Single Subject ODE solving -- differences from multiple subject

Single Subject solving

Originally, rxode2 was only created to solve ODEs for one individual. That is a single system without any changes in individual parameters.

Of course this is still supported, the classic examples are found in rxode2 intro.

This article discusses the differences between multiple subject and single subject solving. There are three differences:

Single solving does not solve each ID in parallel
Single solving lacks the id column in parameters($params) as well as in the actual dataset.
Single solving allows parameter exploration easier because each parameter can be modified. With multiple subject solves, you have to make sure to update each individual parameter.

The first obvious difference is in speed; With multiple subjects you can run each subject ID in parallel. For more information and examples of the speed gains with multiple subject solving see the Speeding up rxode2 vignette.

The next difference is the amount of information output in the final data.

Taking the 2 compartment indirect response model originally in the tutorial:

library(rxode2)
#> rxode2 2.1.2.9000 using 2 threads (see ?getRxThreads)
#>   no cache: create with `rxCreateCache()`

mod1 <- function() {
  ini({
    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
  })
  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
    d/dt(eff)  = Kin - Kout*(1-C2/(EC50+C2))*eff
    eff(0) = 1
  })
}
  
et <- et(amount.units='mg', time.units='hours') %>%
    et(dose=10000, addl=9, ii=12) %>%
    et(amt=20000, nbr.doses=5, start.time=120, dosing.interval=24) %>%
    et(0:240) # sampling

Now a simple solve

x <- rxSolve(mod1, et)
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

print(x)
#> ── Solved rxode2 object ──
#> ── Parameters ($params): ──
#>      KA      CL      V2       Q      V3     Kin    Kout    EC50 
#>   0.294  18.600  40.200  10.500 297.000   1.000   1.000 200.000 
#> ── Initial Conditions ($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

plot(x, C2, eff)

To better see the differences between the single solve, you can solve for 2 individuals

x2 <- rxSolve(mod1, et %>% et(id=1:2), params=data.frame(CL=c(18.6, 7.6)))
print(x2)
#> ── Solved rxode2 object ──
#> ── Parameters ($params): ──
#> # A tibble: 2 × 9
#>   id       KA    CL    V2     Q    V3   Kin  Kout  EC50
#>   <fct> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1     0.294  18.6  40.2  10.5   297     1     1   200
#> 2 2     0.294   7.6  40.2  10.5   297     1     1   200
#> ── Initial Conditions ($inits): ──
#> depot centr  peri   eff 
#>     0     0     0     1 
#> ── First part of data (object): ──
#> # A tibble: 482 × 8
#>      id time    C2    C3  depot centr  peri   eff
#>   <int>  [h] <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl>
#> 1     1    0   0   0     10000     0     0   1   
#> 2     1    1  44.4 0.920  7453. 1784.  273.  1.08
#> 3     1    2  54.9 2.67   5554. 2206.  794.  1.18
#> 4     1    3  51.9 4.46   4140. 2087. 1324.  1.23
#> 5     1    4  44.5 5.98   3085. 1789. 1776.  1.23
#> 6     1    5  36.5 7.18   2299. 1467. 2132.  1.21
#> # ℹ 476 more rows

plot(x2, C2, eff)

By observing the two solves, you can see:

A multiple subject solve contains the id column both in the data frame and then data frame of parameters for each subject.

The last feature that is not as obvious, modifying the individual parameters. For single subject data, you can modify the rxode2 data frame changing initial conditions and parameter values as if they were part of the data frame, as described in the rxode2 Data Frames.

For multiple subject solving, this feature still works, but requires care when supplying each individual’s parameter value, otherwise you may change the solve and drop parameter for key individuals.

Summary of Single solve vs Multiple subject solving

Feature	Single Subject Solve	Multiple Subject Solve
Parallel	None	Each Subject
$params	data.frame with one parameter value	data.frame with one parameter per subject (w/ID column)
solved data	Can modify individual parameters with $ syntax	Have to modify all the parameters to update solved object

2024-04-16

Single Subject solving

Summary of Single solve vs Multiple subject solving