STATISTICS
Limit LoB
LoD LoQ Question answered
How high can an analyte free sample appear to read?
At what low concentration is detection achieved with a stated probability?
At what lowest concentration does the procedure meet predefined quantitative performance?
Table 1. Outline of the information provided by LoB, LoD and LoQ.
LoB under the conditions represented by the study. A result just above the LoB is therefore unlikely to have arisen from the blank distribution alone, but it is not automatically suitable for quantification. For approximately Gaussian blank
results, a familiar calculation is LoB = meanblank
+ 1.645 × SDblank . The
multiplier (1.645) represents the 95th percentile of a one-sided normal distribution. This equation is inappropriate when its assumptions are not met. Blank results are often bounded at zero, rounded, censored or skewed. A percentile or another method justified for the observed distribution may then be preferable. The selected blank materials must also represent the relevant matrix and sources of background response. Reagent water may underestimate the blank behaviour of a biological matrix.
Limit of detection
The LoD is the lowest concentration expected to be detected with a stated probability under defined conditions. The LoB controls the chance that a blank is reported as a measured result, while the LoD is chosen so that approximately 95% of samples at that concentration produce results above the LoB. The LoD therefore must be a property of two distributions: the blank and a low concentration sample.
Stage Define intended use Choose materials Distribute runs Predefine errors and criteria Inspect distributions Estimate uncertainty Again under simple Gaussian
assumptions, the relationship is often shown as LoD = LoB + 1.645 × SDlow
. That
is a teaching approximation, not a universal law. If variance changes with concentration, blank distributions are non-Gaussian, calibration is non-linear near zero or results are censored, the study and analysis must accommodate those features. Probability of detection modelling across several concentrations can be more informative than applying a multiplier to one pooled standard deviation.1–3
Limit of quantitation
The LoQ is the lowest concentration at which a result meets predefined requirements for quantitative use. The requirement may include imprecision, bias, total error, uncertainty or a combination appropriate to the intended use. This makes LoQ partly statistical and partly a performance decision. The data describe what the method does. The acceptance criterion defines what ‘good enough’ means. A fixed rule such as “LoQ is where CV
equals 20%” is not generally defensible. Twenty per cent may be too permissive for a narrow clinical decision and unnecessarily strict for monitoring a large biological change. Relative
Practical design question
Is the result used to detect presence, report a number, classify around a decision point, or monitor change?
Do blanks and low pools behave like patient samples and span relevant matrices or lots?
Are measurements spread across days, runs, operators, reagent lots and calibrations relevant to routine use?
What false positive/false negative probabilities define detection, and what performance defines quantification?
Are results rounded, censored, skewed, heteroscedastic (variance changes) or affected by outliers with clear causes?
How precise is the estimated limit and could plausible sampling variation alter the claim?
Table 2. Steps involved in designing a practical study. 18
WWW.PATHOLOGYINPRACTICE.COM October 2026
imprecision also becomes unstable as the mean approaches zero. Criteria should be set before examining the results and linked to the use of the number. Bias deserves explicit consideration when reference values are available. A reproducible but materially biased low result is not necessarily quantitatively acceptable.
Designing a practical study The design should begin with the claim to be evaluated, and the intended clinical use (Table 2). Establishing a new limit requires enough materials, days and replicates to characterise the relevant distributions. Verifying an existing manufacturer claim is a narrower question. Can the laboratory reproduce the claimed capability under local conditions? The sample numbers and analysis should follow the selected protocol and claim. A small verification dataset should not be presented as a fresh establishment study. The terminology also sits within
broader analytical nomenclature, capability of detection standards and method validation practice.4–7
Those
frameworks are useful context, but they should not be blended into a hybrid calculation without stating which definition, error probabilities and acceptance criteria govern the claim.
Main risk if ignored
A statistically correct limit that does not support the clinical use
Underestimated background or variance from non-commutable material
A repeatability experiment mislabelled as routine detection capability
Post hoc thresholds selected to make the method pass Invalid Gaussian calculations or concealed process failures False confidence in a single decimal value Primary data Blank or analyte free materials Blank plus low level samples
Several low levels spanning the expected boundary
What it does not extablish
Reliable detection or acceptable numerical performance
A result accurate and precise enough to report quantitatively
Linearity across the full measuring interval or clinical usefulness by itself
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