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One of the things that can be helpful is reading NONMEM with rounding errors.

For this example we will take some of the test examples from babelmixr2 to translate to show examples of rounding errors that can be read in to help diagnose what could be happening with the model.

library(nonmem2rx)
library(babelmixr2)
#> Loading required package: nlmixr2
#> Loading required package: nlmixr2data

Step 1: Have a NONMEM model with rounding errors (and .phi or other information about the etas)

The first step is to load a model with rounding errors using nonmem2rx():

# Unzip example with rounding error
# included, but can be accessed with nlmixr2
#
# unzip(system.file("tests/testthat/pk.turnover.emax3-nonmem.zip", package="babelmixr2"))
# Load the model with `nonmem2rx`:
mod <- nonmem2rx("pk.turnover.emax3-nonmem/pk.turnover.emax3.nmctl")
#>  getting information from  'pk.turnover.emax3-nonmem/pk.turnover.emax3.nmctl'
#>  reading in xml file
#>  done
#>  reading in phi file
#>  done
#>  reading in lst file
#>  abbreviated list parsing
#>  done
#>  done
#>  splitting control stream by records
#>  done
#>  Processing record $INPUT
#>  Processing record $MODEL
#>  Processing record $THETA
#>  Processing record $OMEGA
#>  Processing record $SIGMA
#>  Processing record $PROBLEM
#>  Processing record $DATA
#>  Processing record $SUBROUTINES
#>  Processing record $PK
#>  Processing record $DES
#>  Processing record $ERROR
#>  Processing record $ESTIMATION
#>  Ignore record $ESTIMATION
#>  Processing record $COVARIANCE
#>  Ignore record $COVARIANCE
#>  Processing record $TABLE
#>  change initial estimate of `theta1` to `6.24053043162953e-07`
#>  change initial estimate of `theta2` to `-3.00642760553675e-06`
#>  change initial estimate of `theta3` to `-2.00405074386117`
#>  change initial estimate of `theta4` to `2.05188410700476`
#>  change initial estimate of `theta5` to `0.0985804613565218`
#>  change initial estimate of `theta6` to `0.511625249037084`
#>  change initial estimate of `theta7` to `6.4184983102259`
#>  change initial estimate of `theta8` to `0.140763261319656`
#>  change initial estimate of `theta9` to `-2.9534704318737`
#>  change initial estimate of `theta10` to `4.57045413136592`
#>  change initial estimate of `theta11` to `3.71714384851537`
#>  change initial estimate of `eta1` to `0.558129815059436`
#>  change initial estimate of `eta2` to `0.558402321309217`
#>  change initial estimate of `eta3` to `0.0785849119252598`
#>  change initial estimate of `eta4` to `0.0508226905750953`
#>  change initial estimate of `eta5` to `5e-05`
#>  change initial estimate of `eta6` to `0.18426809257979`
#>  change initial estimate of `eta7` to `0.0083631531443303`
#>  change initial estimate of `eta8` to `0.00274561514766752`
#>  read in nonmem input data (for model validation): /home/runner/work/nonmem2rx/nonmem2rx/vignettes/articles/pk.turnover.emax3-nonmem/pk.turnover.emax3.csv
#>  ignoring lines that begin with a letter (IGNORE=@)'
#>  applying names specified by $INPUT
#>  renaming 'dvid' to 'nmdvid'
#>  done
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#>  read in nonmem IPRED data (for model validation): /home/runner/work/nonmem2rx/nonmem2rx/vignettes/articles/pk.turnover.emax3-nonmem/pk.turnover.emax3.pred
#>  done
#>  changing most variables to lower case
#>  done
#>  replace theta names
#>  done
#>  replace eta names
#>  done
#>  renaming compartments
#>  done
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#>  solving ipred problem
#>  done
#>  solving pred problem
#>  done
mod
#>  ── rxode2-based free-form 4-cmt ODE model ────────────────────────────────────── 
#>  ── Initalization: ──  
#> Fixed Effects ($theta): 
#>          tktr           tka           tcl            tv      prop.err 
#>  6.240530e-07 -3.006428e-06 -2.004051e+00  2.051884e+00  9.858046e-02 
#>     pkadd.err         temax         tec50         tkout           te0 
#>  5.116252e-01  6.418498e+00  1.407633e-01 -2.953470e+00  4.570454e+00 
#>     pdadd.err 
#>  3.717144e+00 
#> 
#> Omega ($omega): 
#>            eta.ktr    eta.ka     eta.cl      eta.v eta.emax  eta.ec50
#> eta.ktr  0.5581298 0.0000000 0.00000000 0.00000000    0e+00 0.0000000
#> eta.ka   0.0000000 0.5584023 0.00000000 0.00000000    0e+00 0.0000000
#> eta.cl   0.0000000 0.0000000 0.07858491 0.00000000    0e+00 0.0000000
#> eta.v    0.0000000 0.0000000 0.00000000 0.05082269    0e+00 0.0000000
#> eta.emax 0.0000000 0.0000000 0.00000000 0.00000000    5e-05 0.0000000
#> eta.ec50 0.0000000 0.0000000 0.00000000 0.00000000    0e+00 0.1842681
#> eta.kout 0.0000000 0.0000000 0.00000000 0.00000000    0e+00 0.0000000
#> eta.e0   0.0000000 0.0000000 0.00000000 0.00000000    0e+00 0.0000000
#>             eta.kout      eta.e0
#> eta.ktr  0.000000000 0.000000000
#> eta.ka   0.000000000 0.000000000
#> eta.cl   0.000000000 0.000000000
#> eta.v    0.000000000 0.000000000
#> eta.emax 0.000000000 0.000000000
#> eta.ec50 0.000000000 0.000000000
#> eta.kout 0.008363153 0.000000000
#> eta.e0   0.000000000 0.002745615
#> 
#> States ($state or $stateDf): 
#>   Compartment Number Compartment Name
#> 1                  1            DEPOT
#> 2                  2              GUT
#> 3                  3           CENTER
#> 4                  4           EFFECT
#>  ── Model (Normalized Syntax): ── 
#> function() {
#>     description <- c("translated from babelmixr2", "; comments show mu referenced model in ui$getSplitMuModel")
#>     dfObs <- 483
#>     dfSub <- 32
#>     sigma <- lotri({
#>         eps1 ~ 1
#>     })
#>     validation <- c("IPRED relative difference compared to Nonmem IPRED: 0%; 95% percentile: (0%,0%); rtol=6.13e-06", 
#>         "IPRED absolute difference compared to Nonmem IPRED: 95% percentile: (3.12e-06, 0.000497); atol=6.17e-05", 
#>         "PRED relative difference compared to Nonmem PRED: 0%; 95% percentile: (0%,0%); rtol=6.18e-06", 
#>         "PRED absolute difference compared to Nonmem PRED: 95% percentile: (3.79e-07,0.00313) atol=6.18e-06")
#>     ini({
#>         tktr <- 6.24053043162953e-07
#>         label("1 - tktr")
#>         tka <- -3.00642760553675e-06
#>         label("2 - tka")
#>         tcl <- -2.00405074386117
#>         label("3 - tcl")
#>         tv <- 2.05188410700476
#>         label("4 - tv")
#>         prop.err <- c(0, 0.0985804613565218)
#>         label("5 - prop.err")
#>         pkadd.err <- c(0, 0.511625249037084)
#>         label("6 - pkadd.err")
#>         temax <- 6.4184983102259
#>         label("7 - temax")
#>         tec50 <- 0.140763261319656
#>         label("8 - tec50")
#>         tkout <- -2.9534704318737
#>         label("9 - tkout")
#>         te0 <- 4.57045413136592
#>         label("10 - te0")
#>         pdadd.err <- c(0, 3.71714384851537)
#>         label("11 - pdadd.err")
#>         eta.ktr ~ 0.558129815059436
#>         eta.ka ~ 0.558402321309217
#>         eta.cl ~ 0.0785849119252598
#>         eta.v ~ 0.0508226905750953
#>         eta.emax ~ 5e-05
#>         eta.ec50 ~ 0.18426809257979
#>         eta.kout ~ 0.0083631531443303
#>         eta.e0 ~ 0.00274561514766752
#>     })
#>     model({
#>         cmt(DEPOT)
#>         cmt(GUT)
#>         cmt(CENTER)
#>         cmt(EFFECT)
#>         mu_1 <- tktr
#>         mu_2 <- tka
#>         mu_3 <- tcl
#>         mu_4 <- tv
#>         mu_5 <- temax
#>         mu_6 <- tec50
#>         mu_7 <- tkout
#>         mu_8 <- te0
#>         ktr <- exp(mu_1 + eta.ktr)
#>         ka <- exp(mu_2 + eta.ka)
#>         cl <- exp(mu_3 + eta.cl)
#>         v <- exp(mu_4 + eta.v)
#>         emax <- ((1) - (0)) * (1/(1 + exp(-(mu_5 + eta.emax)))) + 
#>             (0)
#>         ec50 <- exp(mu_6 + eta.ec50)
#>         kout <- exp(mu_7 + eta.kout)
#>         e0 <- exp(mu_8 + eta.e0)
#>         rxini.rxddta4. <- e0
#>         EFFECT(0) <- rxini.rxddta4.
#>         dcp <- CENTER/v
#>         rxdz001 <- (ec50 + dcp)
#>         if (rxdz001 >= 0 && rxdz001 <= 1e-06) {
#>             rxdz001 <- 1e-06
#>         }
#>         if (rxdz001 >= -1e-06 && rxdz001 < 0) {
#>             rxdz001 <- -1e-06
#>         }
#>         pd <- 1 - emax * dcp/rxdz001
#>         kin <- e0 * kout
#>         d/dt(DEPOT) <- -ktr * DEPOT
#>         d/dt(GUT) <- ktr * DEPOT - ka * GUT
#>         d/dt(CENTER) <- ka * GUT - cl/v * CENTER
#>         d/dt(EFFECT) <- kin * pd - kout * EFFECT
#>         cp <- CENTER/v
#>         f <- DEPOT
#>         rxe_dcp <- CENTER/v
#>         rxdze001 <- (ec50 + rxe_dcp)
#>         if (rxdze001 >= 0 && rxdze001 <= 1e-06) {
#>             rxdze001 <- 1e-06
#>         }
#>         if (rxdze001 >= -1e-06 && rxdze001 < 0) {
#>             rxdze001 <- -1e-06
#>         }
#>         rxe_pd <- 1 - emax * rxe_dcp/rxdze001
#>         rxe_kin <- e0 * kout
#>         rxe_cp <- CENTER/v
#>         rx_pf1 <- rxe_cp
#>         rx_pf2 <- EFFECT
#>         rx_ip1 <- rx_pf1
#>         rx_p1 <- rx_ip1
#>         w1 <- sqrt((pkadd.err)^2 + (rx_pf1)^2 * (prop.err)^2)
#>         if (w1 == 0) 
#>             w1 <- 1
#>         rx_ip2 <- rx_pf2
#>         rx_p2 <- rx_ip2
#>         w2 <- sqrt((pdadd.err)^2)
#>         if (w2 == 0) 
#>             w2 <- 1
#>         ipred <- rx_ip1
#>         w <- w1
#>         if (nmdvid == 2) {
#>             ipred <- rx_ip2
#>             w <- w2
#>         }
#>         y <- ipred + w * eps1
#>     })
#> }
#>  ── nonmem2rx translation notes ($notes): ──  
#>    • some etas defaulted to non-mu referenced, possible parsing error: eta.emax as a work-around try putting the mu-referenced expression on a simple line 
#>    • some etas defaulted to non-mu referenced, possible parsing error: eta5 as a work-around try putting the mu-referenced expression on a simple line 
#>    • some NONMEM input has tied times; they are offset by a small offset 
#>    • is.na() applied to non-(list or vector) of type 'language' 
#>    • 'dvid' variable has special meaning in rxode2, renamed to 'nmdvid', rename/copy in your data too 
#>    • $MODEL NCOMPARTMENTS/NEQUILIBRIUM/NPARAMETERS statement(s) ignored 
#>  ── nonmem2rx extra properties: ──  
#> 
#> Sigma ($sigma): 
#>      eps1
#> eps1    1
#> 
#> other properties include: $nonmemData, $etaData
#> captured NONMEM table outputs: $predData, $ipredData
#> NONMEM/rxode2 comparison data: $iwresCompare, $predCompare, $ipredCompare
#> NONMEM/rxode2 composite comparison: $predAtol, $predRtol, $ipredAtol, $ipredRtol, $iwresAtol, $iwresRtol

Step 2: Convert rxode2 model to model with endpoints/residuals specified like nlmixr2

This example has rounding errors and isn’t a fully qualified nlmixr2 model (even though it was generated from nlmixr2).

We can use the model and create an equivalent model with as.nonmem2rx()

mod2 <- function() {
  ini({
    tktr <- 6.24053043162953e-07
    label("1 - tktr")
    tka <- -3.00642760553675e-06
    label("2 - tka")
    tcl <- -2.00405074386117
    label("3 - tcl")
    tv <- 2.05188410700476
    label("4 - tv")
    prop.err <- c(0, 0.0985804613565218)
    label("5 - prop.err")
    pkadd.err <- c(0, 0.511625249037084)
    label("6 - pkadd.err")
    temax <- 6.4184983102259
    label("7 - temax")
    tec50 <- 0.140763261319656
    label("8 - tec50")
    tkout <- -2.9534704318737
    label("9 - tkout")
    te0 <- 4.57045413136592
    label("10 - te0")
    pdadd.err <- c(0, 3.71714384851537)
    label("11 - pdadd.err")
    eta.ktr ~ 0.558129815059436
    eta.ka ~ 0.558402321309217
    eta.cl ~ 0.0785849119252598
    eta.v ~ 0.0508226905750953
    eta.emax ~ 5e-05
    eta.ec50 ~ 0.18426809257979
    eta.kout ~ 0.0083631531443303
    eta.e0 ~ 0.00274561514766752
  })
  model({
    cmt(DEPOT)
    cmt(GUT)
    cmt(CENTER)
    cmt(EFFECT)
    ktr <- exp(tktr + eta.ktr)
    ka <- exp(tka   + eta.ka)
    cl <- exp(tcl   + eta.cl)
    v <- exp(tv     + eta.v)
    emax <- expit(temax + eta.emax) 
    ec50 <- exp(tec50 + eta.ec50)
    kout <- exp(tkout + eta.kout)
    e0 <- exp(te0 + eta.e0)
    EFFECT(0) <- e0
    dcp <- CENTER/v
    pd <- 1 - emax * dcp/(ec50 + dcp)
    kin <- e0 * kout
    d/dt(DEPOT) <- -ktr * DEPOT
    d/dt(GUT) <- ktr * DEPOT - ka * GUT
    d/dt(CENTER) <- ka * GUT - cl/v * CENTER
    d/dt(EFFECT) <- kin * pd - kout * EFFECT
    eff <- EFFECT
    dcp ~ add(pkadd.err)+prop(prop.err)
    eff ~ add(pdadd.err)
  })
}

In the model above, the following modifications were made:

  • The code for protecting for rounding errors was removed

  • Endpoints/residual specifications were added

  • Duplicate code in NONMEM’s $ERROR block was removed from imported model

  • All the rx and nlmixr prefixed items were removed from the model. It is possible that not removing these variables can causenlmixr2 conversion to fail. It is best practice to remove them completely.

Also, it is good practice to make sure the model parses correctly before trying to validate/convert the model. If you find that your model doesn’t parse correctly it definitely won’t validate (and the error may not be as easy to track-down).

The first step is to validate if the translation is correct. This is done below:

new <- as.nonmem2rx(mod, mod2)
#>  copy 'dfSub' to nonmem2rx model
#>  copy 'dfObs' to nonmem2rx model
#>  merging 'dvid' with nlmixr2 'cmt' definition
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#>  solving ipred problem
#>  done
#>  solving pred problem
#>  done
print(new)
#>  ── rxode2-based free-form 4-cmt ODE model ────────────────────────────────────── 
#>  ── Initalization: ──  
#> Fixed Effects ($theta): 
#>          tktr           tka           tcl            tv      prop.err 
#>  6.240530e-07 -3.006428e-06 -2.004051e+00  2.051884e+00  9.858046e-02 
#>     pkadd.err         temax         tec50         tkout           te0 
#>  5.116252e-01  6.418498e+00  1.407633e-01 -2.953470e+00  4.570454e+00 
#>     pdadd.err 
#>  3.717144e+00 
#> 
#> Omega ($omega): 
#>            eta.ktr    eta.ka     eta.cl      eta.v eta.emax  eta.ec50
#> eta.ktr  0.5581298 0.0000000 0.00000000 0.00000000    0e+00 0.0000000
#> eta.ka   0.0000000 0.5584023 0.00000000 0.00000000    0e+00 0.0000000
#> eta.cl   0.0000000 0.0000000 0.07858491 0.00000000    0e+00 0.0000000
#> eta.v    0.0000000 0.0000000 0.00000000 0.05082269    0e+00 0.0000000
#> eta.emax 0.0000000 0.0000000 0.00000000 0.00000000    5e-05 0.0000000
#> eta.ec50 0.0000000 0.0000000 0.00000000 0.00000000    0e+00 0.1842681
#> eta.kout 0.0000000 0.0000000 0.00000000 0.00000000    0e+00 0.0000000
#> eta.e0   0.0000000 0.0000000 0.00000000 0.00000000    0e+00 0.0000000
#>             eta.kout      eta.e0
#> eta.ktr  0.000000000 0.000000000
#> eta.ka   0.000000000 0.000000000
#> eta.cl   0.000000000 0.000000000
#> eta.v    0.000000000 0.000000000
#> eta.emax 0.000000000 0.000000000
#> eta.ec50 0.000000000 0.000000000
#> eta.kout 0.008363153 0.000000000
#> eta.e0   0.000000000 0.002745615
#> 
#> States ($state or $stateDf): 
#>   Compartment Number Compartment Name
#> 1                  1            DEPOT
#> 2                  2              GUT
#> 3                  3           CENTER
#> 4                  4           EFFECT
#>  ── Multiple Endpoint Model ($multipleEndpoint): ──  
#>   variable                cmt                dvid*
#> 1  dcp ~ … cmt='dcp' or cmt=5 dvid='dcp' or dvid=1
#> 2  eff ~ … cmt='eff' or cmt=6 dvid='eff' or dvid=2
#>   * If dvids are outside this range, all dvids are re-numered sequentially, ie 1,7, 10 becomes 1,2,3 etc
#> 
#>  ── μ-referencing ($muRefTable): ──  
#>   theta      eta level
#> 1  tktr  eta.ktr    id
#> 2   tka   eta.ka    id
#> 3   tcl   eta.cl    id
#> 4    tv    eta.v    id
#> 5 temax eta.emax    id
#> 6 tec50 eta.ec50    id
#> 7 tkout eta.kout    id
#> 8   te0   eta.e0    id
#> 
#>  ── Model (Normalized Syntax): ── 
#> function() {
#>     description <- c("translated from babelmixr2", "; comments show mu referenced model in ui$getSplitMuModel")
#>     dfObs <- 483
#>     dfSub <- 32
#>     validation <- c("IPRED relative difference compared to Nonmem IPRED: 0%; 95% percentile: (0%,0%); rtol=6.13e-06", 
#>         "IPRED absolute difference compared to Nonmem IPRED: 95% percentile: (3.12e-06, 0.000497); atol=6.17e-05", 
#>         "PRED relative difference compared to Nonmem PRED: 0%; 95% percentile: (0%,0%); rtol=6.18e-06", 
#>         "PRED absolute difference compared to Nonmem PRED: 95% percentile: (3.79e-07,0.00313) atol=6.18e-06")
#>     ini({
#>         tktr <- 6.24053043162953e-07
#>         label("1 - tktr")
#>         tka <- -3.00642760553675e-06
#>         label("2 - tka")
#>         tcl <- -2.00405074386117
#>         label("3 - tcl")
#>         tv <- 2.05188410700476
#>         label("4 - tv")
#>         prop.err <- c(0, 0.0985804613565218)
#>         label("5 - prop.err")
#>         pkadd.err <- c(0, 0.511625249037084)
#>         label("6 - pkadd.err")
#>         temax <- 6.4184983102259
#>         label("7 - temax")
#>         tec50 <- 0.140763261319656
#>         label("8 - tec50")
#>         tkout <- -2.9534704318737
#>         label("9 - tkout")
#>         te0 <- 4.57045413136592
#>         label("10 - te0")
#>         pdadd.err <- c(0, 3.71714384851537)
#>         label("11 - pdadd.err")
#>         eta.ktr ~ 0.558129815059436
#>         eta.ka ~ 0.558402321309217
#>         eta.cl ~ 0.0785849119252598
#>         eta.v ~ 0.0508226905750953
#>         eta.emax ~ 5e-05
#>         eta.ec50 ~ 0.18426809257979
#>         eta.kout ~ 0.0083631531443303
#>         eta.e0 ~ 0.00274561514766752
#>     })
#>     model({
#>         cmt(DEPOT)
#>         cmt(GUT)
#>         cmt(CENTER)
#>         cmt(EFFECT)
#>         ktr <- exp(tktr + eta.ktr)
#>         ka <- exp(tka + eta.ka)
#>         cl <- exp(tcl + eta.cl)
#>         v <- exp(tv + eta.v)
#>         emax <- expit(temax + eta.emax)
#>         ec50 <- exp(tec50 + eta.ec50)
#>         kout <- exp(tkout + eta.kout)
#>         e0 <- exp(te0 + eta.e0)
#>         EFFECT(0) <- e0
#>         dcp <- CENTER/v
#>         pd <- 1 - emax * dcp/(ec50 + dcp)
#>         kin <- e0 * kout
#>         d/dt(DEPOT) <- -ktr * DEPOT
#>         d/dt(GUT) <- ktr * DEPOT - ka * GUT
#>         d/dt(CENTER) <- ka * GUT - cl/v * CENTER
#>         d/dt(EFFECT) <- kin * pd - kout * EFFECT
#>         eff <- EFFECT
#>         dcp ~ add(pkadd.err) + prop(prop.err)
#>         eff ~ add(pdadd.err)
#>     })
#> }
#>  ── nonmem2rx extra properties: ──  
#> other properties include: $nonmemData, $etaData, $thetaMat
#> captured NONMEM table outputs: $predData, $ipredData
#> NONMEM/rxode2 comparison data: $iwresCompare, $predCompare, $ipredCompare
#> NONMEM/rxode2 composite comparison: $predAtol, $predRtol, $ipredAtol, $ipredRtol, $iwresAtol, $iwresRtol

Step 3: Convert new model to nlmixr2 fit with as.nlmixr2()

Once the translation is complete, and it is validated, you can convert the fit to a full nlmixr2 fit object.

fit <- as.nlmixr2(new)
#> → loading into symengine environment...
#> → pruning branches (`if`/`else`) of full model...
#>  done
#> → finding duplicate expressions in EBE model...
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → optimizing duplicate expressions in EBE model...
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → compiling EBE model...
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#>  done
#> rxode2 2.1.0 using 2 threads (see ?getRxThreads)
#>   no cache: create with `rxCreateCache()`
#> → Calculating residuals/tables
#>  done
#> → compress origData in nlmixr2 object, save 21592
#> → compress parHistData in nlmixr2 object, save 5536

# Once it is loaded remove the directory (we don't need the files any
# more for this example)
#
# In this example, we don't remove, but note where it can be removed
#
# unlink("pk.turnover.emax3-nonmem", recursive = TRUE)

Note this object does not rerun an estimation, but rather imports everything it knows about the fit to rerun the nlmixr2 table steps to calculate the things you need.

Step 4: Explore the data/fit as if it came from nlmixr2

With this information you can see about the properties of the model:

print(fit)
#> ── nlmix nonmem2rx reading NONMEM ver 7.4.3 ──
#> 
#>               OBJF     AIC      BIC Log-likelihood
#> nonmem2rx 439.2156 1364.91 1444.331      -663.4551
#> 
#> ── Time (sec $time): ──
#> 
#>            setup table compress NONMEM as.nlmixr2
#> elapsed 0.026015 0.049    0.013 320.27      3.522
#> 
#> ── Population Parameters ($parFixed or $parFixedDf): ──
#> 
#>                Parameter      Est. Back-transformed BSV(CV% or SD) Shrink(SD)%
#> tktr            1 - tktr  6.24e-07                1           86.5      59.8% 
#> tka              2 - tka -3.01e-06                1           86.5      59.8% 
#> tcl              3 - tcl        -2            0.135           28.6      1.34% 
#> tv                4 - tv      2.05             7.78           22.8      6.44% 
#> prop.err    5 - prop.err    0.0986           0.0986                           
#> pkadd.err  6 - pkadd.err     0.512            0.512                           
#> temax          7 - temax      6.42            0.998        0.00707      100.% 
#> tec50          8 - tec50     0.141             1.15           45.0      6.06% 
#> tkout          9 - tkout     -2.95           0.0522           9.16      32.4% 
#> te0             10 - te0      4.57             96.6           5.24      18.1% 
#> pdadd.err 11 - pdadd.err      3.72             3.72                           
#>  
#>   No correlations in between subject variability (BSV) matrix
#>   Full BSV covariance ($omega) or correlation ($omegaR; diagonals=SDs) 
#>   Distribution stats (mean/skewness/kurtosis/p-value) available in $shrink 
#>   Censoring ($censInformation): No censoring
#>   Minimization message ($message):  
#>     
#> 
#>  WARNINGS AND ERRORS (IF ANY) FOR PROBLEM    1
#> 
#>  (WARNING  2) NM-TRAN INFERS THAT THE DATA ARE POPULATION.
#> 
#>     
#> 0MINIMIZATION TERMINATED
#>  DUE TO ROUNDING ERRORS (ERROR=134)
#>  NO. OF FUNCTION EVALUATIONS USED:     1088
#>  NO. OF SIG. DIGITS UNREPORTABLE
#> 0PARAMETER ESTIMATE IS NEAR ITS BOUNDARY
#> 
#>     IPRED relative difference compared to Nonmem IPRED: 0%; 95% percentile: (0%,0%); rtol=5.09e-06
#>     PRED relative difference compared to Nonmem PRED: 0%; 95% percentile: (0%,0%); rtol=5.29e-06
#>     IPRED absolute difference compared to Nonmem IPRED: 95% percentile: (2.2e-06, 0.000454); atol=3.03e-05
#>     PRED absolute difference compared to Nonmem PRED: 95% percentile: (4.72e-07,0.00361); atol=5.29e-06
#>     there are solving errors during optimization (see '$prderr')
#>     nonmem2rx model file: 'pk.turnover.emax3-nonmem/pk.turnover.emax3.nmctl' 
#> 
#> ── Fit Data (object is a modified tibble): ──
#> # A tibble: 483 × 35
#>   ID     TIME CMT      DV  PRED   RES IPRED   IRES  IWRES eta.ktr eta.ka eta.cl
#>   <fct> <dbl> <fct> <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl>   <dbl>  <dbl>  <dbl>
#> 1 1       0.5 dcp     0    1.16 -1.16 0.444 -0.444 -0.864  -0.506 -0.506  0.699
#> 2 1       1   dcp     1.9  3.37 -1.47 1.45   0.446  0.840  -0.506 -0.506  0.699
#> 3 1       2   dcp     3.3  7.51 -4.21 3.96  -0.660 -1.03   -0.506 -0.506  0.699
#> # ℹ 480 more rows
#> # ℹ 23 more variables: eta.v <dbl>, eta.emax <dbl>, eta.ec50 <dbl>,
#> #   eta.kout <dbl>, eta.e0 <dbl>, dcp <dbl>, eff <dbl>, DEPOT <dbl>, GUT <dbl>,
#> #   CENTER <dbl>, EFFECT <dbl>, ktr <dbl>, ka <dbl>, cl <dbl>, v <dbl>,
#> #   emax <dbl>, ec50 <dbl>, kout <dbl>, e0 <dbl>, pd <dbl>, kin <dbl>,
#> #   tad <dbl>, dosenum <dbl>

In this model you can see:

  • High shrinkage in temax, ktr, ka and moderate shrinkage in kout

By removing these parameters, you could possibly get a successful NONMEM run.

If you want, you can use model piping to remove these parameters as follows:

mod3 <-  fit %>%
  model(ktr <- exp(tktr)) %>%
  model(ka <- exp(tka)) %>%
  model(emax <- expit(temax)) %>%
  model(kout <- exp(tkout))
#> ! remove between subject variability `eta.ktr`
#> ! remove between subject variability `eta.ka`
#> ! remove between subject variability `eta.emax`
#> ! remove between subject variability `eta.kout`

mod3
#>  ── rxode2-based free-form 4-cmt ODE model ────────────────────────────────────── 
#>  ── Initalization: ──  
#> Fixed Effects ($theta): 
#>          tktr           tka           tcl            tv      prop.err 
#>  6.240530e-07 -3.006428e-06 -2.004051e+00  2.051884e+00  9.858046e-02 
#>     pkadd.err         temax         tec50         tkout           te0 
#>  5.116252e-01  6.418498e+00  1.407633e-01 -2.953470e+00  4.570454e+00 
#>     pdadd.err 
#>  3.717144e+00 
#> 
#> Omega ($omega): 
#>              eta.cl      eta.v  eta.ec50      eta.e0
#> eta.cl   0.07858491 0.00000000 0.0000000 0.000000000
#> eta.v    0.00000000 0.05082269 0.0000000 0.000000000
#> eta.ec50 0.00000000 0.00000000 0.1842681 0.000000000
#> eta.e0   0.00000000 0.00000000 0.0000000 0.002745615
#> 
#> States ($state or $stateDf): 
#>   Compartment Number Compartment Name
#> 1                  1            DEPOT
#> 2                  2              GUT
#> 3                  3           CENTER
#> 4                  4           EFFECT
#>  ── Multiple Endpoint Model ($multipleEndpoint): ──  
#>   variable                cmt                dvid*
#> 1  dcp ~ … cmt='dcp' or cmt=5 dvid='dcp' or dvid=1
#> 2  eff ~ … cmt='eff' or cmt=6 dvid='eff' or dvid=2
#>   * If dvids are outside this range, all dvids are re-numered sequentially, ie 1,7, 10 becomes 1,2,3 etc
#> 
#>  ── μ-referencing ($muRefTable): ──  
#>   theta      eta level
#> 1   tcl   eta.cl    id
#> 2    tv    eta.v    id
#> 3 tec50 eta.ec50    id
#> 4   te0   eta.e0    id
#> 
#>  ── Model (Normalized Syntax): ── 
#> function() {
#>     description <- c("translated from babelmixr2", "; comments show mu referenced model in ui$getSplitMuModel")
#>     dfObs <- 483
#>     dfSub <- 32
#>     validation <- c("IPRED relative difference compared to Nonmem IPRED: 0%; 95% percentile: (0%,0%); rtol=6.13e-06", 
#>         "IPRED absolute difference compared to Nonmem IPRED: 95% percentile: (3.12e-06, 0.000497); atol=6.17e-05", 
#>         "PRED relative difference compared to Nonmem PRED: 0%; 95% percentile: (0%,0%); rtol=6.18e-06", 
#>         "PRED absolute difference compared to Nonmem PRED: 95% percentile: (3.79e-07,0.00313) atol=6.18e-06")
#>     ini({
#>         tktr <- 6.24053043162953e-07
#>         label("1 - tktr")
#>         tka <- -3.00642760553675e-06
#>         label("2 - tka")
#>         tcl <- -2.00405074386117
#>         label("3 - tcl")
#>         tv <- 2.05188410700476
#>         label("4 - tv")
#>         prop.err <- c(0, 0.0985804613565218)
#>         label("5 - prop.err")
#>         pkadd.err <- c(0, 0.511625249037084)
#>         label("6 - pkadd.err")
#>         temax <- 6.4184983102259
#>         label("7 - temax")
#>         tec50 <- 0.140763261319656
#>         label("8 - tec50")
#>         tkout <- -2.9534704318737
#>         label("9 - tkout")
#>         te0 <- 4.57045413136592
#>         label("10 - te0")
#>         pdadd.err <- c(0, 3.71714384851537)
#>         label("11 - pdadd.err")
#>         eta.cl ~ 0.0785849119252598
#>         eta.v ~ 0.0508226905750953
#>         eta.ec50 ~ 0.18426809257979
#>         eta.e0 ~ 0.00274561514766752
#>     })
#>     model({
#>         cmt(DEPOT)
#>         cmt(GUT)
#>         cmt(CENTER)
#>         cmt(EFFECT)
#>         ktr <- exp(tktr)
#>         ka <- exp(tka)
#>         cl <- exp(tcl + eta.cl)
#>         v <- exp(tv + eta.v)
#>         emax <- expit(temax)
#>         ec50 <- exp(tec50 + eta.ec50)
#>         kout <- exp(tkout)
#>         e0 <- exp(te0 + eta.e0)
#>         EFFECT(0) <- e0
#>         dcp <- CENTER/v
#>         pd <- 1 - emax * dcp/(ec50 + dcp)
#>         kin <- e0 * kout
#>         d/dt(DEPOT) <- -ktr * DEPOT
#>         d/dt(GUT) <- ktr * DEPOT - ka * GUT
#>         d/dt(CENTER) <- ka * GUT - cl/v * CENTER
#>         d/dt(EFFECT) <- kin * pd - kout * EFFECT
#>         eff <- EFFECT
#>         dcp ~ add(pkadd.err) + prop(prop.err)
#>         eff ~ add(pdadd.err)
#>     })
#> }

Since you have babelmixr2 you could use babelmixr2 to run the model for you in NONMEM (if you have it setup to run NONMEM), or even run the model from nlmixr2 itself. In this example we will choose to use nlmixr2 (since the babelmixr2 example runs NONMEM and shows a reduction in shrinkage)

fit2 <- nlmixr(mod3, new$nonmemData, "focei", foceiControl(print=0))
#> → loading into symengine environment...
#> → pruning branches (`if`/`else`) of full model...
#>  done
#> → calculate jacobian
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → calculate sensitivities
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → calculate ∂(f)/∂(η)
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → calculate ∂(R²)/∂(η)
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → finding duplicate expressions in inner model...
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → optimizing duplicate expressions in inner model...
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → finding duplicate expressions in EBE model...
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → optimizing duplicate expressions in EBE model...
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → compiling inner model...
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#>  done
#> → finding duplicate expressions in FD model...
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → optimizing duplicate expressions in FD model...
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → compiling EBE model...
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#>  done
#> → compiling events FD model...
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#>  done
#> calculating covariance matrix
#> [====|====|====|====|====|====|====|====|====|====] 0:00:29 
#> done
#> → Calculating residuals/tables
#>  done
#> → compress origData in nlmixr2 object, save 21592
#> → compress parHistData in nlmixr2 object, save 14920

fit2
#> ── nlmix FOCEi (outer: nlminb) ──
#> 
#>           OBJF      AIC      BIC Log-likelihood Condition#(Cov) Condition#(Cor)
#> FOCEi 1425.005 2342.699 2405.399       -1156.35        896101.4        262.0511
#> 
#> ── Time (sec fit2$time): ──
#> 
#>            setup optimize covariance table compress   other
#> elapsed 0.003023 29.89559   29.89559 0.065    0.015 75.7248
#> 
#> ── Population Parameters (fit2$parFixed or fit2$parFixedDf): ──
#> 
#>                Parameter   Est.     SE  %RSE Back-transformed(95%CI) BSV(CV%)
#> tktr            1 - tktr 0.0978  0.147   150       1.1 (0.827, 1.47)         
#> tka              2 - tka 0.0229 0.0978   427      1.02 (0.845, 1.24)         
#> tcl              3 - tcl  -2.01   0.05  2.49    0.134 (0.122, 0.148)     27.8
#> tv                4 - tv   2.05 0.0425  2.07       7.79 (7.17, 8.47)     22.7
#> prop.err    5 - prop.err  0.144                                0.144         
#> pkadd.err  6 - pkadd.err  0.616                                0.616         
#> temax          7 - temax    188   5.75  3.06                1 (1, 1)         
#> tec50          8 - tec50  0.143 0.0875  61.1      1.15 (0.972, 1.37)     43.0
#> tkout          9 - tkout  -2.96  0.028 0.945 0.0516 (0.0488, 0.0545)         
#> te0             10 - te0   4.57 0.0105  0.23       96.8 (94.8, 98.8)     5.24
#> pdadd.err 11 - pdadd.err   3.86                                 3.86         
#>           Shrink(SD)%
#> tktr                 
#> tka                  
#> tcl            1.95% 
#> tv             6.61% 
#> prop.err             
#> pkadd.err            
#> temax                
#> tec50          7.90% 
#> tkout                
#> te0            19.4% 
#> pdadd.err            
#>  
#>   Covariance Type (fit2$covMethod): |r|,|s|
#>   No correlations in between subject variability (BSV) matrix
#>   Full BSV covariance (fit2$omega) or correlation (fit2$omegaR; diagonals=SDs) 
#>   Distribution stats (mean/skewness/kurtosis/p-value) available in fit2$shrink 
#>   Information about run found (fit2$runInfo):
#>    • gradient problems with initial estimate and covariance; see $scaleInfo 
#>    • since sandwich matrix is corrected, you may compare to $covR or $covS if you wish 
#>    • S matrix non-positive definite but corrected by S = sqrtm(S%*%S) 
#>    • R matrix non-positive definite but corrected by R = sqrtm(R%*%R) 
#>    • last objective function was not at minimum, possible problems in optimization 
#>    • ETAs were reset to zero during optimization; (Can control by foceiControl(resetEtaP=.)) 
#>    • initial ETAs were nudged; (can control by foceiControl(etaNudge=., etaNudge2=)) 
#>   Censoring (fit2$censInformation): No censoring
#>   Minimization message (fit2$message):  
#>     false convergence (8) 
#>   In an ODE system, false convergence may mean "useless" evaluations were performed.
#>   See https://tinyurl.com/yyrrwkce
#>   It could also mean the convergence is poor, check results before accepting fit
#>   You may also try a good derivative free optimization:
#>     nlmixr2(...,control=list(outerOpt="bobyqa"))
#> 
#> ── Fit Data (object fit2 is a modified tibble): ──
#> # A tibble: 483 × 33
#>   ID     TIME CMT      DV  PRED   RES  WRES IPRED   IRES IWRES CPRED  CRES CWRES
#>   <fct> <dbl> <fct> <dbl> <dbl> <dbl> <dbl> <dbl>  <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1       0.5 dcp     0    1.28 -1.28 -1.82  1.01 -1.01  -1.60  1.25 -1.25 -1.86
#> 2 1       1   dcp     1.9  3.66 -1.76 -1.53  2.89 -0.991 -1.33  3.58 -1.68 -1.71
#> 3 1       2   dcp     3.3  7.91 -4.61 -2.12  6.22 -2.92  -2.68  7.73 -4.43 -2.55
#> # ℹ 480 more rows
#> # ℹ 20 more variables: eta.cl <dbl>, eta.v <dbl>, eta.ec50 <dbl>, eta.e0 <dbl>,
#> #   DEPOT <dbl>, GUT <dbl>, CENTER <dbl>, EFFECT <dbl>, ktr <dbl>, ka <dbl>,
#> #   cl <dbl>, v <dbl>, emax <dbl>, ec50 <dbl>, kout <dbl>, e0 <dbl>, pd <dbl>,
#> #   kin <dbl>, tad <dbl>, dosenum <dbl>

With these modifications the shrinkage is also reduced (just like in the NONMEM case)

Step 5: Get the covariance of the model

Another thing that can be helpful when the fit has been imported into a nlmixr2 fit is to get the variance/covariance matrix. This can be especially helpful to diagnose things to help simplify your model

getVarCov(fit)
#> → loading into symengine environment...
#> → pruning branches (`if`/`else`) of full model...
#>  done
#> → calculate jacobian
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → calculate sensitivities
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → calculate ∂(f)/∂(η)
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → finding duplicate expressions in inner model...
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → optimizing duplicate expressions in inner model...
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → finding duplicate expressions in EBE model...
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → optimizing duplicate expressions in EBE model...
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → compiling inner model...
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#>  done
#> → finding duplicate expressions in FD model...
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → optimizing duplicate expressions in FD model...
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00
#> → compiling EBE model...
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#>  done
#> → compiling events FD model...
#> using C compiler: ‘gcc (Ubuntu 11.4.0-1ubuntu1~22.04) 11.4.0’
#>  done
#> calculating covariance matrix
#> [====|====|====|====|====|====|====|====|====|====] 0:00:05
#> Warning in foceiFitCpp_(.ret): using R matrix to calculate covariance, can
#> check sandwich or S matrix with $covRS and $covS
#> Warning in foceiFitCpp_(.ret): gradient problems with covariance; see
#> $scaleInfo
#> → compress origData in nlmixr2 object, save 21592
#> Updated original fit object fit
#>                tktr           tka           tcl           tv         temax
#> tktr   1.830060e-02 -1.523057e-02 -2.404755e-05 3.183949e-04  0.0011992673
#> tka   -1.523057e-02  1.828061e-02 -2.125855e-05 3.195745e-04  0.0014273042
#> tcl   -2.404755e-05 -2.125855e-05  2.479870e-04 1.184906e-05 -0.0008486078
#> tv     3.183949e-04  3.195745e-04  1.184906e-05 3.183331e-04  0.0011376028
#> temax  1.199267e-03  1.427304e-03 -8.486078e-04 1.137603e-03  7.5951592101
#> tec50  1.333848e-04  1.362464e-04 -3.585788e-04 1.232516e-04  0.0485635015
#> tkout  9.641362e-05  1.069037e-04 -9.755546e-05 1.189674e-04 -0.0189321828
#> te0    1.365383e-05  1.343098e-05 -9.855499e-06 1.252947e-05 -0.0004450840
#>               tec50         tkout           te0
#> tktr   0.0001333848  9.641362e-05  1.365383e-05
#> tka    0.0001362464  1.069037e-04  1.343098e-05
#> tcl   -0.0003585788 -9.755546e-05 -9.855499e-06
#> tv     0.0001232516  1.189674e-04  1.252947e-05
#> temax  0.0485635015 -1.893218e-02 -4.450840e-04
#> tec50  0.0018384895  1.539214e-04 -1.360918e-04
#> tkout  0.0001539214  6.316775e-04  5.255583e-05
#> te0   -0.0001360918  5.255583e-05  8.870276e-05
fit
#> ── nlmix nonmem2rx reading NONMEM ver 7.4.3 ──
#> 
#>               OBJF     AIC      BIC Log-likelihood
#> nonmem2rx 439.2156 1364.91 1444.331      -663.4551
#> 
#> ── Time (sec fit$time): ──
#> 
#>            setup table compress NONMEM as.nlmixr2 covariance
#> elapsed 0.026015 0.049    0.013 320.27      3.522     12.775
#> 
#> ── Population Parameters (fit$parFixed or fit$parFixedDf): ──
#> 
#>                Parameter      Est.      SE     %RSE Back-transformed(95%CI)
#> tktr            1 - tktr  6.24e-07   0.135 2.17e+07          1 (0.767, 1.3)
#> tka              2 - tka -3.01e-06   0.135  4.5e+06          1 (0.767, 1.3)
#> tcl              3 - tcl        -2  0.0157    0.786    0.135 (0.131, 0.139)
#> tv                4 - tv      2.05  0.0178     0.87       7.78 (7.52, 8.06)
#> prop.err    5 - prop.err    0.0986                                   0.0986
#> pkadd.err  6 - pkadd.err     0.512                                    0.512
#> temax          7 - temax      6.42    2.76     42.9        0.998 (0.734, 1)
#> tec50          8 - tec50     0.141  0.0429     30.5       1.15 (1.06, 1.25)
#> tkout          9 - tkout     -2.95  0.0251    0.851 0.0522 (0.0497, 0.0548)
#> te0             10 - te0      4.57 0.00942    0.206       96.6 (94.8, 98.4)
#> pdadd.err 11 - pdadd.err      3.72                                     3.72
#>           BSV(CV% or SD) Shrink(SD)%
#> tktr                86.5      59.8% 
#> tka                 86.5      59.8% 
#> tcl                 28.6      1.34% 
#> tv                  22.8      6.44% 
#> prop.err                            
#> pkadd.err                           
#> temax            0.00707      100.% 
#> tec50               45.0      6.06% 
#> tkout               9.16      32.4% 
#> te0                 5.24      18.1% 
#> pdadd.err                           
#>  
#>   Covariance Type (fit$covMethod): r
#>   No correlations in between subject variability (BSV) matrix
#>   Full BSV covariance (fit$omega) or correlation (fit$omegaR; diagonals=SDs) 
#>   Distribution stats (mean/skewness/kurtosis/p-value) available in fit$shrink 
#>   Censoring (fit$censInformation): No censoring
#>   Minimization message (fit$message):  
#>     
#> 
#>  WARNINGS AND ERRORS (IF ANY) FOR PROBLEM    1
#> 
#>  (WARNING  2) NM-TRAN INFERS THAT THE DATA ARE POPULATION.
#> 
#>     
#> 0MINIMIZATION TERMINATED
#>  DUE TO ROUNDING ERRORS (ERROR=134)
#>  NO. OF FUNCTION EVALUATIONS USED:     1088
#>  NO. OF SIG. DIGITS UNREPORTABLE
#> 0PARAMETER ESTIMATE IS NEAR ITS BOUNDARY
#> 
#>     IPRED relative difference compared to Nonmem IPRED: 0%; 95% percentile: (0%,0%); rtol=5.09e-06
#>     PRED relative difference compared to Nonmem PRED: 0%; 95% percentile: (0%,0%); rtol=5.29e-06
#>     IPRED absolute difference compared to Nonmem IPRED: 95% percentile: (2.2e-06, 0.000454); atol=3.03e-05
#>     PRED absolute difference compared to Nonmem PRED: 95% percentile: (4.72e-07,0.00361); atol=5.29e-06
#>     there are solving errors during optimization (see '$prderr')
#>     nonmem2rx model file: 'pk.turnover.emax3-nonmem/pk.turnover.emax3.nmctl' 
#> 
#> ── Fit Data (object fit is a modified tibble): ──
#> # A tibble: 483 × 35
#>   ID     TIME CMT      DV  PRED   RES IPRED   IRES  IWRES eta.ktr eta.ka eta.cl
#>   <fct> <dbl> <fct> <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl>   <dbl>  <dbl>  <dbl>
#> 1 1       0.5 dcp     0    1.16 -1.16 0.444 -0.444 -0.864  -0.506 -0.506  0.699
#> 2 1       1   dcp     1.9  3.37 -1.47 1.45   0.446  0.840  -0.506 -0.506  0.699
#> 3 1       2   dcp     3.3  7.51 -4.21 3.96  -0.660 -1.03   -0.506 -0.506  0.699
#> # ℹ 480 more rows
#> # ℹ 23 more variables: eta.v <dbl>, eta.emax <dbl>, eta.ec50 <dbl>,
#> #   eta.kout <dbl>, eta.e0 <dbl>, dcp <dbl>, eff <dbl>, DEPOT <dbl>, GUT <dbl>,
#> #   CENTER <dbl>, EFFECT <dbl>, ktr <dbl>, ka <dbl>, cl <dbl>, v <dbl>,
#> #   emax <dbl>, ec50 <dbl>, kout <dbl>, e0 <dbl>, pd <dbl>, kin <dbl>,
#> #   tad <dbl>, dosenum <dbl>

Note this covariance step is not 100% successful since it is not r, s. However, it can give some insights on which parameters are estimated well. In this case you can see that the emax parameter is more poorly estimated than other parameters, which means fixing the parameter or reducing other parameters may help your estimate progress in NONMEM.