic and systolic blood pressure measurements for 1000 individuals, and genotype data at 11 SNPs in a candidate gene for blood pressure. Covariates such as gender (sex) and body mass index (bmi) are included as well.
Let’s first load the file into R. You can read the file directly from the web (if you are connected to the web) using the following command:
BP.df <- fread("https://raw.githubusercontent.com/joellembatchou/SISG2023_Association_Mapping/master/data/bpdata.csv", header=TRUE)Alternatively, you can save the file to your computer and read it into R from the directory where the file is located:
BP.df <- fread("bpdata.csv", header=TRUE)Exercises
Let’s take a look at the dataset:
BP.df %>% head V1 sex sbp dbp snp1 snp2 snp3 snp4 snp5 snp6 snp7 snp8 snp9 snp10 snp11
1: 1 FEMALE 171 89 CC TT TT TT CC GG AA TT TT CC TT
2: 2 MALE 160 99 TT TT CC <NA> CC AG AT CC CT CC CT
3: 3 FEMALE 142 83 CT TT TC CT CC AG TT CC TT CT TT
4: 4 MALE 126 71 CT TT CC <NA> CC AA TT CC TT CT CT
5: 5 FEMALE 126 82 CT TT CC CC CC AA TT CC TT CT CT
6: 6 FEMALE 132 89 CT TT CC CC CC <NA> TT CC TT TT CT
bmi
1: 25
2: 35
3: 34
4: 32
5: 34
6: 25BP.df %>% strClasses 'data.table' and 'data.frame': 1000 obs. of 16 variables:
$ V1 : int 1 2 3 4 5 6 7 8 9 10 ...
$ sex : chr "FEMALE" "MALE" "FEMALE" "MALE" ...
$ sbp : int 171 160 142 126 126 132 136 121 120 136 ...
$ dbp : int 89 99 83 71 82 89 58 87 69 88 ...
$ snp1 : chr "CC" "TT" "CT" "CT" ...
$ snp2 : chr "TT" "TT" "TT" "TT" ...
$ snp3 : chr "TT" "CC" "TC" "CC" ...
$ snp4 : chr "TT" NA "CT" NA ...
$ snp5 : chr "CC" "CC" "CC" "CC" ...
$ snp6 : chr "GG" "AG" "AG" "AA" ...
$ snp7 : chr "AA" "AT" "TT" "TT" ...
$ snp8 : chr "TT" "CC" "CC" "CC" ...
$ snp9 : chr "TT" "CT" "TT" "TT" ...
$ snp10: chr "CC" "CC" "CT" "CT" ...
$ snp11: chr "TT" "CT" "TT" "CT" ...
$ bmi : int 25 35 34 32 34 25 22 33 21 29 ...
- attr(*, ".internal.selfref")=<externalptr> - Perform a linear regression of systolic blood pressure
(
sbp) onSNP3using thelm()function. Compare the estimates, confidence intervals and p-values you get.
- Additive (linear) model: let’s count the number of
Tallele
BP.df %>% select(snp3) %>% tablesnp3
CC TC TT
621 304 35 BP.df <- BP.df %>%
mutate(snp3.add = 1 * (snp3 == "TC") + 2 * (snp3 == "TT"))
lm.add <- lm(sbp ~ snp3.add, data = BP.df)
lm.add %>% summary
Call:
lm(formula = sbp ~ snp3.add, data = BP.df)
Residuals:
Min 1Q Median 3Q Max
-55.974 -12.418 -0.974 10.582 60.582
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 140.4179 0.7219 194.506 <2e-16 ***
snp3.add 2.5556 1.0615 2.407 0.0163 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 18.33 on 958 degrees of freedom
(40 observations deleted due to missingness)
Multiple R-squared: 0.006014, Adjusted R-squared: 0.004976
F-statistic: 5.796 on 1 and 958 DF, p-value: 0.01625lm.add %>% confint.default 2.5 % 97.5 %
(Intercept) 139.0029685 141.832849
snp3.add 0.4750661 4.636205Let’s check how it compares when we count the number of
C alleles.
BP.df <- BP.df %>%
mutate(snp3.add.C = 1 * (snp3 == "TC") + 2 * (snp3 == "CC"))
lm.add.C <- lm(sbp ~ snp3.add.C, data = BP.df)
lm.add.C %>% summary
Call:
lm(formula = sbp ~ snp3.add.C, data = BP.df)
Residuals:
Min 1Q Median 3Q Max
-55.974 -12.418 -0.974 10.582 60.582
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 145.529 1.809 80.446 <2e-16 ***
snp3.add.C -2.556 1.062 -2.407 0.0163 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 18.33 on 958 degrees of freedom
(40 observations deleted due to missingness)
Multiple R-squared: 0.006014, Adjusted R-squared: 0.004976
F-statistic: 5.796 on 1 and 958 DF, p-value: 0.01625- dominant model (for
Tallele)
BP.df <- BP.df %>%
mutate(snp3.dom = 1 * (snp3 == "TC" | snp3 == "TT"))
BP.df %>% select(snp3.dom, snp3) %>% table snp3
snp3.dom CC TC TT
0 621 0 0
1 0 304 35lm.dom <- lm(sbp ~ snp3.dom, data = BP.df)
lm.dom %>% summary
Call:
lm(formula = sbp ~ snp3.dom, data = BP.df)
Residuals:
Min 1Q Median 3Q Max
-56.218 -12.428 -0.823 10.572 60.572
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 140.428 0.736 190.801 <2e-16 ***
snp3.dom 2.790 1.238 2.253 0.0245 *
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 18.34 on 958 degrees of freedom
(40 observations deleted due to missingness)
Multiple R-squared: 0.005269, Adjusted R-squared: 0.00423
F-statistic: 5.074 on 1 and 958 DF, p-value: 0.02451lm.dom %>% confint.default 2.5 % 97.5 %
(Intercept) 138.9858186 141.870864
snp3.dom 0.3624521 5.217443- recessive model (for
Tallele)
BP.df <- BP.df %>%
mutate(snp3.rec = 1 * (snp3 == "TT"))
BP.df %>% select(snp3.rec, snp3) %>% table snp3
snp3.rec CC TC TT
0 621 304 0
1 0 0 35lm.rec <- lm(sbp ~ snp3.rec, data = BP.df)
lm.rec %>% summary
Call:
lm(formula = sbp ~ snp3.rec, data = BP.df)
Residuals:
Min 1Q Median 3Q Max
-54.251 -12.501 -1.251 10.749 59.749
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 141.251 0.604 233.854 <2e-16 ***
snp3.rec 4.463 3.163 1.411 0.159
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 18.37 on 958 degrees of freedom
(40 observations deleted due to missingness)
Multiple R-squared: 0.002074, Adjusted R-squared: 0.001032
F-statistic: 1.991 on 1 and 958 DF, p-value: 0.1586lm.rec %>% confint.default 2.5 % 97.5 %
(Intercept) 140.06697 142.43465
snp3.rec -1.73658 10.66353- 2 parameter model
lm.rec <- lm(sbp ~ snp3, data = BP.df)
lm.rec %>% summary
Call:
lm(formula = sbp ~ snp3, data = BP.df)
Residuals:
Min 1Q Median 3Q Max
-55.931 -12.428 -0.931 10.572 60.572
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 140.4283 0.7361 190.773 <2e-16 ***
snp3TC 2.5026 1.2840 1.949 0.0516 .
snp3TT 5.2859 3.1868 1.659 0.0975 .
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 18.34 on 957 degrees of freedom
(40 observations deleted due to missingness)
Multiple R-squared: 0.006019, Adjusted R-squared: 0.003942
F-statistic: 2.898 on 2 and 957 DF, p-value: 0.05563lm.rec %>% confint.default 2.5 % 97.5 %
(Intercept) 138.98560975 141.871073
snp3TC -0.01405184 5.019211
snp3TT -0.96007686 11.531966- Provide a plot illustrating the relationship between sbp and the three genotypes at SNP3.
BP.df %>%
drop_na(snp3) %>%
ggplot(aes(x = snp3, y = sbp, fill = snp3)) +
geom_boxplot()
For question 3 and 4 below, R also has a ‘formula’ syntax, frequently
used when specifying regression models with many predictors. To regress
an outcome y on several covariates, the syntax is:
outcome ~ covariate1 + covariate2 + covariate3- Now redo the linear regression analysis of
sbpfrom question 1 for the additive model, but this time adjust forsexandbmi. Do the results change?
lm(sbp ~ snp3.add + sex + bmi, data = BP.df) %>% summary
Call:
lm(formula = sbp ~ snp3.add + sex + bmi, data = BP.df)
Residuals:
Min 1Q Median 3Q Max
-58.83 -12.81 -0.82 11.58 57.80
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 145.85380 3.00271 48.574 < 2e-16 ***
snp3.add 2.63566 1.05434 2.500 0.0126 *
sexMALE -4.77580 1.17642 -4.060 5.32e-05 ***
bmi -0.09837 0.09481 -1.038 0.2997
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 18.19 on 955 degrees of freedom
(41 observations deleted due to missingness)
Multiple R-squared: 0.02402, Adjusted R-squared: 0.02096
F-statistic: 7.836 on 3 and 955 DF, p-value: 3.608e-05- What proportion of the heritability of
sbpis explained by all of the 11 SNPs together?
lm(sbp ~ snp1+snp2+snp3+snp4+snp5+snp6+snp7+snp8+snp9+snp10+snp11, data = BP.df) %>% summary
Call:
lm(formula = sbp ~ snp1 + snp2 + snp3 + snp4 + snp5 + snp6 +
snp7 + snp8 + snp9 + snp10 + snp11, data = BP.df)
Residuals:
Min 1Q Median 3Q Max
-50.722 -11.967 -0.703 11.021 61.704
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 133.1726 12.4033 10.737 <2e-16 ***
snp1CT -1.7048 4.5991 -0.371 0.711
snp1TT 1.9319 8.2839 0.233 0.816
snp2AT 0.7347 5.5923 0.131 0.896
snp2TT -0.5118 6.9317 -0.074 0.941
snp3TC 4.7672 5.0211 0.949 0.343
snp3TT 6.6913 9.7904 0.683 0.495
snp4CT -0.4778 3.5501 -0.135 0.893
snp4TT 2.3431 6.4874 0.361 0.718
snp5CT 1.1896 3.0462 0.391 0.696
snp5TT -2.2787 7.5490 -0.302 0.763
snp6AG -3.0266 2.0697 -1.462 0.144
snp6GG 2.1230 4.6650 0.455 0.649
snp7AT -3.0873 3.9148 -0.789 0.431
snp7TT -2.6319 4.3146 -0.610 0.542
snp8CT -1.5509 3.6318 -0.427 0.669
snp8TT -2.5507 7.3228 -0.348 0.728
snp9CT 6.0693 7.6170 0.797 0.426
snp9TT 4.7385 7.4517 0.636 0.525
snp10CT 1.4330 1.6466 0.870 0.384
snp10TT 1.9810 2.0699 0.957 0.339
snp11CT 4.8005 6.5175 0.737 0.462
snp11TT 4.0226 9.2775 0.434 0.665
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 18.2 on 707 degrees of freedom
(270 observations deleted due to missingness)
Multiple R-squared: 0.02633, Adjusted R-squared: -0.003965
F-statistic: 0.8691 on 22 and 707 DF, p-value: 0.6372Let’s check the model if we had used additive coding for all SNPs.
# all allele combinations: C/T, A/T, A/G
BP.df %>% select(snp1:snp11) %>% unlist %>% table.
AA AG AT CC CT GG TC TT
636 335 666 2874 2276 73 304 3428 BP.df %>%
mutate(across(
snp1:snp11,
function(snp) { 1 * (snp == "TC" | snp == "CT" | snp == "AT" | snp == "AG") + 2 * (snp == "TT" | snp == "GG")}
)) %>%
lm(sbp ~ snp1+snp2+snp3+snp4+snp5+snp6+snp7+snp8+snp9+snp10+snp11, data = .) %>%
summary
Call:
lm(formula = sbp ~ snp1 + snp2 + snp3 + snp4 + snp5 + snp6 +
snp7 + snp8 + snp9 + snp10 + snp11, data = .)
Residuals:
Min 1Q Median 3Q Max
-53.638 -12.849 -0.522 11.032 61.683
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 137.36286 9.09141 15.109 <2e-16 ***
snp1 1.88456 4.03838 0.467 0.641
snp2 -1.95639 2.96674 -0.659 0.510
snp3 4.60730 4.65652 0.989 0.323
snp4 0.05946 3.11138 0.019 0.985
snp5 -0.26494 2.58719 -0.102 0.918
snp6 -1.17284 1.80185 -0.651 0.515
snp7 -0.28939 1.78362 -0.162 0.871
snp8 0.70702 2.78030 0.254 0.799
snp9 2.17197 2.54774 0.853 0.394
snp10 0.60685 1.01229 0.599 0.549
snp11 -0.39009 4.15347 -0.094 0.925
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 18.17 on 718 degrees of freedom
(270 observations deleted due to missingness)
Multiple R-squared: 0.01418, Adjusted R-squared: -0.0009268
F-statistic: 0.9386 on 11 and 718 DF, p-value: 0.5022
sessionInfo()R version 4.3.0 (2023-04-21)
Platform: aarch64-apple-darwin20 (64-bit)
Running under: macOS Ventura 13.4
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.3-arm64/Resources/lib/libRlapack.dylib; LAPACK version 3.11.0
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
time zone: Australia/Brisbane
tzcode source: internal
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] ggplot2_3.4.2 tidyr_1.3.0 dplyr_1.1.2 data.table_1.14.8
loaded via a namespace (and not attached):
[1] gtable_0.3.3 jsonlite_1.8.5 highr_0.10 compiler_4.3.0
[5] promises_1.2.0.1 tidyselect_1.2.0 Rcpp_1.0.10 stringr_1.5.0
[9] git2r_0.32.0 later_1.3.1 jquerylib_0.1.4 scales_1.2.1
[13] yaml_2.3.7 fastmap_1.1.1 R6_2.5.1 labeling_0.4.2
[17] generics_0.1.3 curl_5.0.1 workflowr_1.7.0 knitr_1.43
[21] tibble_3.2.1 munsell_0.5.0 rprojroot_2.0.3 bslib_0.5.0
[25] pillar_1.9.0 rlang_1.1.1 utf8_1.2.3 cachem_1.0.8
[29] stringi_1.7.12 httpuv_1.6.11 xfun_0.39 fs_1.6.2
[33] sass_0.4.6 cli_3.6.1 withr_2.5.0 magrittr_2.0.3
[37] grid_4.3.0 digest_0.6.31 rstudioapi_0.14 lifecycle_1.0.3
[41] vctrs_0.6.2 evaluate_0.21 glue_1.6.2 farver_2.1.1
[45] colorspace_2.1-0 fansi_1.0.4 purrr_1.0.1 rmarkdown_2.22
[49] tools_4.3.0 pkgconfig_2.0.3 htmltools_0.5.5