mets (version 1.3.7)

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

Description

We consider the cumulative odds model $$ P(T \leq t | x) = \frac{G(t) \exp(x \beta) }{1 + G(t) exp( x \beta) } $$ or equivalently $$ logit(P(T \leq t | x)) = log(G(t)) + x \beta $$ and we can thus also compute the probability of surviving $$ P(T >t | x) = \frac{1}{1 + G(t) exp( x \beta) } $$

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

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. Note that the regression coefficients are describing the probability of dying before or at time t.

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. Can be used for fitting the usual ordinal regression model (with logit link) that in contrast, however, describes the probibility of surviving time t (thus leads to -beta).

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

Examples

library(mets)
data(ttpd) 
dtable(ttpd,~entry+time2)

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

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

ttpd <- dfactor(ttpd,fentry~entry)
out <- cumoddsreg(fentry~X1+X2+X3+X4,ttpd)
summary(out)
head(iid(out))