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

In kkholst/mets: Analysis of Multivariate Event Times

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

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)

Author(s)

Thomas Scheike

Examples

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)

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

kkholst/mets documentation built on June 14, 2025, 9:19 a.m.