Accommodating Measurements Below a Limit of Detection: A Novel Application of Cox Regression

• Published in: American journal of epidemiology Vol. 179; no. 8; pp. 1018 - 1024
• Main Authors: Dinse, Gregg E., Jusko, Todd A., Ho, Lindsey A., Annam, Kaushik, Graubard, Barry I., Hertz-Picciotto, Irva, Miller, Frederick W., Gillespie, Brenda W., Weinberg, Clarice R.
• Format: Journal Article
• Language: English
• Published: Cary, NC Oxford University Press 15.04.2014; Oxford Publishing Limited (England)
• Subjects: Biological and medical sciences; Biomarkers; Biomarkers - blood; Case-Control Studies; Clinical outcomes; Cohort Studies; Computer Simulation; Confounding Factors, Epidemiologic; Cross-Sectional Studies; Data Interpretation, Statistical; Developmental Disabilities - blood; Developmental Disabilities - chemically induced; Dioxins; Environmental Exposure - analysis; Environmental Pollutants - blood; Environmental Pollutants - toxicity; Epidemiologic Research Design; Epidemiology; Female; General aspects; Health Surveys; Human exposure; Humans; Infant; Limit of Detection; Linear Models; Logistic Models; Male; Mathematical models; Medical sciences; Metabolic diseases; Miscellaneous; Models, Theoretical; Odds Ratio; Polychlorinated Biphenyls - blood; Polychlorinated Biphenyls - toxicity; Polychlorinated Dibenzodioxins - blood; Practice of Epidemiology; Proportional Hazards Models; Prospective Studies; Psychomotor Disorders - blood; Psychomotor Disorders - chemically induced; Public health. Hygiene; Public health. Hygiene-occupational medicine; Regression analysis; Sex Factors; Nutrition; Nutrition survey; hazard identification; Regression; Identification; limit of detection; Epidemiology; 2,3,7,8-tetrachlorodibenzo-p-dioxin; proportional hazards; Feeding; 2,4,4'-trichlorobiphenyl; nondetects; Limit; Detection; National Health and Nutrition Examination Survey; Hazard; Public health; 2,4,4′-trichlorobiphenyl
• ISSN: 0002-9262; 1476-6256; 1476-6256
• DOI: 10.1093/aje/kwu017

In environmental epidemiology, measurements of exposure biomarkers often fall below the assay's limit of detection. Existing methods for handling this problem, including deletion, substitution, parametric regression, and multiple imputation, can perform poorly if the proportion of "nondetects" is high or parametric models are mis-specified. We propose an approach that treats the measured analyte as the modeled outcome, implying a role reversal when the analyte is a putative cause of a health outcome. Following a scale reversal as well, our approach uses Cox regression to model the analyte, with confounder adjustment. The method makes full use of quantifiable analyte measures, while appropriately treating nondetects as censored. Under the proportional hazards assumption, the hazard ratio for a binary health outcome is interpretable as an adjusted odds ratio: the odds for the outcome at any particular analyte concentration divided by the odds given a lower concentration. Our approach is broadly applicable to cohort studies, case-control studies (frequency matched or not), and cross-sectional studies conducted to identify determinants of exposure. We illustrate the method with cross-sectional survey data to assess sex as a determinant of 2,3,7,8-tetrachlorodibenzo-p-dioxin concentration and with prospective cohort data to assess the association between 2,4,4'-trichlorobiphenyl exposure and psychomotor development.