| We present several probability models relating time-varying chemical exposures and measured biomarkers such as blood mercury and hair mercury concentrations, using a discrete approximation to available continuous-time biokinetic models. Equations describing the expectation and variance of "temporal error," the difference between a steady state exposure estimate and the true average exposure in an individual with known kinetic parameters, are presented and used to evaluate the reliability of individual steady state average exposure estimates for several different mercury exposure scenarios involving intermittent seafood consumption. We show that steady state exposure estimates are imprecise under many conditions, supporting the development and use of temporally explicit methods. We examine several statistical approaches that could be used in this setting including saddlepoint estimation, the EM algorithm, generalized estimating equations, and several Bayesian methods, and use simulation studies to examine the properties of estimators based on several of these approaches. Generalized estimating equations appear to be the most practical and reliable approach for this setting at the present time. Bayesian methods are also available but are computationally expensive; we suggest a normal approximation to part of the exposure history in order to hasten computations. Our methods allow for the explicit incorporation of information on biokinetics, exposure intermittency, and measurement error in biomarker based exposure estimation, and allow for estimation of exposure variability as well as average exposures. |
