  Censored quantile regression has emerged as a prominent alternative to
classical Cox's proportional hazards model or accelerated failure time model in
both theoretical and applied statistics. While quantile regression has been
extensively studied for right-censored survival data, methodologies for
analyzing interval-censored data remain limited in the survival analysis
literature. This paper introduces a novel local weighting approach for
estimating linear censored quantile regression, specifically tailored to handle
diverse forms of interval-censored survival data. The estimation equation and
the corresponding convex objective function for the regression parameter can be
constructed as a weighted average of quantile loss contributions at two
interval endpoints. The weighting components are nonparametrically estimated
using local kernel smoothing or ensemble machine learning techniques. To
estimate the nonparametric distribution mass for interval-censored data, a
modified EM algorithm for nonparametric maximum likelihood estimation is
employed by introducing subject-specific latent Poisson variables. The proposed
method's empirical performance is demonstrated through extensive simulation
studies and real data analyses of two HIV/AIDS datasets.
