About detection limits

The low end of a measuring range raises three questions: how high a sample with no analyte can read, how low a concentration the method reliably detects, and how low it measures well enough for the laboratory's purpose. The limit of blank, limit of detection and limit of quantitation answer them in turn. Detection limits runs the study, and the Detection limits reference gives its settings, rules and formulas.

The limit of blank (LoB) is the highest result expected from a sample with no analyte. Only a small share of blank results, α, is expected to read above it.

The limit of detection (LoD) is the lowest concentration that reliably reads above the LoB, so it is built on the LoB. It sits above the LoB by a multiple of the pooled SD of low-level results, chosen so that only a small share of results at the LoD, β, reads at or below the LoB. The multiplier is z(1−β) adjusted for the degrees of freedom behind the pooled SD; more low results bring it closer to 1.645. Pooling assumes the low materials share one SD, and the ratio between the largest and smallest material SD shows how well that holds. The LoB beneath an LoD can come from blanks in the same study or be stated from elsewhere.

The limit of quantitation (LoQ) is the lowest tested concentration whose results meet the laboratory's own precision or accuracy goal and where every higher tested concentration also meets it. It cannot be below a stated LoD.

The percentile method reads the LoB directly from the sorted blank results, so it needs enough blanks for the percentile to fall within them, and more again before the LoB has an upper confidence limit. The Gaussian method, mean + z·SD, works from the blank mean and SD and assumes normally distributed blanks. A blank mean above the median suggests skew, as in the established LoB example, where the two methods give different limits.

A study either establishes a limit from its own data or verifies a claimed limit, for example from a package insert. Establishing gives an estimate with a confidence interval, which the laboratory compares with the largest estimate it accepts.

Verifying an LoB or LoD compares a share with the smallest share the laboratory accepts: blanks at or below the claimed LoB, or low results above the LoB at the claimed LoD. The share implied by α or β is shown for reference, and the laboratory's verification share decides. A verification rests on materials at the claimed concentration. An LoQ is verified by checking the quantitation goal at the claimed LoQ.

Three things weaken any of these results: an LoB from few blanks, a large SD ratio between low materials, and a share whose lower confidence bound is well below the reference share.

Near the low end, a result can be reported only as below a limit, such as <0.01. The study ranks such a result below every exact result and never replaces it with a number. A rank is enough for a percentile, so a percentile LoB can use censored blanks as long as the percentile falls above them. A mean and SD need exact values, so calculations built on them can't. Censored results lists how each limit treats them, and Handle missing and censored values covers the other studies.