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

## remove surgery type "orthopedic"
surgery2 <- subset(surgery, surgtype %in% 2:3)
surgery2$surgtype <- surgery2$surgtype[drop = TRUE]

logistic <- glm(complication ~ surgtype - 1,
                family = binomial,
                data = surgery2)

## n_j and S_j
t <- table(surgery2$surgtype, surgery2$complication)
addmargins(t)

## estimates on probability scale with corresponding standard deviations
est <- predict(logistic,
               ## predicting the probability for both surgery types
               data.frame(surgtype = factor(2:3)),
               type = "response",
               se.fit = T)

## lower confidence limits (normal approximation)
est$fit - 1.96 * est$se.fit

## upper confidence limits
est$fit + 1.96 * est$se.fit