Evaluation of statistical treatments of left-censored environmental data using coincident uncensored data sets: I. Summary statistics

Environ Sci Technol. 2008 May 15;42(10):3732-8. doi: 10.1021/es071301c.


The main classes of statistical treatment of below-detection limit (left-censored) environmental data for the determination of basic statistics that have been used in the literature are substitution methods, maximum likelihood, regression on order statistics (ROS), and nonparametric techniques. These treatments, along with using all instrument-generated data (even those below detection), were evaluated by examining data sets in which the true values of the censored data were known. It was found that for data sets with less than 70% censored data, the best technique overall for determination of summary statistics was the nonparametric Kaplan-Meier technique. ROS and the two substitution methods of assigning one-half the detection limit value to censored data or assigning a random number between zero and the detection limitto censored data were adequate alternatives. The use of these two substitution methods, however, requires a thorough understanding of how the laboratory censored the data. The technique of employing all instrument-generated data--including numbers below the detection limit--was found to be less adequate than the above techniques. At high degrees of censoring (greater than 70% censored data), no technique provided good estimates of summary statistics. Maximum likelihood techniques were found to be far inferior to all other treatments except substituting zero or the detection limit value to censored data.

Publication types

  • Evaluation Study

MeSH terms

  • Environmental Monitoring / statistics & numerical data*
  • Likelihood Functions
  • Sensitivity and Specificity