Interval-censored Linear Quantile Regression

Censored quantile regression has emerged as a prominent alternative toclassical Cox's proportional hazards model or accelerated failure time model inboth theoretical and applied statistics. While quantile regression has beenextensively studied for right-censored survival data, methodologies foranalyzing interval-censored data remain limited in the survival analysisliterature. This paper introduces a novel local weighting approach forestimating linear censored quantile regression, specifically tailored to handlediverse forms of interval-censored survival data. The estimation equation andthe corresponding convex objective function for the regression parameter can beconstructed as a weighted average of quantile loss contributions at twointerval endpoints. The weighting components are nonparametrically estimatedusing local kernel smoothing or ensemble machine learning techniques. Toestimate the nonparametric distribution mass for interval-censored data, amodified EM algorithm for nonparametric maximum likelihood estimation isemployed by introducing subject-specific latent Poisson variables. The proposedmethod's empirical performance is demonstrated through extensive simulationstudies and real data analyses of two HIV/AIDS datasets.