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.

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Published in Statistics in Medicine, v. 36, issue 18, p. 2935-2946.

Copyright © 2017 John Wiley & Sons, Ltd.

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This is the peer reviewed version of the following article: Yang, Y., Shelton, B. J., Tucker, T. T., Li, L., Kryscio, R., & Chen, L. (2017). Estimation of exposure distribution adjusting for association between exposure level and detection limit. Statistics in Medicine, 36(18), 2935-2946, which has been published in final form at https://doi.org/10.1002/sim.7335. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.

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This research was supported by the National Cancer Institute under grants R03CA179661 and P30CA177558. The colon cancer study was supported by the National Cancer Institute under grant R01CA136726.