Linear regression model with a randomly censored predictor:Estimation procedures

TL;DR

This paper evaluates various estimation methods for linear regression models with randomly censored covariates, comparing their efficiency and bias through simulations and real data application.

Contribution

It adapts existing estimation methods to handle random censoring in covariates and compares their performance under different scenarios.

Findings

Parametric, semiparametric, and nonparametric methods vary in bias and efficiency.

Simulation results highlight the impact of censoring mechanisms on estimation accuracy.

Application to Framingham data demonstrates practical differences among methods.

Abstract

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.