In Novartis/xgxr: Exploratory Graphics for Pharmacometrics

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

Overview

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).

Required Packages

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

Traceability: annotating and saving plots and tables

Annotating figures

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 function is: * xgx_annotate_status allows for the addition of text (like the word draft) to the plots * The caption is set to contain the file directory, program name, output name, and time of creation

caption = paste("File_Directory","\n",
                "Progam_Name.Rmd", "\n",
                "Output_Name.html","\n",
                paste(Sys.time()),
                collapse = "\n")
ggcaption = list(labs(caption = caption),
                 theme(plot.caption = element_text(hjust = 0.5)))

data <- data.frame(x = 1:1000, y = stats::rnorm(1000))
g <- xgx_plot(data = data, aes(x = x, y = y)) +
  geom_point() + 
  xgx_annotate_status(status = "DRAFT") + 
  ggcaption

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")

Graphics helpers

xgx theme

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))

Confidence intervals

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)

Nonlinear smoothing (e.g. Emax), and ordinal response smoothing

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())

Nice log scale

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()

Reverse log transform

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)

Nice scale for percent change data

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")

Scaling x-axis as a time scale

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)

Novartis/xgxr documentation built on Oct. 20, 2023, 4:35 a.m.