Gprop.odds: Fit Generalized Semiparametric Proportional 0dds Model

In timereg: Flexible Regression Models for Survival Data

Fit Generalized Semiparametric Proportional 0dds Model

Description

Fits a semiparametric proportional odds model:

logit(1-S_{X,Z}(t)) = log(X^T A(t)) + \beta^T Z

where A(t) is increasing but otherwise unspecified. Model is fitted by maximising the modified partial likelihood. A goodness-of-fit test by considering the score functions is also computed by resampling methods.

Usage

Gprop.odds(
  formula = formula(data),
  data = parent.frame(),
  beta = 0,
  Nit = 50,
  detail = 0,
  start.time = 0,
  max.time = NULL,
  id = NULL,
  n.sim = 500,
  weighted.test = 0,
  sym = 0,
  mle.start = 0
)

Arguments

formula	a formula object, with the response on the left of a '~' operator, and the terms on the right. The response must be a survival object as returned by the ‘Surv’ function.
data	a data.frame with the variables.
beta	starting value for relative risk estimates
Nit	number of iterations for Newton-Raphson algorithm.
detail	if 0 no details is printed during iterations, if 1 details are given.
start.time	start of observation period where estimates are computed.
max.time	end of observation period where estimates are computed. Estimates thus computed from [start.time, max.time]. This is very useful to obtain stable estimates, especially for the baseline. Default is max of data.
id	For timevarying covariates the variable must associate each record with the id of a subject.
n.sim	number of simulations in resampling.
weighted.test	to compute a variance weighted version of the test-processes used for testing time-varying effects.
sym	to use symmetrized second derivative in the case of the estimating equation approach (profile=0). This may improve the numerical performance.
mle.start	starting values for relative risk parameters.

Details

An alternative way of writing the model :

S_{X,Z}(t)) = \frac{ \exp( - \beta^T Z )}{ (X^T A(t)) + \exp( - \beta^T Z) }

such that \beta is the log-odds-ratio of dying before time t, and A(t) is the odds-ratio.

The modelling formula uses the standard survival modelling given in the survival package.

The data for a subject is presented as multiple rows or "observations", each of which applies to an interval of observation (start, stop]. The program essentially assumes no ties, and if such are present a little random noise is added to break the ties.

Value

returns an object of type 'cox.aalen'. With the following arguments:

cum	cumulative timevarying regression coefficient estimates are computed within the estimation interval.
var.cum	the martingale based pointwise variance estimates.
robvar.cum	robust pointwise variances estimates.
gamma	estimate of proportional odds parameters of model.
var.gamma	variance for gamma.
robvar.gamma	robust variance for gamma.
residuals	list with residuals. Estimated martingale increments (dM) and corresponding time vector (time).
obs.testBeq0	observed absolute value of supremum of cumulative components scaled with the variance.
pval.testBeq0	p-value for covariate effects based on supremum test.
sim.testBeq0	resampled supremum values.
obs.testBeqC	observed absolute value of supremum of difference between observed cumulative process and estimate under null of constant effect.
pval.testBeqC	p-value based on resampling.
sim.testBeqC	resampled supremum values.
obs.testBeqC.is	observed integrated squared differences between observed cumulative and estimate under null of constant effect.
pval.testBeqC.is	p-value based on resampling.
sim.testBeqC.is	resampled supremum values.
conf.band	resampling based constant to construct robust 95% uniform confidence bands.
test.procBeqC	observed test-process of difference between observed cumulative process and estimate under null of constant effect over time.
loglike	modified partial likelihood, pseudo profile likelihood for regression parameters.
D2linv	inverse of the derivative of the score function.
score	value of score for final estimates.
test.procProp	observed score process for proportional odds regression effects.
pval.Prop	p-value based on resampling.
sim.supProp	re-sampled supremum values.
sim.test.procProp	list of 50 random realizations of test-processes for constant proportional odds under the model based on resampling.

Author(s)

Thomas Scheike

References

Scheike, A flexible semiparametric transformation model for survival data, Lifetime Data Anal. (to appear).

Martinussen and Scheike, Dynamic Regression Models for Survival Data, Springer (2006).

Examples

data(sTRACE)

### runs slowly and is therefore donttest 
data(sTRACE)
# Fits Proportional odds model with stratified baseline
age.c<-scale(sTRACE$age,scale=FALSE); 
## out<-Gprop.odds(Surv(time,status==9)~-1+factor(diabetes)+prop(age.c)+prop(chf)+
##                 prop(sex)+prop(vf),data=sTRACE,max.time=7,n.sim=50)
## summary(out) 
## par(mfrow=c(2,3))
## plot(out,sim.ci=2); plot(out,score=1) 

timereg documentation built on Sept. 11, 2024, 8:35 p.m.