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

Journal of Exposure Science & Environmental Epidemiology volume 22, pages 299–303 (2012)Cite this article

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A Corrigendum to this article was published on 18 April 2018

Abstract

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.

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Abbreviations

NHANES:

National Health and Nutrition Examination Survey

PFOA:

perfluorooctanoate

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Acknowledgements

Although no contract or grant funding supported this work, the author would like to acknowledge the C8 Science Panel and the C8 Class Action Settlement Agreement (Circuit Court of Wood County, WV) for funding his residential perfluorooctanoate half-life study that serves as one of the motivating examples.

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  1. Program in Public Health and Department of Statistics, University of California, Irvine, California, USA

    Scott M Bartell

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  1. Scott M Bartell
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Correspondence to Scott M Bartell.

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Appendix

Appendix

Equation (4) can be written more simply in terms of the random variables ɛi and several constants (values that may vary over time, but are fixed quantities not random variables):

 Let . Because ɛi is normally distributed with mean 0, ɛ* must also be normally distributed with mean 0. Thus, explaining why the error term does not appear in Eqs. (5), (6) and (7).

 The bias in the half-life estimate is a function of a quantity that depends on the error variances and is more difficult to calculate. For errors that are small relative to the predicted log biomarker concentrations, the denominator is approximately equal to c1 so the approximation used in Eqs. (8) and (9).

 Alternatively, the delta method states that for functions g(.) with existent second derivatives.17 The result of this method is thus:

 Therefore with either a relatively small error variance, often a reasonable assumption, or for studies with large enough sample sizes, an underlying assumption for most statistical methods, Eqs. (8) and (9) provide close approximations to the bias in half-life estimates from background exposures under the single compartment pharmacokinetic model for evenly spaced samples.

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Bartell, S. Bias in half-life estimates using log concentration regression in the presence of background exposures, and potential solutions. J Expo Sci Environ Epidemiol 22, 299–303 (2012). https://doi.org/10.1038/jes.2012.2

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