Estimation in generalized linear models under censored covariates with an application to MIREC data

Abstract

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.

Prediction Methods for High Dimensional Data with Censored Covariates

“…While the Tobit model was initially introduced to handle censored responses, the concept can be applied also for censored covariates, such as for instance in [23]. While maximum likelihood approaches extend to cases with several censored covariates present [22], [26] and can therefore be considered scalable in theory, they are usually computationally heavy and therefore have limited scaling potential in practice.…”

“…Linear regression is used to obtain maximum likelihood estimates for right and left censored data in [23], and the method can handle censoring in both the response and the covariates. [22] presents a more general approach than ordinary linear regression which instead uses generalized linear models suitable for the case when potentially all covariates are subject to censoring.…”

Bayesian Prediction with Covariates Subject to Detection Limits

“…Moreover, much of the existing literature on covariates subject to detection limits is limited to situations with a small number of covariates, and the focus is typically parameter inference rather than prediction and decision making. Lee et al (2018) handle data where potentially all covariates are subject to detection limits using a generalized linear model estimated with maximum likelihood. A similar approach is developed in de Lima Taga and Singer (2018) for a Gaussian linear regression model.…”

Nonparametric regression with right‐censored covariate via conditional density function

“…To obtain robust and more efficient estimators, Kong and Nan 16 proposed a two‐step semiparametric likelihood‐based approach to fit the generalized linear models. By taking into account all possible values below the limit of detection, Lee et al 17 incorporated a weight function into the likelihood function. Moreover, Wang and Feng 5 and Bernhardt et al 18 examined parametric regression (linear models or AFT models) through multiple imputation, but with covariates just subject to detection limits.…”