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     `echo: true`, which shows every code chunk. Regenerate both PDFs with
     `quarto render` from the exercises/ folder. -->

---
title: "Vancomycin exposure — a mini report (solution)"
author: "Your Name"
date: today
format:
  pdf:
    toc: false
    number-sections: true
execute:
  echo: true
---

# Introduction

A single intravenous dose of a drug that follows first-order elimination is described by
@eq-decay, where $D$ is the dose, $V_d$ the volume of distribution and $k_e$ the
elimination rate constant.

$$C(t) = \frac{D}{V_d}\,e^{-k_e t}$$ {#eq-decay}

# Methods

Concentrations were read from `data/patient-concentrations.csv`. The elimination rate
constant was estimated by least squares on the log-transformed concentrations, and the
half-life followed from @eq-thalf.

$$t_{1/2} = \frac{\ln 2}{k_e}$$ {#eq-thalf}

```{r}
#| label: fit

conc <- read.csv("data/patient-concentrations.csv")

fit <- lm(log(conc_mgL) ~ time_h, data = conc)
c0 <- exp(unname(coef(fit)[1]))
k_el <- -unname(coef(fit)[2])
half_life <- log(2) / k_el
```

# Results

@fig-conc shows the observed concentrations with the fitted curve. The fitted initial
concentration is `r round(c0, 1)` mg/L and the estimated half-life is
`r round(half_life, 1)` h.

```{r}
#| label: fig-conc
#| fig-cap: "Observed concentrations and the fitted mono-exponential decay."
#| fig-width: 6
#| fig-height: 3.4

tt <- seq(0, 12, length.out = 200)

par(mar = c(4, 4.2, 1, 1), las = 1)
plot(conc$time_h, conc$conc_mgL,
  pch = 19, col = "#1b6ca8", cex = 1.1,
  xlab = "Time after dose (h)", ylab = "Concentration (mg/L)"
)
lines(tt, c0 * exp(-k_el * tt), col = "#b3502a", lwd = 2)
```

# Summary

| Quantity | Estimate |
|--------------------|---------:|
| $C_0$ (mg/L)       | `r round(c0, 1)` |
| $k_e$ (h$^{-1}$)   | `r round(k_el, 3)` |
| $t_{1/2}$ (h)      | `r round(half_life, 1)` |

: Fitted parameters {#tbl-params}

The fitted values in @tbl-params are computed at render time, so they cannot drift out of
step with the figure in @fig-conc.