  We consider linear regression model estimation where the covariate of
interest is randomly censored. Under a non-informative censoring mechanism, one
may obtain valid estimates by deleting censored observations. However, this
comes at a cost of lost information and decreased efficiency, especially under
heavy censoring. Other methods for dealing with censored covariates, such as
ignoring censoring or replacing censored observations with a fixed number,
often lead to severely biased results and are of limited practicality.
Parametric methods based on maximum likelihood estimation as well as
semiparametric and non-parametric methods have been successfully used in linear
regression estimation with censored covariates where censoring is due to a
limit of detection.
  In this paper, we adapt some of these methods to handle randomly censored
covariates and compare them under different scenarios to recently-developed
semiparametric and nonparametric methods for randomly censored covariates.
Specifically, we consider both dependent and independent randomly censored
mechanisms as well as the impact of using a non-parametric algorithm on the
distribution of the randomly censored covariate. Through extensive simulation
studies, we compare the performance of these methods under different scenarios.
Finally, we illustrate and compare the methods using the Framingham Health
Study data to assess the association between low-density lipoprotein (LDL) in
offspring and parental age at onset of a clinically-diagnosed cardiovascular
event.
