Nondetects, Detection Limits, and the Probability of Detection

Abstract

When chemists cannot quantify the concentration in a field sample, they report nondetect instead of a numerical measurement. A data analyst faced with environmental data containing nondetects might assume that all nondetects are zeros, all nondetects are smaller than the smallest detect (numerical measurement), or, if a detection limit is reported, that all nondetects are below the detection limit. This article shows that these assumptions can be incorrect and suggests better alternatives. The measurements that are likely to be reported as nondetect can be described by a new concept, the probability of acceptance, where acceptance means that a measurement passes the requirements for being reported as a detect. The 90th percentile of the probability of acceptance curve is a reasonable upper bound or censoring limit for a measurement reported as nondetect. The probability of acceptance also suggests the complexity of the data analysis task. For example, assuming that all nondetects are smaller than the smallest detect is reasonable if the probability of acceptance rises sharply from 0 to 1, but not if the probability of acceptance is nonmonotone. We show how to estimate the probability of acceptance and interpret the estimated probabilities for five soil pollutants from the 1988 Love Canal study. These examples show that, over the range of measurements seen in a study, the probability of acceptance need not be monotone. Statisticians must understand which measurements are likely to be reported as nondetect, because data analysis involves combining nondetects and numerical measurements. But health effects depend on true concentration, not measured concentration, and the public and toxicologists are more concerned with which true, field concentrations are likely to be detected. Since field concentrations are often measured with bias and imprecision, the probability of acceptance does not describe the probability of detection. We show how to estimate the probability of detection from field measurements and quality control data. We compare its 90th percentile, here called the minimum reliably detected concentration, to the detection limit that chemists usually report to describe which field concentrations can be detected. In the Love Canal study, for example, we find that the estimated probability of detecting a field concentration at the detection limit was sometimes almost 1 but sometimes only .5.

Key Words:

• Censored data
• Chemometrics
• Environmental data
• Interlaboratory comparison
• Local logistic regression
• Quality control
• Smoothing
• Threshold