timereg (version 1.8.6)

Gprop.odds.subdist: Fit Generalized Semiparametric Proportional 0dds Model for the competing risks subdistribution

Description

Fits a semiparametric proportional odds model: $$logit(F_1(t;X,Z)) = log(X^T A(t)) + \beta^T Z$$ 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.

An alternative way of writing the model : $$F_1(t;X,Z) = \frac{ \exp( \beta^T Z )}{ (X^T A(t)) + \exp( \beta^T Z) }$$ such that $\beta$ is the log-odds-ratio of cause 1 before time t, and $A(t)$ is the odds-ratio.

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

Usage

Gprop.odds.subdist(formula=formula(data),data=sys.parent(),cause=NULL,
                   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,causeS=1,
		   cens.code=0,cens.model="KM")

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.

cause

cause indicator for competing risks.

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.

causeS

specifies cause of interst. numeric value.

cens.code

specifies censoring code.

cens.model

specifies censoring model. So far only Kaplan-Meier "KM".

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.

Details

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.

References

Scheike, A flexible semiparametric transformation model for survival data, Lifetime Data Anal. (2007).

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

Examples

data(bmt)
# Fits Proportional odds model 
out <- Gprop.odds.subdist(Surv(time,cause==1)~prop(platelet)+prop(age)+prop(tcell),data=bmt,
		 cause=bmt$cause,cens.code=0,cens.model="KM",causeS=1,detail=0,n.sim=1000)
summary(out) 
par(mfrow=c(2,3))
plot(out,sim.ci=2); plot(out,score=1) 

# Fits Proportional odds model with stratified baseline
out <- Gprop.odds.subdist(Surv(time,cause==1)~-1+factor(platelet)+prop(age)+prop(tcell),data=bmt,
		 cause=bmt$cause,cens.code=0,cens.model="KM",causeS=1,detail=0,n.sim=1000)
summary(out) 
par(mfrow=c(2,3))
plot(out,sim.ci=2); plot(out,score=1)