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Estimation of exposure distribution adjusting for association between exposure level and detection limit
Author(s) -
Yang Yuchen,
Shelton Brent J.,
Tucker Thomas T.,
Li Li,
Kryscio Richard,
Chen Li
Publication year - 2017
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.7335
Subject(s) - statistics , limit (mathematics) , estimation , distribution (mathematics) , association (psychology) , econometrics , computer science , mathematics , psychology , economics , mathematical analysis , management , psychotherapist
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.