Much ado about next to nothing: incorporating nondetects in science.

A great many papers and one textbook have been published on the topic of how to incorporate 'nondetects', low-level values reported only as below a detection limit, into statistical analyses. This is of interest not only in occupational hygiene but also in environmental sciences and astronomy, among other fields. Here, the literature is reviewed from the earliest known publication on the topic >40 years ago and recommendations contrasted. I have tried to pull some unifying conclusions out of the mix, ending with four suggestions I believe all can agree on. See if you agree with me.

[1]  Masoud Kayhanian,et al.  Statistical approaches to estimating mean water quality concentrations with detection limits. , 2002, Environmental science & technology.

[2]  A. Cohen,et al.  Tables for Maximum Likelihood Estimates: Singly Truncated and Singly Censored Samples , 1961 .

[3]  R. A. Crovelli,et al.  An objective replacement method for censored geochemical data , 1993 .

[4]  D. Helsel,et al.  Estimation of Distributional Parameters for Censored Trace Level Water Quality Data: 2. Verification and Applications , 1986 .

[5]  A. T. Miesch.  Methods of computation for estimating geochemical abundance , 1967 .

[6]  Thomas Mathew,et al.  Model-based imputation approach for data analysis in the presence of non-detects. , 2009, The Annals of occupational hygiene.

[7]  Murray M Finkelstein,et al.  Asbestos fibre concentrations in the lungs of brake workers: another look. , 2008, The Annals of occupational hygiene.

[8]  Robert J. Gilliom,et al.  Estimation of Distributional Parameters for Censored Trace Level Water Quality Data: 1. Estimation Techniques , 1986 .

[9]  R. J. Gilliom,et al.  ESTIMATION OF DISTRIBUTIONAL PARAMETERS FOR CENSORED TRACE-LEVEL WATER-QUALITY DATA , 1984 .

[10]  R. O N A L,et al.  Evaluation of Statistical Treatments of Left-Censored Environmental Data using Coincident Uncensored Data Sets : I . Summary Statistics , 2008 .

[11]  A. Cohen,et al.  ON THE SOLUTION OF ESTIMATING EQUATIONS FOR TRUNCATED AND CENSORED SAMPLES FROM NORMAL POPULATIONS , 1957 .

[12]  Michael R Flynn,et al.  Analysis of censored exposure data by constrained maximization of the Shapiro-Wilk W statistic. , 2010, The Annals of occupational hygiene.

[13]  Dennis R. Helsel,et al.  Less than obvious - statistical treatment of data below the detection limit , 1990 .

[14]  Scott Clark,et al.  Imputation of Data Values That are Less Than a Detection Limit , 2004, Journal of occupational and environmental hygiene.

[15]  Timothy A. Cohn,et al.  Estimation of descriptive statistics for multiply censored water quality data , 1988 .

[16]  P. I. Nelson,et al.  Statistical methods for astronomical data with upper limits. I - Univariate distributions , 1985 .

[17]  Dennis R. Helsel,et al.  Nondetects and data analysis : statistics for censored environmental data , 2004 .

[18]  P. Hewett,et al.  A comparison of several methods for analyzing censored data. , 2007, The Annals of occupational hygiene.