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

Description

$l o g i t (P (T > t | x)) = l o g (G (t)) + x β$ $P (T > t | x) = \frac{1}{1 + G (t) e x p (x β)}$

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 $P (T \leq t | x) = \frac{G (t) \exp (x β)}{1 + G (t) e x p (x β)}$

The baseline $G (t)$ is written as $c u m s u m (e x p (α))$ 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: $\prod P (T_{i} > t_{i l} | x) - P (T_{i} > t_{i r} | x)$

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)