Fit Semiparametric Proportional 0dds Model

Description

Fits a semiparametric proportional odds model:

logit(1-S_Z(t)) = log(G(t)) + β^T Z

where G(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.

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

For large data sets use the divide.conquer.timereg of the mets package to run the model on splits of the data, or the alternative estimator by the cox.aalen function.

Usage

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prop.odds(formula,data=sys.parent(),beta=NULL,
Nit=20,detail=0,start.time=0,max.time=NULL,id=NULL,n.sim=500,weighted.test=0,
profile=1,sym=0,baselinevar=1,clusters=NULL,max.clust=1000,weights=NULL)

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 Event object as returned by the ‘Event’ function.

data

a data.frame with the variables.

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.

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.

profile

if profile is 1 then modified partial likelihood is used, profile=0 fits by simple estimating equation. The modified partial likelihood is recommended.

sym

to use symmetrized second derivative in the case of the estimating equation approach (profile=0). This may improve the numerical performance.

baselinevar

set to 0 to omit calculations of baseline variance.

clusters

to compute cluster based standard errors.

max.clust

number of maximum clusters to be used, to save time in iid decomposition.

weights

weights for score equations.

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.

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

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

Examples

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data(sTRACE)
# Fits Proportional odds model 
out<-prop.odds(Event(time,status==9)~age+diabetes+chf+vf+sex,
sTRACE,max.time=7,n.sim=100)
summary(out)

par(mfrow=c(2,3))
plot(out,sim.ci=2)
plot(out,score=1) 

pout <- predict(out,Z=c(70,0,0,0,0))
plot(pout)

### alternative estimator for large data sets 
form <- Surv(time,status==9)~age+diabetes+chf+vf+sex
pform <- timereg.formula(form)
out2<-cox.aalen(pform,data=sTRACE,max.time=7,
	propodds=1,n.sim=0,robust=0,detail=0,Nit=40)
summary(out2)

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