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<h1 class="title toc-ignore">PD, Oncology, RECIST - continuous, binary
and categorical endpoints</h1>
<h4 class="author">Fariba Khanshan, Andrew Stein</h4>
</div>
<div id="overview" class="section level2">
<h2>Overview</h2>
<!--START_EXPLANATION-->
<p>The purpose of this document is to provide exploratory plots and R
code for assessing dose-response and exposure-response using the RECIST
(Response Evaluation Criteria In Solid Tumors) endpoint data. These
plots provide insight into whether a dose-response relationship is
observable. In Phase 1, often no dose-response relationship is observed
due to high inter-subject variability. In that situation, we recommened
that no longitudinal, NLME modeling be performed as it is unlikely to
add much value. Furthermore, even if an exposure-response relationship
is detected, it must be interpreted with extreme caution when it cannot
be confirmed with simple explortaory graphics.</p>
<p>The plots presented here are based on blinded merged RECIST data (<a
href="Data/Oncology_Efficacy_Data.csv">download dataset</a>) with nmpk
and and dose history datasets (<a
href="Data/Oncology_Efficacy_Dose.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/Oncology_Efficacy_Plots.Rmd">Rmarkdown-Template</a>.</p>
<p>Standard statistical plots for summarizing recist (e.g. Waterfall)
are presented elsewhere. <!--END_EXPLANATION--></p>
</div>
<div id="setup" class="section level2">
<h2>Setup</h2>
<pre class="r"><code>library(ggplot2)
library(dplyr)
library(tidyr)
library(gridExtra)
library(zoo)
library(xgxr)
#flag for labeling figures as draft
status = "DRAFT"
## ggplot settings
xgx_theme_set()</code></pre>
</div>
<div id="load-dataset" class="section level2">
<h2>Load Dataset</h2>
<pre class="r"><code>recist.data <- read.csv("../Data/Oncology_Efficacy_Data.csv")
dose_record <- read.csv("../Data/Oncology_Efficacy_Dose.csv")
recist.data$MONO_DOSE_label <- paste(recist.data$DOSE_ABC,"mg")
recist.data$COMBO_DOSE_label <- paste(recist.data$DOSE_DEF,"mg")
recist.data = recist.data %>%
arrange(MONO_DOSE_label,COMBO_DOSE_label) %>%
mutate(MONO_DOSE_label_low2high = factor(MONO_DOSE_label, levels = unique(MONO_DOSE_label)),
MONO_DOSE_label_high2low = factor(MONO_DOSE_label, levels = rev(unique(MONO_DOSE_label))),
COMBO_DOSE_label_low2high = factor(COMBO_DOSE_label, levels = unique(COMBO_DOSE_label)),
COMBO_DOSE_label_high2low = factor(COMBO_DOSE_label, levels = rev(unique(COMBO_DOSE_label))))
#ensure dataset has all the necessary columns
recist.data = recist.data %>%
mutate(IDSHORT = IDSHORT, #ID column
BOR = BOR, #Best Overal Response
BPCHG = BPCHG, #Best Percent Change from Baseline
OR = OR , #Overall Response
BORNUM = BORNUM, #Best Overall Response Value
psld = psld, #Percent Change in Sum of Longest Diameters
DOSE_ABC = DOSE_ABC, #Dose of Agent 1 (numeric)
DOSE_DEF = DOSE_DEF, #Dose of Agent 2 (numeric)
DOSE_combo = DOSE_combo, #ARM of the study (character)
binary_BOR = binary_BOR, #Binary Best Overall Response
PR_rate = PR_rate, #Partial Response rate
n = n, #The number of total subjects in each dose group
count_cr_pr = count_cr_pr, #Count the number of CR or PR subjects in each dose group
TIME = TIME, #Evaluation time
TIME_OR = TIME_OR, #Overall Response evaluation time
auc0_24 = auc0_24, #AUC-24
)
dose_record = dose_record %>%
mutate(IDSHORT = IDSHORT, #ID column
DOSE = DOSE, #Dose amount
TIME = TIME, #Dosing time
COMB = COMB, #Single agent or combo
)
# make single agent and combo datsets
recist.data.monotherapy = recist.data %>% filter(COMB=="Single")
recist.data.combo = recist.data %>% filter(COMB=="Combo")
# Dose record data preparation for making step function plot
# in order to show any dose reduction during the study
# the idea is that at each time point, you have both the current dose and the previous dose
# the dplyr::lag command implements this
data_areaStep <- bind_rows(old = dose_record,
new = dose_record %>%
group_by(IDSHORT) %>%
mutate(DOSE = lag(DOSE)),
.id = "source") %>%
arrange(IDSHORT, TIME, source) %>%
ungroup() %>%
mutate(DOSE = ifelse(lag(IDSHORT)!=IDSHORT, NA, DOSE),
TIME = TIME/24) #convert to days
data_areaStep.monotherapy = filter(data_areaStep,COMB=="Single")
# calculate average dose intensity up to the first assessment:
# "TIME==57"" is the first assessment time in this dataset
first.assess.time = 57
dose_record <- dose_record %>%
group_by(IDSHORT) %>%
mutate(ave_dose_intensity = mean(DOSE[TIME/24 < first.assess.time]))
dose_intensity <- dose_record[c("IDSHORT","COMB","ave_dose_intensity")]
dose_intensity <- subset(dose_intensity, !duplicated(IDSHORT))
#units and labels
time_units_dataset = "hours"
time_units_plot = "days"
trtact_label = "Dose"
dose_label = "Dose (mg)"
time_label = "Time(Days)"
timemonth_label = "Time (months)"
sld_label = "Percent Change in\nSum of Longest Diameters"
mono_dose_label = "ABC123 Dose (mg)"
combo_dose_label = "DEF456 Dose (mg)"
bpchg_label = "Best Percent Change \n in Tumor Size (%)"
mono_auc_label = "ABC123 AUC0-24 (ng.h/ml)"
mono_aveauc_label = "Average ABC123 dose (mg) \n up to the first assessment"
first_pchg_label = " Percent Change in Tumor Size \n up to the first assessment"
rr_label = "Response Rate (%)"
#directories for saving individual graphs
dirs = list(
parent_dir= tempdir(),
rscript_dir = "./",
rscript_name = "Example.R",
results_dir = "./",
filename_prefix = "",
filename = "Example.png")</code></pre>
</div>
<div id="introduction-to-recist" class="section level2">
<h2>Introduction to RECIST</h2>
<!--START_EXPLANATION-->
<p>RECIST (Response Evaluation Criteria in Solid Tumor) uses an
image-based assessment from X-ray Computed Tomography (CT) scans. and
has three components:</p>
<ol style="list-style-type: decimal">
<li>Sum of the longest diameter of the target lesions (continuous
measure),</li>
<li>Assessment of the non target lesions (categorical measure), and</li>
<li>Appearance of a new lesion (binary yes/no measure).</li>
</ol>
<p>An example patient and the criteria for assigning a response
category, is shown below. <!--END_EXPLANATION--></p>
<p><img src="SiteResources/RECIST.png" style="width:80.0%" /></p>
<div class="figure">
<img src="SiteResources/response_category.png" style="width:80.0%"
alt="" />
<p class="caption">Figure 1: Example RECIST assessment for
individualpatient and response category identified</p>
</div>
</div>
<div id="overview-of-all-data" class="section level2">
<h2>Overview of all data</h2>
<div id="spaghetti-plots-of-change-from-baseline"
class="section level3">
<h3>Spaghetti plots of change from baseline</h3>
<!--START_EXPLANATION-->
<p>We recommend stratifying the spaghetti plots of target lesion
kinetics by dose so that one can observe if there is more tumor
shrinkage at the higher dose groups. In this case, no obvious
relationship is observed and it is likely a longitudinal model will not
be helpful. <!--END_EXPLANATION--></p>
<pre class="r"><code>gg <- ggplot(data= recist.data.monotherapy,aes(x=TIME, y=psld))
gg <- gg + geom_line(aes(group=IDSHORT, color =factor(MONO_DOSE_label_high2low)))
gg <- gg + geom_point(alpha=.3,colour="black")
gg <- gg + guides(color=guide_legend(""),fill=guide_legend(""))
gg <- gg + geom_hline(yintercept = 0.0, linetype="dashed")
gg <- gg + xgx_scale_x_time_units(units_dataset = "day", units_plot ="month")
gg <- gg + theme(text = element_text(size=15))
gg <- gg + labs(x= timemonth_label, y= sld_label)
gg <- gg + xgx_annotate_status(status)
gg</code></pre>
<p><img src="Oncology_Efficacy_Plots_files/figure-html/unnamed-chunk-3-1.png" width="768" /></p>
</div>
<div id="change-from-baseline-plot-faceted-by-dose"
class="section level3">
<h3>Change from baseline plot, faceted by Dose</h3>
<pre class="r"><code>gg <- ggplot(data=recist.data.monotherapy,aes(x=TIME, y=psld))
gg <- gg + geom_line(aes(group=IDSHORT))
gg <- gg + geom_point(alpha=.3,colour="black")
gg <- gg + guides(color=guide_legend(""),fill=guide_legend(""))
gg <- gg + facet_grid(~MONO_DOSE_label)
gg <- gg + geom_hline(yintercept = 0.0, linetype="dashed")
gg <- gg + theme(text = element_text(size=15))
gg <- gg + xgx_scale_x_time_units(units_dataset = "day", units_plot ="month")
gg <- gg + labs(x= timemonth_label, y= sld_label)
gg <- gg + xgx_annotate_status(status)
gg</code></pre>
<p><img src="Oncology_Efficacy_Plots_files/figure-html/unnamed-chunk-4-1.png" width="960" /></p>
</div>
<div
id="individual-plots-of-percent-change-from-baseline-including-dosing-history-labeled-by-overall-response"
class="section level3">
<h3>Individual plots of percent change from baseline, including dosing
history, labeled by “Overall Response”</h3>
<!--START_EXPLANATION-->
<p>These plots allow one to look for subtle trends in the individual
trajectories. If changes in the tumor trajectory occur often after a
dose reduction, a longitudinal model may be useful for assessing
dose-response. However, caution is needed because both dose reductions
and resistance acquisition can occur at later times and it may not be
easy to deterimne which is the cause of the change in tumor
trajectory.</p>
<p>In the first plot below, it is difficult to see a trend of dose
changes impacting response and a longitudinal tumor-size model will
likely not be informative. But in the second plot below, a trend of
tumor shrinkage followed by tumor growth after a dose reduction was
observed and a longitudinal model was useful for characterizing this
data. <a
href="https://bmccancer.biomedcentral.com/articles/10.1186/1471-2407-12-311">see
reference</a> <!--END_EXPLANATION--></p>
<p>Example 1, longitudinal model won’t be informative:</p>
<pre class="r"><code># This part is optional to label "OR" in the plot
# "OR" can be substituted with other information, such as non-target, new target lesions
# make the OR label for the plot
recist.data.label <- recist.data %>%
group_by(IDSHORT) %>%
mutate(label_psld = as.numeric(ifelse(TIME==TIME_OR , psld,""))) %>%
filter(!(is.na(label_psld) | label_psld==""))
dose_shift = 50
dose_scale = 1.2
data_areaStep.monotherapy = data_areaStep.monotherapy %>%
mutate(dose_shift = DOSE/dose_scale+dose_shift)
dose_unique = c(0,unique(recist.data.monotherapy$DOSE_ABC))
data_tumor = recist.data.monotherapy
data_dose_step = data_areaStep.monotherapy
gg <- ggplot(data = data_tumor)
gg <- gg + geom_point(mapping = aes(y= psld, x= TIME))
gg <- gg + geom_text(data= recist.data.label,aes(y= label_psld, x= TIME_OR, label=OR), vjust=-.5)
gg <- gg + geom_hline(aes(yintercept = 0),size=0.25,linetype="dashed", colour="red")
gg <- gg + geom_line(mapping = aes(y= psld, x= TIME))
gg <- gg + geom_ribbon(data = data_dose_step,
aes( ymin = 50, ymax = dose_shift , x= TIME),
fill="palegreen2", color = "black", alpha=0.5 )
gg <- gg + facet_wrap(~IDSHORT, ncol = 6)
gg <- gg + labs(y = sld_label, x= timemonth_label)
gg <- gg + xgx_scale_x_time_units(units_dataset = "day", units_plot ="month")
gg <- gg + scale_y_continuous(
sec.axis = sec_axis(~(.-dose_shift)*dose_scale, name = "Dose(mg)", breaks = dose_unique))
gg <- gg + theme(text = element_text(size=15))
gg <- gg + xgx_annotate_status(status)
gg</code></pre>
<p><img src="Oncology_Efficacy_Plots_files/figure-html/unnamed-chunk-5-1.png" width="960" /></p>
<p>Example 2, dose reduction was followed by growth of tumor and
longitudinal model would help.</p>
<div class="figure">
<img src="SiteResources/Stein12_RAD001.png" style="width:100.0%"
alt="" />
<p class="caption">Example data where dose reduction was followed by
growth of tumor</p>
</div>
</div>
</div>
<div id="dose-response-monotherapy" class="section level2">
<h2>Dose-Response: Monotherapy</h2>
<!--START_EXPLANATION-->
<p>To visualize dose-response (exposure-response), we recommend plotting
the assigned dose group (or exposure) vs best overall change in tumor
size.</p>
<p><strong>Warning:</strong> If you see what appears to be a linear
dose-response relationship (e.g. more tumor shrinkage with increasing
dose), be very cautious when trying to extrapolate outside this range,
as Emax may not have been observed yet. <!--END_EXPLANATION--></p>
<pre class="r"><code>gg <- ggplot()
gg <- gg + geom_point(data=recist.data.monotherapy,aes(x=DOSE_ABC,y=BPCHG),color="tomato")
gg <- gg + scale_x_continuous(breaks=unique(recist.data.monotherapy$DOSE_ABC))
gg <- gg + geom_hline(yintercept=0,color="grey50", linetype = "dashed")
gg <- gg + scale_y_continuous(labels=scales::percent)
gg <- gg + labs(x=mono_dose_label, y=bpchg_label)
gg <- gg + theme(legend.title=element_blank())
gg <- gg + theme(text = element_text(size=15))
gg <- gg + xgx_annotate_status(status)
gg</code></pre>
<p><img src="Oncology_Efficacy_Plots_files/figure-html/unnamed-chunk-6-1.png" width="768" /></p>
<pre class="r"><code>gg <- ggplot()
gg <- gg + geom_point(data=recist.data.monotherapy,aes(x=auc0_24,y=BPCHG), color="tomato")
gg <- gg + geom_hline(yintercept=0,color="grey50", linetype = "dashed")
gg <- gg + scale_y_continuous(labels=scales::percent)
gg <- gg + labs(x=mono_auc_label, y=bpchg_label)
gg <- gg + theme(legend.title=element_blank())
gg <- gg + theme(text = element_text(size=15))
gg <- gg + xgx_annotate_status(status)
gg</code></pre>
<p><img src="Oncology_Efficacy_Plots_files/figure-html/unnamed-chunk-7-1.png" width="768" /></p>
<!--START_EXPLANATION-->
<p>Best overall change is commonly reported in Waterfall plots. And the
reason we recommend using the randomized dose group as opposed to
something like average dose-intensity is that the latter can be
confounded. For instance, consider the following scenario. There are two
patients that both start at 10 mg. One has 30% tumor growth at the first
assessment and progresses. The other responds, but at month 6, they are
dose reduced to 5 mg due to an adverse event, and then followed for
another 6 months. In this case, the responder would have a dose
intensity of 7.5 mg while the non-responder had a dose-intensity of 10
mg, and thus one might conclude from a simple plot of these two patients
that lower doses are better.</p>
<p>One way to avoid this issue is to plot average dose intensity up to
the first assessment vs percent change at the first assessment and this
could be considered if there are a large number of dose reductions
before the first assessment. <!--END_EXPLANATION--></p>
<pre class="r"><code># Do it only for monoteraphy, it can be repeated for combo
dose_intensity <- dose_intensity[dose_intensity$COMB=="Single",]
recist.data.assessment <- recist.data.monotherapy %>%
merge(dose_intensity ,by="IDSHORT")
gg <- ggplot()
gg <- gg + geom_point(data=recist.data.assessment %>% subset(TIME==first.assess.time,),
aes(x=ave_dose_intensity ,
y=psld),color="tomato")
gg <- gg + scale_x_continuous(breaks=c(20,40, 60, 74,78,90))
gg <- gg + geom_hline(yintercept=0,color="grey50", linetype = "dashed")
gg <- gg + labs(x=mono_aveauc_label, y= first_pchg_label)
gg <- gg + theme(legend.title=element_blank())
gg <- gg + theme(text = element_text(size=15))
gg <- gg + xgx_annotate_status(status)
gg</code></pre>
<p><img src="Oncology_Efficacy_Plots_files/figure-html/unnamed-chunk-8-1.png" width="768" /></p>
</div>
<div id="dose-response-combo" class="section level2">
<h2>Dose-Response: Combo</h2>
<!--START_EXPLANATION-->
<p>When two drugs are combined (ABC123 + DEF456), it can be a useful
first step to look at the dose-response relationship of each drug.
However, it should be noted that provide only a limited understanding of
the data. <!--END_EXPLANATION--></p>
<pre class="r"><code>gg <- ggplot()
gg <- gg + geom_point(data=recist.data.combo,aes(x=DOSE_ABC,y=BPCHG,
color = paste0("ABC123 + ", COMBO_DOSE_label_high2low, " DEF456")))
gg <- gg + geom_point(data=recist.data.monotherapy,aes(x=DOSE_ABC,y=BPCHG, color="ABC123"))
gg <- gg + labs(color = "DEF456 (mg) dose:")
gg <- gg + geom_hline(yintercept=0,color="grey50", linetype = "dashed")
gg <- gg + scale_x_continuous(breaks=unique(recist.data.monotherapy$DOSE_ABC))
gg <- gg + labs(x=mono_dose_label,y=bpchg_label)
gg <- gg + scale_y_continuous(labels=scales::percent)
gg <- gg + theme(text = element_text(size=15))
gg <- gg + xgx_annotate_status(status)
gg</code></pre>
<p><img src="Oncology_Efficacy_Plots_files/figure-html/unnamed-chunk-9-1.png" width="960" /></p>
<pre class="r"><code>gg <- ggplot(data=recist.data.combo,aes(x=DOSE_DEF,y=BPCHG))
gg <- gg + geom_point(aes( color= paste0("+ ", MONO_DOSE_label_low2high, " ABC123")))
gg <- gg + geom_hline(yintercept=0,color="grey50", linetype = "dashed")
gg <- gg + scale_x_continuous(breaks=unique(recist.data.combo$DOSE_DEF))
gg <- gg + labs(x=combo_dose_label,y=bpchg_label)
gg <- gg + scale_y_continuous(labels=scales::percent)
gg <- gg + theme(legend.title=element_blank())
gg <- gg + theme(text = element_text(size=15))
gg <- gg + xgx_annotate_status(status)
gg</code></pre>
<p><img src="Oncology_Efficacy_Plots_files/figure-html/unnamed-chunk-10-1.png" width="960" /></p>
<div id="responder-rate-95-ci-vs-dose" class="section level3">
<h3>Responder rate (95% CI) vs dose</h3>
<!--START_EXPLANATION-->
<p>For most of the oncology clinical trials, the standard primary and
secondary endpoints are Overall Survival (OS), Progression Free Survival
(PFS), duration without progression (PD) or death, and Overall Response
Rate (ORR). Dose vs ORR at each dose can be informative.
<!--END_EXPLANATION--></p>
<pre class="r"><code>gg <- ggplot(data = recist.data.combo, aes(x=DOSE_ABC,y=PR_rate))
gg <- gg + xgx_stat_ci(mapping = aes(x = DOSE_ABC, y = binary_BOR ,group=DOSE_ABC),
conf_level = 0.95, distribution = "binomial", geom = c("point"), size = 4, color="tomato")
gg <- gg + xgx_stat_ci(mapping = aes(x = DOSE_ABC, y = binary_BOR , group=DOSE_ABC),
conf_level = 0.95, distribution = "binomial", geom = c("errorbar"), size = 0.5)
gg <- gg + scale_x_continuous(breaks=unique(recist.data[recist.data$COMB=="Combo",]$DOSE_ABC))
gg <- gg + scale_y_continuous(labels=scales::percent)
gg <- gg + labs(x= mono_dose_label, y= rr_label)
gg <- gg + theme(text = element_text(size=15))
gg <- gg + xgx_annotate_status(status)
gg</code></pre>
<p><img src="Oncology_Efficacy_Plots_files/figure-html/unnamed-chunk-11-1.png" width="768" /></p>
</div>
<div id="best-overall-response-bor-plot-for-combo-therapy"
class="section level3">
<h3>Best Overall Response (BOR) plot for combo therapy</h3>
<pre class="r"><code>gg <- ggplot(data=recist.data.combo,aes(x=DOSE_ABC ,y=DOSE_DEF,fill=PR_rate))
gg <- gg + scale_fill_gradient(low="orange", high="green")
gg <- gg + geom_segment(data=recist.data.combo, aes(x=-Inf,xend=20,y=30,yend=30), color=rgb(0.5,0.5,0.5))
gg <- gg + geom_segment(data=recist.data.combo, aes(x=20,xend=20,y=-Inf,yend=30), color=rgb(0.5,0.5,0.5))
gg <- gg + geom_segment(data=recist.data.combo, aes(x=-Inf,xend=40,y=30,yend=30), color=rgb(0.5,0.5,0.5))
gg <- gg + geom_segment(data=recist.data.combo, aes(x=40,xend=40,y=-Inf,yend=30), color=rgb(0.5,0.5,0.5))
gg <- gg + geom_segment(data=recist.data.combo, aes(x=-Inf,xend=60,y=30,yend=30), color=rgb(0.5,0.5,0.5))
gg <- gg + geom_segment(data=recist.data.combo, aes(x=60,xend=60,y=-Inf,yend=30), color=rgb(0.5,0.5,0.5))
gg <- gg + geom_segment(data=recist.data.combo, aes(x=-Inf,xend=40,y=40,yend=40), color=rgb(0.5,0.5,0.5))
gg <- gg + geom_segment(data=recist.data.combo, aes(x=40,xend=40,y=-Inf,yend=40), color=rgb(0.5,0.5,0.5))
gg <- gg + geom_label(data=unique(recist.data.combo[,c("DOSE_DEF","DOSE_ABC","PR_rate","n","count_cr_pr")]),
aes(x=DOSE_ABC ,y=DOSE_DEF*1.00,fontface=2, label=paste0(round(PR_rate,2)*100,
"% ORR \nn=",n,"\nn(CR|PR)=",count_cr_pr)))
gg <- gg + scale_x_continuous(breaks=c(20, 40, 60))
gg <- gg + scale_y_continuous(breaks=c(30, 40))
gg <- gg + labs(x=mono_dose_label , y= combo_dose_label)
gg <- gg + theme(legend.title = element_blank(),
plot.title=element_text(hjust=0.5),
text = element_text(size=20),
title = element_text(size=20))
gg <- gg + guides(fill=FALSE)
gg <- gg + xgx_annotate_status(status)
gg </code></pre>
<p><img src="Oncology_Efficacy_Plots_files/figure-html/unnamed-chunk-12-1.png" width="1344" /></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] 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 stringr_1.4.1
## [10] 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 dplyr_1.0.10
## [19] ggplot2_3.3.6
##
## loaded via a namespace (and not attached):
## [1] googledrive_2.0.0 colorspace_2.0-3 ggsignif_0.6.2 deldir_1.0-6 rio_0.5.27 ellipsis_0.3.2 class_7.3-19
## [8] htmlTable_2.2.1 markdown_1.2 base64enc_0.1-3 fs_1.5.2 gld_2.6.2 rstudioapi_0.14 proxy_0.4-26
## [15] farver_2.1.1 Deriv_4.1.3 fansi_1.0.3 mvtnorm_1.1-3 lubridate_1.8.0 xml2_1.3.3 codetools_0.2-18
## [22] splines_4.1.0 cachem_1.0.6 rootSolve_1.8.2.2 Formula_1.2-4 jsonlite_1.8.3 km.ci_0.5-2 binom_1.1-1
## [29] cluster_2.1.3 dbplyr_2.2.1 png_0.1-7 compiler_4.1.0 httr_1.4.4 backports_1.4.1 assertthat_0.2.1
## [36] Matrix_1.5-1 fastmap_1.1.0 gargle_1.2.1 cli_3.4.1 prettyunits_1.1.1 htmltools_0.5.3 tools_4.1.0
## [43] gtable_0.3.1 glue_1.6.2 lmom_2.8 Rcpp_1.0.9 carData_3.0-4 cellranger_1.1.0 jquerylib_0.1.4
## [50] vctrs_0.5.0 nlme_3.1-160 crosstalk_1.2.0 xfun_0.34 openxlsx_4.2.4 rvest_1.0.3 lifecycle_1.0.3
## [57] rstatix_0.7.0 googlesheets4_1.0.1 MASS_7.3-58.1 scales_1.2.1 hms_1.1.2 expm_0.999-6 RColorBrewer_1.1-3
## [64] curl_4.3.3 yaml_2.3.6 Exact_2.1 KMsurv_0.1-5 pander_0.6.4 sass_0.4.2 rpart_4.1.16
## [71] reshape_0.8.8 latticeExtra_0.6-30 stringi_1.7.8 highr_0.9 e1071_1.7-8 checkmate_2.1.0 zip_2.2.0
## [78] boot_1.3-28 rlang_1.0.6 pkgconfig_2.0.3 bitops_1.0-7 evaluate_0.17 lattice_0.20-45 htmlwidgets_1.5.4
## [85] labeling_0.4.2 tidyselect_1.2.0 GGally_2.1.2 plyr_1.8.7 magrittr_2.0.3 R6_2.5.1 DescTools_0.99.42
## [92] generics_0.1.3 Hmisc_4.7-0 DBI_1.1.3 pillar_1.8.1 haven_2.5.1 foreign_0.8-82 withr_2.5.0
## [99] mgcv_1.8-41 abind_1.4-5 RCurl_1.98-1.4 nnet_7.3-17 car_3.0-11 crayon_1.5.2 modelr_0.1.9
## [106] survMisc_0.5.5 interp_1.1-2 utf8_1.2.2 tzdb_0.3.0 rmarkdown_2.17 progress_1.2.2 jpeg_0.1-9
## [113] grid_4.1.0 readxl_1.4.1 minpack.lm_1.2-1 data.table_1.14.2 reprex_2.0.2 digest_0.6.30 xtable_1.8-4
## [120] munsell_0.5.0 bslib_0.4.0</code></pre>
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