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. (
Journal of Exposure Science and Environmental Epidemiology
INTRODUCTIONRegression of log serum concentrations on time is a long practiced method for estimating first-order elimination rates of contaminants and drugs after exposure ceases. 1 --8 Similar methods are used for urine concentrations and other biomarkers. After exposure ceases, the first-order elimination implies the following equation:where C t is the serum concentration at time t, C 0 is the serum concentration at baseline (time 0), and k is the elimination rate constant. Therefore, if the errors are independent, normally distributed, and homoscedastic, the slope from linear regression of log concentrations reliably estimates Àk, and the intercept estimates ln C 0 . The apparent half-life t 1/2 ¼ ln(2)/k. Adjustment for covariate effects on the serum concentrations is easily handled by adding additional terms to the model on the right hand side of Eq.(1), provided that the covariates have constant multiplicative effects on serum concentrations over time. 7 Studies of post-shift workers, 2,5 retired workers, 4 fasting subjects, 6 and subjects undergoing exposure interventions 7,9 have used regression of log biomarker concentrations on time to estimate elimination rate constants and corresponding half-lives for environmental contaminants. However, Eq. (1) does not apply when any of the exposures are continuing, as occurs in many studies of environmental contaminants because of ongoing background exposures. With a constant background exposure that continues after some larger exposure ceases, as might be expected for retired workers, residents who leave a contaminated community, or anyone who has undergone an exposure intervention that eliminates most but not all exposure to a toxicant, the first-order elimination model implies the following:where C N is the background contribution to the serum concentration at any point in time. 10 When C N is very small relative to C 0 , Eqs. (1) and (2) are approximately eq...