Use of multiple assays subject to detection limits with regression modeling in assessing the relationship between exposure and outcome

BACKGROUND: The goal of many studies in environmental epidemiology is to assess the relationship between chemical exposure and disease outcome. Often various assays can be used to measure a particular environmental exposure, with some assays being more invasive or expensive than others. METHODS: We consider the situation in which 2 assays can be used to measure an environmental exposure. The first assay has measurement error and is subject to a lower detection limit (LOD), and the second assay has less measurement error and is not subject to a lower LOD. In this situation, the first assay is less invasive or less expensive and is measured in all study participants, whereas the second assay is more invasive or more expensive and is only measured in a subset of individuals. We develop a flexible class of regression models that incorporates both sets of assay measurements and allows for continuous or binary outcomes. We explore different design strategies for selecting the subset of patients in whom to measure the second assay. One design strategy is to measure the second more invasive or expensive assay only when the first assay is below LOD. We compare these designs with a simple design in which the second assay is measured in a random subset of patients without regard to the results of the first assay. RESULTS: We develop estimation approaches for these regression models. We demonstrate through simulations that there are efficiency advantages of measuring the second assay in at least a fraction of cases in which the first assay is above LOD. We illustrate the methodology by using data from a study examining the effect of environmental polychlorinated biphenyl exposure on the risk of endometriosis. CONCLUSION: The proposed methodology has good statistical properties and will be a useful methodological technique for studying the effect of exposure on outcome when exposure assays are subject to LOD.