Statistical Method for Missing Covariates
Date Issued
2012
Date
2012
Author(s)
Liu, Ting-Yin
Abstract
In many environmental and laboratory studies, instrument detection limits often lead to missing values of the data. The existing methods for the regression analysis for the data with at most two covariates subject to detection limits include simple substitution, imputation, and model-based methods. While either multiple continuous covariates or multiple categorical covariates alone are subject to detection limits, the most common approaches are the model-based method, Expectation-Maximization (EM) algorithm, and a Monte Carlo version of EM algorithm to obtain the maximum likelihood estimates via sampling.
In this paper, we consider a more complex case of missing covariates that both multiple continuous covariates subject to detection limits and categorical covariates with missing at random mechanism are presented in the logistic regression analysis. The aim of this paper is to provide a method for estimating the parameters of regression models for data with covariates subject to detection limit and missing at random mechanism. We use the Monte Carlo version for the E-step of the EM algorithm to tackle the high dimensional integration and summation due to the missing covariates subject to detection limits and random missing. We conduct a simulation study to compare the performance of the proposed Monte Carlo EM algorithm approach with the complete-case method and the imputation method proposed by Schisterman et al. (2006).
The results of the simulation study showed that the proposed approach resulted in relatively unbiased estimates with smaller standard error than the complete-case method and the imputation method by Schisterman et al, (2006).
Subjects
detection limits
maximum likelihood estimation
missing at random
Newton-Raphson methods
Type
thesis
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