Accommodating measurements below a limit of detection: A novel application of cox regression

Gregg E. Dinse, Todd A. Jusko, Lindsey A. Ho, Kaushik Annam, Barry I. Graubard, Irva Hertz-Picciotto, Frederick W. Miller, Brenda W. Gillespie, Clarice R. Weinberg

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


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 misspecified. 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.

Original languageEnglish (US)
Pages (from-to)1018-1024
Number of pages7
JournalAmerican Journal of Epidemiology
Issue number8
StatePublished - Apr 15 2014


  • 2,3,7,8-tetrachlorodibenzo-p-dioxin
  • 2,4,4′-trichlorobiphenyl
  • hazard identification
  • limit of detection
  • National Health and Nutrition Examination Survey
  • nondetects
  • proportional hazards

ASJC Scopus subject areas

  • Epidemiology


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