Linear regression with left-censored covariates and outcome using a pseudolikelihood approach

Area of Science:

• Environmental Science
• Biostatistics
• Toxicology

Background:

• Environmental toxicology studies frequently encounter data below the limit of quantification (left-censored data).
• Left-censored data pose significant challenges for standard regression analyses in toxicology.
• These challenges include censored covariates, non-normal toxicant distributions, and complex relationships between variables.

Purpose of the Study:

• To develop novel statistical methods for analyzing left-censored data in environmental toxicology.
• To address the complexities of censored outcomes, covariates, and recursive toxicant relationships.
• To provide accurate estimation of means and covariance matrices for censored toxicological data.

Main Methods:

• Proposed marginal and pseudo-likelihood based methods for estimating means and covariance matrices.
• Developed linear regression methods for outcomes and covariates as linear combinations of left-censored measures.
• Extended methods to handle recursive systems of modeling equations and employed bootstrap for standard errors and confidence intervals.

Main Results:

• Simulation studies confirmed the accuracy of the proposed methods across various study designs and censoring probabilities.
• The methods demonstrated effectiveness in handling complex scenarios involving left-censored environmental toxicological data.
• Accurate estimation of parameters was achieved even with high probabilities of left-censoring.

Conclusions:

• The developed statistical methods offer robust solutions for analyzing left-censored data in environmental toxicology.
• These methods improve the reliability of regression analyses when dealing with data below quantification limits.
• The approach was successfully illustrated using a community study on polychlorinated biphenyls exposure.