Epidemiologic Evaluation of Measurement Data in the Presence of Detection Limits

Abstract

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.

Airborne concentrations of benzene for dock workers at the ExxonMobil refinery and chemical plant, Baton Rouge, Louisiana, USA (1977–2005)

“…The ROS method was developed by Helsel & Cohn (25) and is the method that Hewett (26) refers to as the robust multiple censoring point log probit regression method, one of the censored data methods used in the IH DataAnalyst (IHDA) program. The ROS method was used because it is fairly robust even when the percentage of data below detection is fairly high (50-70%), and even with moderate deviations from the distribution assumptions (27)(28)(29)(30)(31). The benzene concentration data were tested Widner et al for distribution fit using the Kolmogorov-Smirnov goodness-of-fit test for normal, lognormal, and gamma distributions.…”

Pre‐diagnostic blood immune markers, incidence and progression of B‐cell lymphoma and multiple myeloma: Univariate and functionally informed multivariate analyses

“…Median intra class correlation coefficient (ICC) of the measured analytes was 0.87 and was above 0.5, except for MDC and FGF‐2 (0.16 and 0.43, respectively) (Supporting Information Table S1). Cytokine levels measured out of range of the calibration curve (either too low: <limit of detection (LOD), or too high) and missing values for covariate (body mass index [ n  = 8], smoking status [ n  = 14], education [ n  = 16], alcohol intake [ n  = 41], physical activity [ n  = 2]) were imputed based on a maximum likelihood estimation method which was informed by the observed correlation structure within the data 22. Imputation of samples <LOD was carried out using the empirical LOD across all plates as the upper bound.…”

Sensitization and chronic beryllium disease at a primary manufacturing facility, part 1: historical exposure reconstruction

“…The general area data (N=76 349 for the years 1994-1999) were collected from 274 fixed locations within the 24 process areas (identified in table 1) across all production and selected non-production units. General area air samples were collected using three sampling methods including: high volume (200-400 Lpm), continuous (10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20), and low-flow (2 Lpm) sampling methods (14). While information on sampling methods was not available, sampling durations of the general area samples included: 1-5 days (4.5%), 10-24 hours (10%), 6-10 hours (76%), <6 hours (9.5%).…”

“…The trends in exposure over time were evaluated using the general area data in regression models to estimate the overall and process-specific annual change in exposure for the years 1994-1998, compared to the baseline year of 1999. A large fraction of the general area data were below the LOD in the different process areas (table 1), thus the temporal factors for the years by process areas (TF pa,y ) were estimated using Tobit regression models (15). Tobit regression uses the maximum likelihood estimate (MLE) method to provide estimates of the temporal factors while accounting for the measurement data below the LOD.…”