Correction for bias introduced by truncation in pharmacokinetics studies of environmental contaminants

Pharmacokinetic studies of biomarkers for environmental contaminants in humans are generally restricted to a few measurements per subject taken after the initial exposure. Subjects are selected for inclusion in the study if their measured body burden is above a threshold determined by the distribution of the biomarker in a control population. Such selection procedures introduce bias in the ordinary weighted least squares estimate of the decay rate λ caused by the truncation. We show that if the data are conditioned to lie above a line with slope - λ on the log scale then the weighted least squares estimate of λ is unbiased. We given an iterative estimation algorithm that produces this unbiased estimate with commercially available software for fitting a repeated measures linear model. The estimate and its efficacy are discussed in the context of a pharmacokinetic study of 2,3,7,8-tetrachlorodibenzo-p-dioxin. Unbiasedness and efficiency are demonstrated with a simulation.