# cox.adapt: Compute the extreme quantile procedure for Cox model In extremefit: Estimation of Extreme Conditional Quantiles and Probabilities

## Description

Compute the extreme quantile procedure for Cox model

## Usage

 ```1 2 3``` ```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.

`coxph`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```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) ```