Temporal error in biomarker-based mean exposure estimates for individuals

Biomarker measurements from single time points are often used to make inferences about longer periods of toxicant intake. However, toxicant exposures rarely, if ever, occur under steady-state conditions, and biomarkers are typically most sensitive to recent toxicant exposures. Moreover, toxicant exposures are typically episodic and vary in magnitude over time. While it is often believed that the error introduced by the steady-state assumption is minimal and can safely be ignored, no rationale is typically presented to support this belief. Moreover, no guidelines have been established for determining a de minimus error level or for estimating the degree of error potentially introduced by a fallacious steady-state assumption in biomarker interpretation. We present a statistical framework for evaluating the potential magnitude of the error introduced by the steady-state fallacy and demonstrate applications of the framework to blood mercury and hair mercury exposure biomarkers in human adults. The magnitude of error clearly depends on many factors, including the exposure frequency, exposure magnitude, exposure duration, and exposure inference duration. Graphical presentation of the error as a function of those factors provides insight into the interpretation of mercury exposure biomarkers. We describe a general approach for determining the mean and variance of temporal error, present explicit solutions for several special cases, and demonstrate an example using the framework to evaluate the error resulting from the use of a steady-state model to estimate time-varying exposure from mercury biomarkers.