% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/LogrankSIS.R
\name{LogrankSIS}
\alias{LogrankSIS}
\title{Generalized Log-rank Sure Independence Screening for Ultrahigh-Dimensional
Interval-Censored Response}
\usage{
LogrankSIS(X, L, R, nsis = floor(dim(X)[1]/log(dim(X)[1])))
}
\arguments{
\item{X}{The design matrix of dimensions \eqn{n \times p}.  Each row is an
observation vector.  Predictors should be binary (0/1), as commonly
arising from SNP minor-allele encoding or word-segmentation of job
postings.}

\item{L}{A numeric vector of length \eqn{n} giving the \strong{lower}
endpoints of the observed intervals \eqn{(L_i, R_i]}.  For left-censored
observations (event known to have occurred no later than \eqn{R_i}), set
\code{L[i] = 0} or \code{L[i] = -Inf} as appropriate for the application.}

\item{R}{A numeric vector of length \eqn{n} giving the \strong{upper}
endpoints of the observed intervals.  Set \code{R[i] = Inf} for
right-censored observations (event not yet observed by the end of
follow-up).}

\item{nsis}{Number of predictors recruited by \code{LogrankSIS}.  The
default is \code{floor(n / log(n))}.}
}
\value{
An integer vector of length \code{nsis} containing the
  \strong{column indices} of the top-ranked predictors in \code{X},
  ordered by decreasing marginal utility \eqn{\hat\omega_k}.
}
\description{
A computationally efficient and statistically robust feature screening
procedure for ultrahigh-dimensional Case II interval-censored responses
with binary predictors (e.g., SNP indicators or text-derived skill words).

The marginal utility is the \emph{variance-adjusted generalized log-rank
statistic}
\deqn{\hat\omega_k = \frac{|\hat U_k|}{n\,\hat\pi_k(1-\hat\pi_k)},}
where \eqn{\hat U_k} is the generalized log-rank score of Sun (1996)
evaluated at the pooled NPMLE \eqn{\hat{\mathbf p}} fitted once to the
full sample under the null hypothesis of no covariate effect.  Because
\eqn{\hat{\mathbf p}} and the resulting posterior weights \eqn{w_{ij}} are
shared across all \eqn{p} features, evaluating each feature reduces to
simple vector operations, achieving dramatic speed-ups over ADD-SIS
(Zhong et al., 2023), which requires \eqn{2p} stratified NPMLE fits.
}
\examples{
## ---- Example 1: Balanced binary predictors, linear model ----
set.seed(2025)
n   <- 200
p   <- 1000
rho <- 0.5

## Toeplitz covariance for latent continuous predictors
data <- GendataIC(n, p, rho, model = "linear", balanced = TRUE)
X <- data[[1]]   # n x p binary design matrix
L <- data[[2]]   # lower bounds
R <- data[[3]]   # upper bounds (Inf = right-censored)

## Run LogrankSIS (active predictors are indices 1, 2, 3, 19, 20)
result <- LogrankSIS(X, L, R, nsis = floor(n / log(n)))
cat("Active predictors recovered:", intersect(result, c(1, 2, 3, 19, 20)), "\n")

## ---- Example 2: Imbalanced binary predictors, Cox model ----
set.seed(2025)
data2 <- GendataIC(n, p, rho, model = "cox", balanced = FALSE)
X2 <- data2[[1]]; L2 <- data2[[2]]; R2 <- data2[[3]]

result2 <- LogrankSIS(X2, L2, R2, nsis = floor(n / log(n)))
cat("Active predictors recovered:", intersect(result2, c(1, 2, 3, 19, 20)), "\n")

}
\references{
Sun, J. (1996). A non-parametric test for interval-censored failure time
data with application to AIDS studies.
\emph{Statistics in Medicine}, \strong{15}, 1387--1395.

Zhao, Q. and Sun, J. (2004). Generalized log-rank test for mixed
interval-censored failure time data.
\emph{Statistics in Medicine}, \strong{23}(10), 1621--1629.

Zhong, W., Qian, C., Liu, W., Zhu, L., and Li, R. (2023). Feature
screening for interval-valued response with application to study
association between posted salary and required skills.
\emph{Journal of the American Statistical Association},
\strong{118}, 805--817.

Fan, J. and Lv, J. (2008). Sure independence screening for ultrahigh
dimensional feature space.
\emph{Journal of the Royal Statistical Society: Series B},
\strong{70}(5), 849--911.
}
