Individual Covariates
If there is an individual covariate you wish to solve for you may
specify it by the iCov dataset:
## rxode2 2.0.13.9000 using 1 threads (see ?getRxThreads)
## no cache: create with `rxCreateCache()`## udunits database from /usr/share/xml/udunits/udunits2.xml
library(xgxr)
mod3 <- rxode2({
KA=2.94E-01;
## Clearance with individuals
CL=1.86E+01 * (WT / 70) ^ 0.75;
V2=4.02E+01;
Q=1.05E+01;
V3=2.97E+02;
Kin=1;
Kout=1;
EC50=200;
## The linCmt() picks up the variables from above
C2 = linCmt();
Tz= 8
amp=0.1
eff(0) = 1 ## This specifies that the effect compartment starts at 1.
d/dt(eff) = Kin - Kout*(1-C2/(EC50+C2))*eff;
})## using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
ev <- et(amount.units="mg", time.units="hours") %>%
et(amt=10000, cmt=1) %>%
et(0,48,length.out=100) %>%
et(id=1:4);
set.seed(10)
rxSetSeed(10)
## Now use iCov to simulate a 4-id sample
r1 <- solve(mod3, ev,
# Create individual covariate data-frame
iCov=data.frame(id=1:4, WT=rnorm(4, 70, 10)))
print(r1)## ── Solved rxode2 object ──
## ── Parameters ($params): ──
## KA V2 Q V3 Kin Kout EC50 Tz amp
## 0.294 40.200 10.500 297.000 1.000 1.000 200.000 8.000 0.100
## ── Initial Conditions ($inits): ──
## eff
## 1
## ── First part of data (object): ──
## # A tibble: 400 × 6
## id time CL C2 eff WT
## <int> [h] <dbl> <dbl> <dbl> <dbl>
## 1 1 0 18.6 249. 1 70.2
## 2 1 0.485 18.6 175. 1 70.2
## 3 1 0.970 18.6 124. 1 70.2
## 4 1 1.45 18.6 87.9 1 70.2
## 5 1 1.94 18.6 62.7 1 70.2
## 6 1 2.42 18.6 45.1 1 70.2
## # ℹ 394 more rows
plot(r1, C2, log="y")
Time Varying Covariates
Covariates are easy to specify in rxode2, you can specify them as a variable. Time-varying covariates, like clock time in a circadian rhythm model, can also be used. Extending the indirect response model already discussed, we have:
library(rxode2)
library(units)
mod3 <- rxode2({
KA=2.94E-01;
CL=1.86E+01;
V2=4.02E+01;
Q=1.05E+01;
V3=2.97E+02;
Kin0=1;
Kout=1;
EC50=200;
## The linCmt() picks up the variables from above
C2 = linCmt();
Tz= 8
amp=0.1
eff(0) = 1 ## This specifies that the effect compartment starts at 1.
## Kin changes based on time of day (like cortosol)
Kin = Kin0 +amp *cos(2*pi*(ctime-Tz)/24)
d/dt(eff) = Kin - Kout*(1-C2/(EC50+C2))*eff;
})
ev <- eventTable(amount.units="mg", time.units="hours") %>%
add.dosing(dose=10000, nbr.doses=1, dosing.to=1) %>%
add.sampling(seq(0,48,length.out=100));
## Create data frame of 8 am dosing for the first dose This is done
## with base R but it can be done with dplyr or data.table
ev$ctime <- (ev$time+set_units(8,hr)) %% 24Now there is a covariate present in the event dataset, the system can be solved by combining the dataset and the model:
r1 <- solve(mod3, ev, covsInterpolation="linear")
print(r1)
#> ── Solved rxode2 object ──
#> ── Parameters ($params): ──
#> KA CL V2 Q V3 Kin0 Kout
#> 0.294000 18.600000 40.200000 10.500000 297.000000 1.000000 1.000000
#> EC50 Tz amp pi
#> 200.000000 8.000000 0.100000 3.141593
#> ── Initial Conditions ($inits): ──
#> eff
#> 1
#> ── First part of data (object): ──
#> # A tibble: 100 × 5
#> time C2 Kin eff ctime
#> [h] <dbl> <dbl> <dbl> [h]
#> 1 0 249. 1.1 1 8
#> 2 0.485 175. 1.10 1.04 8.48
#> 3 0.970 124. 1.10 1.06 8.97
#> 4 1.45 88.0 1.09 1.07 9.45
#> 5 1.94 62.9 1.09 1.08 9.94
#> 6 2.42 45.2 1.08 1.08 10.4
#> # ℹ 94 more rowsWhen solving ODE equations, the solver may sample times outside of
the data. When this happens, this ODE solver can use linear
interpolation between the covariate values. It is equivalent to R’s
approxfun with method="linear".
plot(r1,C2, ylab="Central Concentration")
Note that the linear approximation in this case leads to some kinks in the solved system at 24-hours where the covariate has a linear interpolation between near 24 and near 0. While linear seems reasonable, cases like clock time make other interpolation methods more attractive.
In rxode2 the default covariate interpolation is be the last
observation carried forward (locf), or constant
approximation. This is equivalent to R’s approxfun with
method="constant".
r1 <- solve(mod3, ev,covsInterpolation="locf")
print(r1)
#> ── Solved rxode2 object ──
#> ── Parameters ($params): ──
#> KA CL V2 Q V3 Kin0 Kout
#> 0.294000 18.600000 40.200000 10.500000 297.000000 1.000000 1.000000
#> EC50 Tz amp pi
#> 200.000000 8.000000 0.100000 3.141593
#> ── Initial Conditions ($inits): ──
#> eff
#> 1
#> ── First part of data (object): ──
#> # A tibble: 100 × 5
#> time C2 Kin eff ctime
#> [h] <dbl> <dbl> <dbl> [h]
#> 1 0 249. 1.1 1 8
#> 2 0.485 175. 1.10 1.04 8.48
#> 3 0.970 124. 1.10 1.06 8.97
#> 4 1.45 88.0 1.09 1.08 9.45
#> 5 1.94 62.9 1.09 1.08 9.94
#> 6 2.42 45.2 1.08 1.08 10.4
#> # ℹ 94 more rowswhich gives the following plots:
plot(r1,C2, ylab="Central Concentration", xlab="Time")
plot(r1,eff, ylab="Effect", xlab="Time")
In this case, the plots seem to be smoother.
You can also use NONMEM’s preferred interpolation style of next observation carried backward (NOCB):
r1 <- solve(mod3, ev,covsInterpolation="nocb")
print(r1)
#> ── Solved rxode2 object ──
#> ── Parameters ($params): ──
#> KA CL V2 Q V3 Kin0 Kout
#> 0.294000 18.600000 40.200000 10.500000 297.000000 1.000000 1.000000
#> EC50 Tz amp pi
#> 200.000000 8.000000 0.100000 3.141593
#> ── Initial Conditions ($inits): ──
#> eff
#> 1
#> ── First part of data (object): ──
#> # A tibble: 100 × 5
#> time C2 Kin eff ctime
#> [h] <dbl> <dbl> <dbl> [h]
#> 1 0 249. 1.1 1 8
#> 2 0.485 175. 1.10 1.04 8.48
#> 3 0.970 124. 1.10 1.06 8.97
#> 4 1.45 88.0 1.09 1.07 9.45
#> 5 1.94 62.9 1.09 1.08 9.94
#> 6 2.42 45.2 1.08 1.08 10.4
#> # ℹ 94 more rowswhich gives the following plots:
plot(r1,C2, ylab="Central Concentration", xlab="Time")
plot(r1,eff, ylab="Effect", xlab="Time")