In nlmixrdevelopment/nlmixr: Nonlinear Mixed Effects Models in Population PK/PD

knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  message = FALSE,
  warning = FALSE,
  out.width = "100%"
  )

## These options cache the models and the model simulations in R
## To run the actual models on your system, take the save options off.
## nlmixrVersion <- as.character(packageVersion("nlmixr"));
## options(nlmixr.save=TRUE,
##         nlmixr.save.dir=file.path(system.file(package="nlmixr"), nlmixrVersion));
## if (!dir.exists(getOption("nlmixr.save.dir")))
    ## dir.create(getOption("nlmixr.save.dir"))

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(nlmixr)

one.compartment <- function() {
  ini({
    tka <- 0.45 # Log Ka
    tcl <- 1 # Log Cl
    ## This works with interactive models
    ## You may also label the preceding line with label("label text")
    tv <- 3.45; # log V
    ## the label("Label name") works with all models
    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))

print(fit)

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:

Change parameter estimates before or after running a model. (ie ini(tka=0.5))
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))

print(one.ka.0.5)

## 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))

print(one.ka.0.5)

## 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))

print(one.ka.0.7)

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))

print(noEta)

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))

print(addBackKa)

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

addBackKa$omega

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 %>% ## FIXME could be based on if it finds the covarite in the last used nlmixr data.
  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))

print(wt70)

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))

print(addPropModel)