README.Rmd

---
title: "FMI330"
output: github_document
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```

> Example R scripts to create a dose-response curve and extract EC~X~-values.

## Installing and loading packages

Before the fun-part of dose-response modelling, a handful of add-on packages have to be installed. `tidyverse` and `readxl` provide functionalities for easy data handling and reading straight from .xlsx files, respectively. `drc` is used to perform dose-response modelling, and `lmtest` and `sandwich` provide additional functionalities for standard error and confidence interval estimations.

```{r,eval=FALSE}
install.packages(c("tidyverse", "multcomp", "drc", "lmtest", "sandwich"))
```

After succesful installation, the packages need to be loaded by using the `library()` functionality. 

```{r,message=FALSE}
library(multcomp)
library(tidyverse)
library(readxl)
library(drc)
library(lmtest)
library(sandwich)
```

We are now ready to load the data!

## Loading and cleaning up the data

First, we load the raw data and inspect it.

```{r}
data <- read_xlsx(path = "Data/Diuron_DRC_Data_RevLee.xlsx", sheet = "Summary") %>% 
  select(-SampleName, -Replicate) %>% 
  rename(Concentration = concentration, 
         Fronds_number_inhibition = FN_Normalization_PERCENT,
         Frond_size_inhibition = FS_Normalization_PERCENT,
         Photosystem_II_inhibition = PSII_Normalization_PERCENT,
         ROS_formation = `ROS_Formation_Fold increase`,
         Chlorophyll_A_inhibition = `Chlorophyll a_inhibition_PERCENT`,
         Chlorophyll_B_inhibition = `Chlorophyll b_inhibition_PERCENT`, 
         Carotenoids_inhibition = Carotenoids_inhibition_PERCENT) %>% 
  filter(!str_detect(Note, "CT")) %>% 
  select(-Note)

data
```


# Fronds number
## Visualizing the raw data

Let's take a look at the reproduction along the stressor gradient. Note that this plot is meant to help you understand the data, and is not part of your reports!
```{r}
data %>% 
  ggplot() +
  geom_point(mapping = aes(x = Concentration, y = Fronds_number_inhibition), size = 2, alpha = 0.5) +
  labs(x = "Diuron (mg/L)", 
       y = "Fronds number inhibition (%)") +
  theme_light()
```

## LOEC and NOEC derivation

Based on the figure of the raw data, we can see that there is a strong decreasing trend in reproduction with increasing Concentration. To find out statistically significant differences, we need to run a ANOVA with Dunnett's *post hoc* test.

In the first step, we have to transfrom the `Concentration` from a numeric column to a (categorical) factor column; otherwise it is not possible to run a *post hoc* analysis. This happens inside the `mutate()` function. In the next step, we run a ANOVA. But instead of using a convenience function, we do it more manual, by fitting a linear model using `lm()`. Note that a ANOVA is nothing else than a linear model. Within the linear model, the contrast treatment specifies that Concentration `"0"` contains the control values. The linear model is then used in a generalized linear hypothesis test with the `glht()` function. Inside this function, the multiple comparison is set to Dunnett's contrasts (everything vs. the control), and variance-covariance matrix is updated using the sandwich estimator. In the final step, the *p*-values are adjusted for multiple comparisons using Holm's method. 

```{r}
data %>% 
  mutate(Concentration = fct_relevel(as.character(Concentration), "0")) %>% 
  lm(formula = Fronds_number_inhibition ~ Concentration, data = ., contrasts = list(Concentration = "contr.treatment")) %>% 
  glht(linfct = mcp(Concentration = "Dunnett"), vcov = sandwich) %>% 
  summary(test = adjusted(type = "holm"))
```

From the results we can deduce that the LOEC has a concentration of 0.01 mg/L. As this is the lowest treatment concentration, the NOEC has to be < 0.01 mg/L.

## Dose-response model fitting

From the visualization of the raw data, we see a very clear monotonic dose-response pattern! Let's fit a four-parametric log-logistic model using the `drc` package. We then take a look at the results (i.e., the four parameters, or coefficients) using `coeftest` with adjusted variance-covariance matrix.

```{r}
fronds_number_inhibition.drm <- data %>% 
  drm(formula = Fronds_number_inhibition ~ Concentration, data = .,
      fct = LL.4(names = c("Slope", "Lower Limit", "Upper Limit", "EC50")))

fronds_number_inhibition.drm %>% 
  coeftest(vcov. = sandwich)
```

The fitted values for the parameters seem to make sense. The lower and upper limit are in accordance with what we observe in the raw data, and the EC~50~ value is also realistic. 

## EC~X~ derivation

Let's take a look at the corrected parameter estimates and the EC~5~, EC~10~, and EC~50~ values with 95% confidence limits.
```{r}
fronds_number_inhibition.drm %>% 
  ED(respLev = c(5, 10, 50), interval = "delta", vcov. = sandwich)
```

## Plotting of the dose-response curve

Now that we got all necessary information, let's plot the dose-response curve. This is *not* straight forward, as it requires advanced use of the `predict()` function, so feel free to copy-paste.

```{r}
data.frame(Concentration = seq(from = min(data$Concentration),
                               to = max(data$Concentration),
                               length.out = 1000)) %>% 
  mutate(fit = predict(fronds_number_inhibition.drm, newdata = .), 
         lwr = predict(fronds_number_inhibition.drm, newdata = ., interval = "confidence", vcov. = sandwich)[, 2], 
         upr = predict(fronds_number_inhibition.drm, newdata = ., interval = "confidence", vcov. = sandwich)[, 3]) %>% 
  ggplot() +
  geom_ribbon(mapping = aes(x = Concentration, ymin = lwr, ymax = upr), alpha = 0.2) +
  geom_line(mapping = aes(x = Concentration, y = fit), size = 1) +
  geom_point(mapping = aes(x = Concentration, y = Fronds_number_inhibition), data = data, size = 2, alpha = 0.5) +
  labs(x = "Diuron (mg/L)", 
       y = "Fronds number inhibition (%)") +
  theme_light()
```

Looks good, so let's save the plot.
```{r}
ggsave("Figures/Fronds number inhibition.png", height = 5.25, width = 7, units = "in", dpi = 600, type = "cairo-png")
```