Use mrgsolve to replace NONMEM simulations
Kenta Yoshida
2020-09-30
Setup
knitr::opts_chunk$set(echo = TRUE, fig.width=6, fig.height=4)
knitr::opts_knit$set(root.dir = rprojroot::find_rstudio_root_file())
library(tidyverse)
library(glue)
library(xpose)
library(mrgsolve)
library(xgxr)
library(tidyvpc)
theme_set(theme_linedraw(base_size = 12))
geomean <- function(x){exp(mean(log(x)))}
quibble <- function(x, q = c(0.05, 0.5, 0.95)) {
tibble("{{ x }}" := quantile(x, q),
"{{ x }}_q" := paste0("P",
formatC(q * 100, width = 2, format = "d", flag = "0")))
}
# summarize(data, quibble(x))Preface
See https://github.com/Genentech/mrgsolve_replace_NMsim for the code & files needed to run the examples in your environment
mrgsolve applications covered in this document
In this file, the following four types of mrgsolve applications has been demonstrated:
- Draw smooth PK profiles by adding observation time points in simulations
- Clinical trial simulation with new dose amount and schedules
- Obtain summary PK metrics (e.g. AUCss, Cmin,ss, Cmin,ss) based on protocol-defined dosing schedules and empirical Bayes estimates (EBE) of individual ETA
- This is useful for generating metrics for E-R analysis
- VPC
Notes
- The model & data were from:
- Nonlinear Mixed‐Effects Model Development and Simulation Using nlmixr and Related R Open‐Source Packages, Fidler et al., CPT Pharmacometrics Syst Pharmacol. 2019 Sep;8(9):621-633.
- https://doi.org/10.1002/psp4.12445
mrgsolveversion >= 0.10.4 is required- In these workflows, THETA (& SIGMA) is updated with values in input data frames, while OMEGA is updated with omat function to be applied on
mrgmodobject
Preparations
CSV data import
First modify data
examplomycin.csv is obtained from Supplementary File 1 of the above article
Modification needed to be compatible with NONMEM
df.raw <- read_csv("data/examplomycin.csv")
unique(df.raw$EVID)
df.raw %>%
mutate(CMT = ifelse(EVID == 101, 1, 2),
EVID = ifelse(EVID == 101, 1, 0),
PHASE = ifelse(TIME < 24, "SD", "MD")) %>%
relocate(CMT, .after = DV) %>%
rename(NMID = ID) %>%
write_csv("data/examplomycin2.csv")Import modified data
df.nm <- read_csv("data/examplomycin2.csv")## Parsed with column specification:
## cols(
## NMID = col_double(),
## TIME = col_double(),
## DV = col_double(),
## CMT = col_double(),
## WT = col_double(),
## SEX = col_double(),
## AMT = col_double(),
## EVID = col_double(),
## PHASE = col_character()
## )df.nm.dose<- filter(df.nm, EVID == 1)
df.nm.obs <- filter(df.nm, EVID == 0)
time_units_dataset = "hours"
time_units_plot = "days"Load model files
mrgsolve
mod_pk <- mread("mrgsolve/examplomycin_2cmt_covs_2020-07-08.cpp")## Building examplomycin_2cmt_covs_2020-07-08_cpp ... done.see(mod_pk)##
## Model file: examplomycin_2cmt_covs_2020-07-08.cpp
## [PROB]
## Source: mrgsolve model library
##
## Two-compartment model for oral dosing
##
## Comment:
## Time unit: hour
## Volume units: L
##
## [GLOBAL]
## #define C2 (CENT / V2)
##
## [CMT] @annotated
## DEPOT : Extravascular compartment
## CENT : Central compartment
## PERIPH : Peripheral compartment (mass)
## AUCCENT: AUC in the central compartment
##
## [PARAM] @annotated
## TVCL : 0.1 : Clearance (L/hour)
## TVV2 : 2 : Central volume of distribution (L)
## TVV3 : 5 : Peripheral volume of distribution (L)
## TVQ : 0.3 : Inter-compartmental clearnace (L/hour)
## TVKA : 1 : Absorption rate constant (1/hour)
## TVALAG1: 0 : Lag time - EV dose
## WT : 70 : Individual weight (kg)
## WTref : 70 : Reference body weight (kg)
## WTCL : 0.75 : Effect of WT on CL
## SEX : 0 : 1 = male, 0 = female
## SEXV2 : -0.2 : Effect of SEX=1 (male) on central compartment volume
## PROP : 0.1 : Proportional error (SD)
## ADD : 0 : Additive error (SD)
##
## // ETA for sim with EBE
## E_CLi : 0 : ETA on CL
## E_V2i : 0 : ETA on V2
## E_V3i : 0 : ETA on V3
## E_Qi : 0 : ETA on Q
## E_KAi : 0 : ETA on KA
##
## [OMEGA] @annotated @block @name group1
## // note: if you want to enter off-diagonal elements as correlations, add "@correlation" to this block
## E_CL : 0.1 : ETA on CL
## E_V2 : 0.03 0.1 : ETA on V2
##
## [OMEGA] @annotated @name group2
## E_V3 : 0.1 : ETA on V3
## E_Q : 0.1 : ETA on Q
## E_KA : 0.1 : ETA on KA
##
## [SIGMA] 1
##
## [MAIN]
## // covariate effects on parameters
## double CLCOV = pow(WT/WTref, WTCL);
## double V2COV = exp(SEXV2 * SEX);
##
## double CL = TVCL * CLCOV * exp(E_CL + E_CLi);
## double V2 = TVV2 * V2COV * exp(E_V2 + E_V2i);
## double V3 = TVV3 * exp(E_V3 + E_V3i);
## double Q = TVQ * exp(E_Q + E_Qi);
## double KA = TVKA * exp(E_KA + E_KAi);
##
## double K = CL/V2;
## double K23 = Q/V2;
## double K32 = Q/V3;
##
## ALAG_DEPOT = TVALAG1;
##
## [ODE]
## dxdt_DEPOT =-KA*DEPOT;
## dxdt_CENT = KA*DEPOT - (K+K23)*CENT + K32*PERIPH;
## dxdt_PERIPH = K23 *CENT - K32*PERIPH;
##
## dxdt_AUCCENT= C2;
##
## [TABLE]
##
## double IPRED = C2;
## double SD = sqrt(PROP*PROP*IPRED*IPRED + ADD*ADD);
## double DV = IPRED + EPS(1) * SD;
##
## [CAPTURE] @annotated
## IPRED : Concentration without residual variability
## DV : Concentration with residual variability
##
## [CAPTURE] E_CL E_V2 E_V3 E_Q E_KA CL V2NONMEM fit
This is needed to extract population parameter estimates (THETA, OMEGA) as well as individuals (ETA).
Alternatively you can manually modify population parameters in the mrgsolve model file.
For ETA you most likely need to load NONMEM fit (unless you get EBE using R).
xpdb <- xpose_data(runno = "006", dir = "nm")## Warning: Duplicated column names deduplicated: 'DV' => 'DV_1' [21]df.theta <-
get_prm(xpdb, transform = FALSE, quiet = TRUE) %>%
filter(type == "the") %>%
select(name, value) %>%
pivot_wider() %>%
rename(TVCL = THETA1,
TVV2 = THETA2,
TVV3 = THETA3,
TVQ = THETA4,
TVKA = THETA5,
PROP = THETA6,
ADD = THETA7,
WTCL = THETA11,
SEXV2= THETA12)
df.eta <-
get_data(xpdb, quiet = TRUE) %>%
select(NMID,
E_CLi = ETA1,
E_V2i = ETA2,
E_V3i = ETA3,
E_Qi = ETA4,
E_KAi = ETA5) %>%
distinct()
omega.vec <-
get_prm(xpdb, transform = FALSE, quiet = TRUE) %>%
filter(type == "ome") %>%
pull(value)
d.omat <-
omat(group1 = bmat(omega.vec[1:3]), group2 = dmat(omega.vec[4:6]))Draw smooth individual PK curve
See https://mrgsolve.github.io/user_guide/topics.html#topic-designs for more details of specifying sampling designs
Run
# Set-up datasets
df.sim.act.dose <-
df.nm %>%
# Add parameter values
expand_grid(df.theta) %>%
mutate(ID = NMID)
df.sim.act.dose.eta <-
df.nm %>%
# Add parameter and ETA values
expand_grid(df.theta) %>%
left_join(df.eta, by = "NMID") %>%
mutate(ID = NMID)
# Model run setting
mod_pk.act.dose <-
mod_pk %>%
# Set Omega and Sigma to zero
zero_re() %>%
# Keep these variables in the output
# a.u.g is a flag for augmented sampling timepoints
carry_out(NMID, AMT, EVID, WT, SEX, a.u.g) %>%
# Specify that we want to add augmented timepoints (defined with delta)
obsaug()
# PRED
## IPRED in output here is PRED because E_XXi is left at 0 and
## SIGMA and OMEGA were also set as 0
mrgsim.pred.act.dose <-
mod_pk.act.dose %>%
data_set(df.sim.act.dose) %>%
mrgsim(end = 200, delta = 1,
recover = "PHASE")
df.mrgsim.pred.act.dose <-
as_tibble(mrgsim.pred.act.dose) %>%
rename(PRED = IPRED)
# IPRED
mrgsim.ipred.act.dose <-
mod_pk.act.dose %>%
data_set(df.sim.act.dose.eta) %>%
mrgsim(end = 200, delta = 1,
recover = "PHASE")
df.mrgsim.ipred.act.dose <-
as_tibble(mrgsim.ipred.act.dose)Plot
df.mrgsim.ipred.act.dose %>%
ggplot(aes(TIME, IPRED)) +
geom_line() +
geom_line(data = df.mrgsim.pred.act.dose,
aes(y = PRED),
linetype = "dashed") +
geom_point(data = df.nm.obs,
aes(y = DV)) +
# Only show the first 12 subjects
facet_wrap_paginate(~NMID, nrow = 4, ncol = 4, page = 1,
labeller = "label_both") +
xgx_scale_x_time_units(units_dataset = time_units_dataset,
units_plot = time_units_plot) +
labs(y = "Concentration",
caption = "Solid line: IPRED, Dashed line: PRED, Circles: Obs")
Simulate new dose or schedules
Regular NONMEM-format data frame (which you would export to CSV & use in NONMEM $SIM) would likely work as it is.
If you want to utilize mrgsolve’s helper functions to generate datasets, see https://mrgsolve.github.io/user_guide/data-set-chapter.html#creating-data-sets for details.
Dose ranging
Generate sim data
set.seed(1234)
n.subj.per.dose <- 1000
doses <- c(600, 1200, 2400)
dosetime <- (0:14) * 24
n.subj.all <- n.subj.per.dose * length(doses)
# Generate dosing records
df.dose <-
tibble(AMT = rep(doses, each = n.subj.per.dose)) %>%
mutate(NMID = row_number()) %>%
mutate(CMT = 1, EVID = 1) %>%
expand_grid(TIME = dosetime)
# Here we are resampling covariates from the observed data
df.cov <-
df.nm %>%
select(NMID, WT, SEX) %>%
distinct() %>%
slice_sample(n = n.subj.all, replace = TRUE) %>%
mutate(NMID = row_number())
df.sim.dose.range <-
full_join(df.dose, df.cov, by = "NMID") %>%
# Add parameter values
expand_grid(df.theta) %>%
mutate(ID = NMID,
NAMT = AMT)Run
mrgsim.dose.range <-
mod_pk %>%
carry_out(NMID, NAMT, AMT, EVID, WT, SEX) %>%
data_set(df.sim.dose.range) %>%
omat(d.omat) %>%
mrgsim(end = max(dosetime) + 24, delta = 1)
df.mrgsim.dose.range <-
as_tibble(mrgsim.dose.range) %>%
filter(EVID == 0) %>%
mutate(NAMT = factor(NAMT))Plot
df.mrgsim.dose.range.qtile <-
df.mrgsim.dose.range %>%
group_by(NAMT, TIME) %>%
summarize(quibble(IPRED),
n = n(),
.groups = "drop") %>%
pivot_wider(names_from = IPRED_q, values_from = IPRED)
df.mrgsim.dose.range.qtile %>%
ggplot(aes(TIME, P50, color = NAMT)) +
geom_line() +
geom_ribbon(aes(ymax = P95, ymin = P05, fill = NAMT),
alpha = .3, color = NA) +
xgx_scale_x_time_units(units_dataset = time_units_dataset,
units_plot = time_units_plot) +
facet_wrap(~NAMT, labeller = "label_both", nrow = 1) +
labs(title = "Simulated PK with three dose levels",
y = "Concentration")
Generate exporure metrics
This can be used for showing PK variability or as input for E-R predictions
exposure.metrics.dose.range <-
df.mrgsim.dose.range %>%
filter(TIME >= max(dosetime),
TIME <= max(dosetime) + 24) %>%
group_by(NMID, NAMT) %>%
summarize(AUCss = max(AUCCENT) - min(AUCCENT),
Cmaxss = max(IPRED),
Cminss = min(IPRED),
.groups = "drop")
exposure.metrics.dose.range## # A tibble: 3,000 x 5
## NMID NAMT AUCss Cmaxss Cminss
## <dbl> <fct> <dbl> <dbl> <dbl>
## 1 1 600 2421. 219. 52.9
## 2 2 600 3903. 288. 96.9
## 3 3 600 4750. 319. 132.
## 4 4 600 3037. 211. 80.4
## 5 5 600 5466. 384. 161.
## 6 6 600 5096. 395. 151.
## 7 7 600 2923. 254. 64.9
## 8 8 600 7162. 422. 217.
## 9 9 600 7186. 443. 222.
## 10 10 600 4365. 345. 108.
## # … with 2,990 more rowsexposure.metrics.qtile <-
exposure.metrics.dose.range %>%
pivot_longer(AUCss:Cminss, names_to = "metric") %>%
group_by(NAMT, metric) %>%
summarize(quibble(value), .groups = "drop") %>%
pivot_wider(names_from = value_q, values_from = value)
exposure.metrics.qtile## # A tibble: 9 x 5
## NAMT metric P05 P50 P95
## <fct> <chr> <dbl> <dbl> <dbl>
## 1 600 AUCss 3077. 4779. 7551.
## 2 600 Cmaxss 241. 344. 489.
## 3 600 Cminss 72.2 133. 240.
## 4 1200 AUCss 6241. 9789. 15130.
## 5 1200 Cmaxss 506. 697. 957.
## 6 1200 Cminss 145. 277. 477.
## 7 2400 AUCss 12418. 19322. 30597.
## 8 2400 Cmaxss 961. 1376. 1956.
## 9 2400 Cminss 295. 543. 974.exposure.metrics.dose.range %>%
ggplot(aes(AUCss, NAMT, fill = NAMT, color = NAMT)) +
ggridges::geom_density_ridges(alpha = 0.5) +
scale_y_discrete(expand = c(0, 0)) +
ggridges::theme_ridges()## Picking joint bandwidth of 724
Different treatment intervals
You can use ii and addl statements like NONMEM
Generate sim data
set.seed(1234)
n.subj.per.dose <- 1000
df.dose.interval.setting <-
tribble(~AMT, ~II, ~ADDL, ~NDOSE,
600, 12, 29, "600mg BID",
1200, 24, 14, "1200mg QD")
time.sim.end <- 15 * 24
n.subj.all <- n.subj.per.dose * nrow(df.dose.interval.setting)
# Generate dosing records
df.dose <-
df.dose.interval.setting %>%
expand_grid(IDdummy = 1:n.subj.per.dose) %>%
select(-IDdummy) %>%
mutate(NMID = row_number(),
TIME = 0, CMT = 1, EVID = 1)
# Here we are resampling covariates from the observed data
df.cov <-
df.nm %>%
select(NMID, WT, SEX) %>%
distinct() %>%
slice_sample(n = n.subj.all, replace = TRUE) %>%
mutate(NMID = row_number())
df.sim.dose.intervals <-
full_join(df.dose, df.cov, by = "NMID") %>%
# Add parameter values
expand_grid(df.theta) %>%
mutate(ID = NMID)Run
mrgsim.dose.intervals <-
mod_pk %>%
carry_out(NMID, AMT, EVID, WT, SEX) %>%
data_set(df.sim.dose.intervals) %>%
omat(d.omat) %>%
mrgsim(end = time.sim.end, delta = 1,
recover = "NDOSE")
df.mrgsim.dose.intervals <-
as_tibble(mrgsim.dose.intervals) %>%
filter(EVID == 0)Plot
df.mrgsim.dose.intervals.qtile <-
df.mrgsim.dose.intervals %>%
group_by(NDOSE, TIME) %>%
summarize(quibble(IPRED),
n = n(),
.groups = "drop") %>%
pivot_wider(names_from = IPRED_q, values_from = IPRED)
df.mrgsim.dose.intervals.qtile %>%
ggplot(aes(TIME, P50, color = NDOSE)) +
geom_line() +
geom_ribbon(aes(ymax = P95, ymin = P05, fill = NDOSE),
alpha = .3, color = NA) +
xgx_scale_x_time_units(units_dataset = time_units_dataset,
units_plot = time_units_plot) +
# facet_wrap(~DFREQ, labeller = "label_both", nrow = 1) +
labs(title = "Simulated PK with two dosing intervals",
y = "Concentration")
Calc individual PK metrics
Sometimes we want to generate PK metrics for each individual (e.g. AUCss, Cmin,ss, Cmin,ss) with empirical Bayes estimates (EBE), using protocol-defined dosing schedules rather than actual dosing records.
This may be preferred in some situations where we want to avoid post-randomization bias.
Run
# 15-day QD dosing of 1200mg
df.sim.prot.dose <-
df.nm %>%
select(NMID, WT, SEX) %>%
distinct() %>%
mutate(TIME = 0, AMT = 1200, II = 24, ADDL = 14, CMT = 1, EVID = 1) %>%
# Add parameter and ETA values
expand_grid(df.theta) %>%
left_join(df.eta, by = "NMID") %>%
mutate(ID = NMID)
time.sim.end <- 16 * 24
# Model run setting
mod_pk.prot.dose <-
mod_pk %>%
# Set Omega and Sigma to zero
zero_re() %>%
# Keep these variables in the output
# a.u.g is a flag for augmented sampling timepoints
carry_out(NMID, AMT, EVID, WT, SEX, a.u.g) %>%
# Specify that we want to add augmented timepoints (defined with delta)
obsaug()
# IPRED
mrgsim.ipred.prot.dose <-
mod_pk.prot.dose %>%
data_set(df.sim.prot.dose) %>%
mrgsim(end = time.sim.end, delta = 1)
df.mrgsim.ipred.prot.dose <-
as_tibble(mrgsim.ipred.prot.dose)Exporure metrics for individual subjects
This can be used for E-R analysis
# You can use PKNCA::pk.calc.auc if the mrgsolve model does not calculate AUC in ODE
# exposure.metrics.ipred.prot.dose <-
# df.mrgsim.ipred.prot.dose %>%
# filter(TIME >= 15 * 24) %>%
# mutate(TAD = TIME -15 * 24) %>%
# group_by(NMID) %>%
# summarize(AUCss = PKNCA::pk.calc.auc(IPRED, TAD),
# Cmaxss = max(IPRED),
# Cminss = min(IPRED),
# .groups = "drop")
# If mrgsolve calculate cumulative AUC, then max(AUC) - min(AUC)
# is AUC for the time interval
exposure.metrics.ipred.prot.dose <-
df.mrgsim.ipred.prot.dose %>%
filter(TIME >= 15 * 24,
TIME <= 16 * 24) %>%
group_by(NMID) %>%
summarize(AUCss = max(AUCCENT) - min(AUCCENT),
Cmaxss = max(IPRED),
Cminss = min(IPRED),
.groups = "drop")
exposure.metrics.ipred.prot.dose.plot <-
exposure.metrics.ipred.prot.dose %>%
pivot_longer(Cmaxss:Cminss) %>%
mutate(x = rep(1:2, times = nrow(exposure.metrics.ipred.prot.dose)),
xj = jitter(x, amount = 0.09)) %>%
select(-AUCss, -x)
exposure.metrics.ipred.prot.dose.plot %>%
pivot_wider(names_from = name,
values_from = c(value, xj)) %>%
ggplot() +
geom_line(data = exposure.metrics.ipred.prot.dose.plot,
aes(x = xj, y = value, group = NMID),
alpha = 0.3) +
geom_point(aes(xj_Cmaxss, value_Cmaxss), color = "dodgerblue", size = 2, alpha = 0.6) +
geom_point(aes(xj_Cminss, value_Cminss), color = "darkorange", size = 2, alpha = 0.6) +
expand_limits(y = 0) +
scale_x_continuous(breaks = 1:2,
labels = c("Cmax", "Cmin"),
limits = c(0.5, 2.5)) +
labs(x = "Individual exposure metrics",
y = "")
exposure.metrics.ipred.prot.dose## # A tibble: 40 x 4
## NMID AUCss Cmaxss Cminss
## <dbl> <dbl> <dbl> <dbl>
## 1 1 9123. 428. 337.
## 2 2 3929. 197. 135.
## 3 3 10316. 475. 390.
## 4 4 10215. 474. 381.
## 5 5 4382. 222. 149.
## 6 6 3530. 179. 121.
## 7 7 5381. 262. 191.
## 8 8 2720. 149. 83.7
## 9 9 4493. 230. 150.
## 10 10 7514. 368. 264.
## # … with 30 more rowsVPC
Here I used tidyvpc package
Run sim
# Sim for VPC
n.vpc <- 1000
df.sim.vpc <-
df.nm %>%
# Add parameter values
expand_grid(df.theta) %>%
# Duplicate all records n.vpc times
# Need to give different ID#
expand_grid(REP = 1:n.vpc) %>%
mutate(ID = NMID * n.vpc + REP) %>%
arrange(REP, NMID, TIME, EVID)
mrgsim.vpc <-
mod_pk %>%
carry_out(REP, NMID, AMT, EVID, WT, SEX) %>%
data_set(df.sim.vpc) %>%
omat(d.omat) %>%
mrgsim(tad = TRUE, recover = "PHASE")
df.mrgsim.vpc <-
as_tibble(mrgsim.vpc) %>%
filter(EVID == 0)
# Sim PRED (required for tidyvpc)
df.sim.pred.for.vpc <-
df.nm %>%
# Add parameter values
expand_grid(df.theta) %>%
mutate(ID = NMID)
mrgsim.pred.for.vpc <-
mod_pk %>%
carry_out(NMID, AMT, EVID) %>%
data_set(df.sim.pred.for.vpc) %>%
zero_re() %>%
mrgsim(tad = TRUE, recover = "PHASE")
df.tad.pred <-
mrgsim.pred.for.vpc %>%
filter(EVID == 0) %>%
# Here IPRED is PRED as zero_re was used
select(tad, PRED = IPRED)Generate VPC
vpc <-
df.nm.obs %>%
bind_cols(df.tad.pred) %>%
mutate(PHASE = factor(PHASE, levels = c("SD", "MD"))) %>%
observed(x=TIME, y=DV) %>%
simulated(df.mrgsim.vpc, y=DV) %>%
stratify(~PHASE) %>%
# binning(bin = NTIM) %>%
binning(bin = "breaks", breaks = c(0, 1, 4, 5, 12, 24, 171, 185, 200)) %>%
vpcstats()
plot(vpc) +
xgx_scale_x_time_units(units_dataset = time_units_dataset,
units_plot = time_units_plot,
breaks = (0:40) * 6)
VPC with TAD
We can use time after dose (TAD) calculated in mrgsim() and use that for VPC plot, even if you don’t have TAD in your original dataset
vpc <-
df.nm.obs %>%
bind_cols(df.tad.pred) %>%
mutate(PHASE = factor(PHASE, levels = c("SD", "MD"))) %>%
observed(x=tad, y=DV) %>%
simulated(df.mrgsim.vpc, y=DV) %>%
binning(bin = "breaks", breaks = c(0, 1, 4, 5, 12, 22, 30)) %>%
predcorrect(pred=PRED) %>%
vpcstats()
plot(vpc) +
xgx_scale_x_time_units(units_dataset = time_units_dataset,
units_plot = time_units_plot,
breaks = (0:40) * 6) +
labs(x = "Time after the last dose (Days)")
Session info
devtools::session_info()## ─ Session info ───────────────────────────────────────────────────────────────
## setting value
## version R version 4.0.2 (2020-06-22)
## os macOS Catalina 10.15.6
## system x86_64, darwin17.0
## ui X11
## language (EN)
## collate en_US.UTF-8
## ctype en_US.UTF-8
## tz America/Los_Angeles
## date 2020-09-30
##
## ─ Packages ───────────────────────────────────────────────────────────────────
## package * version date lib source
## assertthat 0.2.1 2019-03-21 [1] CRAN (R 4.0.0)
## backports 1.1.7 2020-05-13 [1] CRAN (R 4.0.0)
## binom 1.1-1 2014-01-02 [1] CRAN (R 4.0.0)
## blob 1.2.1 2020-01-20 [1] CRAN (R 4.0.0)
## broom 0.7.0 2020-07-09 [1] CRAN (R 4.0.2)
## callr 3.4.3 2020-03-28 [1] CRAN (R 4.0.0)
## cellranger 1.1.0 2016-07-27 [1] CRAN (R 4.0.0)
## cli 2.0.2 2020-02-28 [1] CRAN (R 4.0.0)
## colorspace 1.4-1 2019-03-18 [1] CRAN (R 4.0.0)
## crayon 1.3.4 2017-09-16 [1] CRAN (R 4.0.0)
## data.table * 1.12.8 2019-12-09 [1] CRAN (R 4.0.0)
## DBI 1.1.0 2019-12-15 [1] CRAN (R 4.0.0)
## dbplyr 1.4.4 2020-05-27 [1] CRAN (R 4.0.0)
## desc 1.2.0 2018-05-01 [1] CRAN (R 4.0.0)
## devtools 2.3.0 2020-04-10 [1] CRAN (R 4.0.0)
## digest 0.6.25 2020-02-23 [1] CRAN (R 4.0.0)
## dplyr * 1.0.2 2020-08-18 [1] CRAN (R 4.0.2)
## ellipsis 0.3.1 2020-05-15 [1] CRAN (R 4.0.0)
## evaluate 0.14 2019-05-28 [1] CRAN (R 4.0.0)
## fansi 0.4.1 2020-01-08 [1] CRAN (R 4.0.0)
## farver 2.0.3 2020-01-16 [1] CRAN (R 4.0.0)
## forcats * 0.5.0 2020-03-01 [1] CRAN (R 4.0.0)
## fs 1.4.1 2020-04-04 [1] CRAN (R 4.0.0)
## generics 0.0.2 2018-11-29 [1] CRAN (R 4.0.0)
## ggforce 0.3.1 2019-08-20 [1] CRAN (R 4.0.0)
## ggplot2 * 3.3.2 2020-06-19 [1] CRAN (R 4.0.2)
## ggridges 0.5.2 2020-01-12 [1] CRAN (R 4.0.0)
## glue * 1.4.1 2020-05-13 [1] CRAN (R 4.0.0)
## gtable 0.3.0 2019-03-25 [1] CRAN (R 4.0.0)
## haven 2.3.1 2020-06-01 [1] CRAN (R 4.0.0)
## hms 0.5.3 2020-01-08 [1] CRAN (R 4.0.0)
## htmltools 0.5.0 2020-06-16 [1] CRAN (R 4.0.0)
## httr 1.4.1 2019-08-05 [1] CRAN (R 4.0.0)
## jsonlite 1.6.1 2020-02-02 [1] CRAN (R 4.0.0)
## knitr 1.28 2020-02-06 [1] CRAN (R 4.0.0)
## labeling 0.3 2014-08-23 [1] CRAN (R 4.0.0)
## lattice 0.20-41 2020-04-02 [1] CRAN (R 4.0.2)
## lifecycle 0.2.0 2020-03-06 [1] CRAN (R 4.0.0)
## lubridate 1.7.8 2020-04-06 [1] CRAN (R 4.0.0)
## magrittr * 1.5 2014-11-22 [1] CRAN (R 4.0.0)
## MASS 7.3-51.6 2020-04-26 [1] CRAN (R 4.0.2)
## Matrix 1.2-18 2019-11-27 [1] CRAN (R 4.0.2)
## MatrixModels 0.4-1 2015-08-22 [1] CRAN (R 4.0.0)
## memoise 1.1.0 2017-04-21 [1] CRAN (R 4.0.0)
## modelr 0.1.8 2020-05-19 [1] CRAN (R 4.0.0)
## mrgsolve * 0.10.4 2020-06-19 [1] CRAN (R 4.0.0)
## munsell 0.5.0 2018-06-12 [1] CRAN (R 4.0.0)
## pander 0.6.3 2018-11-06 [1] CRAN (R 4.0.0)
## pillar 1.4.4 2020-05-05 [1] CRAN (R 4.0.0)
## pkgbuild 1.0.8 2020-05-07 [1] CRAN (R 4.0.0)
## pkgconfig 2.0.3 2019-09-22 [1] CRAN (R 4.0.0)
## pkgload 1.1.0 2020-05-29 [1] CRAN (R 4.0.0)
## plyr 1.8.6 2020-03-03 [1] CRAN (R 4.0.0)
## png 0.1-7 2013-12-03 [1] CRAN (R 4.0.0)
## polyclip 1.10-0 2019-03-14 [1] CRAN (R 4.0.0)
## prettyunits 1.1.1 2020-01-24 [1] CRAN (R 4.0.0)
## processx 3.4.2 2020-02-09 [1] CRAN (R 4.0.0)
## ps 1.3.3 2020-05-08 [1] CRAN (R 4.0.0)
## purrr * 0.3.4 2020-04-17 [1] CRAN (R 4.0.0)
## quantreg * 5.55 2020-04-01 [1] CRAN (R 4.0.0)
## R6 2.4.1 2019-11-12 [1] CRAN (R 4.0.0)
## Rcpp 1.0.5 2020-07-06 [1] CRAN (R 4.0.2)
## RcppArmadillo 0.9.900.3.0 2020-09-03 [1] CRAN (R 4.0.2)
## readr * 1.3.1 2018-12-21 [1] CRAN (R 4.0.0)
## readxl 1.3.1 2019-03-13 [1] CRAN (R 4.0.0)
## remotes 2.1.1 2020-02-15 [1] CRAN (R 4.0.0)
## reprex 0.3.0 2019-05-16 [1] CRAN (R 4.0.1)
## reticulate 1.16 2020-05-27 [1] CRAN (R 4.0.2)
## rlang 0.4.7 2020-07-09 [1] CRAN (R 4.0.2)
## rmarkdown 2.3 2020-06-18 [1] CRAN (R 4.0.2)
## rprojroot 1.3-2 2018-01-03 [1] CRAN (R 4.0.0)
## rstudioapi 0.11 2020-02-07 [1] CRAN (R 4.0.0)
## rvest 0.3.5 2019-11-08 [1] CRAN (R 4.0.0)
## scales 1.1.1 2020-05-11 [1] CRAN (R 4.0.0)
## sessioninfo 1.1.1 2018-11-05 [1] CRAN (R 4.0.0)
## SparseM * 1.78 2019-12-13 [1] CRAN (R 4.0.0)
## stringi 1.4.6 2020-02-17 [1] CRAN (R 4.0.0)
## stringr * 1.4.0 2019-02-10 [1] CRAN (R 4.0.0)
## testthat 2.3.2 2020-03-02 [1] CRAN (R 4.0.0)
## tibble * 3.0.3 2020-07-10 [1] CRAN (R 4.0.2)
## tidyr * 1.1.2 2020-08-27 [1] CRAN (R 4.0.2)
## tidyselect 1.1.0 2020-05-11 [1] CRAN (R 4.0.0)
## tidyverse * 1.3.0 2019-11-21 [1] CRAN (R 4.0.2)
## tidyvpc * 1.0.0 2020-03-26 [1] CRAN (R 4.0.0)
## tweenr 1.0.1 2018-12-14 [1] CRAN (R 4.0.0)
## usethis 1.6.1 2020-04-29 [1] CRAN (R 4.0.0)
## utf8 1.1.4 2018-05-24 [1] CRAN (R 4.0.0)
## vctrs 0.3.4 2020-08-29 [1] CRAN (R 4.0.2)
## withr 2.2.0 2020-04-20 [1] CRAN (R 4.0.0)
## xfun 0.17 2020-09-09 [1] CRAN (R 4.0.2)
## xgxr * 1.0.9 2020-04-14 [1] CRAN (R 4.0.0)
## xml2 1.3.2 2020-04-23 [1] CRAN (R 4.0.0)
## xpose * 0.4.11 2020-07-22 [1] CRAN (R 4.0.2)
## yaml 2.2.1 2020-02-01 [1] CRAN (R 4.0.0)
##
## [1] /Library/Frameworks/R.framework/Versions/4.0/Resources/library