逻辑回归中不同因素的致死剂量 (LD50)

Question

我有一个逻辑回归模型，其中包含一个连续变量和一个具有各种 levels/factors 的定性变量。有没有办法计算每个因素的 LD50？

library(dplyr)
library(ggeffects)
library(MASS)

# Produce a table with data
set.seed(321)

x1 <- rnorm(400)
x2 <- 3*x1^3 + 2*x1^2 + x1 + 1
x3 <- 1/(1 + exp(-x2))
x4 = rbinom(400, 1, x3) 

dt <- tibble(binary = x4,
             continuous = x1,
             qualitative = sample(c("white", "pink", "lime"), 400, TRUE))

# Logistic model
mdl <- glm(binary ~ continuous + qualitative, family = "binomial", data = dt)

# Calculate LD50, which gives the lethal dose for the whole model
dose.p(mdl) # -0.58 ± 0.11 se

# Plot regression model by factor of the qualitative variable
newdat <- ggpredict(mdl, terms = c("continuous[all]", "qualitative"))
plot(newdat)

我如何计算每个因素的 LD50 ± SE（石灰的 LD50、粉红色的 LD50 等）？

Answer 1

下面为每个因素拟合二元模型与连续模型，并得出 LD50 和 SE：

get_LD50 = function(fit){
   data.frame(
   LD50 = dose.p(fit)[1],
   SE = attributes(dose.p(fit))$SE[,1]
   )
}

dt %>% group_by(qualitative) %>% 
do(get_LD50(glm(binary ~ continuous, family = "binomial", data = .)))

# A tibble: 3 x 3
# Groups:   qualitative [3]
  qualitative   LD50    SE
  <chr>        <dbl> <dbl>
1 lime        -0.578 0.115
2 pink        -0.479 0.104
3 white       -0.392 0.116

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逻辑回归中不同因素的致死剂量 (LD50)

Lethal Dose (LD50) for the different factors in a logistic regression

r

glm

logistic-regression