Estimation of exposure distribution adjusting for association between exposure level and detection limit

In environmental exposure studies, it is common to observe a portion of exposure measurements to fall below experimentally determined detection limits (DLs). The reverse Kaplan-Meier estimator, which mimics the well-known Kaplan-Meier estimator for right-censored survival data with the scale reversed, has been recommended for estimating the exposure distribution for the data subject to DLs because it does not require any distributional assumption. However, the reverse Kaplan-Meier estimator requires the independence assumption between the exposure level and DL and can lead to biased results when this assumption is violated. We propose a kernel-smoothed nonparametric estimator for the exposure distribution without imposing any independence assumption between the exposure level and DL. We show that the proposed estimator is consistent and asymptotically normal. Simulation studies demonstrate that the proposed estimator performs well in practical situations. A colon cancer study is provided for illustration. Copyright © 2017 John Wiley & Sons, Ltd.