Little 2008 proposes that the best fit to atomic bomb surivor data is a linear-quadratic-exponential fit. What does this look like?

a = 0.164
B = 0.683
y = -0.412

dose = seq(0, 4, 0.1)
err = function(D, a, B, y) {
  (a * D + B * D^2) * exp(y * D)
}
response = err(dose, a, B, y)

library(ggplot2)
ggplot(NULL, aes(dose, response)) + 
  geom_path()

A sigmodial curve!

This makes sense because the atomic bomb survivor data curves down at high doses. Unfortunately, the relavant (and dubious) part of this dose response is it’s fit to low dose exposures. It implies that low dose exposures are pretty safe, but it’s not clear if the true data implies the same thing.