In many biological experiments, certain values of a biomarker are often nondetectable due to low concentrations of an analyte or the limitations of a chemical analysis device, resulting in left-censored values. There is an increasing demand for the analysis of data subject to detection limits in clinical and environmental studies. In this paper, we develop a novel statistical method for the maximum likelihood estimation in generalized linear models with covariates subject to detection limits. Simulations are carried out to study the relative performance of the proposed estimators, as compared to other existing estimators. The proposed method is also applied to a real dataset from the Maternal-Infant Research on Environmental Chemicals cohort study, where we investigate how different chemical mixtures affect the health outcomes of infants and pregnant women.

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Keywords generalized linear model, limit of detection, logistic regression, maximum likelihood estimate
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Journal Statistics in Medicine
Lee, W.-C. (Wan-Chen), Sinha, S. K, Arbuckle, T.E. (Tye E.), & Fisher, M. (Mandy). (2018). Estimation in generalized linear models under censored covariates with an application to MIREC data. Statistics in Medicine. doi:10.1002/sim.7942