knitr::opts_chunk$set( collapse = TRUE, comment = "#>", fig.width = 7 )

The xgxr package supports a structured approach to exploring PKPD data (outlined here). It also contains helper functions for enabling the modeler to follow best R practices (by appending the program name, figure name location, and draft status to each plot) and enabling the modeler to follow best graphical practices (by providing an xgx theme that reduces chart ink, and by providing time-scale, log-scale, and reverse-log-transform-scale functions for more readable axes).

library(tidyr) library(dplyr) library(ggplot2) library(xgxr)

Our best practices require that we mark plots as "DRAFT" if not yet final,
and also list the program that created the plot and the location where the
plot is stored. This helps with the traceability of the work, by ensuring
that the following information is available for every plot in a report: the
R script used to create the figure, the location where the figure is stored,
and the time and date when the figure was created. The key functions here are:
* `xgx_annotate_status`

allows for the addition of text (like the word draft)
to the plots
* `xgx_annotate_filenames`

allows for printing the filenames as a caption for
the plot. It requires an input list `dirs`

with particular fields, as shown
below.

The function `xgx_save`

calls both of the above functions and it is
illustrated below.

This function also requires the user to input a width and height for the graph.
This is because often, the plots that are created have font that is so small
that it's impossible to read the x and y axes. We've found that the easiest
way to set the font size is "indirectly" by specifying the height and width
of the graph. Note that if you have a plot window open, you can get the
height and width by typing `dev.size()`

dirs <- list( parent_dir = tempdir(), rscript_dir = tempdir(), rscript_name = "example.R", results_dir = tempdir(), filename_prefix = "example_") data <- data.frame(x = 1:1000, y = stats::rnorm(1000)) g <- xgx_plot(data = data, aes(x = x, y = y)) + geom_point() xgx_save(width = 4, height = 4, dirs = dirs, filename_main = "example_plot", status = "DRAFT")

The the function `xgx_save`

works only with ggplot objects. If the figure
that is created is not a ggplot object, it will not work. An alternative
is to use `xgx_annotate_status_png`

to add the status and filename to png files.

data <- data.frame(x = 1:1000, y = stats::rnorm(1000)) g <- xgx_plot(data = data, aes(x = x, y = y)) + geom_point() filename = file.path(tempdir(), "png_example.png") ggsave(filename, plot = g, height = 4, width = 4, dpi = 75) xgx_annotate_status_png(filename, "./ExampleScript.R")

We also provide a function `xgx_save_table`

for annotating the relevant
information to csv files. The annotated table is shown below.

x <- data.frame(ID = c(1, 2), SEX = c("male", "female")) data <- xgx_save_table(x, dirs = dirs, filename_main = "ExampleTable") knitr::kable(data)

The `xgx_theme()`

function includes the xGx recommended plot settings.
It sets the background to white with light grey lines for the major and
minor breaks. This minimizes chart ink as recommended by Edward Tufte.
You can add `xgx_theme()`

to an existing `ggplot`

object, or you can
call `xgx_plot()`

in place of `ggplot()`

for all of your plot initiations.

xgx_plot(mtcars, aes(x = cyl, y = mpg)) + geom_point()

You may wish to set the theme to `xgx_theme`

for your R session, as we do below.

theme_set(xgx_theme()) ## Alternative, equivalent function: xgx_theme_set()

# time <- rep(seq(1,10),5) # id <- sort(rep(seq(1,5), 10)) # conc <- exp(-time)*sort(rep(rlnorm(5),10)) # # data <- data.frame(time = time, concentration = conc, id = factor(id)) # xgx_plot() + xgx_geom_spaghetti(data = data, mapping = aes(x = time, y = concentration, group = id, color = id)) # # xgx_spaghetti(data = data, mapping = aes(x = time, y = concentration, group = id, color = id))

The code for confidence intervals is a bit complex and hard to remember.
Rather than copy-pasting this code we provide the function `xgx_stat_ci`

for calculating and plotting default confidence intervals and also `xgx_geom_ci`

for percentile intervals. `xgx_stat_ci`

allows the definition of multiple `geom`

options in one function call, defined through a list. The default is `geom = list("point","line","errorbar")`

.
Additional ggplot options can be fed through the `ggplot`

object call, or
the `xgx_stat_ci`

layer. (Note that `xgx_stat_ci`

and `xgx_geom_ci`

are
equivalent). `xgx_stat_pi`

and `xgx_geom_pi`

work in a similar fashion but for percentile intervals.

data <- data.frame(x = rep(c(1, 2, 3), each = 20), y = rep(c(1, 2, 3), each = 20) + stats::rnorm(60), group = rep(1:3, 20)) xgx_plot(data,aes(x = x, y = y)) + xgx_stat_ci(conf_level = .95) xgx_plot(data,aes(x = x, y = y)) + xgx_stat_pi(percent = .95) xgx_plot(data,aes(x = x, y = y)) + xgx_stat_ci(conf_level = .95, geom = list("pointrange","line")) xgx_plot(data,aes(x = x, y = y)) + xgx_stat_ci(conf_level = .95, geom = list("ribbon","line")) xgx_plot(data,aes(x = x, y = y, group = group, color = factor(group))) + xgx_stat_ci(conf_level = .95, alpha = 0.5, position = position_dodge(width = 0.5))

The default settings calculate the confidence interval based on the
Student t Distribution (assuming normally distributed data). You can also
specify "lognormal"", "binomial"" or "multinomial"" for the `distribution`

. The first will
perform the confidence interval operation on the log-scaled data, the second
uses the binomial exact confidence interval calculation from the `binom`

package, and the
third uses `MultinomCI`

from the `DescTools`

package. The "multinomial"" option
is used for ordinal response or categorical data.

Note: you DO NOT need to use both `distribution = "lognormal"`

and `scale_y_log10()`

, choose only one of these.

# plotting lognormally distributed data data <- data.frame(x = rep(c(1, 2, 3), each = 20), y = 10^(rep(c(1, 2, 3), each = 20) + stats::rnorm(60)), group = rep(1:3, 20)) xgx_plot(data, aes(x = x, y = y)) + xgx_stat_ci(conf_level = 0.95, distribution = "lognormal") # note: you DO NOT need to use both distribution = "lognormal" and scale_y_log10() xgx_plot(data,aes(x = x, y = y)) + xgx_stat_ci(conf_level = 0.95) + xgx_scale_y_log10() # plotting binomial data data <- data.frame(x = rep(c(1, 2, 3), each = 20), y = rbinom(60, 1, rep(c(0.2, 0.6, 0.8), each = 20)), group = rep(1:3, 20)) xgx_plot(data, aes(x = x, y = y)) + xgx_stat_ci(conf_level = 0.95, distribution = "binomial") # Example plotting the percent of subjects in a categorical covariate group by treatment. set.seed(12345) data = data.frame(x = 120*exp(rnorm(100,0,1)), response = sample(c("Trt1", "Trt2", "Trt3"), 100, replace = TRUE), covariate = factor(sample(c("White","Black","Asian","Other"), 100, replace = TRUE), levels = c("White", "Black", "Asian", "Other"))) xgx_plot(data = data) + xgx_stat_ci(mapping = aes(x = response, response = covariate), distribution = "ordinal") + xgx_stat_ci(mapping = aes(x = 1, response = covariate), geom = "hline", distribution = "ordinal") + scale_y_continuous(labels = scales::percent_format()) + facet_wrap(~covariate) + xlab("Treatment group") + ylab("Percent of subjects by category")

`xgx_stat_ci`

can now also cut data by quantiles of `x`

using the `bins`

option, e.g. `bins = 4`

will cut the data by quartiles of `x`

. You can also supply your own breaks to cut the data.

# plotting set.seed(12345) data = data.frame(x = 120*exp(rnorm(100,0,1)), response = sample(c("Mild","Moderate","Severe"), 100, replace = TRUE), covariate = sample(c("Male","Female"), 100, replace = TRUE)) %>% mutate(y = (50 + 20*x/(200 + x))*exp(rnorm(100, 0, 0.3))) # plotting a lognormally distributed variable by quartiles of x xgx_plot(data = data) + xgx_stat_ci(mapping = aes(x = x, y = y, colour = covariate), distribution = "lognormal", bins = 4) # plotting ordinal or multinomial data, by quartiles of x xgx_plot(data = data) + xgx_stat_ci(mapping = aes(x = x, response = response, colour = covariate), distribution = "ordinal", bins = 4) + scale_y_continuous(labels = scales::percent_format()) + facet_wrap(~response) xgx_plot(data = data) + xgx_stat_ci(mapping = aes(x = x, response = response, colour = response), distribution = "ordinal", bins = 4) + scale_y_continuous(labels = scales::percent_format()) + facet_wrap(~covariate)

The current ggplot2::geom_smooth does not allow for plotting confidence bands for method = "nls", as ggplot2 does not supply a `predictdf`

for an object of class `nls`

, which geom_smooth silently calls to calculate the ymin and ymax for the confidence bands. The xgxr package includes a definition of `predictdf.nls`

, allowing for confidence bands for method = "nls".

set.seed(123456) Nsubj <- 10 Doses <- c(0, 25, 50, 100, 200) Ntot <- Nsubj*length(Doses) times <- c(0,14,30,60,90) dat1 <- data.frame(ID = 1:(Ntot), DOSE = rep(Doses, Nsubj), E0 = 50*rlnorm(Ntot, 0, 0.3), Emax = 100*rlnorm(Ntot, 0, 0.3), ED50 = 50*rlnorm(Ntot, 0, 0.3)) %>% dplyr::mutate(Response = (E0 + Emax*DOSE/(DOSE + ED50))*rlnorm(Ntot, 0, 0.3) ) %>% merge(data.frame(ID = rep(1:(Ntot), each = length(times)), Time = times), by = "ID") gg <- xgx_plot(data = dat1, aes(x = DOSE, y = Response)) gg <- gg + geom_point() gg gg + geom_smooth(method = "nlsLM", formula = y ~ E0 + Emax*x/(ED50 + x), method.args = list(start = list(E0 = 1, ED50 = 1, Emax = 1), lower = c(-Inf, 0, -Inf)))

xgxr also includes an Emax smooth function called `xgx_geom_smooth_emax`

which utilizes the "nlsLM" method, and silently calls the `predictdf.nls`

defined by xgxr.

gg + xgx_geom_smooth_emax() gg + xgx_geom_smooth_emax(geom = "ribbon", color = "black", fill = NA, linetype = "dashed") + xgx_geom_smooth_emax(geom = "line", color = "red")

xgxr also modifies the stats method `predict.nls`

for `nls`

objects in order to include confidence interval prediction. Upon loading the xgxr package, the `predict`

method for class `nls`

should be updated to the xgxr version, and include functionality to supply confidence intervals. In order to output the confidence intervals, be sure to specify `interval = "confidence"`

. The output will contain a "fit" data.frame with values for "fit", "lwr" and "upr" representing the prediction and lower and upper confidence intervals.

mod <- nlsLM(formula = Response ~ E0 + Emax * DOSE / (ED50 + DOSE), data = dat1, start = list(E0 = 1, ED50 = 1, Emax = 1), lower = c(-Inf, 0, -Inf)) predict(mod, newdata = data.frame(DOSE = c(0, 25, 50, 100, 200)), se.fit = TRUE) predict(mod, newdata = data.frame(DOSE = c(0, 25, 50, 100, 200)), se.fit = TRUE, interval = "confidence", level = 0.95)

xgxr also includes ordinal response smoothing as an option under the `xgx_stat_smooth`

function, indicated by `method = "polr"`

. This requires a dataset of x values and response values, to be defined in the mapping. This method also allows defining of color, fill, facet, linetype, etc. by the response category, while preserving the ordinal response fit across these categories.

# example with ordinal data (method = "polr") set.seed(12345) data = data.frame(x = 120*exp(stats::rnorm(100,0,1)), response = sample(c("Mild","Moderate","Severe"), 100, replace = TRUE), covariate = sample(c("Male","Female"), 100, replace = TRUE)) %>% dplyr::mutate(y = (50 + 20*x/(200 + x))*exp(stats::rnorm(100, 0, 0.3))) # example coloring by the response categories xgx_plot(data = data) + xgx_stat_smooth(mapping = ggplot2::aes(x = x, response = response, colour = response, fill = response), method = "polr") + ggplot2::scale_y_continuous(labels = scales::percent_format()) # example faceting by the response categories, coloring by a different covariate xgx_plot(data = data) + xgx_stat_smooth(mapping = ggplot2::aes(x = x, response = response, colour = covariate, fill = covariate), method = "polr", level = 0.80) + ggplot2::facet_wrap(~response) + ggplot2::scale_y_continuous(labels = scales::percent_format())

This version of the log scale function shows the tick marks between the major breaks (i.e. at 1, 2, 3, ... 10, instead of just 1 and 10). It also uses $$10^x$$ notation when the labels are base 10 and are very small or very large (<.001 or >9999)

df <- data.frame(x = c(0, stats::rlnorm(1000, 0, 1)), y = c(0, stats::rlnorm(1000, 0, 3))) xgx_plot(data = df, aes(x = x, y = y)) + geom_point() + xgx_scale_x_log10() + xgx_scale_y_log10()

This transform is useful for plotting data on a percentage scale that can approach 100% (such as receptor occupancy data).

conc <- 10^(seq(-3, 3, by = 0.1)) ec50 <- 1 data <- data.frame(concentration = conc, bound_receptor = 1 * conc / (conc + ec50)) gy <- xgx_plot(data, aes(x = concentration, y = bound_receptor)) + geom_point() + geom_line() + xgx_scale_x_log10() + xgx_scale_y_reverselog10() gx <- xgx_plot(data, aes(x = bound_receptor, y = concentration)) + geom_point() + geom_line() + xgx_scale_y_log10() + xgx_scale_x_reverselog10() gridExtra::grid.arrange(gy, gx, nrow = 1)

This transform is useful for plotting percent change from baseline data. Percent change data can range from -100% to +Inf%, and depending on the range of the data, a linear scale can lose the desired resolution. This transform plots percent change data on a scale of log10(PCHG + 100%), similar to a log scale of ratio to baseline.

Nsubj <- 10 Doses <- c(0, 25, 50, 100, 200) Ntot <- Nsubj*length(Doses) times <- c(0,14,30,60,90) dat1 <- data.frame(ID = 1:(Ntot), DOSE = rep(Doses, Nsubj), PD0 = rlnorm(Ntot, log(100), 1), Kout = exp(rnorm(Ntot,-2, 0.3)), Imax = 1, ED50 = 25) %>% dplyr::mutate(PDSS = PD0*(1 - Imax*DOSE/(DOSE + ED50))*exp(rnorm(Ntot, 0.05, 0.3)) ) %>% merge(data.frame(ID = rep(1:(Ntot), each = length(times)), Time = times), by = "ID") %>% dplyr::mutate(PD = ((PD0 - PDSS)*(exp(-Kout*Time)) + PDSS), PCHG = (PD - PD0)/PD0) ggplot2::ggplot(dat1 %>% subset(Time == 90), ggplot2::aes(x = DOSE, y = PCHG, group = DOSE)) + ggplot2::geom_boxplot() + xgx_theme() + xgx_scale_y_percentchangelog10() + ylab("Percent Change from Baseline") + xlab("Dose (mg)") ggplot2::ggplot(dat1, ggplot2::aes(x = Time, y = PCHG, group = ID, color = factor(DOSE))) + ggplot2::geom_line() + xgx_theme() + xgx_scale_y_percentchangelog10() + guides(color = guide_legend(title = "Dose (mg)")) + ylab("Percent Change from Baseline") dat2 <- data.frame(ID = 1:(Ntot), DOSE = rep(Doses, Nsubj), PD0 = rlnorm(Ntot, log(100), 1), Kout = exp(rnorm(Ntot,-2, 0.3)), Emax = 50*rlnorm(Ntot, 0, 0.3), ED50 = 300) %>% dplyr::mutate(PDSS = PD0*(1 + Emax*DOSE/(DOSE + ED50))*exp(rnorm(Ntot, -1, 0.3)) ) %>% merge(data.frame(ID = rep(1:(Ntot), each = length(times)), Time = times), by = "ID") %>% dplyr::mutate(PD = ((PD0 - PDSS)*(exp(-Kout*Time)) + PDSS), PCHG = (PD - PD0)/PD0) ggplot2::ggplot(dat2, ggplot2::aes(x = DOSE, y = PCHG, group = DOSE)) + ggplot2::geom_boxplot() + xgx_theme() + xgx_scale_y_percentchangelog10() + ylab("Percent Change from Baseline") + xlab("Dose (mg)") ggplot2::ggplot(dat2, ggplot2::aes(x = Time, y = PCHG, group = ID, color = factor(DOSE))) + ggplot2::geom_line() + xgx_theme() + xgx_scale_y_percentchangelog10() + guides(color = guide_legend(title = "Dose (mg)")) + ylab("Percent Change from Baseline")

For time, it's often good for the x ticks to be spaced in a particular way.
For instance, for hours, subdividing in increments by 24, 12, 6, and 3 hours
can make more sense than by 10 or 100. Similarly for days, increments of 7
or 28 days are preferred over 5 or 10 days. `xgx_scale_x_time_units`

allows
for this, where it is the input and output units.

data <- data.frame(x = 1:1000, y = stats::rnorm(1000)) g <- xgx_plot(data = data, aes(x = x, y = y)) + geom_point() g1 <- g + xgx_scale_x_time_units(units_dataset = "hours", units_plot = "hours") g2 <- g + xgx_scale_x_time_units(units_dataset = "hours", units_plot = "days") g3 <- g + xgx_scale_x_time_units(units_dataset = "hours", units_plot = "weeks") g4 <- g + xgx_scale_x_time_units(units_dataset = "hours", units_plot = "months") gridExtra::grid.arrange(g1, g2, g3, g4, nrow = 2)

We've found that during exploration, it can be extremely important to
check the dataset for issues. This can be done using the `xgx_check_data`

or `xgx_summarize_data`

function (the two functions are identical).

data <- mad_missing_duplicates %>% filter(CMT %in% c(1, 2, 3)) %>% rename(DV = LIDV, YTYPE = CMT, USUBJID = ID) covariates <- c("WEIGHTB", "SEX") check <- xgx_check_data(data, covariates) knitr::kable(check$summary) knitr::kable(head(check$data_subset))

You can also get an overview of the covariates in the dataset
with `xgx_summarize_covariates`

. The covariate summaries are also provided
in the `xgx_check_data`

and `xgx_summarize_data`

functions.

covar <- xgx_summarize_covariates(data,covariates) knitr::kable(covar$cts_covariates) knitr::kable(covar$cat_covariates)

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