## 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($params) as well as in the actual dataset. • Single solving allows parameter exploration easier because each parameter can be modified. With multiple subject solves, you have to make sure to update each individual parameter. The first obvious difference is in speed; With multiple subjects you can run each subject ID in parallel. For more information and examples of the speed gains with multiple subject solving see the Speeding up rxode2 vignette. The next difference is the amount of information output in the final data. Taking the 2 compartment indirect response model originally in the tutorial: library(rxode2) #> rxode2 2.1.3.9000 using 2 threads (see ?getRxThreads) #> no cache: create with rxCreateCache()  mod1 <- function() { ini({ KA=2.94E-01 CL=1.86E+01 V2=4.02E+01 Q=1.05E+01 V3=2.97E+02 Kin=1 Kout=1 EC50=200 }) model({ C2 = centr/V2 C3 = peri/V3 d/dt(depot) =-KA*depot d/dt(centr) = KA*depot - CL*C2 - Q*C2 + Q*C3 d/dt(peri) = Q*C2 - Q*C3 d/dt(eff) = Kin - Kout*(1-C2/(EC50+C2))*eff eff(0) = 1 }) } et <- et(amount.units='mg', time.units='hours') %>% et(dose=10000, addl=9, ii=12) %>% et(amt=20000, nbr.doses=5, start.time=120, dosing.interval=24) %>% et(0:240) # sampling Now a simple solve x <- rxSolve(mod1, et) x #> ── Solved rxode2 object ── #> ── Parameters (x$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