Plotting RxODE models

Plotting in RxODE

Setting up model for plotting explanation

The first step to explain the RxODE model plots is to setup:

An RxODE model
An event table
A solved object

library(RxODE)

## RxODE 1.1.1 using 1 threads (see ?getRxThreads)
##   no cache: create with `rxCreateCache()`

## Model from RxODE tutorial
m1 <- RxODE({
  KA <- 2.94E-01
  CL <- 1.86E+01
  V2 <- 4.02E+01
  Q <- 1.05E+01
  V3 <- 2.97E+02
  Kin <- 1
  Kout <- 1
  EC50 <- 200
  ## Added modeled bioavaiblity, duration and rate
  fdepot <- 1
  durDepot <- 8
  rateDepot <- 1250
  C2 <- centr / V2
  C3 <- peri / V3
  d/dt(depot) <- -KA * depot
  f(depot) <- fdepot
  dur(depot) <- durDepot
  rate(depot) <- rateDepot
  d/dt(centr) <- KA * depot - CL * C2 - Q * C2 + Q * C3
  d/dt(peri) <- Q * C2 - Q * C3
  d/dt(eff) <- Kin - Kout * (1 - C2 / (EC50 + C2)) * eff
  eff(0) <- 1
})

ev <- et(timeUnits = "hr") %>%
  et(amt = 10000, ii = 12, until = 24) %>%
  et(seq(0, 24, length.out = 100))

s <- rxSolve(m1, ev)

Default RxODE plot

The default plot in RxODE is to plot time versus state or calculated lhs values:

plot(s)

Things to note:

First, these plots are actually ggplot2 plots and can be modified by the standard ggplot2 grammar of graphics

Also note that the plot method for rxSolve objects can currently use some of the arguments of the default plot method:

log a character string which contains "x" if the x axis is to be logarithmic, "y" if the y axis is to be logarithmic and "xy" or "yx" if both axes are to be logarithmic. If available, this will use the xgxr xgx_scale_x_log10() and xgx_scale_y_log10() functions.
xlab This is a bit different than simply supplying the x-label through ggplot2, it will retain the unit information originally supplied in the event table. Also note, if available, this unit information is used will be used to have more meaningful ticks with xgx_scale_x_time_units()
ylab This supplies the y label

The following are currently unsupported: a. type b. xlim c. ylim d. main e. sub f. ann g. axes

Subsetting plots

While this is very interesting, it is often more useful to subset plots based on values you are more interested in; For example, it is more interesting in this plot to eff and C2. To do this, you simply specify the interesting items after the plot function. For instance:

plot(s, C2, eff)

Semi-log plots

Semi-log plots of PK concentrations are very common; To do this you simply need to use log="y"

plot(s, C2, log="y", ylab="Concentration")

## Warning: Transformation introduced infinite values in continuous y-axis

This uses the xgx_scale_y_log10() when available to more clearly show the semi-log nature of the plot.

Plots with multi-subject plots

If you have multi-subject plots you can easily plot applying the same principles as above. To illustrate this plot, lets expand an event table to include a plot of 4 subjects with lognormal random variability between subjects;

# Setup the new problem
m2 <- RxODE({
  KA <- 2.94E-01
  CL <- 1.86E+01 * exp(eta.Cl)
  V2 <- 4.02E+01
  Q <- 1.05E+01
  V3 <- 2.97E+02
  Kin <- 1
  Kout <- 1
  EC50 <- 200
  ## Added modeled bioavaiblity, duration and rate
  fdepot <- 1
  durDepot <- 8
  rateDepot <- 1250
  C2 <- centr / V2
  C3 <- peri / V3
  d / dt(depot) <- -KA * depot
  f(depot) <- fdepot
  dur(depot) <- durDepot
  rate(depot) <- rateDepot
  d / dt(centr) <- KA * depot - CL * C2 - Q * C2 + Q * C3
  d / dt(peri) <- Q * C2 - Q * C3
  d / dt(eff) <- Kin - Kout * (1 - C2 / (EC50 + C2)) * eff
  eff(0) <- 1
})

# Add the between subject variability:
omega <- lotri(eta.Cl ~ 0.4^2)

# Create the event table
ev <- et(timeUnits = "hr") %>%
  et(amt = 10000, until = units::set_units(3, days), ii = 12) %>% # loading doses
  et(seq(0, 48, length.out = 200)) %>%
  et(id = 1:4)

s <- rxSolve(m2, ev, omega=omega)

Once that is complete, you may plot it by the same method:

plot(s, C2, eff)

Notice that this is colored by each individual and labeled with a legend.

If you are only interested in the concentration, it produces a similar plot:

plot(s, C2, log="y", ylab="Concentration")

## Warning: Transformation introduced infinite values in continuous y-axis

Notice that this plot each individual is labeled by an attached id to let you know where the individual comes from. This is done by ggrepel if it is available, otherwise a legend is retained.

Multi-subject plots with large number of subjects

This can get a bit much when there are many subjects that are solved (in this example lets simulate 100)

ev <- et(timeUnits = "hr") %>%
  et(amt = 10000, until = units::set_units(3, days), ii = 12) %>% # loading doses
  et(seq(0, 48, length.out = 200)) %>%
  et(id = 1:100) # 100 subjects

s <- rxSolve(m2, ev, omega=omega)

plot(s, C2, log="y", ylab="Concentration")

## Warning: Transformation introduced infinite values in continuous y-axis

In this case, all the individuals are put on the plot in transparent greyscale and plot on the same pane. This allows the places where more subjects are present to be darker.

The number of individuals where the plots switch from legend to grayscale is controlled by changing the options for RxODE.spaghetti. ie. options(RxODE.spaghetti=7). 7 individuals is the default value when the plotting changes from individual to grayscale spaghetti plots.

You can also create a confidence interval of these simulations with confint:

s2 <- confint(s, parm="C2")

## ! in order to put confidence bands around the intervals, you need at least 2500 simulations

## summarizing data...done

And plot this with plot

plot(s2)

Matthew Fidler

2021-09-01