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.

Original languageEnglish
Pages (from-to)2935-2946
Number of pages12
JournalStatistics in Medicine
Issue number18
StatePublished - Aug 15 2017

Bibliographical note

Publisher Copyright:
Copyright © 2017 John Wiley & Sons, Ltd.


  • detection limits
  • environmental exposure
  • kernel smoothing
  • left-censored data
  • nonparametric estimator

ASJC Scopus subject areas

  • Epidemiology
  • Statistics and Probability


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