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.
Highlights
Modeling continuous outcome data using linear regression usually assumes in theory that the values of the covariates are fully observed
To illustrate the methods proposed in this paper, we study the association between low\density lipo protein (LDL) in offspring and age at onset of clinically diagnosed cardiovascular even tin parents, using data from the Framingham Heart Study data base and looking at both the Original and Offspring cohorts [51]
Most of the literature on censored covariates deals with the issue of limits of detection, the point at which observations below this limit cannot be measured or detected and are instead recorded at the limit of detection value. [13,21,25] In this paper, we considered the estimation of linear regression models when the covariate of interest is randomly censored
Summary
Modeling continuous outcome data using linear regression usually assumes in theory that the values of the covariates are fully observed. We use simulation studies to compare this newly developed method to the methods proposed by Sampene & Folefac [20] in which randomly censored covariate values are replaced by a nonparametric and a semiparametric estimations of E (X|X≥τ) or E (X|X≥τ,Y), where τ denotes the maximum observation time for the variable X, and the outcome of interest Y. For this purpose, we will consider both dependent and independent censoring mechanism, which occurred depending on whether such a censoring mechanism depends or not on the outcome of interest. In practice, the data a than d contain a set of additional fully- observed (i.e. non-censored) covariates, Z, the method discussed here could be extended to accommodate such covariates
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