False positive vs. false negative trade off plot

Question

I'm working on a decision making analysis where I'm trying to illustrate the trade off between false positive (false go) vs. false negative (false no-go) using R. I have created a density plot with null and alternative hypothesis curves, but would like to further illustrate the relationship via the example plots like these. Would appreciate the help in creating plots like example 1 and 2, especially example 1. Thank you!

Density plot

Example 1

Example 2

Answer 1

I used two offset normal distributions, the premise carries into whatever curves you can imagine.

library(ggplot2)

xs <- seq(-2, 4, length.out = 201)
dat <- do.call(rbind,
  list(data.frame(x=xs, y=dnorm(xs), id="1"),
       data.frame(x=xs, y=dnorm(xs, 2), id="2")))

---

plot 1

vline <- 1
eps <- 1e-3

ggplot(dat, aes(x, y, group = id, color = id)) +
  geom_line() +
  geom_area(aes(fill = id),
            data = ~ subset(., (id == "1" & x > (vline+eps)) | (id == "2" & x < (vline-eps)))) +
  geom_vline(xintercept = vline, linetype = "dashed") +
  labs(x = "Hazard Ratio", y = NULL) +
  guides(color = "none", fill = "none") +
  theme_classic() +
  theme(
    axis.line.y = element_blank(),
    axis.text.y = element_blank(),
    axis.ticks.y = element_blank()
  )

The vline is the differentiating line here, if it is not at the intersection then it can still be useful. For instance,

vline <- 1.2

plot 2

rng <- c(0.75, 0.85)
rngdat <- do.call(rbind,
  by(dat, dat$id, function(z) with(z, data.frame(approx(x, y, xout = rng), id = id[1]))))
rngdat$otherx <- fifelse(rngdat$id == "1", Inf, -Inf)

ggplot(dat, aes(x, y, group = id, color = id)) +
  geom_line(na.rm = TRUE) +
  geom_segment(aes(xend = x, yend = 0),
               data = subset(rngdat, id == 1),
               color = "black", linetype = "dashed") +
  geom_segment(aes(xend = otherx, yend = y),
               data = rngdat, linetype = "dashed") +
  coord_cartesian(xlim = c(0, 2)) +
  scale_x_continuous(name = "HR gate") +
  scale_y_continuous(
    name = "False Go Probability",
    sec.axis = sec_axis(~ ., name = "False No-Go Probability")) +
  scale_color_manual(values = c("1" = "blue", "2" = "red")) +
  guides(color = "none") +
  theme_classic() +
  theme(
    axis.line.y.left = element_line(color = "red"),
    axis.line.y.right = element_line(color = "blue")
  )

plot 3

offset <- max(rngdat$y[rngdat$id == "1"]) + 0.1
cutoff <- 0
dat <- transform(
  dat,
  yoff = ifelse(id == "1", 0.05 + offset, 0),
  cat = ifelse(id == "1",
               ifelse(x < cutoff, "True Positive", "False Negative"),
               ifelse(x < cutoff, "False Positive", "True Negative")))

ggplot(dat, aes(x, y = y + yoff)) +
  geom_ribbon(aes(ymin = yoff, ymax = y + yoff,
                  group = cat, fill = cat, alpha = cat),
              na.rm = TRUE) +
  geom_vline(xintercept = cutoff) +
  scale_fill_manual(
    name = NULL,
    values = c("True Positive" = "red", "False Negative" = "red",
               "False Positive" = "blue", "True Negative" = "blue")) +
  scale_alpha_manual(
    name = NULL,
    values = c("True Positive" = 1, "False Negative" = 0.2,
               "False Positive" = 0.2, "True Negative" = 1)) +
  labs(x = NULL, y = NULL) +
  theme(
    legend.position = "bottom",
    axis.text.y = element_blank(),
    axis.ticks.y = element_blank()
  )

Answer 2

It looks like your sticking point is figuring out how to access the values of the density curve at a given value of x or y.

You can use ggplot_build() to access the underlying data.frame constructed by the geom_density function. Here is some further discussion.