New insights into modeling exposure measurements below the limit of detection

In environmental epidemiology, it is of interest to assess the health effects of environmental exposures. Some exposure analytes present values that are below the laboratory limit of detection (LOD). There have been many methods proposed for handling this issue to incorporate exposures subject to LOD in risk modeling using logistic regression. We present a fresh look at proposed methods to handle exposure analytes that present values that are below the LOD.

We performed comparisons through an extensive simulation study and a cancer epidemiology example. The methods we considered were a maximum-likelihood approach, multiple imputation, Cox regression, complete case analysis, filling in values below the LOD with , and a missing indicator method.

We found that the logistic regression coefficient associated with the exposure (subject to LOD) can be severely biased when underlying assumptions are not met, even with a relatively small proportion (under 20%) of measurements below the LOD.

We propose the use of a simple method where the relationship between the analyte and disease risk is modeled only above the detection limit with an intercept term at the LOD and a slope parameter, which makes no assumptions about what happens below the LOD. In most practical situations, our results suggest that this simple method may be the best choice for analyzing analytes with detection limits.