emmeans_ED {LabApplStat}

Make emmeans object for an expected dose

Description

Solves linear equations in continuous explanatory variables in order to find the expected dose. A typical application could be to find LD50, i.e. the lethal dose killing 50 percent of the population, from a probit analysis fitted by glm. The associated variance-covariance matrix is found using the Delta method.

Usage

emmeans_ED(
  object,
  specs = ~0,
  left = NULL,
  right = NULL,
  tran = NULL,
  p = 0.5,
  p.name = "probability"
)

Arguments

object

An object that can be given to emmeans. Typically a model fitted by glm.

specs

As for emmeans. Typically as one-sided formula. Defaults to ~0.

left

A list specifying the left end point of the linear span of continuous variables in which to measure the ED values. Defaults to NULL.

right

A list specifying the right end point of the linear span of continuous variables in which to measure the ED values. Defaults to NULL.

tran

Possible transformation of the scale of the ED values. If given then backtransformation can be done using the technology of the emmeans. The default value tran=NULL corresponds to no transformation.

p

Numeric vector given the targeted predictions. Typically probabilities, where the default value p=0.5 corresponds to ED50.

p.name

The name of the variable containing p. If p contains more than one value, then this will also appear in @misc$by.vars in the emmGrid object. Defaults to p.name="probability".

Details

Find the 'expected dose' along a gradient in the space of numeric predictor variables. The options 'left' and 'right' specify the endpoints of this gradient. Typically these endpoints should be chosen as 0 and 1 for the numeric predictor of interest. If both endpoints are chosen as NULL then these choices are taken for all numeric predictors.

Value

An object of class emmGrid-class.

Author(s)

Bo Markussen

Examples

# Data from: C.I. Bliss, "The calculation of the dose-mortality curve", 
# Annals of Applied Biology, 134–167, 1935.

# import data from dobson package
library(dobson)
data(beetle)
m0 <- glm(cbind(y,n-y)~x,data=beetle,family=binomial(link="cloglog"))
# ED50 computation
summary(emmeans_ED(m0,tran="log10"),type="response")
# Visualization using the tidyverse
library(tidyverse)
LCL <- Vectorize(function(y,n) binom.test(y,n)$conf.int[1])
UCL <- Vectorize(function(y,n) binom.test(y,n)$conf.int[2])
beetle <- mutate(beetle,LCL=LCL(y,n),UCL=UCL(y,n))
emmeans_ED(m0,p=seq(0.001,0.999,length.out=100),tran="log10") %>% 
  summary(type="response") %>% as.data.frame() %>% 
  mutate(probability=as.numeric(as.character(probability))) %>%
  ggplot(aes(x=probability,y=response,ymin=asymp.LCL,ymax=asymp.UCL)) + 
  geom_ribbon(alpha=0.2,fill="blue") + geom_line() +
  xlab("Death probability") +
  ylab(expression(expected~dose~CS[2]~mg/l)) +
  geom_errorbarh(aes(xmin=LCL,xmax=UCL,y=10^x),beetle,inherit.aes=FALSE) +
  geom_point(aes(x=y/n,y=10^x),beetle,inherit.aes=FALSE)