A note on comparing exposure data to a regulatory limit in the presence of unexposed and a limit of detection

In some occupational health studies, observations occur in both exposed and unexposed individuals. If the levels of all exposed individuals have been detected, a two-part zero-inflated log-normal model is usually recommended, which assumes that the data has a probability mass at zero for unexposed individuals and a continuous response for values greater than zero for exposed individuals. However, many quantitative exposure measurements are subject to left censoring due to values falling below assay detection limits. A zero-inflated log-normal mixture model is suggested in this situation since unexposed zeros are not distinguishable from those exposed with values below detection limits. In the context of this mixture distribution, the information contributed by values falling below a fixed detection limit is used only to estimate the probability of unexposed. We consider sample size and statistical power calculation when comparing the median of exposed measurements to a regulatory limit. We calculate the required sample size for the data presented in a recent paper comparing the benzene TWA exposure data to a regulatory occupational exposure limit. A simulation study is conducted to investigate the performance of the proposed sample size calculation methods.