source("http://192.38.117.59/~linearpredictors/datafiles/readFever.R")

## logistic regression using alcohol intake as covariate
logistic <- glm(death ~ alco,
                family = binomial,
                data = fever)
summary(logistic)

## Wald test for the slope = 0
b <- logistic$coef["alco"]
se.b <- summary(logistic)$coefficients["alco", "Std. Error"]
(W.logistic <- (b/se.b)^2)

## the p-value
1 - pchisq(W.logistic, df = 1)

## logistic regression using a scored alcohol intake

## means of bilirubin within quintile groups of bilirubin
means <- tapply(fever$alco, fever$alcogroup, mean)
names(means) <- NULL
fever$scoredalco <- means[as.numeric(fever$alcogroup)]

scoredlogistic <- glm(death ~ scoredalco,
                      family = binomial,
                      data = fever)
summary(scoredlogistic)

## Wald test for the slope = 0
b <- scoredlogistic$coef["scoredalco"]
se.b <- summary(scoredlogistic)$coefficients["scoredalco", "Std. Error"]
(W.scoredlogistic <- (b/se.b)^2)

## the p-value
1 - pchisq(W.scoredlogistic, df = 1)