gumbel {discSurv}

Gumbel Link Function

Description

Constructs the link function with gumbel distribution in approriate format for use in generalized, linear models.

Usage

gumbel()

Details

Insert this function into a binary regression model

Author(s)

Thomas Welchowski [e-mail]

Matthias Schmid [e-mail]

References

Tutz G, Schmid M (2016). Modeling discrete time-to-event data. Springer Series in Statistics.

See Also

glm

Examples

# Example with copenhagen stroke study
library(pec)
data(cost)
head(cost)

# Take subsample and convert time to months
costSub <- cost [1:50, ]
costSub$time <- ceiling(costSub$time/30)
costLong <- dataLong(dataShort = costSub, timeColumn = "time", eventColumn = "status",
timeAsFactor=TRUE)
gumbelModel <- glm(formula = y ~ timeInt + diabetes, data = costLong, 
family = binomial(link = gumbel()))

# Estimate hazard given prevStroke and no prevStroke
hazPrevStroke <- predict(gumbelModel, newdata=data.frame(timeInt = factor(1:143), 
diabetes = factor(rep("yes", 143), levels = c("no", "yes"))), type = "response")
hazWoPrevStroke <- predict(gumbelModel, newdata = data.frame(timeInt = factor(1:143), 
diabetes=factor(rep("no", 143), levels = c("no", "yes"))), type = "response")

# Estimate survival function
SurvPrevStroke <- cumprod(1 - hazPrevStroke)
SurvWoPrevStroke <- cumprod(1 - hazWoPrevStroke)

# Example graphics of survival curves with and without diabetes
plot(x = 1:143, y = SurvWoPrevStroke, type = "l", xlab = "Months", 
ylab = "S (t|x)", las = 1, lwd = 2, ylim = c(0,1))
lines(x = 1:143, y = SurvPrevStroke, col = "red", lwd = 2)
legend("topright", legend = c("Without diabetes", "Diabetes"), 
lty = 1, lwd =2, col = c("black", "red"))