# res.mean: Residual mean life (restricted)

Description Usage Arguments Details Value Author(s) References Examples

### 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

 1 2 3 4 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.

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

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 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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