---
title: "Theophylline population PK model"
output:
  bookdown::word_document2:
    number_sections: false
  bookdown::html_document2:
    number_sections: false
  bookdown::pdf_document2:
    number_sections: false
    toc: false
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(echo = FALSE, message = FALSE, warning = FALSE,
                      fig.width = 6, fig.height = 4)
options(knitr.kable.NA = "")
library(nlmixr2)
library(nlmixr2plot)
library(nlmixr2extra)

# Model equations that work in Word, HTML and PDF.  Pandoc drops a bare
# align* environment when writing .docx, but converts display math
# ($$ ... $$) to native Word equations, so use an aligned block in
# display math for every format.  For Word, drop the alignment points
# (&, but not an escaped \& inside text) so the equations also display
# correctly in LibreOffice.
modelEquations <- function(x) {
  eq <- knitr::knit_print(x)
  if (knitr::pandoc_to("docx")) {
    eq <- gsub("(?<!\\\\)&", "", eq, perl = TRUE)
  }
  eq <- sub("\\begin{align*}", "$$\n\\begin{aligned}", eq, fixed = TRUE)
  eq <- sub("\\end{align*}", "\\end{aligned}\n$$", eq, fixed = TRUE)
  knitr::asis_output(eq)
}
```

```{r fit, include = FALSE}
one.cmt <- function() {
  ini({
    tka <- log(1.57)
    tcl <- log(2.72)
    tv <- log(31.5)
    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(central) <- ka * depot - cl / v * central
    cp <- central / v
    cp ~ add(add.sd)
  })
}
fit <- nlmixr2(one.cmt, nlmixr2data::theo_sd, est = "saem",
               control = saemControl(print = 0))
```

# Methods

Theophylline concentrations from `r length(unique(fit$ID))` subjects
were described by a one-compartment model with first-order absorption
(Figure \@ref(fig:diagram)), estimated with `r toupper(fit$est)` in nlmixr2.

```{r diagram, fig.cap = "Structure of the final model."}
modelDiagram(fit, engine = "ggplot2", labels = TRUE)
```

The model is defined by the following equations:

```{r equations}
modelEquations(fit)
```

# Results

The objective function value was `r round(fit$objf, 2)`.  Table
\@ref(tab:estimates) lists the final parameter estimates.

```{r estimates}
knitr::kable(fit$parFixedDf[, c("Back-transformed", "CI Lower",
                                "CI Upper", "%RSE", "BSV(CV%)")],
             digits = 3, caption = "Final parameter estimates.")
```