cox.adapt {extremefit}

Compute the extreme quantile procedure for Cox model

Description

Compute the extreme quantile procedure for Cox model

Usage

cox.adapt(X, cph, cens = rep(1, length(X)), data = rep(0, length(X)),
  initprop = 1/10, gridlen = 100, r1 = 1/4, r2 = 1/20,
  CritVal = 10)

Arguments

X

a numeric vector of data values.

cph

an output object of the function coxph from the package survival.

cens

a binary vector corresponding to the censored values.

data

a data frame containing the covariates values.

initprop

the initial proportion at which we begin to test the model.

gridlen

the length of the grid for which the test is done.

r1

a proportion value of the data from the right that we skip in the test statistic.

r2

a proportion value of the data from the left that we skip in the test statistic.

CritVal

the critical value assiociated to procedure.

Details

Given a vector of data, a vector of censorship and a data frame of covariates, this function compute the adaptive procedure described in Grama and Jaunatre (2018).

We suppose that the data are in the domain of attraction of the Frechet-Pareto type and that the hazard are somewhat proportionals. Otherwise, the procedure will not work.

Value

coefficients

the coefficients of the coxph procedure.

Xsort

the sorted vector of the data.

sortcens

the sorted vector of the censorship.

sortebz

the sorted matrix of the covariates.

ch

the Hill estimator associated to the baseline function.

TestingGrid

the grid used for the statistic test.

TS, TS1, TS.max, TS1.max

respectively the test statistic, the likelihood ratio test, the maximum of the test statistic and the maximum likelihood ratio test.

window1, window2

indices from which the threshold was chosen.

Paretodata

logical: if TRUE the distribution of the data is a Pareto distribution.

Paretotail

logical: if TRUE a Pareto tail was detected.

madapt

the first indice of the TestingGrid for which the test statistic exceeds the critical value.

kadapt

the adaptive indice of the threshold.

kadapt.maxlik

the maximum likelihood corresponding to the adaptive threshold in the selected testing grid.

hadapt

the adaptive weighted parameter of the Pareto distribution after the threshold.

Xadapt

the adaptive threshold.

Author(s)

Ion Grama, Kevin Jaunatre

References

Grama, I. and Jaunatre, K. (2018). Estimation of Extreme Survival Probabilities with Cox Model. arXiv:1805.01638.

See Also

coxph

Examples

library(survival)
data(bladder)

X <- bladder2$stop-bladder2$start
Z <- as.matrix(bladder2[, c(2:4, 8)])
delta <- bladder2$event

ord <- order(X)
X <- X[ord]
Z <- Z[ord,]
delta <- delta[ord]

cph<-coxph(Surv(X, delta) ~ Z)

ca <- cox.adapt(X, cph, delta, Z)