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nlmixr

Changing models via piping

As in the running nlmixr vignette, Let’s start with a very simple PK example, using the single-dose theophylline dataset generously provided by Dr. Robert A. Upton of the University of California, San Francisco:

library(nlmixr2)

one.compartment <- function() {
  ini({
    tka <- 0.45; label("Ka")
    tcl <- 1; label("Cl")
    tv <- 3.45; label("V")
    eta.ka ~ 0.6
    eta.cl ~ 0.3
    eta.v ~ 0.1
    add.sd <- 0.7
  })
  model({
    ka <- exp(tka + eta.ka)
    cl <- exp(tcl + eta.cl)
    v <- exp(tv + eta.v)
    d/dt(depot) = -ka * depot
    d/dt(center) = ka * depot - cl / v * center
    cp = center / v
    cp ~ add(add.sd)
  })
}

We can try the First-Order Conditional Estimation with Interaction (FOCEi) method to find a good solution:

fit <- nlmixr(one.compartment, theo_sd, est="focei",
              control=list(print=0),
              table=list(npde=TRUE, cwres=TRUE))
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#> 
#> calculating covariance matrix
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> done

print(fit)
#> ── nlmix FOCEi (outer: nlminb) ──
#> 
#>           OBJF      AIC     BIC Log-likelihood Condition#(Cov) Condition#(Cor)
#> FOCEi 116.8116 373.4114 393.591      -179.7057        115.6797        9.731882
#> 
#> ── Time (sec $time): ──
#> 
#>            setup optimize covariance table compress    other
#> elapsed 0.013786 0.485915   0.485916 0.752    0.011 5.071383
#> 
#> ── Population Parameters ($parFixed or $parFixedDf): ──
#> 
#>        Parameter  Est.     SE  %RSE Back-transformed(95%CI) BSV(CV%)
#> tka           Ka 0.474  0.199  42.1       1.61 (1.09, 2.38)     69.2
#> tcl           Cl  1.01 0.0742  7.34       2.75 (2.38, 3.18)     26.8
#> tv             V  3.46 0.0337 0.973         31.8 (29.8, 34)     14.0
#> add.sd           0.695                                0.695         
#>        Shrink(SD)%
#> tka        0.659% 
#> tcl         4.19% 
#> tv          10.6% 
#> add.sd            
#>  
#>   Covariance Type ($covMethod): r,s
#>   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 $shrink 
#>   Information about run found ($runInfo):
#>    • gradient problems with initial estimate and covariance; see $scaleInfo 
#>    • ETAs were reset to zero during optimization; (Can control by foceiControl(resetEtaP=.)) 
#>    • initial ETAs were nudged; (can control by foceiControl(etaNudge=., etaNudge2=)) 
#>   Censoring ($censInformation): No censoring
#>   Minimization message ($message):  
#>     relative convergence (4) 
#> 
#> ── Fit Data (object is a modified tibble): ──
#> # A tibble: 132 × 28
#>   ID     TIME    DV EPRED   ERES   NPDE    NPD    PDE    PD  PRED    RES   WRES
#>   <fct> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl>  <dbl> <dbl> <dbl>  <dbl>  <dbl>
#> 1 1      0     0.74 0.114  0.626  0.468  0.866 0.68   0.807  0     0.74   1.06 
#> 2 1      0.25  2.84 3.66  -0.816 -0.431 -0.394 0.333  0.347  3.29 -0.451 -0.242
#> 3 1      0.57  6.57 5.97   0.604 -1.79   0.332 0.0367 0.63   5.87  0.702  0.284
#> # ℹ 129 more rows
#> # ℹ 16 more variables: IPRED <dbl>, IRES <dbl>, IWRES <dbl>, CPRED <dbl>,
#> #   CRES <dbl>, CWRES <dbl>, eta.ka <dbl>, eta.cl <dbl>, eta.v <dbl>,
#> #   depot <dbl>, center <dbl>, ka <dbl>, cl <dbl>, v <dbl>, tad <dbl>,
#> #   dosenum <dbl>

Changing and fixing parameter values in models

Something that you may want to do is change initial estimates with a model. It is simple to modify the model definition and change them yourself, but you may also want to change them in a specific way; For example try a range of starting values to see how the system behaves (either by full estimation or by a posthoc estimation). In these situations it can be come tedious to modify the models by hand.

nlmixr provides the ability to:

  1. Change parameter estimates before or after running a model. (ie ini(tka=0.5))
  2. Fix parameters to arbitrary values, or estimated values (ie ini(tka=fix(0.5)) or ini(tka=fix))

The easiest way to illustrate this is by showing a few examples of piping changes to the model:

## Example 1 -- Set inital estimate to 0.5 (shown w/posthoc)
one.ka.0.5 <- fit %>%
    ini(tka=0.5) %>%
    nlmixr(est="posthoc", control=list(print=0),
           table=list(cwres=TRUE, npde=TRUE))

print(one.ka.0.5)
## Example 2 -- Fix tka to 0.5 and re-estimate.
one.ka.0.5 <- fit %>%
    ini(tka=fix(0.5)) %>%
    nlmixr(est="focei", control=list(print=0),
           table=list(cwres=TRUE, npde=TRUE))
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#> 
#> calculating covariance matrix
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> done

print(one.ka.0.5)
#> ── nlmix FOCEi (outer: nlminb) ──
#> 
#>           OBJF      AIC      BIC Log-likelihood Condition#(Cov) Condition#(Cor)
#> FOCEi 116.8471 371.4469 388.7437      -179.7234        17.52287        12.09477
#> 
#> ── Time (sec $time): ──
#> 
#>            setup optimize covariance table compress    other
#> elapsed 0.001421 0.288283   0.288285 0.734    0.011 2.658011
#> 
#> ── Population Parameters ($parFixed or $parFixedDf): ──
#> 
#>        Parameter  Est.    SE  %RSE Back-transformed(95%CI) BSV(CV%) Shrink(SD)%
#> tka           Ka   0.5 FIXED FIXED                     0.5     69.2     0.600% 
#> tcl           Cl  1.01 0.312  30.9       2.75 (1.49, 5.07)     26.8      4.21% 
#> tv             V  3.46 0.174  5.04       31.8 (22.6, 44.7)     14.0      10.6% 
#> add.sd           0.695                               0.695                     
#>  
#>   Covariance Type ($covMethod): s
#>   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 $shrink 
#>   Information about run found ($runInfo):
#>    • gradient problems with initial estimate and covariance; see $scaleInfo 
#>    • using S matrix to calculate covariance, can check sandwich or R matrix with $covRS and $covR 
#>    • last objective function was not at minimum, possible problems in optimization 
#>    • ETAs were reset to zero during optimization; (Can control by foceiControl(resetEtaP=.)) 
#>    • initial ETAs were nudged; (can control by foceiControl(etaNudge=., etaNudge2=)) 
#>   Censoring ($censInformation): No censoring
#>   Minimization message ($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 is a modified tibble): ──
#> # A tibble: 132 × 28
#>   ID     TIME    DV EPRED   ERES   NPDE    NPD   PDE    PD  PRED    RES   WRES
#>   <fct> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl>
#> 1 1      0     0.74 0.114  0.626  0.468  0.866  0.68 0.807  0     0.74   1.06 
#> 2 1      0.25  2.84 3.72  -0.885 -0.358 -0.422  0.36 0.337  3.36 -0.520 -0.275
#> 3 1      0.57  6.57 6.04   0.526 -1.75   0.253  0.04 0.6    5.96  0.610  0.246
#> # ℹ 129 more rows
#> # ℹ 16 more variables: IPRED <dbl>, IRES <dbl>, IWRES <dbl>, CPRED <dbl>,
#> #   CRES <dbl>, CWRES <dbl>, eta.ka <dbl>, eta.cl <dbl>, eta.v <dbl>,
#> #   depot <dbl>, center <dbl>, ka <dbl>, cl <dbl>, v <dbl>, tad <dbl>,
#> #   dosenum <dbl>
## Example 3 -- Fix tka to model estimated value and re-estimate.
one.ka.0.5 <- fit %>%
    ini(tka=fix) %>%
    nlmixr(est="focei", control=list(print=0),
           table=list(cwres=TRUE, npde=TRUE))
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#> 
#> calculating covariance matrix
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> done

print(one.ka.0.5)
#> ── nlmix FOCEi (outer: nlminb) ──
#> 
#>           OBJF      AIC      BIC Log-likelihood Condition#(Cov) Condition#(Cor)
#> FOCEi 116.8131 371.4128 388.7096      -179.7064        17.54673        12.12971
#> 
#> ── Time (sec $time): ──
#> 
#>            setup optimize covariance table compress   other
#> elapsed 0.001276 0.284691   0.284693 0.732     0.01 2.73934
#> 
#> ── Population Parameters ($parFixed or $parFixedDf): ──
#> 
#>        Parameter  Est.    SE  %RSE Back-transformed(95%CI) BSV(CV%) Shrink(SD)%
#> tka           Ka 0.474 FIXED FIXED                   0.474     69.2     0.670% 
#> tcl           Cl  1.01 0.313  30.9       2.75 (1.49, 5.08)     26.8      4.19% 
#> tv             V  3.46 0.175  5.05       31.8 (22.6, 44.8)     14.0      10.6% 
#> add.sd           0.695                               0.695                     
#>  
#>   Covariance Type ($covMethod): s
#>   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 $shrink 
#>   Information about run found ($runInfo):
#>    • gradient problems with initial estimate and covariance; see $scaleInfo 
#>    • using S matrix to calculate covariance, can check sandwich or R matrix with $covRS and $covR 
#>    • last objective function was not at minimum, possible problems in optimization 
#>    • ETAs were reset to zero during optimization; (Can control by foceiControl(resetEtaP=.)) 
#>    • initial ETAs were nudged; (can control by foceiControl(etaNudge=., etaNudge2=)) 
#>   Censoring ($censInformation): No censoring
#>   Minimization message ($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 is a modified tibble): ──
#> # A tibble: 132 × 28
#>   ID     TIME    DV EPRED   ERES   NPDE    NPD    PDE    PD  PRED    RES   WRES
#>   <fct> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl>  <dbl> <dbl> <dbl>  <dbl>  <dbl>
#> 1 1      0     0.74 0.114  0.626  0.468  0.866 0.68   0.807  0     0.74   1.06 
#> 2 1      0.25  2.84 3.66  -0.816 -0.431 -0.394 0.333  0.347  3.29 -0.451 -0.242
#> 3 1      0.57  6.57 5.97   0.604 -1.79   0.332 0.0367 0.63   5.87  0.702  0.284
#> # ℹ 129 more rows
#> # ℹ 16 more variables: IPRED <dbl>, IRES <dbl>, IWRES <dbl>, CPRED <dbl>,
#> #   CRES <dbl>, CWRES <dbl>, eta.ka <dbl>, eta.cl <dbl>, eta.v <dbl>,
#> #   depot <dbl>, center <dbl>, ka <dbl>, cl <dbl>, v <dbl>, tad <dbl>,
#> #   dosenum <dbl>
## Example 4 -- Change tka to 0.7 in orginal model function and then estimate
one.ka.0.7 <- one.compartment %>%
    ini(tka=0.7) %>%
    nlmixr(theo_sd, est="focei", control=list(print=0),
           table=list(cwres=TRUE, npde=TRUE))
#> calculating covariance matrix
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> done

print(one.ka.0.7)
#> ── nlmix FOCEi (outer: nlminb) ──
#> 
#>           OBJF     AIC      BIC Log-likelihood Condition#(Cov) Condition#(Cor)
#> FOCEi 116.9872 373.587 393.7666      -179.7935        77.33962        11.86369
#> 
#> ── Time (sec $time): ──
#> 
#>            setup optimize covariance table compress    other
#> elapsed 0.001139 0.494094   0.494095 0.339     0.01 2.323672
#> 
#> ── Population Parameters ($parFixed or $parFixedDf): ──
#> 
#>        Parameter  Est.     SE %RSE Back-transformed(95%CI) BSV(CV%) Shrink(SD)%
#> tka           Ka 0.481  0.213 44.2       1.62 (1.07, 2.46)     70.5      1.61% 
#> tcl           Cl  1.02 0.0737 7.22         2.77 (2.4, 3.2)     28.0      7.96% 
#> tv             V  3.46 0.0516 1.49       31.8 (28.8, 35.2)     15.3      15.1% 
#> add.sd           0.693                               0.693                     
#>  
#>   Covariance Type ($covMethod): r,s
#>   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 $shrink 
#>   Information about run found ($runInfo):
#>    • gradient problems with initial estimate and covariance; see $scaleInfo 
#>    • last objective function was not at minimum, possible problems in optimization 
#>    • ETAs were reset to zero during optimization; (Can control by foceiControl(resetEtaP=.)) 
#>    • initial ETAs were nudged; (can control by foceiControl(etaNudge=., etaNudge2=)) 
#>   Censoring ($censInformation): No censoring
#>   Minimization message ($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 is a modified tibble): ──
#> # A tibble: 132 × 28
#>   ID     TIME    DV EPRED   ERES   NPDE    NPD    PDE    PD  PRED    RES   WRES
#>   <fct> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl>  <dbl> <dbl> <dbl>  <dbl>  <dbl>
#> 1 1      0     0.74 0.113  0.627  0.468  0.878 0.68   0.81   0     0.74   1.07 
#> 2 1      0.25  2.84 3.68  -0.845 -0.332 -0.394 0.37   0.347  3.31 -0.468 -0.246
#> 3 1      0.57  6.57 5.99   0.582 -1.83   0.297 0.0333 0.617  5.89  0.680  0.270
#> # ℹ 129 more rows
#> # ℹ 16 more variables: IPRED <dbl>, IRES <dbl>, IWRES <dbl>, CPRED <dbl>,
#> #   CRES <dbl>, CWRES <dbl>, eta.ka <dbl>, eta.cl <dbl>, eta.v <dbl>,
#> #   depot <dbl>, center <dbl>, ka <dbl>, cl <dbl>, v <dbl>, tad <dbl>,
#> #   dosenum <dbl>

Changing parameter labels and order

For aesthetic reasons, sometimes it is preferred to update parameter labels and the order of parameters. These changes do not affect the estimation of the parameters. They only affect the output tables and order of parameters.

By using these, you can modify a model with model piping and still have the desired output table format ready to use in a report.

For example, you can change the label from "Ka" to "Absorption rate" as follows:

fit %>%
  ini(
    tka <- label("Absorption rate")
  )
#>  ── rxode2-based free-form 2-cmt ODE model ────────────────────────────────────── 
#>  ── Initalization: ──  
#> Fixed Effects ($theta): 
#>       tka       tcl        tv    add.sd 
#> 0.4741772 1.0112664 3.4593293 0.6952432 
#> 
#> Omega ($omega): 
#>           eta.ka    eta.cl      eta.v
#> eta.ka 0.3913202 0.0000000 0.00000000
#> eta.cl 0.0000000 0.0695591 0.00000000
#> eta.v  0.0000000 0.0000000 0.01935147
#> 
#> States ($state or $stateDf): 
#>   Compartment Number Compartment Name
#> 1                  1            depot
#> 2                  2           center
#>  ── μ-referencing ($muRefTable): ──  
#>   theta    eta level
#> 1   tka eta.ka    id
#> 2   tcl eta.cl    id
#> 3    tv  eta.v    id
#> 
#>  ── Model (Normalized Syntax): ── 
#> function() {
#>     ini({
#>         tka <- 0.474177171359262
#>         label("Absorption rate")
#>         tcl <- 1.01126635373108
#>         label("Cl")
#>         tv <- 3.45932933156061
#>         label("V")
#>         add.sd <- c(0, 0.695243197595218)
#>         eta.ka ~ 0.391320225986854
#>         eta.cl ~ 0.0695590964689484
#>         eta.v ~ 0.019351468331187
#>     })
#>     model({
#>         ka <- exp(tka + eta.ka)
#>         cl <- exp(tcl + eta.cl)
#>         v <- exp(tv + eta.v)
#>         d/dt(depot) = -ka * depot
#>         d/dt(center) = ka * depot - cl/v * center
#>         cp = center/v
#>         cp ~ add(add.sd)
#>     })
#> }

And, if you’d prefer for volume to come before clearance in the parameter table (fit$parFixed), you can change that, too.

fit %>%
  ini(
    tv <- label("Central volume"),
    append = "tcl"
  )
#>  ── rxode2-based free-form 2-cmt ODE model ────────────────────────────────────── 
#>  ── Initalization: ──  
#> Fixed Effects ($theta): 
#>       tka       tcl        tv    add.sd 
#> 0.4741772 1.0112664 3.4593293 0.6952432 
#> 
#> Omega ($omega): 
#>           eta.ka    eta.cl      eta.v
#> eta.ka 0.3913202 0.0000000 0.00000000
#> eta.cl 0.0000000 0.0695591 0.00000000
#> eta.v  0.0000000 0.0000000 0.01935147
#> 
#> States ($state or $stateDf): 
#>   Compartment Number Compartment Name
#> 1                  1            depot
#> 2                  2           center
#>  ── μ-referencing ($muRefTable): ──  
#>   theta    eta level
#> 1   tka eta.ka    id
#> 2   tcl eta.cl    id
#> 3    tv  eta.v    id
#> 
#>  ── Model (Normalized Syntax): ── 
#> function() {
#>     ini({
#>         tka <- 0.474177171359262
#>         label("Ka")
#>         tcl <- 1.01126635373108
#>         label("Cl")
#>         tv <- 3.45932933156061
#>         label("Central volume")
#>         add.sd <- c(0, 0.695243197595218)
#>         eta.ka ~ 0.391320225986854
#>         eta.cl ~ 0.0695590964689484
#>         eta.v ~ 0.019351468331187
#>     })
#>     model({
#>         ka <- exp(tka + eta.ka)
#>         cl <- exp(tcl + eta.cl)
#>         v <- exp(tv + eta.v)
#>         d/dt(depot) = -ka * depot
#>         d/dt(center) = ka * depot - cl/v * center
#>         cp = center/v
#>         cp ~ add(add.sd)
#>     })
#> }

See the documentation for ini for more about how you can modify parameters with model piping.

Changing model features

When developing models, often you add and remove between subject variability to parameters, add covariates to the effects, and/or change the residual errors. You can change lines in the model by piping the fit or the nlmixr model specification function to a model

Adding or Removing between subject variability

Often in developing a model you add and remove between subject variability to certain model parameters. For example, you could remove the between subject variability in the ka parameter by changing that line in the model;

For example to remove a eta from a prior fit or prior model specification function, simply pipe it to the model function. You can then re-estimate by piping it to the nlmixr function again.

## Remove eta.ka on ka
noEta <- fit %>%
    model(ka <- exp(tka)) %>%
    nlmixr(est="focei", control=list(print=0),
           table=list(cwres=TRUE, npde=TRUE))
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> 
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
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#> 
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> 
#> calculating covariance matrix
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> done

print(noEta)
#> ── nlmix FOCEi (outer: nlminb) ──
#> 
#>           OBJF      AIC      BIC Log-likelihood Condition#(Cov) Condition#(Cor)
#> FOCEi 176.5777 431.1775 448.4743      -209.5887        33.12954        7.050454
#> 
#> ── Time (sec $time): ──
#> 
#>            setup optimize covariance table compress    other
#> elapsed 0.001353 0.303991   0.303992 0.751    0.009 3.568664
#> 
#> ── Population Parameters ($parFixed or $parFixedDf): ──
#> 
#>        Parameter  Est.     SE %RSE Back-transformed(95%CI) BSV(CV%) Shrink(SD)%
#> tka           Ka 0.433  0.167 38.6       1.54 (1.11, 2.14)                     
#> tcl           Cl 0.988  0.076  7.7       2.69 (2.31, 3.12)     30.4      7.95% 
#> tv             V  3.48 0.0481 1.38       32.4 (29.5, 35.6)     15.4      7.24% 
#> add.sd            1.02                                1.02                     
#>  
#>   Covariance Type ($covMethod): r,s
#>   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 $shrink 
#>   Information about run found ($runInfo):
#>    • gradient problems with initial estimate and covariance; see $scaleInfo 
#>    • last objective function was not at minimum, possible problems in optimization 
#>    • ETAs were reset to zero during optimization; (Can control by foceiControl(resetEtaP=.)) 
#>    • initial ETAs were nudged; (can control by foceiControl(etaNudge=., etaNudge2=)) 
#>   Censoring ($censInformation): No censoring
#>   Minimization message ($message):  
#>     relative convergence (4) 
#> 
#> ── Fit Data (object is a modified tibble): ──
#> # A tibble: 132 × 27
#>   ID     TIME    DV EPRED   ERES   NPDE    NPD    PDE    PD  PRED    RES   WRES
#>   <fct> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl>  <dbl> <dbl> <dbl>  <dbl>  <dbl>
#> 1 1      0     0.74 0.167  0.573  0.126  0.477 0.55   0.683  0     0.74   0.724
#> 2 1      0.25  2.84 3.18  -0.342 -1.36  -0.253 0.0867 0.4    3.12 -0.282 -0.250
#> 3 1      0.57  6.57 5.68   0.888 -0.524  0.674 0.3    0.75   5.62  0.954  0.722
#> # ℹ 129 more rows
#> # ℹ 15 more variables: IPRED <dbl>, IRES <dbl>, IWRES <dbl>, CPRED <dbl>,
#> #   CRES <dbl>, CWRES <dbl>, eta.cl <dbl>, eta.v <dbl>, depot <dbl>,
#> #   center <dbl>, ka <dbl>, cl <dbl>, v <dbl>, tad <dbl>, dosenum <dbl>

Of course you could also add an eta on a parameter in the same way;

addBackKa <- noEta %>%
    model({ka <- exp(tka + bsv.ka)}) %>%
    ini(bsv.ka=0.1) %>%
    nlmixr(est="focei", control=list(print=0),
           table=list(cwres=TRUE, npde=TRUE))
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
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#> 
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> 
#> calculating covariance matrix
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> done

print(addBackKa)
#> ── nlmix FOCEi (outer: nlminb) ──
#> 
#>           OBJF      AIC      BIC Log-likelihood Condition#(Cov) Condition#(Cor)
#> FOCEi 116.8978 373.4976 393.6772      -179.7488        50.95108        7.394634
#> 
#> ── Time (sec $time): ──
#> 
#>            setup optimize covariance table compress    other
#> elapsed 0.001378 0.479759   0.479761 0.774    0.011 4.982102
#> 
#> ── Population Parameters ($parFixed or $parFixedDf): ──
#> 
#>        Parameter  Est.     SE %RSE Back-transformed(95%CI) BSV(CV%) Shrink(SD)%
#> tka           Ka 0.462  0.207 44.9       1.59 (1.06, 2.38)     69.1     0.451% 
#> tcl           Cl  1.01 0.0715 7.08       2.74 (2.39, 3.16)     27.4      6.47% 
#> tv             V  3.46 0.0505 1.46       31.9 (28.9, 35.2)     15.0      13.8% 
#> add.sd           0.693                               0.693                     
#>  
#>   Covariance Type ($covMethod): r,s
#>   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 $shrink 
#>   Information about run found ($runInfo):
#>    • gradient problems with initial estimate and covariance; see $scaleInfo 
#>    • last objective function was not at minimum, possible problems in optimization 
#>    • ETAs were reset to zero during optimization; (Can control by foceiControl(resetEtaP=.)) 
#>    • initial ETAs were nudged; (can control by foceiControl(etaNudge=., etaNudge2=)) 
#>   Censoring ($censInformation): No censoring
#>   Minimization message ($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 is a modified tibble): ──
#> # A tibble: 132 × 28
#>   ID     TIME    DV EPRED   ERES   NPDE    NPD   PDE    PD  PRED    RES   WRES
#>   <fct> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl>
#> 1 1      0     0.74 0.114  0.626  0.468  0.878 0.68  0.81   0     0.74   1.07 
#> 2 1      0.25  2.84 3.66  -0.825 -0.866 -0.271 0.193 0.393  3.25 -0.411 -0.222
#> 3 1      0.57  6.57 5.96   0.611 -1.48   0.314 0.07  0.623  5.81  0.758  0.306
#> # ℹ 129 more rows
#> # ℹ 16 more variables: IPRED <dbl>, IRES <dbl>, IWRES <dbl>, CPRED <dbl>,
#> #   CRES <dbl>, CWRES <dbl>, eta.cl <dbl>, eta.v <dbl>, bsv.ka <dbl>,
#> #   depot <dbl>, center <dbl>, ka <dbl>, cl <dbl>, v <dbl>, tad <dbl>,
#> #   dosenum <dbl>

You can see the name change by examining the omega matrix:

addBackKa$omega
#>            eta.cl      eta.v    bsv.ka
#> eta.cl 0.07240395 0.00000000 0.0000000
#> eta.v  0.00000000 0.02217241 0.0000000
#> bsv.ka 0.00000000 0.00000000 0.3907193

Note that new between subject variability parameters are distinguished from other types of parameters (ie population parameters, and individual covariates) by their name. Parameters starting or ending with the following names are assumed to be between subject variability parameters:

  • eta (from NONMEM convention)
  • ppv (per patient variability)
  • psv (per subject variability)
  • iiv (inter-individual variability)
  • bsv (between subject variability)
  • bpv (between patient variability)

Adding Covariate effects

## Note currently cov is needed as a prefix so nlmixr knows this is an
## estimated parameter not a parameter
wt70 <- fit %>%
  model({cl <- exp(tcl + eta.cl)*(WT/70)^covWtPow}) %>%
  ini(covWtPow=fix(0.75)) %>%
  ini(tka=fix(0.5)) %>%
  nlmixr(est="focei", control=list(print=0),
         table=list(cwres=TRUE, npde=TRUE))
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> 
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#> 
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> 
#> calculating covariance matrix
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> done

print(wt70)
#> ── nlmix FOCEi (outer: nlminb) ──
#> 
#>           OBJF      AIC      BIC Log-likelihood Condition#(Cov) Condition#(Cor)
#> FOCEi 116.2103 370.8101 388.1069      -179.4051        3.142512        2.615431
#> 
#> ── Time (sec $time): ──
#> 
#>            setup optimize covariance table compress    other
#> elapsed 0.001354 0.294427   0.294428  0.74    0.009 3.417791
#> 
#> ── Population Parameters ($parFixed or $parFixedDf): ──
#> 
#>          Parameter  Est.     SE  %RSE Back-transformed(95%CI) BSV(CV%)
#> tka             Ka   0.5  FIXED FIXED                     0.5     69.4
#> tcl             Cl  1.02 0.0777  7.62       2.77 (2.38, 3.23)     26.8
#> tv               V  3.46 0.0576  1.66       31.8 (28.4, 35.6)     14.0
#> add.sd             0.695                                0.695         
#> covWtPow            0.75  FIXED FIXED                    0.75         
#>          Shrink(SD)%
#> tka           1.26% 
#> tcl           6.79% 
#> tv            12.6% 
#> add.sd              
#> covWtPow            
#>  
#>   Covariance Type ($covMethod): r,s
#>   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 $shrink 
#>   Information about run found ($runInfo):
#>    • gradient problems with initial estimate and covariance; see $scaleInfo 
#>    • last objective function was not at minimum, possible problems in optimization 
#>    • ETAs were reset to zero during optimization; (Can control by foceiControl(resetEtaP=.)) 
#>    • initial ETAs were nudged; (can control by foceiControl(etaNudge=., etaNudge2=)) 
#>   Censoring ($censInformation): No censoring
#>   Minimization message ($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 is a modified tibble): ──
#> # A tibble: 132 × 29
#>   ID     TIME    DV EPRED   ERES   NPDE    NPD    PDE    PD  PRED    RES   WRES
#>   <fct> <dbl> <dbl> <dbl>  <dbl>  <dbl>  <dbl>  <dbl> <dbl> <dbl>  <dbl>  <dbl>
#> 1 1      0     0.74 0.114  0.626  0.422  0.866 0.663  0.807  0     0.74   1.06 
#> 2 1      0.25  2.84 3.72  -0.885 -0.297 -0.422 0.383  0.337  3.36 -0.520 -0.274
#> 3 1      0.57  6.57 6.03   0.541 -1.79   0.271 0.0367 0.607  5.95  0.622  0.252
#> # ℹ 129 more rows
#> # ℹ 17 more variables: IPRED <dbl>, IRES <dbl>, IWRES <dbl>, CPRED <dbl>,
#> #   CRES <dbl>, CWRES <dbl>, eta.ka <dbl>, eta.cl <dbl>, eta.v <dbl>,
#> #   depot <dbl>, center <dbl>, ka <dbl>, cl <dbl>, v <dbl>, tad <dbl>,
#> #   dosenum <dbl>, WT <dbl>

Changing residual errors

Changing the residual errors is also just as easy, by simply specifying the error you wish to change:

## Since there are 0 predictions in the data, these are changed to
## 0.0150 to show proportional error change.
d <- theo_sd
d$DV[d$EVID == 0 & d$DV == 0] <- 0.0150

addPropModel <- fit %>%
    model({cp ~ add(add.err)+prop(prop.err)}) %>%
    ini(prop.err=0.1) %>%
    nlmixr(d,est="focei",
           control=list(print=0),
           table=list(cwres=TRUE, npde=TRUE))
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> 
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> 
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> 
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> 
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#> 
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#> 
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#> 
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> 
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> 
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> 
#> calculating covariance matrix
#> [====|====|====|====|====|====|====|====|====|====] 0:00:00 
#> done

print(addPropModel)
#> ── nlmix FOCEi (outer: nlminb) ──
#> 
#>           OBJF     AIC      BIC Log-likelihood Condition#(Cov) Condition#(Cor)
#> FOCEi 104.9613 363.561 386.6235      -173.7805        29.38653        16.08647
#> 
#> ── Time (sec $time): ──
#> 
#>            setup optimize covariance table compress    other
#> elapsed 0.001299 0.531543   0.531545 0.796     0.01 7.862613
#> 
#> ── Population Parameters ($parFixed or $parFixedDf): ──
#> 
#>          Parameter  Est.    SE %RSE Back-transformed(95%CI) BSV(CV%)
#> tka             Ka 0.424 0.326 76.9       1.53 (0.806, 2.9)     72.2
#> tcl             Cl  1.02 0.111 10.9       2.77 (2.23, 3.44)     26.4
#> tv               V  3.46 0.176 5.08       31.8 (22.6, 44.9)     13.4
#> add.err            0.315                              0.315         
#> prop.err            0.12                               0.12         
#>          Shrink(SD)%
#> tka           3.73% 
#> tcl           1.93% 
#> tv            14.3% 
#> add.err             
#> prop.err            
#>  
#>   Covariance Type ($covMethod): r,s
#>   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 $shrink 
#>   Information about run found ($runInfo):
#>    • gradient problems with initial estimate and covariance; see $scaleInfo 
#>    • last objective function was not at minimum, possible problems in optimization 
#>    • ETAs were reset to zero during optimization; (Can control by foceiControl(resetEtaP=.)) 
#>    • initial ETAs were nudged; (can control by foceiControl(etaNudge=., etaNudge2=)) 
#>   Censoring ($censInformation): No censoring
#>   Minimization message ($message):  
#>     relative convergence (4) 
#> 
#> ── Fit Data (object is a modified tibble): ──
#> # A tibble: 132 × 28
#>   ID     TIME    DV  EPRED   ERES   NPDE    NPD   PDE    PD  PRED    RES   WRES
#>   <fct> <dbl> <dbl>  <dbl>  <dbl>  <dbl>  <dbl> <dbl> <dbl> <dbl>  <dbl>  <dbl>
#> 1 1      0     0.74 0.0516  0.688  0.954  2.22  0.83  0.987  0     0.74   2.35 
#> 2 1      0.25  2.84 3.52   -0.679 -0.573 -0.305 0.283 0.38   3.16 -0.317 -0.177
#> 3 1      0.57  6.57 5.82    0.751 -0.515  0.358 0.303 0.64   5.69  0.885  0.350
#> # ℹ 129 more rows
#> # ℹ 16 more variables: IPRED <dbl>, IRES <dbl>, IWRES <dbl>, CPRED <dbl>,
#> #   CRES <dbl>, CWRES <dbl>, eta.ka <dbl>, eta.cl <dbl>, eta.v <dbl>,
#> #   depot <dbl>, center <dbl>, ka <dbl>, cl <dbl>, v <dbl>, tad <dbl>,
#> #   dosenum <dbl>

There is much more you can do with piping. For a more complete discussion see see rxode2 piping documentation. Since rxode2 and nlmixr2 models can share the same functional form the piping applies to fits as well as model definitions.