faft {fastAFT}

Fast censored linear regression for the accelerated failure time (AFT) model

Description

An implementation of the fast censored linear regression in Huang (2013).

Usage

faft(x,dlt,z,weight="logrank",ynci=0,epl=0.95,epu=0.05)

Arguments

x

follow-up time.

dlt

censoring indicator: 1 - event, 0 - censored.

z

matrix of covariates: each column corresponds to a covariate.

weight

either "logrank" or "Gehan" estimating function.

ynci

compute test inversion-based 95% CI's? 1 - yes, 0 - no.

epl

parameter in (0,1) for determining the lower quantile from censored quantile regression (Huang 2010) for the preparatory estimation: sum of squared covariates for at-risk uncensored individuals is about $epl^(dim(z)[2]+1)$ in determinant.

epu

parameter in (0,1) for determining the upper quantile from censored quantile regression (Huang 2010) for the preparatory estimation: sum of squared covariates for at-risk uncensored individuals is about $epu^(dim(z)[2]+1)$ in determinant.

Value

weight

either "logrank" or "Gehan" estimating function.

beta

estimated regression coefficient (the proposed).

va

sandwich variance estimate for beta.

qif

quadratic score statistic at beta.

ci95

test inversion-based 95% CI's, only available if requested and successful.

message

point estimation: "success", "error - algorithm fails", or "warning - singular hessian".

imsg

numerical code for point and test inversion-based interval estimation: 0 - success in point and interval, 1 - error in point where algorithm fails, 2 - warning in point with singular hessian, 3 - success in point but failure in interval.

beta1stp

the one-step estimator.

qif1stp

quadratic score statistic at beta1stp.

betainit

the initial estimator.

qifinit

quadratic score statistic at betainit.

Author(s)

Yijian Huang

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 of size 100 with 2 covariates
size <- 100
npred <- 2
beta <- rep(1,npred)

cvt <- matrix(rnorm(size*npred),ncol=npred)
resid <- log(rexp(size))
event.t <- resid + cvt %*% beta
censr.t <- log(runif(size, 0, 6))
x <- pmin(event.t, censr.t)
dlt <- as.numeric(event.t<=censr.t)

## run censored linear regression
fit.g <- faft(x,dlt,cvt,weight="Gehan")
fit.l <- faft(x,dlt,cvt,weight="logrank")