The Limitations due to Exposure Detection Limits for Regression Models

Abstract

Biomarker use in exposure assessment is increasingly common, and consideration of related issues is of growing importance. Exposure quantification may be compromised when measurement is subject to a lower threshold. Statistical modeling of such data requires a decision regarding the handling of such readings. Various authors have considered this problem. In the context of linear regression analysis, Richardson and Ciampi (Am J Epidemiol 2003;157:355-63) proposed replacement of data below a threshold by a constant equal to the expectation for such data to yield unbiased estimates. Use of such an imputation has some limitations; distributional assumptions are required, and bias reduction in estimation of regression parameters is asymptotic, thereby presenting concerns about small studies. In this paper, the authors propose distribution-free methods for managing values below detection limits and evaluate the biases that may result when exposure measurement is constrained by a lower threshold. The authors utilize an analytical approach and a simulation study to assess the effects of the proposed replacement method on estimates. These results may inform decisions regarding analytical plans for future studies and provide a possible explanation for some amount of the discordance seen in extant literature.

Exposure to Ethylene Oxide in Hospitals: Biological Monitoring and Influence of Glutathione S-Transferase and Epoxide Hydrolase Polymorphisms

“…Attributing a fixed value to samples with HEMA concentrations below the detection limit may be a source of error (33,34). Therefore, regression equations were carried out again in the subgroup with HEMA concentrations above the limit of detection in both urine samples included in the regression model (1 and 2, and 2 and 3, respectively).…”

Associations between IVF outcomes and essential trace elements measured in follicular fluid and urine: a pilot study

“…Method detection limits (MDL) for trace elements were calculated based on three times the standard deviation of the mean values of trace elements at low concentrations (i.e., matrix blank). We did not impute quantities below the MDL, but used the instrument generated data (including zeros and negative values) to avoid the introduction of bias that can occur with the former approach [22]. The laboratory staff was blinded to clinical data and to the study outcomes.…”

Associations between toxic metals in follicular fluid and in vitro fertilization (IVF) outcomes

“…The limits of detection (LODs) were defined as three times the standard deviation of the quantity measured in matrix blanks and are equal to 0.2 μg/L for Hg, 0.02 μg/L for Cd, and 0.03 μg/L for Pb. All laboratory values were reported irrespective of the LODs; this distribution-free approach precludes bias that may be introduced into regression models by censoring values below LODs [29]. Specimens were carefully examined for potential blood contamination; two pink specimens were excluded.…”