blogit: Bounded link functions

Description

Alternate link functions that impose bounds on the input of their link function

Usage

blogit(edge = 0.05)
bprobit(edge= 0.05)
bcloglog(edge=.05)
blog(edge=.05)

Arguments

edge

input values less than the cutpoint are replaces with the cutpoint. For all be blog input values greater than (1-edge) are replaced with (1-edge)

Value

a family object of the same form as make.family.

Details

When using survival psuedovalues for binomial regression, the raw data can be outside the range (0,1), yet we want to restrict the predicted values to lie within that range. A natural way to deal with this is to use glm with family = gaussian(link= "logit"). But this will fail. The reason is that the family object has a component linkfun that does not accept values outside of (0,1).

This function is only used to create initial values for the iteration step, however. Mapping the offending input argument into the range of (egde, 1-edge) before computing the link results in starting estimates that are good enough. The final result of the fit will be no different than if explicit starting estimates were given using the etastart or mustart arguments. These functions create copies of the logit, probit, and complimentary log-log families that differ from the standard ones only in this use of a bounded input argument, and are called a "bounded logit" = blogit, etc.

The same argument hold when using RMST (area under the curve) pseudovalues along with a log link to ensure positive predictions, though in this case only the lower boundary needs to be mapped.

Examples

Run this code

# NOT RUN {
py <- pseudo(survfit(Surv(time, status) ~1, lung), time=730) #2 year survival
range(py)
pfit <- glm(py ~ ph.ecog, data=lung, family=gaussian(link=blogit()))
# For each +1 change in performance score, the odds of 2 year survival
#  are multiplied by 1/2  = exp of the coefficient.
# }