Bias in half-life estimates using log concentration regression in the presence of background exposures, and potential solutions

Regression of log serum concentrations or log urine concentrations on time elapsed after primary exposure ceases is a common method for estimating the elimination rates and corresponding half-lives for environmental contaminants. However, this method produces bias in the presence of ongoing background exposures. A general formula for the amount of bias introduced by background exposures under any single compartment pharmacokinetic model is derived here, and simpler expressions and graphical results are presented for the special case of regularly spaced biomarker measurements. The formulas are also applied to evaluate the potential bias from background exposures in recently published half-life estimates for perfluorooctanoate. These published half-lives are likely to be overestimated because of bias from background exposures, by about 1-26%. Background exposures can contribute substantial bias to half-life estimates based on longer follow-up times, even when the background contribution constitutes a small fraction of total exposure at baseline.