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<h1 class="title toc-ignore">PK - Single Ascending Dose</h1>
<h4 class="author">Alison Margolskee, Andy Stein</h4>
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<div id="overview" class="section level2">
<h2>Overview</h2>
<!--START_EXPLANATION-->
<p>This document contains exploratory plots for single ascending dose PK
data as well as the R code that generates these graphs. The plots
presented here are based on simulated data (<a
href="PKPD_Datasets.html">see: PKPD Datasets</a>). You may also download
the Single Ascending Dose PK dataset for your reference (<a
href="Data/Single_Ascending_Dose_Dataset2.csv">download dataset</a>).
Data specifications can be accessed on <a
href="Datasets.html">Datasets</a> and Rmarkdown template to generate
this page can be found on <a
href="Rmarkdown/Single_Ascending_Dose_PK.Rmd">Rmarkdown-Template</a>.
<!--END_EXPLANATION--></p>
</div>
<div id="setup" class="section level2">
<h2>Setup</h2>
<pre class="r"><code>library(ggplot2)
library(dplyr)
library(tidyr)
library(xgxr)
#flag for labeling figures as draft
status = "DRAFT"
# ggplot settings
xgx_theme_set()
#directories for saving individual graphs
dirs = list(
parent_dir = "Parent_Directory",
rscript_dir = "./",
rscript_name = "Example.R",
results_dir = "./",
filename_prefix = "",
filename = "Example.png")</code></pre>
</div>
<div id="load-dataset" class="section level2">
<h2>Load Dataset</h2>
<pre class="r"><code>#load dataset
pkpd_data <- read.csv("../Data/Single_Ascending_Dose_Dataset2.csv")
#ensure dataset has all the necessary columns
pkpd_data = pkpd_data %>%
mutate(ID = ID, #ID column
TIME = TIME, #TIME column name, time relative to first dose
NOMTIME = NOMTIME,#NOMINAL TIME column name
EVID = EVID ,#EVENT ID, >=1 is dose, otherwise measurement
LIDV = LIDV, #DEPENDENT VARIABLE column name
CENS = CENS, #CENSORING column name
CMT = CMT, #COMPARTMENT column
DOSE = DOSE, #DOSE column here (numeric value)
TRTACT = TRTACT, #DOSE REGIMEN column here (character, with units),
LIDV_NORM = LIDV/DOSE,
LIDV_UNIT = ifelse(CMT==2, "ng/ml", NA )
)
#create a factor for the treatment variable for plotting
pkpd_data = pkpd_data %>%
arrange(DOSE) %>%
mutate(TRTACT_low2high = factor(TRTACT, levels = unique(TRTACT)),
TRTACT_high2low = factor(TRTACT, levels = rev(unique(TRTACT)))) %>%
select(-TRTACT)
#create pk dataset
pk_data <- pkpd_data %>%
filter(CMT==2)
#perform NCA, for additional plots
NCA = pk_data %>%
group_by(ID, DOSE) %>%
filter(!is.na(LIDV)) %>%
summarize(AUC_last = caTools::trapz(TIME,LIDV),
Cmax = max(LIDV),
SEX = SEX[1], #this part just keeps the SEX and WEIGHTB covariates
WEIGHTB = WEIGHTB[1]) %>%
gather(PARAM, VALUE,-c(ID, DOSE, SEX, WEIGHTB)) %>%
ungroup() %>%
mutate(VALUE_NORM = VALUE/DOSE)
#units and labels
time_units_dataset = "hours"
time_units_plot = "days"
trtact_label = "Dose"
dose_label = "Dose (mg)"
conc_units = "ng/ml"
AUC_units = paste0("h.", conc_units)
conc_label = paste0("Concentration (", conc_units, ")")
concnorm_label = paste0("Normalized Concentration (", conc_units, ")/mg")</code></pre>
</div>
<div id="provide-an-overview-of-the-data" class="section level2">
<h2>Provide an overview of the data</h2>
<!--START_EXPLANATION-->
<p>Summarize the data in a way that is easy to visualize the general
trend of PK over time and between doses. Using summary statistics can be
helpful, e.g. Mean +/- SE, or median, 5th & 95th percentiles.
Consider either coloring by dose or faceting by dose. Depending on the
amount of data one graph may be better than the other.</p>
<p>When looking at summaries of PK over time, there are several things
to observe. Note the number of doses and number of time points or
sampling schedule. Observe the overall shape of the average profiles.
What is the average Cmax per dose? Tmax? Does the elimination phase
appear to be parallel across the different doses? Is there separation
between the profiles for different doses? Can you make a visual estimate
of the number of compartments that would be needed in a PK model?</p>
<p>For PK data, we recommend plotting both on a linear scale, and on a
log scale. Linear scale will help you better to see the Cmax, while log
scale will help you to detect number of compartments, half-life and
potential nonlinearity of clearance. <!--END_EXPLANATION--></p>
<div id="concentration-over-time-colored-by-dose-mean---95-ci"
class="section level3">
<h3>Concentration over time, colored by Dose, mean +/- 95% CI</h3>
<pre class="r"><code>gg <- ggplot(data = pk_data, aes(x = NOMTIME, y = LIDV, group= TRTACT_high2low, color = TRTACT_high2low))
gg <- gg + xgx_stat_ci(conf_level = .95)
gg <- gg + xgx_scale_x_time_units(units_dataset = time_units_dataset,
units_plot = time_units_plot)
gg <- gg + labs(y=conc_label,color = trtact_label)
gg <- gg + xgx_annotate_status(status)
gg <- gg + xgx_annotate_filenames(dirs)
#if saving copy of figure, replace xgx_annotate lines with xgx_save() shown below:
#xgx_save(width,height,dirs,"filename_main",status)
print(gg)</code></pre>
<p><img src="Single_Ascending_Dose_PK_files/figure-html/unnamed-chunk-3-1.png" width="768" /></p>
<pre class="r"><code>print(gg + xgx_scale_y_log10() )</code></pre>
<p><img src="Single_Ascending_Dose_PK_files/figure-html/unnamed-chunk-3-2.png" width="768" /></p>
</div>
<div
id="concentration-over-time-faceted-by-dose-mean---95-ci-overlaid-on-gray-spaghetti-plots"
class="section level3">
<h3>Concentration over time, faceted by Dose, mean +/- 95% CI, overlaid
on gray spaghetti plots</h3>
<pre class="r"><code>gg <- ggplot(data = pk_data, aes(x = TIME, y = LIDV))
gg <- gg + geom_line(aes(group = ID), color = rgb(0.5,0.5,0.5), size = 1, alpha = 0.3)
gg <- gg + geom_point(aes(color = factor(CENS), shape = factor(CENS), alpha = 0.3), size = 2, alpha = 0.3)
gg <- gg + scale_shape_manual(values=c(1,8))
gg <- gg + scale_color_manual(values=c("grey50","red"))
gg <- gg + xgx_stat_ci(aes(x = NOMTIME, color=NULL, group=NULL), conf_level = 0.95)
gg <- gg + xgx_scale_y_log10()
gg <- gg + xgx_scale_x_time_units(units_dataset = time_units_dataset,
units_plot = time_units_plot)
gg <- gg + labs(y=conc_label,color = trtact_label)
gg <- gg + theme(legend.position="none") + facet_grid(.~TRTACT_low2high)
gg <- gg + xgx_annotate_status(status)
gg <- gg + xgx_annotate_filenames(dirs)
#if saving copy of figure, replace xgx_annotate lines with xgx_save() shown below:
#xgx_save(width,height,dirs,"filename_main",status)
print(gg)</code></pre>
<p><img src="Single_Ascending_Dose_PK_files/figure-html/unnamed-chunk-4-1.png" width="960" /></p>
</div>
</div>
<div id="assess-the-dose-linearity-of-exposure" class="section level2">
<h2>Assess the dose linearity of exposure</h2>
<div
id="dose-normalized-concentration-over-time-colored-by-dose-mean---95-ci"
class="section level3">
<h3>Dose Normalized Concentration over time, colored by Dose, mean +/-
95% CI</h3>
<pre class="r"><code>gg <- ggplot(data = pk_data,
aes(x = NOMTIME, y = LIDV_NORM,
group = TRTACT_high2low, color = TRTACT_high2low))
gg <- gg + xgx_stat_ci(conf_level = 0.95, alpha = 0.5, position = position_dodge(1))
gg <- gg + xgx_scale_y_log10()
gg <- gg + xgx_scale_x_time_units(units_dataset = time_units_dataset,
units_plot = time_units_plot)
gg <- gg + labs(y=concnorm_label, color = trtact_label)
gg <- gg + xgx_annotate_status(status)
gg <- gg + xgx_annotate_filenames(dirs)
#if saving copy of figure, replace xgx_annotate lines with xgx_save() shown below:
#xgx_save(width,height,dirs,"filename_main",status)
print(gg)</code></pre>
<p><img src="Single_Ascending_Dose_PK_files/figure-html/unnamed-chunk-5-1.png" width="768" /></p>
</div>
<div id="nca-of-dose-normalized-auc-and-cmax-vs-dose"
class="section level3">
<h3>NCA of dose normalized AUC and Cmax vs Dose</h3>
<!--START_EXPLANATION-->
<p>Observe the dose normalized AUC and Cmax over different doses. Does
the relationship appear to be constant across doses or do some doses
stand out from the rest? Can you think of reasons why some would stand
out? For example, the lowest dose may have dose normalized AUC much
higher than the rest, could this be due to BLQ observations? If the
highest doses have dose normalized AUC much higher than the others,
could this be due to nonlinear clearance, with clearance saturating at
higher doses? If the highest doses have dose normalized AUC much lower
than the others, could there be saturation of bioavailability, reaching
the maximum absorbable dose? <!--END_EXPLANATION--></p>
<pre class="r"><code>gg <- ggplot(data = NCA, aes(x = DOSE, y = VALUE_NORM))
gg <- gg + geom_boxplot(aes(group = DOSE))
gg <- gg + geom_smooth(method = "lm", color = "black")
gg <- gg + facet_wrap(~PARAM, scales = "free_y")
gg <- gg + labs(x = dose_label, y = concnorm_label)
gg <- gg + xgx_annotate_status(status)
gg <- gg + xgx_annotate_filenames(dirs)
#if saving copy of figure, replace xgx_annotate lines with xgx_save() shown below:
#xgx_save(width,height,dirs,"filename_main",status)
print(gg)</code></pre>
<p><img src="Single_Ascending_Dose_PK_files/figure-html/unnamed-chunk-6-1.png" width="768" /></p>
</div>
</div>
<div id="explore-variability" class="section level2">
<h2>Explore variability</h2>
<!--START_EXPLANATION-->
<p>Now that the overall trends in the mean data have been observed, look
into the between subject variability by plotting spaghetti plots.
Consider again whether to color by dose or facet by dose. If coloring by
dose, do the individuals in the different dose groups overlap across
doses? Does there seem to be more variability at higher or lower
concentrations? <!--END_EXPLANATION--></p>
<div
id="concentration-over-time-colored-by-dose-dots-and-lines-grouped-by-individual"
class="section level3">
<h3>Concentration over time, colored by Dose, dots and lines grouped by
individual</h3>
<pre class="r"><code>gg <- ggplot(data = pk_data, aes(x = TIME, y = LIDV))
gg <- gg + geom_line(aes(group = ID, color = factor(TRTACT_high2low)), size = 1, alpha = 0.5)
gg <- gg + geom_point(data = pk_data %>% filter(CENS==0), aes(color = TRTACT_high2low), size = 2, alpha = 0.5)
gg <- gg + geom_point(data = pk_data %>% filter(CENS==1), color="red", shape=8, size = 2, alpha = 0.5)
gg <- gg + xgx_scale_y_log10()
gg <- gg + xgx_scale_x_time_units(units_dataset = time_units_dataset,
units_plot = time_units_plot)
gg <- gg + labs(y = conc_label, color = trtact_label)
gg <- gg + xgx_annotate_status(status)
gg <- gg + xgx_annotate_filenames(dirs)
#if saving copy of figure, replace xgx_annotate lines with xgx_save() shown below:
#xgx_save(width,height,dirs,"filename_main",status)
print(gg)</code></pre>
<p><img src="Single_Ascending_Dose_PK_files/figure-html/unnamed-chunk-7-1.png" width="768" /></p>
</div>
<div
id="concentration-over-time-faceted-by-dose-dots-and-lines-grouped-by-individual"
class="section level3">
<h3>Concentration over time, faceted by Dose, dots and lines grouped by
individual</h3>
<pre class="r"><code>gg <- ggplot(data = pk_data, aes(x = TIME, y = LIDV))
gg <- gg + geom_line(aes(group = ID), size = 1, alpha = 0.2)
gg <- gg + geom_point(aes(color = factor(CENS), shape = factor(CENS), alpha = 0.3), size = 2, alpha = 0.2)
gg <- gg + scale_shape_manual(values=c(1,8))
gg <- gg + scale_color_manual(values=c("grey50","red"))
gg <- gg + xgx_scale_y_log10()
gg <- gg + xgx_scale_x_time_units(units_dataset = time_units_dataset,
units_plot = time_units_plot)
gg <- gg + labs(y = conc_label, shape = "BLQ", color = "BLQ")
gg <- gg + facet_grid(.~TRTACT_low2high)
gg <- gg + xgx_annotate_status(status)
gg <- gg + xgx_annotate_filenames(dirs)
#if saving copy of figure, replace xgx_annotate lines with xgx_save() shown below:
#xgx_save(width,height,dirs,"filename_main",status)
print(gg)</code></pre>
<p><img src="Single_Ascending_Dose_PK_files/figure-html/unnamed-chunk-8-1.png" width="960" /></p>
</div>
</div>
<div id="explore-irregularities-in-profiles" class="section level2">
<h2>Explore irregularities in profiles</h2>
<!--START_EXPLANATION-->
<p>Plot individual profiles in order to inspect them for any
irregularities. Inspect the profiles for outlying data points that may
skew results or bias conclusions. Looking at the shapes of the
individual profiles now, do they support your observations made about
the mean profile (e.g. number of compartments, typical Cmax, Tmax)?</p>
<p>Plotting individual profiles on top of gray spaghetti plots puts
individual profiles into context, and may help identify outlying
individuals for further inspection. Are there any individuals that
appear to have very high or low Cmax compared to others within the same
dose group? What about the timing of Cmax? What about the slope of the
elimination phase? Does it appear that any subjects could have received
an incorrect dose? <!--END_EXPLANATION--></p>
<div
id="concentration-over-time-faceted-by-individual-individual-line-plots-overlaid-on-gray-spaghetti-plots-for-that-dose-group"
class="section level3">
<h3>Concentration over time, faceted by individual, individual line
plots overlaid on gray spaghetti plots for that dose group</h3>
<pre class="r"><code>pk_data_rep_by_trt <- list()
for(id in unique(pk_data$ID)){
indiv_data <- pk_data %>% subset(ID == id)
itrtact = unique(indiv_data$TRTACT_low2high)
pk_data_rep_by_trt[[as.character(id)]] <- pk_data %>%
subset(TRTACT_low2high == itrtact) %>%
mutate(ID_rep_by_trt = ID, ID = id)
}
pk_data_rep_by_trt <- bind_rows(pk_data_rep_by_trt)
gg <- ggplot(mapping = aes(x = TIME, y = LIDV))
gg <- gg + geom_line(data = pk_data_rep_by_trt,
aes(group = ID_rep_by_trt),
size = 1, color = rgb(0.5,0.5,0.5), alpha = 0.3)
gg <- gg + geom_line(data = pk_data,
aes(group = ID), size = 1)
gg <- gg + geom_point(data = pk_data %>% filter(CENS==1),
color="red", shape=8, size = 2)
gg <- gg + xgx_scale_y_log10()
gg <- gg + xgx_scale_x_time_units(units_dataset = time_units_dataset,
units_plot = time_units_plot)
gg <- gg + labs(y = conc_label)
gg <- gg + theme(legend.position="none")
gg <- gg + facet_wrap(~ID + TRTACT_low2high,
ncol = 10 )
gg <- gg + theme(panel.grid.minor.x = ggplot2::element_line(color = rgb(0.9,0.9,0.9)),
panel.grid.minor.y = ggplot2::element_line(color = rgb(0.9,0.9,0.9)))
gg <- gg + xgx_annotate_status(status, fontsize = 4, color=rgb(0.5,0.5,1))
gg <- gg + xgx_annotate_filenames(dirs)
#if saving copy of figure, replace xgx_annotate lines with xgx_save() shown below:
#xgx_save(width,height,dirs,"filename_main",status)
print(gg)</code></pre>
<p><img src="Single_Ascending_Dose_PK_files/figure-html/unnamed-chunk-9-1.png" width="960" /></p>
</div>
</div>
<div id="explore-covariate-effects-on-pk" class="section level2">
<h2>Explore covariate effects on PK</h2>
<div
id="concentration-over-time-colored-by-categorical-covariate-mean---95-ci"
class="section level3">
<h3>Concentration over time, colored by categorical covariate, mean +/-
95% CI</h3>
<pre class="r"><code>gg <- ggplot(data = pk_data, aes(x = NOMTIME, y = LIDV, color = SEX))
gg <- gg + xgx_stat_ci(conf_level = 0.95)
gg <- gg + xgx_scale_y_log10()
gg <- gg + xgx_scale_x_time_units(units_dataset = time_units_dataset,
units_plot = time_units_plot)
gg <- gg + labs(y = conc_label)
gg <- gg + facet_grid(.~TRTACT_low2high)
gg <- gg + xgx_annotate_status(status)
gg <- gg + xgx_annotate_filenames(dirs)
#if saving copy of figure, replace xgx_annotate lines with xgx_save() shown below:
#xgx_save(width,height,dirs,"filename_main",status)
print(gg)</code></pre>
<p><img src="Single_Ascending_Dose_PK_files/figure-html/unnamed-chunk-10-1.png" width="960" /></p>
<pre class="r"><code>print(gg + aes(group= WEIGHTB>70, color = WEIGHTB>70) )</code></pre>
<p><img src="Single_Ascending_Dose_PK_files/figure-html/unnamed-chunk-10-2.png" width="960" /></p>
</div>
<div
id="dose-normalized-concentration-over-time-colored-by-categorical-covariate-mean---95-ci"
class="section level3">
<h3>Dose Normalized Concentration over time, colored by categorical
covariate, mean +/- 95% CI</h3>
<pre class="r"><code>gg <- ggplot(data = pk_data,
aes(x = NOMTIME,
y = LIDV_NORM,
color = SEX))
gg <- gg + xgx_stat_ci(conf_level = 0.95)
gg <- gg + xgx_scale_y_log10()
gg <- gg + xgx_scale_x_time_units(units_dataset = time_units_dataset,
units_plot = time_units_plot)
gg <- gg + ylab(concnorm_label)
gg <- gg + xgx_annotate_status(status)
gg <- gg + xgx_annotate_filenames(dirs)
#if saving copy of figure, replace xgx_annotate lines with xgx_save() shown below:
#xgx_save(width,height,dirs,"filename_main",status)
print(gg)</code></pre>
<p><img src="Single_Ascending_Dose_PK_files/figure-html/unnamed-chunk-11-1.png" width="768" /></p>
<pre class="r"><code>print(gg+ aes(color = WEIGHTB>70))</code></pre>
<p><img src="Single_Ascending_Dose_PK_files/figure-html/unnamed-chunk-11-2.png" width="768" /></p>
<pre class="r"><code>gg <- ggplot(data = NCA, aes(x = SEX, y = VALUE_NORM))
gg <- gg + geom_boxplot(aes(group = SEX))
gg <- gg + ylab("") + xlab("Sex")
gg <- gg + facet_wrap(~PARAM, scales = "free_y")
gg <- gg + xgx_annotate_status(status)
gg <- gg + xgx_annotate_filenames(dirs)
#if saving copy of figure, replace xgx_annotate lines with xgx_save() shown below:
#xgx_save(width,height,dirs,"filename_main",status)
print(gg)</code></pre>
<p><img src="Single_Ascending_Dose_PK_files/figure-html/unnamed-chunk-12-1.png" width="768" /></p>
<pre class="r"><code>gg <- ggplot(data = NCA, aes(x = WEIGHTB, y = VALUE_NORM))
gg <- gg + geom_point()
gg <- gg + ylab("") + xlab("Body Weight (kg)")
gg <- gg + facet_wrap(~PARAM, scales = "free_y")
gg <- gg + geom_smooth(method="lm")
gg <- gg + xgx_annotate_status(status)
gg <- gg + xgx_annotate_filenames(dirs)
#if saving copy of figure, replace xgx_annotate lines with xgx_save() shown below:
#xgx_save(width,height,dirs,"filename_main",status)
print(gg)</code></pre>
<p><img src="Single_Ascending_Dose_PK_files/figure-html/unnamed-chunk-13-1.png" width="768" /></p>
<pre class="r"><code>gg + aes(color = SEX)</code></pre>
<p><img src="Single_Ascending_Dose_PK_files/figure-html/unnamed-chunk-13-2.png" width="768" /></p>
</div>
</div>
<div id="r-session-info" class="section level2">
<h2>R Session Info</h2>
<pre class="r"><code>sessionInfo()</code></pre>
<pre><code>## R version 4.1.0 (2021-05-18)
## Platform: x86_64-pc-linux-gnu (64-bit)
## Running under: Red Hat Enterprise Linux Server 7.9 (Maipo)
##
## Matrix products: default
## BLAS/LAPACK: /CHBS/apps/EB/software/imkl/2019.1.144-gompi-2019a/compilers_and_libraries_2019.1.144/linux/mkl/lib/intel64_lin/libmkl_gf_lp64.so
##
## locale:
## [1] LC_CTYPE=en_US.UTF-8 LC_NUMERIC=C LC_TIME=en_US.UTF-8 LC_COLLATE=en_US.UTF-8 LC_MONETARY=en_US.UTF-8
## [6] LC_MESSAGES=en_US.UTF-8 LC_PAPER=en_US.UTF-8 LC_NAME=C 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] RxODE_1.1.1 survminer_0.4.9 ggpubr_0.4.0 survival_3.4-0 knitr_1.40 broom_1.0.1 caTools_1.18.2 DT_0.26 forcats_0.5.2
## [10] stringr_1.4.1 purrr_0.3.5 readr_2.1.3 tibble_3.1.8 tidyverse_1.3.2 xgxr_1.1.1 zoo_1.8-11 gridExtra_2.3 tidyr_1.2.1
## [19] dplyr_1.0.10 ggplot2_3.3.6
##
## loaded via a namespace (and not attached):
## [1] readxl_1.4.1 backports_1.4.1 Hmisc_4.7-0 plyr_1.8.7 splines_4.1.0 RApiSerialize_0.1.0 crosstalk_1.2.0
## [8] digest_0.6.30 htmltools_0.5.3 fansi_1.0.3 magrittr_2.0.3 checkmate_2.1.0 memoise_2.0.1 googlesheets4_1.0.1
## [15] cluster_2.1.3 tzdb_0.3.0 openxlsx_4.2.4 modelr_0.1.9 RcppParallel_5.1.5 prettyunits_1.1.1 jpeg_0.1-9
## [22] colorspace_2.0-3 rvest_1.0.3 PreciseSums_0.5 haven_2.5.1 xfun_0.34 crayon_1.5.2 RCurl_1.98-1.4
## [29] jsonlite_1.8.3 Exact_2.1 stringfish_0.15.7 glue_1.6.2 gtable_0.3.1 gargle_1.2.1 car_3.0-11
## [36] abind_1.4-5 scales_1.2.1 mvtnorm_1.1-3 DBI_1.1.3 GGally_2.1.2 rstatix_0.7.0 Rcpp_1.0.9
## [43] xtable_1.8-4 progress_1.2.2 htmlTable_2.2.1 foreign_0.8-82 proxy_0.4-26 km.ci_0.5-2 Formula_1.2-4
## [50] dparser_1.3.1-5 htmlwidgets_1.5.4 httr_1.4.4 RColorBrewer_1.1-3 ellipsis_0.3.2 pkgconfig_2.0.3 reshape_0.8.8
## [57] lotri_0.4.2 farver_2.1.1 nnet_7.3-17 sass_0.4.2 dbplyr_2.2.1 binom_1.1-1 deldir_1.0-6
## [64] utf8_1.2.2 tidyselect_1.2.0 labeling_0.4.2 rlang_1.0.6 munsell_0.5.0 cellranger_1.1.0 tools_4.1.0
## [71] cachem_1.0.6 cli_3.4.1 generics_0.1.3 evaluate_0.17 fastmap_1.1.0 sys_3.4 yaml_2.3.6
## [78] fs_1.5.2 zip_2.2.0 pander_0.6.4 survMisc_0.5.5 rootSolve_1.8.2.2 nlme_3.1-160 xml2_1.3.3
## [85] compiler_4.1.0 rstudioapi_0.14 curl_4.3.3 png_0.1-7 e1071_1.7-8 ggsignif_0.6.2 reprex_2.0.2
## [92] bslib_0.4.0 DescTools_0.99.42 stringi_1.7.8 highr_0.9 lattice_0.20-45 Matrix_1.5-1 markdown_1.2
## [99] KMsurv_0.1-5 vctrs_0.5.0 pillar_1.8.1 lifecycle_1.0.3 jquerylib_0.1.4 data.table_1.14.2 bitops_1.0-7
## [106] lmom_2.8 R6_2.5.1 latticeExtra_0.6-30 qs_0.25.3 rio_0.5.27 gld_2.6.2 codetools_0.2-18
## [113] boot_1.3-28 MASS_7.3-58.1 assertthat_0.2.1 minpack.lm_1.2-1 withr_2.5.0 Deriv_4.1.3 mgcv_1.8-41
## [120] expm_0.999-6 hms_1.1.2 grid_4.1.0 rpart_4.1.16 class_7.3-19 rmarkdown_2.17 carData_3.0-4
## [127] googledrive_2.0.0 lubridate_1.8.0 base64enc_0.1-3 interp_1.1-2</code></pre>
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$('tr.odd').parent('tbody').parent('table').addClass('table table-condensed');
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$(document).ready(function () {
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