res.mean: Residual mean life (restricted)

In timereg: Flexible Regression Models for Survival Data

Residual mean life (restricted)

Description

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

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

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

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

where Y_j = \sum_j Y I(\epsilon=j) + \infty * I(\epsilon=0) or (estimator=2)

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

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

Usage

res.mean(
  formula,
  data = parent.frame(),
  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-06,
  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

Uses the IPCW for the score equations based on

w(t) \Delta(\tau)/P(\Delta(\tau)=1| T,\epsilon,X,Z) ( Y(t) - h_1(t,X,Z))

and where \Delta(\tau) is the at-risk indicator given data and requires a IPCW model.

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

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=bmtw$cw,cens.weights=1/bmtw$weights); 
summary(out)

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