interval.logitsurv.discrete: Discrete time to event interval censored data

Description

$$ logit(P(T >t | x)) = log(G(t)) + x \beta $$ $$ P(T >t | x) = \frac{1}{1 + G(t) exp( x \beta) } $$

Usage

interval.logitsurv.discrete(
  formula,
  data,
  beta = NULL,
  no.opt = FALSE,
  method = "NR",
  stderr = TRUE,
  weights = NULL,
  offsets = NULL,
  exp.link = 1,
  increment = 1,
  ...
)

Arguments

formula: formula
data: data
beta: starting values
no.opt: optimization TRUE/FALSE
method: NR, nlm
stderr: to return only estimate
weights: weights following id for GLM
offsets: following id for GLM
exp.link: parametrize increments exp(alpha) > 0
increment: using increments dG(t)=exp(alpha) as parameters
...: Additional arguments to lower level funtions lava::NR optimizer or nlm

Author

Thomas Scheike

Details

This is thus also the cumulative odds model, since $$ P(T \leq t | x) = \frac{G(t) \exp(x \beta) }{1 + G(t) exp( x \beta) } $$

The baseline $G(t)$ is written as $cumsum(exp(\alpha))$ and this is not the standard parametrization that takes log of $G(t)$ as the parameters.

Input are intervals given by ]t_l,t_r] where t_r can be infinity for right-censored intervals When truly discrete ]0,1] will be an observation at 1, and ]j,j+1] will be an observation at j+1

Likelihood is maximized: $$ \prod P(T_i >t_{il} | x) - P(T_i> t_{ir}| x) $$

Examples

Run this code

data(ttpd) 
dtable(ttpd,~entry+time2)
out <- interval.logitsurv.discrete(Interval(entry,time2)~X1+X2+X3+X4,ttpd)
summary(out)

pred <- predictlogitSurvd(out,se=FALSE)
plotSurvd(pred)

Run the code above in your browser using DataLab