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The non-parametric maximum likelihood estimator and semi-parametric regression models are fundamental estimators for interval censored data, along with standard fullyparametric regression models. The R package icenReg is introduced which contains fast, reliable algorithms for fitting these models. In addition, the package contains functions for imputation of the censored response variables and diagnostics of both regression effects and baseline distribution.
Clifford Anderson-Bergman (Sun,) studied this question.