cequre {cequre}

Censored quantile regression of Huang (2010)

Description

Implementation of censored quantile regression of Huang (2010), with incorporation of an upper bound related to the identification limit on probability scale as described in Huang (2013).

Usage

cequre(x,dlt,z,epsi=0.05,taus=numeric(0),res=0,
  resam.dist=FALSE,nbps=3*length(x))

Arguments

x

follow-up time.

dlt

censoring indicator: 1 - event, 0 - censored.

z

matrix of covariates (intercept not included): each column corresponds to a covariate.

epsi

parameter for the upper bound related to the identification limit on probability scale.

taus

(increasing) tau values at which quantile coefficient is of interest.

res

number of resampling iterations for variance estimation: res=200 is typically sufficient for variance estimation, but res needs to be much larger for confidence band construction.

resam.dist

resampling distribution to be reported or not.

nbps

maximum storage size for quantile coefficient: 3*length(x is typically sufficient.

Value

curve

estimated (piecewise-constant) quantile coefficient: each column corresponds to a jump point (the intercept is followed by slope coefficients, and final element is tau, the probability index.)

tau.bnd

upper bound of tau such that determinant of the at-risk matrix (for uncensored observations) is at least epsi^# regression coefficients times the initial value, subject to provided storage limit (nbps).

bt

estimated quantile coefficient at taus, only available if taus is specified.

va

variance estimate associated with bt, only available if taus is specified and res>0. As is resampling based, the variance estimate can be slightly different over multiple runs unless seed for the random number generator is reset each time.

dist

resampling distribution with res resampled curves: dist[ , ,1] through dist[ , ,res], only available if res>0 and resam.dist=TRUE.

dist.lgth

lengths of resampled curves, only available if res>0 and resam.dist=TRUE.

References

Huang, Y. (2010) Quantile calculus and censored regression, The Annals of Statistics 38, 1607–1637.

Huang, Y. (2013) Fast censored linear regression. Scandinavian Journal of Statistics 40, 789–806.

Examples

## simulate a dataset following Scenario 1 of Table 1 in Huang (2010)
num <- 200
beta <- c(.5, .5)

cvt.1 <- as.numeric(runif(num)<0.5)
cvt.2 <- runif(num)
resid <- rexp(num)
tres <- 1-exp(-resid)
event.t <- log(resid)+beta[1]*cvt.1*ifelse(tres<.4,tres/.4,1)+beta[2]*cvt.2
censr.t <- log(runif(num, 0, 5))
x <- pmin(event.t, censr.t)
dlt <- as.numeric(event.t<=censr.t)

## run censored quantile regression
fit <- cequre(x,dlt,cbind(cvt.1,cvt.2),taus=.1*seq(1,7,2),res=200)