Detection limits

Run this study#

Bring: blank and low-level materials in your sample matrix, their assigned concentrations, each individual reading and the reagent lot. Use one lot per study.

Decide first: which limit (Which limit, in the New study dialog) and whether you are establishing it or verifying a claim (Objective, on Set up). Under Acceptance limits, choose Enter your own limit: the largest acceptable limit when establishing, or the smallest acceptable Verification share when verifying an LoB or LoD. LoQ verification needs no limit: its quantitation goal decides.

Enter the results: on Data, choose Import a file and choose your file (start from Blank template (CSV) or the CSV layout linked for your limit below). Answer any question the dialog asks, then choose Import into this study.

Finish: choose Calculate results and review Results. On Report, choose Download PDF.

These are suggested starting plans. Adjust the counts to your goal and the precision you need. The calculation minimums are the fewest results that can be calculated.

LoB: how high can a blank read?#

1. Test 4 blank materials × 4 replicates per day × 5 days = 80 blank results. Enter material, role blank, result, lot, day, run and replicate in the LoB CSV layout.
2. Choose the percentile or Gaussian method. To verify, also enter the claimed LoB.
3. Calculate and check the blank distribution and interval. The calculation minimum is 2 blanks. At default settings, a nonparametric LoB needs 72 blanks for an upper confidence limit, so 80 leaves a margin.

LoD: how low can the method detect?#

1. Test 3 low materials near the expected LoD × 4 replicates per day × 5 days = 60 low results. If you estimate the LoB in the same study, add the 80 blanks above: 140 results total. Or use a stated LoB.
2. Enter each low material's assigned concentration and exact readings in the LoD CSV layout. To verify, prepare all three low materials at the claimed LoD, enter the claim, and give each material an assigned concentration equal to the claim, on any one of its rows. Without it, verification is Undecided.
3. Calculate and check the low-level SDs and detection shares. Each low material needs 2 exact results for its SD. The LoD comes from the LoB and the pooled low-level SD.

LoQ: how low can the method quantify acceptably?#

1. Test 5 low concentrations spanning the point where results start to meet your goal × 4 replicates per day × 5 days = 100 results in the LoQ CSV layout. To verify, include a material assigned exactly at the claim.
2. Set a CV, bias-plus-CV or total-error goal before testing. Assigned concentrations must be above zero. Keep every individual reading.
3. Check the goal result for each concentration. You need at least 2 low materials, each with 2 exact results for SD-based goals. The LoQ is one of the concentrations you tested. If every level passes, test lower. If none passes, test higher.

Purpose#

• Limit of blank (LoB): the highest result expected from a sample with no analyte.
• Limit of detection (LoD): the lowest concentration that reliably reads above the LoB.
• Limit of quantitation (LoQ): the lowest concentration whose results meet your own precision or accuracy goal.

You can establish each limit from your data or verify a claimed limit, for example from a package insert. One study covers one limit and one objective.

When to use it#

Use it for the LoB, LoD or LoQ of a quantitative method. For a qualitative cutoff, use Near-cutoff precision. For performance higher in the range, use Linearity or Repeatability.

Study setup#

1. In your project choose New study. Enter Analyte and Unit, select Detection limits under Measuring range, choose Which limit, then Create study, or Create and import data if you already have results.
2. On Set up, under Detection capability, choose the Objective (Establish from study data or Verify a claimed limit). α · false-positive error probability shows when the LoB is estimated, and β · false-negative error probability for the LoD. To verify, enter Claimed LoB, Claimed LoD or Claimed LoQ.
3. For the LoD, choose LoB source: Estimate from blank rows in this study or Use a stated LoB, with Stated LoB.
4. When the LoB is estimated, choose the LoB method, Nonparametric · empirical percentile or Parametric · mean + z·SD (Gaussian). For every limit, choose a Censoring policy.
5. For the LoQ, under Quantitation goal, choose the Goal type (Imprecision · CV, Bias and imprecision · |bias| and CV or Total error · (|bias| + k·SD) / assigned) and enter its values (CV goal (%), Bias goal (%), Total-error goal (%) with SD multiplier k). No goal value is preset. Stated LoD (optional) sets a floor: the LoQ can't be below it.
6. Under Acceptance limits, choose Enter your own limit (see Acceptance limits).

Blank readings are often negative, so Permit negative results, under Calculation settings, starts ticked.

Give blank materials the role blank and low-level materials the role low. Each material has one role and one assigned concentration.

Entering data#

Day, Run and Replicate are for your records. See Importing a file and Corrections and exclusions.

Censored results#

Censoring policy decides what happens to results such as <0.01:

• Refuse “<” results (row errors) (default): correct or exclude the marked row.
• Rank “<” results below exact results: use it where ranking is enough.
  • Nonparametric LoB: censored blanks take the lowest ranks. Use it when every exact blank is at or above the bounds and the percentile falls above the censored results.
  • LoB verification: a bound at or below the claim counts as at or below the claim.
  • Parametric LoB: can't be calculated, because a mean and SD need exact values.
  • LoD: low-level results must be exact.
  • LoQ: the material becomes indeterminate.

Results starting with > or ≥ are row errors under either policy.

Statistics#

• z(1−α) and z(1−β) are standard-normal quantiles (1.6449 at 0.05).
• Nonparametric LoB: type-7 percentile (Hyndman–Fan, NumPy "linear") at 1 − α, with an exact binomial order-statistic CI and its achieved coverage.
• Parametric LoB: mean + z(1−α)·SD. CI ± t(N−1)·SD·√(1/N + z²/(2(N − 1))), a normal-theory approximation.
• Pooled SD_L = √(Σ(nᵢ − 1)sᵢ² / Σ(nᵢ − 1)), with chi-square CI [s√(df/χ²₍₁₊c₎/₂), s√(df/χ²₍₁₋c₎/₂)] (NIST/SEMATECH §1.3.5.8). LoD = LoB + z(1−β)·SD_L.
• Detection share = 100·count/N with a two-sided Wilson score interval (NIST/SEMATECH §7.2.4.1).
• LoQ for each material: CV% = 100·SD/mean, bias = mean − assigned, bias% = 100·bias/assigned, TE% = 100·(\|bias\| + k·SD)/assigned. Goal checks compare point estimates from the entered decimal results with the goal, before display rounding. A value equal to the goal meets it.

See Methods and sources.

Acceptance limits#

Enter your own limit offers the estimated LoB, LoD or LoQ when establishing and the Verification share when verifying an LoB or LoD. The dialog and its choices are in Acceptance limits. What is specific to detection limits:

• Establishing: the limit is the largest acceptable estimate. An LoD study with an estimated LoB can also limit the LoB: choose More statistics and Limit of blank.
• Verifying an LoB or LoD: the Verification share is the smallest acceptable share.
• Verifying a LoQ: no limit applies. The quantitation goal at the claimed LoQ decides and is listed as Quantitation goal at the claimed LoQ.
• A limit that doesn't fit the study, for example an LoB limit when the LoB is stated, is Not applicable.
• A LoD or LoQ limit needs at least 2 low materials, and a share limit at least 2 results. With fewer, the limit is Undecided. So is a LoQ limit when no LoQ was reached. See Limit outcomes.
• Without a Verification share, an LoB or LoD verification shows its share but gives no pass or fail, and a note says verification is not decided.

Worked example#

Three synthetic troponin I files (ng/L, reagent lot L2401), Permit negative results ticked, α = β = 0.05, 95 %. A limit's outcome reads Met, Not met or Undecided; the study reads Criteria met, Criteria not met or Undecided.

LoB, established. detection_lob.csv: 40 blank results, 20 each on BLK-A and BLK-B. Nonparametric, refuse censored. Acceptance limit: Limit of blank ≤ 0.3 ng/L.

An upper confidence limit needs 72 blanks, so 40 give none, and a note says so. With Parametric · mean + z·SD (Gaussian) the LoB is 0.191 ng/L, 95 % CI 0.156–0.226. That assumes normally distributed blanks. Here the mean, 0.075, is above the median, 0.05, which suggests skew.

LoB, verified. Same file, Claimed LoB 0.3, acceptance limit Verification share ≥ 90 %:

LoD, established. detection_lod.csv: 20 blanks (BLK-A, BLK-B) and 10 results each on LOW-1 (assigned 0.30), LOW-2 (0.40) and LOW-3 (0.55). Estimated nonparametric LoB. Acceptance limit: Limit of detection ≤ 0.5 ng/L.

A note says the LoD, 0.291 ng/L, is below every material mean (lowest 0.305 ng/L), so detection at the LoD was not tested directly. A LoD verification study with material at the LoD tests it. With a stated LoB of 0.2 ng/L, the LoD is 0.294 ng/L.

LoD, verified. Claimed LoD 0.4 ng/L, acceptance limit Verification share ≥ 90 %:

• With only the blanks and LOW-2 (assigned 0.4): 10 of 10 low results exceed the LoB 0.197 ng/L, share 100.0% (95 % Wilson CI 72.2–100.0%), Met.
• On the full file, LOW-1 (0.3) and LOW-3 (0.55) are off the claim, so the outcome is Undecided even though the share would meet it.

LoQ, established. detection_loq.csv: 10 results each on Q-0.5, Q-1, Q-2 and Q-4 (assigned 0.5, 1, 2 and 4 ng/L). Imprecision · CV, CV goal (%) 20. Acceptance limit: Limit of quantitation ≤ 1.5 ng/L.

The LoQ is 1 ng/L: Q-1 and every higher material meet the goal. The limit is Met; the study status is Criteria met.

LoQ, verified. Claimed LoQ 1 ng/L with CV ≤ 20 %: Goal met at the claimed LoQ (CV 12.766 %). The limit Quantitation goal at the claimed LoQ is Met; the study status is Criteria met.

Reading the results#

Results by material plots each result by material: circles for blanks, diamonds for low materials, triangles for censored values at their bound. Lines mark the LoB, LoD and any claim. The panel beside it, Establish the LoB (or LoD, LoQ; Verify the claimed … when verifying), holds the estimate. Blank materials, Low-level materials or Material results and goal status lists the materials, and Settings (Claim and settings when verifying) records what was used.

• LoB and its CI. If an interval end reads "not estimable", add blank results. The note above the results says how many. For a parametric LoB, compare mean and median to check for skew.
• SD_L. Pooling assumes the low materials share one SD. Check the SD ratio.
• LoD. A note appears if it lies outside the studied materials.
• Detection share (verification). For an LoB, the share of blanks at or below the claim. For an LoD, the share of low results above the LoB. The share implied by α or β is for reference.
• Precision profile (LoQ). CV or total error for each material against the goal line: circles meet the goal, diamonds don't.

LoQ rule. The LoQ is the lowest tested concentration where that material and all higher ones meet the goal, at or above any stated LoD. A material is indeterminate with censored results, fewer than 2 exact results, zero spread or a mean at or below zero. A note flags a lower material that passes while a higher one fails.

LoQ verification verdicts: Goal met at the claimed LoQ, Goal not met at the claimed LoQ, Indeterminate at the claimed LoQ, or Claim below the stated LoD.

Look out for a LoB from few blanks, a large SD ratio between low materials, or a share whose lower bound is well below the reference.

If a limit fails, check roles, shared material IDs, the unit and the reagent lot first. For a failed verification, confirm the material is at the claimed concentration.

Calculations follow Armbruster and Pry (2008).