Residual mean life (restricted)

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Description

Fits a semiparametric model for the residual life (estimator=1):

E( \min(Y,τ) -t | Y>=t) = h_1( g(t,x,z) )

or cause specific years lost of Andersen (2012) (estimator=3)

E( τ- \min(Y_j,τ) | Y>=0) = \int_0^t (1-F_j(s)) ds = h_2( g(t,x,z) )

where Y_j = ∑_j Y I(ε=j) + ∞ * I(ε=0) or (estimator=2)

E( τ- \min(Y_j,τ) | Y<τ, ε=j) = h_3( g(t,x,z) ) = h_2(g(t,x,z)) F_j(τ,x,z)

where F_j(s,x,z) = P(Y<τ, ε=j | x,z ) for a known link-function h() and known prediction-function g(t,x,z)

Uses the IPCW for the score equations based on

w(t) Δ(τ)/P(Δ(τ)=1| T,ε,X,Z) ( Y(t) - h_1(t,X,Z))

and where Δ(τ) is the at-risk indicator given data and requires a IPCW model.

Usage

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res.mean(formula,data=sys.parent(),cause=1,restricted=NULL,times=NULL,Nit=50,
clusters=NULL,gamma=0,n.sim=0,weighted=0,model="additive",detail=0,interval=0.01,
resample.iid=1,cens.model="KM",cens.formula=NULL,time.pow=NULL,time.pow.test=NULL,
silent=1,conv=1e-6,estimator=1,cens.weights=NULL,conservative=1,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 survival object as returned by the ‘Event’ function. The status indicator is not important here. Time-invariant regressors are specified by the wrapper const(), and cluster variables (for computing robust variances) by the wrapper cluster().

data

a data.frame with the variables.

cause

For competing risk models specificies which cause we consider.

restricted

gives a possible restriction times for means.

times

specifies the times at which the estimator is considered. Defaults to all the times where an event of interest occurs, with the first 10 percent or max 20 jump points removed for numerical stability in simulations.

Nit

number of iterations for Newton-Raphson algorithm.

clusters

specifies cluster structure, for backwards compability.

gamma

starting value for constant effects.

n.sim

number of simulations in resampling.

weighted

Not implemented. To compute a variance weighted version of the test-processes used for testing time-varying effects.

model

"additive", "prop"ortional.

detail

if 0 no details are printed during iterations, if 1 details are given.

interval

specifies that we only consider timepoints where the Kaplan-Meier of the censoring distribution is larger than this value.

resample.iid

to return the iid decomposition, that can be used to construct confidence bands for predictions

cens.model

specified which model to use for the ICPW, KM is Kaplan-Meier alternatively it may be "cox" or "aalen" model for further flexibility.

cens.formula

specifies the regression terms used for the regression model for chosen regression model. When cens.model is specified, the default is to use the same design as specified for the competing risks model. "KM","cox","aalen","weights". "weights" are user specified weights given is cens.weight argument.

time.pow

specifies that the power at which the time-arguments is transformed, for each of the arguments of the const() terms, default is 1 for the additive model and 0 for the proportional model.

time.pow.test

specifies that the power the time-arguments is transformed for each of the arguments of the non-const() terms. This is relevant for testing if a coefficient function is consistent with the specified form A_l(t)=beta_l t^time.pow.test(l). Default is 1 for the additive model and 0 for the proportional model.

silent

if 0 information on convergence problems due to non-invertible derviates of scores are printed.

conv

gives convergence criterie in terms of sum of absolute change of parameters of model

estimator

specifies what that is estimated.

cens.weights

censoring weights for estimating equations.

conservative

for slightly conservative standard errors.

weights

weights for estimating equations.

Details

Since timereg version 1.8.4. the response must be specified with the Event function instead of the Surv function and the arguments.

Value

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

cum

cumulative timevarying regression coefficient estimates are computed within the estimation interval.

var.cum

pointwise variances estimates.

gamma

estimate of proportional odds parameters of model.

var.gamma

variance for gamma.

score

sum of absolute value of scores.

gamma2

estimate of constant effects based on the non-parametric estimate. Used for testing of constant effects.

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.

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.

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.

conf.band

resampling based constant to construct 95% uniform confidence bands.

B.iid

list of iid decomposition of non-parametric effects.

gamma.iid

matrix of iid decomposition of parametric effects.

test.procBeqC

observed test process for testing of time-varying effects

sim.test.procBeqC

50 resample processes for for testing of time-varying effects

conv

information on convergence for time points used for estimation.

Author(s)

Thomas Scheike

References

Andersen (2013), Decomposition of number of years lost according to causes of death, Statistics in Medicine, 5278-5285.

Scheike, and Cortese (2015), Regression Modelling of Cause Specific Years Lost,

Scheike, Cortese and Holmboe (2015), Regression Modelling of Restricted Residual Mean with Delayed Entry,

Examples

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data(bmt); 
tau <- 100 

### residual restricted mean life
out<-res.mean(Event(time,cause>=1)~factor(tcell)+factor(platelet),data=bmt,cause=1,
	      times=0,restricted=tau,n.sim=0,model="additive",estimator=1); 
summary(out)

out<-res.mean(Event(time,cause>=1)~factor(tcell)+factor(platelet),data=bmt,cause=1,
	      times=seq(0,90,5),restricted=tau,n.sim=0,model="additive",estimator=1); 
par(mfrow=c(1,3))
plot(out)

### restricted years lost given death
out21<-res.mean(Event(time,cause)~factor(tcell)+factor(platelet),data=bmt,cause=1,
	      times=0,restricted=tau,n.sim=0,model="additive",estimator=2); 
summary(out21)
out22<-res.mean(Event(time,cause)~factor(tcell)+factor(platelet),data=bmt,cause=2,
	      times=0,restricted=tau,n.sim=0,model="additive",estimator=2); 
summary(out22)


### total restricted years lost 
out31<-res.mean(Event(time,cause)~factor(tcell)+factor(platelet),data=bmt,cause=1,
	      times=0,restricted=tau,n.sim=0,model="additive",estimator=3); 
summary(out31)
out32<-res.mean(Event(time,cause)~factor(tcell)+factor(platelet),data=bmt,cause=2,
	      times=0,restricted=tau,n.sim=0,model="additive",estimator=3); 
summary(out32)


### delayed entry 
nn <- nrow(bmt)
entrytime <- rbinom(nn,1,0.5)*(bmt$time*runif(nn))
bmt$entrytime <- entrytime

bmtw <- prep.comp.risk(bmt,times=tau,time="time",entrytime="entrytime",cause="cause")

out<-res.mean(Event(time,cause>=1)~factor(tcell)+factor(platelet),data=bmtw,cause=1,
	      times=0,restricted=tau,n.sim=0,model="additive",estimator=1,
              cens.model="weights",weights=bmt$cw,cens.weights=1/bmtw$weights); 
summary(out)

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