Epidemiologic evaluation of measurement data in the presence of detection limits

Quantitative measurements of environmental factors greatly improve the quality of epidemiologic studies but can pose challenges because of the presence of upper or lower detection limits or interfering compounds, which do not allow for precise measured values. We consider the regression of an environmental measurement (dependent variable) on several covariates (independent variables). Various strategies are commonly employed to impute values for interval-measured data, including assignment of one-half the detection limit to nondetected values or of "fill-in" values randomly selected from an appropriate distribution. On the basis of a limited simulation study, we found that the former approach can be biased unless the percentage of measurements below detection limits is small (5-10%). The fill-in approach generally produces unbiased parameter estimates but may produce biased variance estimates and thereby distort inference when 30% or more of the data are below detection limits. Truncated data methods (e.g., Tobit regression) and multiple imputation offer two unbiased approaches for analyzing measurement data with detection limits. If interest resides solely on regression parameters, then Tobit regression can be used. If individualized values for measurements below detection limits are needed for additional analysis, such as relative risk regression or graphical display, then multiple imputation produces unbiased estimates and nominal confidence intervals unless the proportion of missing data is extreme. We illustrate various approaches using measurements of pesticide residues in carpet dust in control subjects from a case-control study of non-Hodgkin lymphoma.