load(url("http://ls.home.amu.edu.pl/data_sets/liver_data.RData"))
head(liver_data)

liver_data$condition <- ifelse(liver_data$condition == "Yes", 1, 0)
model_1 <- glm(condition ~ bilirubin + ldh, data = liver_data, family = 'binomial')
model_1

summary(model_1)

step(model_1)

exp(coef(model_1)[2])
exp(coef(model_1)[3])

install.packages("ROCR")
library(ROCR) 
pred_1 <- prediction(model_1$fitted, liver_data$condition) 
plot(performance(pred_1, 'tpr', 'fpr'), main = "Model 1")
performance(pred_1, 'auc')@y.values


liver_data_new <- data.frame(bilirubin = c(0.9, 2.1, 3.4), ldh = c(100, 200, 300))
(predict_glm <- stats::predict(model_1, 
                               liver_data_new, 
                               type = 'response'))
model_1_hat <- coef(model_1)[1] + 
  coef(model_1)[2] * liver_data$bilirubin + 
  coef(model_1)[3] * liver_data$ldh
model_1_temp <- seq(min(model_1_hat) - 1, max(model_1_hat) + 2.5, length.out = 100)
condition_temp <- exp(model_1_temp) / (1 + exp(model_1_temp))
plot(model_1_temp, condition_temp, type = "l", xlab = "X beta", ylab = "condition", 
     xlim = c(-6, 9), ylim = c(-0.1, 1.1))
points(model_1_hat, liver_data$condition, pch = 16)
points(coef(model_1)[1] + 
         coef(model_1)[2] * liver_data_new$bilirubin + 
         coef(model_1)[3] * liver_data_new$ldh, 
       predict_glm, pch = 16, col = "red")