Each individual pollutant has different degrees of measurement error. Exposure measurement errors are generally non-differential when the errors are independent of each other and the disease status [66]. Therefore, it is expected that environmental pollutants measured with less non-differential measurement error such as those with lower temporal variability are more likely to be detected (e.g., PCBs vs. phthalates). However, differential measurement errors may occur when exposure measurement errors are not independent because some of the effects of more poorly measured exposures may be transferred to the effect estimates of better-measured exposures [67]. In addition, most of the pollutant variables used in our study are subject to a limit of detection (LOD). Several ad hoc substitution methods, such as substitution of LOD/2 or LOD/√2 for values below LOD, are widely used (NHANES used LOD/√2). These ad hoc methods, however, can lead to bias especially when the proportion of values below LOD is high [68]. Maximum likelihood estimation based on a parametric joint distribution assumption for all the exposures, for example, multivariate normal distribution, may reduce potential bias if the parametric distribution assumption is correct [69].
