rxode2 is an R package for solving and simulating from ode-based models. These models are convert the rxode2 mini-language to C and create a compiled dll for fast solving. ODE solving using rxode2 has a few key parts:
rxode2()
which creates the C code for fast ODE solving based on a simple syntax related to Leibnitz notation.- The event data, which can be:
- a
NONMEM
ordeSolve
compatible data frame, or - created with
et()
oreventTable()
for easy simulation of events - The data frame can be augmented by adding
time-varying
or adding individual
covariates
(
iCov=
as needed)
- a
rxSolve()
which solves the system of equations using initial conditions and parameters to make predictions- With multiple subject data, this may be parallelized.
- With single subject the output data frame is adaptive
- Covariances and other metrics of uncertanty can be used to simulate while solving
You can install the released version of rxode2 from CRAN with:
install.packages("rxode2")
The fastest way to install the development version of rxode2
is to use
the r-universe
service. This service compiles binaries of the
development version for MacOS and for Windows so you don’t have to wait
for package compilation:
install.packages(c("dparser", "rxode2ll", "rxode2parse",
"rxode2random", "rxode2et", "rxode2"),
repos=c(nlmixr2="https://nlmixr2.r-universe.dev",
CRAN="https://cloud.r-project.org"))
If this doesn’t work you install the development version of rxode2 with
devtools::install_github("nlmixr2/rxode2parse")
devtools::install_github("nlmixr2/rxode2random")
devtools::install_github("nlmixr2/rxode2et")
devtools::install_github("nlmixr2/rxode2ll")
devtools::install_github("nlmixr2/rxode2")
To build models with rxode2, you need a working c compiler. To use parallel threaded solving in rxode2, this c compiler needs to support open-mp.
You can check to see if R has working c compiler you can check with:
## install.packages("pkgbuild")
pkgbuild::has_build_tools(debug = TRUE)
If you do not have the toolchain, you can set it up as described by the platform information below:
In windows you may simply use installr to install rtools:
install.packages("installr")
library(installr)
install.rtools()
Alternatively you can download and install rtools directly.
To get the most speed you need OpenMP enabled and compile rxode2 with
that compiler. There are various options and the most up to date
discussion about this is likely the data.table installation FAQ for
MacOS.
The last thing to keep in mind is that rxode2
uses the code very
similar to the original lsoda
which requires the gfortran
compiler
to be setup as well as the OpenMP
compilers.
If you are going to be using rxode2
and nlmixr
together and have an
older mac computer, I would suggest trying the following:
library(symengine)
If this crashes your R session then the binary does not work with your
Mac machine. To be able to run nlmixr, you will need to compile this
package manually. I will proceed assuming you have homebrew
installed
on your system.
On your system terminal you will need to install the dependencies to
compile symengine
:
brew install cmake gmp mpfr libmpc
After installing the dependencies, you need to re-install symengine
:
install.packages("symengine", type="source")
library(symengine)
To install on linux make sure you install gcc
(with openmp support)
and gfortran
using your distribution’s package manager.
For installation on R versions 4.0.x and 4.1.x, please see the
instructions on how to install symengine
in the nlmixr2
installation
instructions:
https://github.com/nlmixr2/nlmixr2#r-package-installation
Since the development version of rxode2 uses StanHeaders, you will need to make sure your compiler is setup to support C++14, as described in the rstan setup page. For R 4.0, I do not believe this requires modifying the windows toolchain any longer (so it is much easier to setup).
Once the C++ toolchain is setup appropriately, you can install the development version from GitHub with:
# install.packages("devtools")
devtools::install_github("nlmixr2/rxode2parse")
devtools::install_github("nlmixr2/rxode2random")
devtools::install_github("nlmixr2/rxode2et")
devtools::install_github("nlmixr2/rxode2ll")
devtools::install_github("nlmixr2/rxode2")
The model equations can be specified through a text string, a model file
or an R expression. Both differential and algebraic equations are
permitted. Differential equations are specified by d/dt(var_name) =
.
Each equation can be separated by a semicolon.
To load rxode2
package and compile the model:
library(rxode2)
#> rxode2 2.0.13.9000 using 8 threads (see ?getRxThreads)
#> no cache: create with `rxCreateCache()`
mod1 <- function() {
ini({
# central
KA=2.94E-01
CL=1.86E+01
V2=4.02E+01
# peripheral
Q=1.05E+01
V3=2.97E+02
# effects
Kin=1
Kout=1
EC50=200
})
model({
C2 <- centr/V2
C3 <- peri/V3
d/dt(depot) <- -KA*depot
d/dt(centr) <- KA*depot - CL*C2 - Q*C2 + Q*C3
d/dt(peri) <- Q*C2 - Q*C3
eff(0) <- 1
d/dt(eff) <- Kin - Kout*(1-C2/(EC50+C2))*eff
})
}
Model parameters may be specified in the ini({})
model block, initial
conditions can be specified within the model with the cmt(0)= X
, like
in this model eff(0) <- 1
.
You may also specify between subject variability initial conditions and
residual error components just like nlmixr2. This allows a single
interface for nlmixr2
/rxode2
models. Also note, the classic rxode2
interface still works just like it did in the past (so don’t worry about
breaking code at this time).
In fact, you can get the classic rxode2
model $simulationModel
in
the ui object:
mod1 <- mod1() # create the ui object (can also use `rxode2(mod1)`)
mod1
summary(mod1$simulationModel)
rxode2
provides a simple and very flexible way to specify dosing and
sampling through functions that generate an event table. First, an empty
event table is generated through the “et()” function. This has an
interface that is similar to NONMEM event tables:
ev <- et(amountUnits="mg", timeUnits="hours") %>%
et(amt=10000, addl=9,ii=12,cmt="depot") %>%
et(time=120, amt=2000, addl=4, ii=14, cmt="depot") %>%
et(0:240) # Add sampling
You can see from the above code, you can dose to the compartment named in the rxode2 model. This slight deviation from NONMEM can reduce the need for compartment renumbering.
These events can also be combined and expanded (to multi-subject events
and complex regimens) with rbind
, c
, seq
, and rep
. For more
information about creating complex dosing regimens using rxode2 see the
rxode2 events
vignette.
The ODE can now be solved using rxSolve
:
x <- mod1 %>% rxSolve(ev)
x
#> ── Solved rxode2 object ──
#> ── Parameters (x$params): ──
#> KA CL V2 Q V3 Kin Kout EC50
#> 0.294 18.600 40.200 10.500 297.000 1.000 1.000 200.000
#> ── Initial Conditions (x$inits): ──
#> depot centr peri eff
#> 0 0 0 1
#> ── First part of data (object): ──
#> # A tibble: 241 × 7
#> time C2 C3 depot centr peri eff
#> [h] <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 0 0 0 10000 0 0 1
#> 2 1 44.4 0.920 7453. 1784. 273. 1.08
#> 3 2 54.9 2.67 5554. 2206. 794. 1.18
#> 4 3 51.9 4.46 4140. 2087. 1324. 1.23
#> 5 4 44.5 5.98 3085. 1789. 1776. 1.23
#> 6 5 36.5 7.18 2299. 1467. 2132. 1.21
#> # ℹ 235 more rows
This returns a modified data frame. You can see the compartment values in the plot below:
library(ggplot2)
plot(x,C2) + ylab("Central Concentration")
Or,
plot(x,eff) + ylab("Effect")
Note that the labels are automatically labeled with the units from the
initial event table. rxode2 extracts units
to label the plot (if they
are present).
This is a brief comparison of pharmacometric ODE solving R packages to
rxode2
.
There are several R packages for differential equations. The most popular is deSolve.
However for pharmacometrics-specific ODE solving, there are only 2 packages other than rxode2 released on CRAN. Each uses compiled code to have faster ODE solving.
-
mrgsolve, which uses C++ lsoda solver to solve ODE systems. The user is required to write hybrid R/C++ code to create a mrgsolve model which is translated to C++ for solving.
In contrast,
rxode2
has a R-like mini-language that is parsed into C code that solves the ODE system.Unlike
rxode2
,mrgsolve
does not currently support symbolic manipulation of ODE systems, like automatic Jacobian calculation or forward sensitivity calculation (rxode2
currently supports this and this is the basis of nlmixr2’s FOCEi algorithm) -
dMod, which uses a unique syntax to create “reactions”. These reactions create the underlying ODEs and then created c code for a compiled deSolve model.
In contrast
rxode2
defines ODE systems at a lower level.rxode2
’s parsing of the mini-language comes from C, whereasdMod
’s parsing comes from R.Like
rxode2
,dMod
supports symbolic manipulation of ODE systems and calculates forward sensitivities and adjoint sensitivities of systems.Unlike
rxode2
,dMod
is not thread-safe sincedeSolve
is not yet thread-safe. -
PKPDsim which defines models in an R-like syntax and converts the system to compiled code.
Like
mrgsolve
,PKPDsim
does not currently support symbolic manipulation of ODE systems.PKPDsim
is not thread-safe.
The open pharmacometrics open source community is fairly friendly, and the rxode2 maintainers has had positive interactions with all of the ODE-solving pharmacometric projects listed.
rxode2
supports 1-3 compartment models with gradients (using stan
math’s auto-differentiation). This currently uses the same equations as
PKADVAN
to allow time-varying covariates.
rxode2
can mix ODEs and solved systems.
-
mrgsolve currently has 1-2 compartment (poly-exponential models) models built-in. The solved systems and ODEs cannot currently be mixed.
-
pmxTools currently have 1-3 compartment (super-positioning) models built-in. This is a R-only implementation.
-
PKPDsim uses 1-3 “ADVAN” solutions using non-superpositioning.
-
PKPDmodels has a one-compartment model with gradients.
- PKADVAN Provides 1-3 compartment models using non-superpositioning. This allows time-varying covariates.