dmso-analysis.qmd

---
title: "Analysis of DMSO data"
format: pdf
execute:
  eval: false
editor_options: 
  chunk_output_type: console
---

# Setup

```{r}
# Packages used
library(tidyverse)
library(nimble)
library(MCMCvis)
library(ggdist)
library(patchwork)

# Data
data <- 
  read_csv("dmso.csv") |>
  mutate(Species = factor(Species, levels = c("S. pneumoniae", "P. aeruginosa")),
         Antibiotic = factor(Antibiotic, levels = c("Ampicillin", "Getamycin")))

# Metadata
n.species <- 2
n.dmso <- 4
alpha <- 0.5  # Scale parameter for hormesis

# Prediction ranges for plots
n.pred <- 200
xd <- 10 ^ seq(log10(0.0375), log10(37.5), length.out = n.pred)  # DMSO
xa <- 10 ^ seq(log10(0.0225), log10(24), length.out = n.pred)    # Antibiotic
```

# Models

## Experiment 1: DMSO only

```{r}
# Data prep
#data1 <- 
  data |>
  filter(Type == "Variable",
         Concentration == 0) |>
  mutate(Trial = sort(c(rep(1:14, 10))))
# Exclude outliers for model
data1.i <- 
  data1 |>
  filter(Inhibition > -100)
```

### Absorbance

#### Model

```{r}
a1code <- nimbleCode({
  
  # PRIORS
  
  # Intercepts (species-specific)
  for (i in 1:n.species) {
      
    # Start and end absorbance
    c.alpha[i] <- 0
    d.alpha[i] ~ dnorm(1, 1)
    
    # Hormesis
    w.alpha[i] ~ dbern(0.5)
    f.alpha[i] ~ dexp(1)
    
    # e and slope
    e.alpha[i] ~ dunif(0, max.x)
    b.alpha[i] ~ dexp(0.1)

  } # i
  
  # Non-centered parameterization for multivariate random trial effects
  for (j in 1:4) {
    sigma.trial[j] ~ dexp(1)
  }
  chol[1:4,1:4] ~ dlkj_corr_cholesky(1.5, 4)
  cor[1:4,1:4] <- t(chol[1:4,1:4]) %*% chol[1:4,1:4]  # Correlation matrix
  for (i in 1:n.trial) {
    for (j in 1:4) {
      z[j,i] ~ dnorm(0, 1)
    } # j
    eps.trial[1:4,i] <- diag(sigma.trial[1:4]) %*% t(chol[1:4,1:4]) %*% z[1:4,i]
  } # i
  
  # Residual
  sigma ~ dexp(1)
  
  # LIKELIHOOD
  
  for (i in 1:n.obs) {
    
    # Start and end inhibition
    c[i] <- c.alpha[species[i]]
    d[i] <- d.alpha[species[i]] + eps.trial[1,trial[i]]
    
    # Hormesis and RJMCMC inclusion
    f[i] <- f.alpha[species[i]] + eps.trial[2,trial[i]]
    w[i] <- w.alpha[species[i]]
    
    # e and slope
    e[i] <- e.alpha[species[i]] + eps.trial[3,trial[i]]
    b[i] <- b.alpha[species[i]] + eps.trial[4,trial[i]]
    
    # Cedergreen–Ritz–Streibig model
    mu[i] <- c[i] + (d[i] - c[i] + w[i] * f[i] * exp(-1 / x[i] ^ alpha)) / (1 + (x[i] / e[i]) ^ b[i])
    y[i] ~ dnorm(mu[i], sd = sigma)
    
  } # i
  
  # DERIVED QUANTITIES
  
  e.diff <- e.alpha[2] - e.alpha[1]
  
})

# Data
str(a1data <- list(y = data1$Absorbance))

# Constant
str(a1consts <- list(n.obs = nrow(data1),
                     n.species = n.species,
                     n.trial = max(data1$Trial),
                     x = data1$DMSO,
                     max.x = max(data1$DMSO),
                     species = as.numeric(data1$Species),
                     trial = data1$Trial,
                     alpha = alpha))

# Initial values
a1inits <- list(d.alpha = rep(1, n.species),
                sigma.trial = rep(0.1, 4))

# Parameters to monitor
a1mons <- c("b.alpha", "c.alpha", "d.alpha", "e.alpha", "f.alpha", "w.alpha",
            "sigma.trial", "cor", "sigma",
            "e.diff")

# Model
Ca1model <- compileNimble(nimbleModel(a1code, a1consts, a1data, a1inits))
a1conf <- configureMCMC(Ca1model, monitors = a1mons)
configureRJ(a1conf, "f.alpha", "w.alpha")
Ca1mcmc <- compileNimble(buildMCMC(a1conf), project = Ca1model)

# Run
a1samples <- runMCMC(Ca1mcmc, niter = 60000, nburnin = 10000, thin = 10, nchains = 2)

# Summary and traceplots
print(a1sum <- MCMCsummary(a1samples, round = 3))
write.csv(a1sum, "a1sum.csv")
#MCMCtrace(adSamples, pdf = F, Rhat = T, n.eff = T, ind = T)
```

#### Plot

```{r}
# Setup
a1draws <- do.call(rbind, a1samples)

# Predictions
a1pred <- array(NA, c(n.pred, nrow(a1draws), n.species))
for (i in 1:n.pred) {
  for (k in 1:n.species) {
      
      a1pred[i,,k] <- a1draws[,paste0("c.alpha[", k, "]")] + (a1draws[,paste0("d.alpha[", k, "]")] - a1draws[,paste0("c.alpha[", k, "]")] + a1draws[,paste0("f.alpha[", k, "]")] * exp(-1 / xd[i] ^ alpha)) / (1 + (xd[i] / a1draws[,paste0("e.alpha[", k, "]")]) ^ a1draws[,paste0("b.alpha[", k, "]")])
      
  } # k
} # i

# Plot 1a
a1plot1 <- 
  tibble(pred = c(a1pred[,,1]),
         dmso = rep(xd, nrow(a1draws))) |>
  ggplot(aes(x = dmso)) +
  geom_jitter(aes(x = DMSO, y = Absorbance),
              data = data1 |> filter(Species == "S. pneumoniae"),
              color = "#333333",
              shape = 16,
              size = 3/4,
              width = 1/50,
              alpha = 3/4) +
  stat_lineribbon(aes(y = pred),
                  .width = 0.95,
                  point_interval = median_qi,
                  color = "#333333",
                  fill = "#333333",
                  size = 3/4,
                  alpha = 1/3,
                  show.legend = F) +
  scale_x_log10(expand = c(0, 0)) +
  scale_y_continuous(breaks = seq(0, 0.5, 0.5),
                     expand = c(0, 0)) +
  coord_cartesian(ylim = c(-0.1, 0.6)) +
  labs(subtitle = expression(italic("S. pneumoniae")),
       x = "DMSO (%)",
       y = "Absorbance (OD 595)")

# Plot 1b
a1plot2 <- 
  tibble(pred = c(a1pred[,,2]),
         dmso = rep(xd, nrow(a1draws))) |>
  ggplot(aes(x = dmso)) +
  geom_jitter(aes(x = DMSO, y = Absorbance),
              data = data1 |> filter(Species == "P. aeruginosa", Concentration == 0),
              shape = 16,
              size = 3/4,
              width = 1/50,
              alpha = 2/3) +
  stat_lineribbon(aes(y = pred),
                  .width = 0.95,
                  point_interval = median_qi,
                  color = "#333333",
                  fill = "#333333",
                  size = 3/4,
                  alpha = 1/3,
                  show.legend = F) +
  scale_x_log10(expand = c(0, 0)) +
  scale_y_continuous(breaks = seq(0, 1.5, 0.5),
                     expand = c(0, 0)) +
  coord_cartesian(ylim = c(-0.1, 1.6)) +
  labs(subtitle = expression(italic("P. aeruginosa")),
       x = "DMSO (%)",
       y = "Absorbance (OD 595)")
```

### Inhibition

#### Model

```{r}
# Code
i1code <- nimbleCode({
  
  # PRIORS
  
  # Intercepts (species-specific)
  for (i in 1:n.species) {
    
    # Start and end inhibition
    c.alpha[i] <- 100
    d.alpha[i] ~ dnorm(0, 100)
    
    # Hormesis and RJMCMC inclusion
    f.alpha[i] ~ dexp(0.01)
    w.alpha[i] ~ dbern(0.5)
    
    # ED50 and slope
    e.alpha[i] ~ dunif(0, max.x)
    b.alpha[i] ~ dexp(0.1)
    
  } # i
  
  # Non-centered parameterization for multivariate random trial effects
  for (j in 1:4) {
    sigma.trial[j] ~ dexp(0.1)
  }
  chol[1:4,1:4] ~ dlkj_corr_cholesky(1.5, 4)
  cor[1:4,1:4] <- t(chol[1:4,1:4]) %*% chol[1:4,1:4]  # Correlation matrix
  for (i in 1:n.trial) {
    for (j in 1:4) {
      z[j,i] ~ dnorm(0, 1)
    } # j
    eps.trial[1:4,i] <- diag(sigma.trial[1:4]) %*% t(chol[1:4,1:4]) %*% z[1:4,i]
  } # i
  
  # Residual
  sigma ~ dexp(0.1)
  
  # LIKELIHOOD
  
  for (i in 1:n.obs) {
    
    # Start and end inhibition
    c[i] <- c.alpha[species[i]]
    d[i] <- d.alpha[species[i]] + eps.trial[1,trial[i]]
    
    # Hormesis and RJMCMC inclusion
    f[i] <- f.alpha[species[i]] + eps.trial[2,trial[i]]
    w[i] <- w.alpha[species[i]]
    
    # ED50 and slope
    e[i] <- e.alpha[species[i]] + eps.trial[3,trial[i]]
    b[i] <- b.alpha[species[i]] + eps.trial[4,trial[i]]
    
    # Cedergreen–Ritz–Streibig model
    mu[i] <- c[i] - (c[i] - d[i] + w[i] * f[i] * exp(-1 / x[i] ^ alpha)) / (1 + (x[i] / e[i]) ^ b[i])
    y[i] ~ dnorm(mu[i], sd = sigma)
    
  } # i
  
  # DERIVED QUANTITIES

  e.diff <- e.alpha[2] - e.alpha[1]
  
})

# Data
str(i1data <- list(y = data1.i$Inhibition))

# Constants
str(i1consts <- list(n.obs = nrow(data1.i),
                     n.species = n.species,
                     x = data1.i$DMSO,
                     max.x = max(data1.i$DMSO),
                     species = as.numeric(data1.i$Species),
                     trial = data1.i$Trial,
                     n.trial = length(unique(data1.i$Trial)),
                     alpha = alpha))

# Initial values
i1inits <- list(d.alpha = rep(0, n.species),
                sigma.trial = rep(0.1, 4))

# Parameters to monitor
i1mons <- c("b.alpha", "c.alpha", "d.alpha", "e.alpha", "f.alpha", "w.alpha", 
            "sigma.trial", "cor", "sigma",
            "e.diff")

# Model
Ci1model <- compileNimble(nimbleModel(i1code, i1consts, i1data, i1inits))
i1conf <- configureMCMC(Ci1model, monitors = i1mons)
configureRJ(i1conf, "f.alpha", "w.alpha")
Ci1mcmc <- compileNimble(buildMCMC(i1conf), project = Ci1model)

# Run
i1samples <- runMCMC(Ci1mcmc, niter = 60000, nburnin = 10000, thin = 10, nchains = 2)

# Summary and traceplots
print(i1sum <- MCMCsummary(i1samples, round = 3))
write.csv(i1sum, "i1sum.csv")
#MCMCtrace(i1samples, pdf = F, Rhat = T, n.eff = T, ind = T, iter = 10000)
```

#### Plot

```{r}
# Setup
i1draws <- do.call(rbind, i1samples)

# Predictions
i1pred <- array(NA, c(n.pred, nrow(i1draws), n.species))
for (i in 1:n.pred) {
  for (k in 1:n.species) {
      
      i1pred[i,,k] <- i1draws[,paste0("c.alpha[", k, "]")] - (i1draws[,paste0("c.alpha[", k, "]")] - i1draws[,paste0("d.alpha[", k, "]")] + i1draws[,paste0("f.alpha[", k, "]")] * exp(-1 / xd[i] ^ alpha)) / (1 + (xd[i] / i1draws[,paste0("e.alpha[", k, "]")]) ^ i1draws[,paste0("b.alpha[", k, "]")])
      
  } # k
} # i

# Plot 1a
i1plot1 <- 
  tibble(pred = c(i1pred[,,1]),
         dmso = rep(xd, nrow(i1draws))) |>
  ggplot(aes(x = dmso)) +
  geom_jitter(aes(x = DMSO, y = Inhibition),
              data = data1 |> filter(Species == "S. pneumoniae"),
              color = "#333333",
              shape = 16,
              size = 3/4,
              width = 1/50,
              alpha = 3/4) +
  stat_lineribbon(aes(y = pred),
                  .width = 0.95,
                  point_interval = median_qi,
                  color = "#333333",
                  fill = "#333333",
                  size = 3/4,
                  alpha = 1/3,
                  show.legend = F) +
  scale_x_log10(expand = c(0, 0)) +
  scale_y_continuous(breaks = seq(0, 100, 50),
                     expand = c(0, 0)) +
  coord_cartesian(ylim = c(-15, 115)) +
  labs(subtitle = expression(italic("S. pneumoniae")),
       x = "DMSO (%)",
       y = "Biofilm inhibition (%)")

# Plot 1b
i1plot2 <- 
  tibble(pred = c(i1pred[,,2]),
         dmso = rep(xd, nrow(i1draws))) |>
  ggplot(aes(x = dmso)) +
  geom_jitter(aes(x = DMSO, y = Inhibition, color = Inhibition < -100),
              data = data1 |> filter(Species == "P. aeruginosa"),
              shape = 16,
              size = 3/4,
              width = 1/50,
              alpha = 3/4,
              show.legend = F) +
  stat_lineribbon(aes(y = pred),
                  .width = 0.95,
                  point_interval = median_qi,
                  color = "#333333",
                  fill = "#333333",
                  size = 3/4,
                  alpha = 1/3,
                  show.legend = F) +
  scale_color_manual(values = c("#333333", "red")) +
  scale_x_log10(expand = c(0, 0)) +
  scale_y_continuous(breaks = seq(-300, 100, 50),
                     expand = c(0, 0)) +
  coord_cartesian(ylim = c(-315, 115)) +
  labs(subtitle = expression(italic("P. aeruginosa")),
       x = "DMSO (%)",
       y = "Biofilm inhibition (%)")
```

## Experiment 2: Anbiotioc with DMSO

```{r}
# Data prep
data2 <- data |>
  filter(Concentration > 0) |>
  mutate(DMSO2 = factor(ifelse(DMSO == 0 | DMSO == 1 | DMSO == 2, DMSO, "Variable")),
         Trial = sort(c(rep(1:35, 10), rep(36:39, 9), rep(40:56, 10))))
```

### Absorbance

#### Model

```{r}
# Code
a2code <- nimbleCode({
  
  # PRIORS
  
  # Intercepts (species- and DMSO-specific)
  for (i in 1:n.species) {
    for (j in 1:n.dmso) {
      
      # Start and end absorbance
      c.alpha[i,j] <- 0
      d.alpha[i,j] ~ dnorm(1, 1)
      
      # Hormesis and RJMCMC inclusion
      w.alpha[i,j] ~ dbern(0.5)
      f.alpha[i,j] ~ dexp(1)
      
      # e and slope
      e.alpha[i,j] ~ dunif(0, max.x)
      b.alpha[i,j] ~ dexp(0.1)
      
    } # j
  } # i
  
  # Non-centered parameterization for multivariate random trial effects
  for (j in 1:4) {
    sigma.trial[j] ~ dexp(1)
  }
  chol[1:4,1:4] ~ dlkj_corr_cholesky(1.5, 4)
  cor[1:4,1:4] <- t(chol[1:4,1:4]) %*% chol[1:4,1:4]  # Correlation matrix
  for (i in 1:n.trial) {
    for (j in 1:4) {
      z[j,i] ~ dnorm(0, 1)
    } # j
    eps.trial[1:4,i] <- diag(sigma.trial[1:4]) %*% t(chol[1:4,1:4]) %*% z[1:4,i]
  } # i
  
  # Residual
  sigma ~ dexp(1)
  
  # LIKELIHOOD
  
  for (i in 1:n.obs) {
    
    # Start and end inhibition
    c[i] <- c.alpha[species[i],dmso[i]]
    d[i] <- d.alpha[species[i],dmso[i]] + eps.trial[1,trial[i]]
    
    # Hormesis and RJMCMC inclusion
    f[i] <- f.alpha[species[i],dmso[i]] + eps.trial[2,trial[i]]
    w[i] <- w.alpha[species[i],dmso[i]]
    
    # ED50 and slope
    e[i] <- e.alpha[species[i],dmso[i]] + eps.trial[3,trial[i]]
    b[i] <- b.alpha[species[i],dmso[i]] + eps.trial[4,trial[i]]
    
    # Cedergreen–Ritz–Streibig model
    mu[i] <- c[i] + (d[i] - c[i] + w[i] * f[i] * exp(-1 / x[i] ^ alpha)) / (1 + (x[i] / e[i]) ^ b[i])
    y[i] ~ dnorm(mu[i], sd = sigma)
    
  } # i
  
  # DERIVED QUANTITIES

  for (i in 1:n.species) {
    
    # Differences in d
    d.diff[i,1] <- d.alpha[i,1] - d.alpha[i,2]
    d.diff[i,2] <- d.alpha[i,1] - d.alpha[i,3]
    d.diff[i,3] <- d.alpha[i,1] - d.alpha[i,4]
    d.diff[i,4] <- d.alpha[i,2] - d.alpha[i,3]
    d.diff[i,5] <- d.alpha[i,2] - d.alpha[i,4]
    d.diff[i,6] <- d.alpha[i,3] - d.alpha[i,4]
    
    # Differences in e
    e.diff[i,1] <- e.alpha[i,1] - e.alpha[i,2]
    e.diff[i,2] <- e.alpha[i,1] - e.alpha[i,3]
    e.diff[i,3] <- e.alpha[i,1] - e.alpha[i,4]
    e.diff[i,4] <- e.alpha[i,2] - e.alpha[i,3]
    e.diff[i,5] <- e.alpha[i,2] - e.alpha[i,4]
    e.diff[i,6] <- e.alpha[i,3] - e.alpha[i,4]
    
  } # i
  
})

# Data
str(a2data <- list(y = data2$Absorbance))

# Constants
str(a2consts <- list(n.obs = nrow(data2),
                     n.species = n.species,
                     n.dmso = n.dmso,
                     n.trial = max(data2$Trial),
                     x = data2$Concentration,
                     max.x = max(data2$Concentration),
                     species = as.numeric(data2$Species),
                     dmso = as.numeric(data2$DMSO2),
                     trial = data2$Trial,
                     alpha = alpha))

# Parameters to monitor
a2mons <- c("b.alpha", "c.alpha", "d.alpha", "e.alpha", "f.alpha", "w.alpha", 
            "sigma.trial", "cor", "sigma",
            "d.diff", "e.diff")

# Initial values
a2inits <- list(d.alpha = array(1, c(n.species, n.dmso)),
                sigma.trial = rep(0.1, 4))

# Model
Ca2model <- compileNimble(nimbleModel(a2code, a2consts, a2data, a2inits))
a2conf <- configureMCMC(Ca2model, monitors = a2mons)
configureRJ(a2conf, "f.alpha", "w.alpha")
Ca2mcmc <- compileNimble(buildMCMC(a2conf), project = Ca2model)

# Run
a2samples <- runMCMC(Ca2mcmc, niter = 60000, nburnin = 10000, thin = 10, nchains = 2)

# Summary and traceplots
print(a2sum <- MCMCsummary(a2samples, round = 3))
write.csv(a2sum, "a2sum.csv")
#MCMCtrace(a2samples, pdf = F, Rhat = T, n.eff = T, ind = T, excl = c("d.diff", "e.diff", "w.alpha"))
```

#### Plot

```{r}
# Setup
a2draws <- do.call(rbind, a2samples)

# Predictions
a2pred <- array(NA, c(n.pred, nrow(a2draws), n.species, n.dmso))
for (i in 1:n.pred) {
  for (k in 1:n.species) {
    for (m in 1:n.dmso) {
      
      a2pred[i,,k,m] <- a2draws[,paste0("c.alpha[", k, ", ", m, "]")] + (a2draws[,paste0("d.alpha[", k, ", ", m, "]")] - a2draws[,paste0("c.alpha[", k, ", ", m, "]")] + a2draws[,paste0("f.alpha[", k, ", ", m, "]")] * exp(-1 / xa[i] ^ alpha)) / (1 + (xa[i] / a2draws[,paste0("e.alpha[", k, ", ", m, "]")]) ^ a2draws[,paste0("b.alpha[", k, ", ", m, "]")])
      
    } # m
  } # k
} # i

# Plot 1a
a2labels1 <- c(expression(0^"A"), expression(1^"A"), expression(2^"A"), expression("Variable"^"A"))
a2plot1 <- 
  tibble(pred = c(a2pred[,,1,]),
         conc = rep(rep(xa, nrow(a2draws)), n.dmso),
         dmso = factor(sort(rep(c(0:2, "Variable"), dim(a2pred)[1] * dim(a2pred)[2])))) |>
  ggplot(aes(x = conc)) +
  geom_jitter(aes(x = Concentration, y = Absorbance, color = DMSO2),
              data = data2 |> filter(Species == "S. pneumoniae"),
              shape = 16,
              size = 3/4,
              width = 1/50,
              alpha = 2/3) +
  stat_lineribbon(aes(y = pred, color = dmso, fill = dmso),
                  point_interval = median_qi,
                  .width = 0.95,
                  size = 3/4,
                  alpha = 1/3) +
  scale_color_manual(values = c("black", "#FFA500", "#005AFF", "#FF005A"),
                     labels = a2labels1) +
  scale_fill_manual(values = c("black", "#FFA500", "#005AFF", "#FF005A"),
                    labels = a2labels1) +
  scale_x_log10(expand = c(0, 0)) +
  scale_y_continuous(breaks = seq(0, 0.5, 0.5),
                     expand = c(0, 0)) +
  coord_cartesian(ylim = c(-0.1, 0.6)) +
  theme(legend.position = c(1, 1),
        legend.justification = c("right", "top")) +
  labs(subtitle = expression(italic("S. pneumoniae")),
       x = bquote(paste("Ampicillin (", mu,"g/mL)")),
       y = "Absorbance (OD 595)",
       color = "DMSO (%)",
       fill = "DMSO (%)")

# Plot 1b
a2labels2 <- c(expression(0^"A"), expression(1^"AB"), expression(2^"B"), expression("Variable"^"C"))
a2plot2 <- 
  tibble(pred = c(a2pred[,,2,]),
         conc = rep(rep(xa, nrow(a2draws)), n.dmso),
         dmso = factor(sort(rep(c(0:2, "Variable"), dim(a2pred)[1] * dim(a2pred)[2])))) |>
  ggplot(aes(x = conc)) +
  geom_jitter(aes(x = Concentration, y = Absorbance, color = DMSO2),
              data = data2 |> filter(Species == "P. aeruginosa"),
              shape = 16,
              size = 3/4,
              width = 1/50,
              alpha = 2/3) +
  stat_lineribbon(aes(y = pred, color = dmso, fill = dmso),
                  point_interval = median_qi,
                  .width = 0.95,
                  size = 3/4,
                  alpha = 1/3) +
  scale_color_manual(values = c("black", "#FFA500", "#005AFF", "#FF005A"),
                     labels = a2labels2) +
  scale_fill_manual(values = c("black", "#FFA500", "#005AFF", "#FF005A"),
                    labels = a2labels2) +
  scale_x_log10(expand = c(0, 0)) +
  scale_y_continuous(breaks = seq(0, 1.5, 0.5),
                     expand = c(0, 0)) +
  coord_cartesian(ylim = c(-0.1, 1.6)) +
  theme(legend.position = c(1, 1),
        legend.justification = c("right", "top")) +
  labs(subtitle = expression(italic("P. aeruginosa")),
       x = bquote(paste("Gentamicin (", mu,"g/mL)")),
       y = "Absorbance (OD 595)",
       color = "DMSO (%)",
       fill = "DMSO (%)")
```

### Inhibition

#### Model

```{r}
# Code
i2code <- nimbleCode({
  
  # PRIORS
  
  # Intercepts (species- and DMSO-specific)
  for (i in 1:n.species) {
    for (j in 1:n.dmso) {
      
      # Start and end inhibition
      c.alpha[i,j] <- 100
      d.alpha[i,j] ~ dnorm(0, 100)
      
      # Hormesis and RJMCMC inclusion
      f.alpha[i,j] ~ dexp(0.01)
      w.alpha[i,j] ~ dbern(0.5)
      
      # e and slope
      e.alpha[i,j] ~ dunif(0, max.x)
      b.alpha[i,j] ~ dexp(0.1)

    } # j
  } # i
  
  # Non-centered parameterization for multivariate random trial effects
  for (j in 1:4) {
    sigma.trial[j] ~ dexp(0.1)
  }
  chol[1:4,1:4] ~ dlkj_corr_cholesky(1.5, 4)
  cor[1:4,1:4] <- t(chol[1:4,1:4]) %*% chol[1:4,1:4]
  for (i in 1:n.trial) {
    for (j in 1:4) {
      z[j,i] ~ dnorm(0, 1)
    } # j
    eps.trial[1:4,i] <- diag(sigma.trial[1:4]) %*% t(chol[1:4,1:4]) %*% z[1:4,i]
  } # i
  
  # Residual
  sigma ~ dexp(0.1)
  
  # LIKELIHOOD
  
  for (i in 1:n.obs) {
    
    # Start and end inhibition
    c[i] <- c.alpha[species[i],dmso[i]]
    d[i] <- d.alpha[species[i],dmso[i]] + eps.trial[1,trial[i]]
    
    # Hormesis and RJMCMC inclusion
    f[i] <- f.alpha[species[i],dmso[i]] + eps.trial[2,trial[i]]
    w[i] <- w.alpha[species[i],dmso[i]]
    
    # e and slope
    e[i] <- e.alpha[species[i],dmso[i]] + eps.trial[3,trial[i]]
    b[i] <- b.alpha[species[i],dmso[i]] + eps.trial[4,trial[i]]
    
    # Cedergreen–Ritz–Streibig model
    mu[i] <- c[i] - (c[i] - d[i] + w[i] * f[i] * exp(-1 / x[i] ^ alpha)) / (1 + (x[i] / e[i]) ^ b[i])
    y[i] ~ dnorm(mu[i], sd = sigma)
    
  } # i
  
  # DERIVED QUANTITIES

  for (i in 1:n.species) {
    
    # Difference in d
    d.diff[i,1] <- d.alpha[i,1] - d.alpha[i,2]
    d.diff[i,2] <- d.alpha[i,1] - d.alpha[i,3]
    d.diff[i,3] <- d.alpha[i,1] - d.alpha[i,4]
    d.diff[i,4] <- d.alpha[i,2] - d.alpha[i,3]
    d.diff[i,5] <- d.alpha[i,2] - d.alpha[i,4]
    d.diff[i,6] <- d.alpha[i,3] - d.alpha[i,4]
    
    # Differences in e
    e.diff[i,1] <- e.alpha[i,1] - e.alpha[i,2]
    e.diff[i,2] <- e.alpha[i,1] - e.alpha[i,3]
    e.diff[i,3] <- e.alpha[i,1] - e.alpha[i,4]
    e.diff[i,4] <- e.alpha[i,2] - e.alpha[i,3]
    e.diff[i,5] <- e.alpha[i,2] - e.alpha[i,4]
    e.diff[i,6] <- e.alpha[i,3] - e.alpha[i,4]
    
  } # i

})

# Data
str(i2data <- list(y = data2$Inhibition))

# Constants
str(i2consts <- list(n.obs = nrow(data2),
                     n.species = n.species,
                     n.dmso = n.dmso,
                     n.trial = max(data2$Trial),
                     x = data2$Concentration,
                     max.x = max(data2$Concentration),
                     species = as.numeric(data2$Species),
                     dmso = as.numeric(data2$DMSO2),
                     trial = data2$Trial,
                     alpha = alpha))

# Initial values
i2inits <- list(d.alpha = array(0, c(n.species, n.dmso)),
                sigma.trial = rep(0.1, 4))

# Parameters to monitor
i2mons <- c("b.alpha", "c.alpha", "d.alpha", "e.alpha", "f.alpha", "w.alpha", 
            "sigma.trial", "cor", "sigma",
            "d.diff", "e.diff")

# Model
Ci2model <- compileNimble(nimbleModel(i2code, i2consts, i2data, i2inits))
i2conf <- configureMCMC(Ci2model, monitors = i2mons)
configureRJ(i2conf, "f.alpha", "w.alpha")
Ci2mcmc <- compileNimble(buildMCMC(i2conf), project = Ci2model)

# Run
i2samples <- runMCMC(Ci2mcmc, niter = 60000, nburnin = 10000, thin = 10, nchains = 2)

# Summary and traceplots
print(i2sum <- MCMCsummary(i2samples, round = 3))
write.csv(i2sum, "i2sum.csv")
#MCMCtrace(i2samples, pdf = F, Rhat = T, n.eff = T, ind = T, excl = "w.alpha")
```

#### Plot

```{r}
# Setup
i2draws <- do.call(rbind, i2samples)

# Predictions
i2pred <- array(NA, c(n.pred, nrow(i2draws), n.species, n.dmso))
for (i in 1:n.pred) {
  for (k in 1:n.species) {
    for (m in 1:n.dmso) {
      
      i2pred[i,,k,m] <- i2draws[,paste0("c.alpha[", k, ", ", m, "]")] - (i2draws[,paste0("c.alpha[", k, ", ", m, "]")] - i2draws[,paste0("d.alpha[", k, ", ", m, "]")] + i2draws[,paste0("f.alpha[", k, ", ", m, "]")] * exp(-1 / xa[i] ^ alpha)) / (1 + (xa[i] / i2draws[,paste0("e.alpha[", k, ", ", m, "]")]) ^ i2draws[,paste0("b.alpha[", k, ", ", m, "]")])
      
    } # m
  } # k
} # i

# Plot 1a
i2labels1 <- c(expression(0^"A"), expression(1^"A"), expression(2^"A"), expression("Variable"^"A"))
i2plot1 <- 
  tibble(pred = c(i2pred[,,1,]),
         conc = rep(rep(xa, nrow(i2draws)), n.dmso),
         dmso = factor(sort(rep(c(0:2, "Variable"), dim(i2pred)[1] * dim(i2pred)[2])))) |>
  ggplot(aes(x = conc)) +
  geom_jitter(aes(x = Concentration, y = Inhibition, color = DMSO2),
              data = data2 |> filter(Species == "S. pneumoniae"),
              shape = 16,
              size = 3/4,
              width = 1/50,
              alpha = 2/3) +
  stat_lineribbon(aes(y = pred, color = dmso, fill = dmso),
                  .width = 0.95,
                  point_interval = median_qi,
                  size = 3/4,
                  alpha = 1/3) +
  scale_color_manual(values = c("black", "#FFA500", "#005AFF", "#FF005A"),
                     labels = i2labels1) +
  scale_fill_manual(values = c("black", "#FFA500", "#005AFF", "#FF005A"),
                    labels = i2labels1) +
  scale_x_log10(expand = c(0, 0)) +
  scale_y_continuous(breaks = seq(0, 100, 50),
                     expand = c(0, 0)) +
  coord_cartesian(ylim = c(-15, 115)) +
  theme(legend.position = c(1, 0.05),
        legend.justification = c("right", "bottom")) +
  labs(subtitle = expression(italic("S. pneumoniae")),
       x = bquote(paste("Ampicillin (", mu,"g/mL)")), 
       y = "Biofilm inhibition (%)",
       color = "DMSO (%)",
       fill = "DMSO (%)")

# Plot 1b
i2labels2 <- c(expression(0^"A"), expression(1^"A"), expression(2^"A"), expression("Variable"^"B"))
i2plot2 <- 
  tibble(pred = c(i2pred[,,2,]),
         conc = rep(rep(xa, nrow(i2draws)), n.dmso),
         dmso = factor(sort(rep(c(0:2, "Variable"), dim(i2pred)[1] * dim(i2pred)[2])))) |>
  ggplot(aes(x = conc)) +
  geom_jitter(aes(x = Concentration, y = Inhibition, color = DMSO2),
              data = data2 |> filter(Species == "P. aeruginosa"),
              shape = 16,
              size = 3/4,
              width = 1/50,
              alpha = 2/3) +
  stat_lineribbon(aes(y = pred, color = dmso, fill = dmso),
                  .width = 0.95,
                  point_interval = median_qi,
                  size = 3/4,
                  alpha = 1/3) +
  scale_color_manual(values = c("black", "#FFA500", "#005AFF", "#FF005A"),
                    labels = i2labels2) +
  scale_fill_manual(values = c("black", "#FFA500", "#005AFF", "#FF005A"),
                    labels = i2labels2) +
  scale_x_log10(expand = c(0, 0)) +
  scale_y_continuous(breaks = seq(-200, 100, 50),
                     expand = c(0, 0)) +
  coord_cartesian(ylim = c(-215, 115)) +
  theme(legend.position = c(1, 0.05),
        legend.justification = c("right", "bottom")) +
  labs(subtitle = expression(italic("P. aeruginosa")),
       x = bquote(paste("Gentamicin (", mu,"g/mL)")), 
       y = "Biofilm inhibition (%)",
       color = "DMSO (%)",
       fill = "DMSO (%)")
```

# Plots

```{r}
# Set theme
theme_set(theme_classic(base_size = 8, 
                        base_family = "Helvetica"))
theme_update(axis.ticks = element_line(color = "#333333"),
             axis.line = element_line(color = "#333333"),
             axis.title = element_text(color = "#333333"),
             axis.text = element_text(color = "#333333"),
             legend.title = element_text(color = "#333333"),
             legend.text = element_text(color = "#333333"),
             legend.position = "none",
             legend.key.size = unit(0.1, "inch"),
             legend.text.align = 0,
             strip.text = element_text(size = rel(1)),
             strip.background = element_rect(color = NA))

# Experiment 1
plot1 <- 
  (a1plot1 | a1plot2) / (i1plot1 | i1plot2) +
  plot_annotation(tag_levels = "A") &
  theme(plot.tag = element_text(face = "bold", color = "#333333"))
ggsave("plot1.jpg", plot1, width = 5, height = 5, units = "in", dpi = 600)

# Experiment 2
plot2 <- 
  (a2plot1 | a2plot2) / (i2plot1 | i2plot2) +
  plot_annotation(tag_levels = "A") &
  theme(plot.tag = element_text(face = "bold", color = "#333333"))
ggsave("plot2.jpg", plot2, width = 5, height = 5, units = "in", dpi = 600)
```