Statistical models for exposure-biomarker relationships with measurement error and censoring

Abstract

Measurements of biomarkers have been used, in conjunction with those of external exposure, to provide information about the rates of human uptake, bioactivation, and detoxification of chemicals. Direct knowledge of these processes is valuable because it can reduce reliance on animal models for making extrapolations about disease risks in humans. In practice, however, valid and precise quantification of exposure—biomarker relationships has been hampered by a number of problems. These include errors in the measurement of true mean exposure and true mean biomarker levels, nonlinear exposure—biomarker relationships, background biomarker levels in unexposed individuals, and response levels that fall below analytic limits of detection. In this article we develop nonlinear mixed models and corresponding likelihood expressions that can address these concerns, and we describe maximum likelihood estimation techniques that permit valid statistical inferences to be made using standard software. The models and methods are applied to both experimental and simulated exposure—biomarker data to illustrate their utility and limitations.