How does one calculate LD50 from a glmer? - r

Question

I am analyzing a data set where ~10 individuals are exposed to a set treatment (Time) and mortality is recorded (Alive, Dead). glmer was used to model the data because Treatments were blocked (Trial).
From the following model I want to predict the Time at which 50% of individuals die.
Trial <- c(1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3)
Time <- c(2, 6, 9, 12, 15, 18, 21, 24, 1, 2, 3, 4, 5, 6, 1.5, 3, 4.5, 6, 39)
Alive <- c(10, 0, 0, 0, 0, 0, 0, 0, 6, 2, 8, 1, 0, 0, 4, 6, 1, 2, 0)
Dead <- c(0, 10, 6, 10, 10, 10, 7, 10, 0, 8, 1, 9, 10, 10, 5, 0, 8, 6, 10)
ostrinaA.glmm<- glmer(cbind(Alive, Dead)~Time+(1|Trial), family = binomial(link="logit"))
summary(ostrinaA.glmm)
If I was simply modelling using glmthe dose.p function from MASS could be used. From a different forum I found generalized code for a dose.p.glmm from Bill Pikounis. It is as follows:
dose.p.glmm <- function(obj, cf = 1:2, p = 0.5) {
eta <- obj$family$linkfun(p)
b <- fixef(obj)[cf]
x.p <- (eta - b[1L])/b[2L]
names(x.p) <- paste("p = ", format(p), ":", sep = "")
pd <- -cbind(1, x.p)/b[2L]
SE <- sqrt(((pd %*% vcov(obj)[cf, cf]) * pd) %*% c(1, 1))
res <- structure(x.p, SE = SE, p = p)
class(res) <- "glm.dose"
res
}
I'm new to coding and need help adjusting this code for my model. My attempt is as follows:
dose.p.glmm <- function(ostrinaA.glmm, cf = 1:2, p = 0.5) {
eta <- ostrinaA.glmm$family$linkfun(p)
b <- fixef(ostrinaA.glmm)[cf]
x.p <- (eta - b[1L])/b[2L]
names(x.p) <- paste("p = ", format(p), ":", sep = "")
pd <- -cbind(1, x.p)/b[2L]
SE <- sqrt(((pd %*% vcov(obj)[cf, cf]) * pd) %*% c(1, 1))
res <- structure(x.p, SE = SE, p = p)
class(res) <- "glm.dose"
res
}
dose.p.glmm(ostrinaA.glmm, cf=1:2, p=0.5)
Error in ostrinaA.glmm$family : $ operator not defined for this S4 class
Any assistance adjusting this code for my model would be greatly appreciated.

Answer 1

At a quick glance I would think replacing
eta <- obj$family$linkfun(p)
with
f <- family(obj)
eta <- f$linkfun(p)
should do the trick.
You also need to replace the res <- ... line with
res <- structure(x.p, SE = matrix(SE), p = p)
This is rather obscure, but is necessary because the print.dose.glm method (from the MASS package) automatically tries to cbind() some stuff together. This fails if SE is a fancy matrix from the Matrix package rather than a vanilla matrix from base R: matrix() does the conversion.
If you are very new to coding, you might not realize that you don't have to change the obj variable name in the code you've copied to ostrina.glmm. In other words, Pikounis's code should work perfectly well with only the two modifications I suggested above.