1. Define the capability being claimed
A detection limit addresses the lowest amount or concentration detected under defined conditions; it does not promise reliable quantitation. A quantitation limit addresses the lowest level quantified with suitable defined performance.
LLOQ often means the lower validated or reportable calibration level in a specific context. Define DL, LOD, QL, LOQ, or LLOQ in the procedure instead of treating the names as interchangeable.
2. Confirm that the linear estimate applies
The worked formula below uses a response standard deviation σ and calibration slope S under one conventional linear approach. Define how σ is estimated, which fitted range supplies S, and why that combination represents the procedure near the proposed limit.
Retain the source responses, units, calculation, calibration version, and any transformations. A plausible formula with mismatched variability or slope inputs does not produce a meaningful limit.
Conventional linear estimate: DL = 3.3σ ÷ S; QL = 10σ ÷ S3. Calculate the proposed DL and QL
With response standard deviation σ = 0.006 response units and slope S = 0.020 response units per ng/mL, DL = 3.3 × 0.006 ÷ 0.020 = 0.99 ng/mL and QL = 10 × 0.006 ÷ 0.020 = 3.0 ng/mL.
The calculation proposes 0.99 ng/mL for detection and 3.0 ng/mL for quantitation. It does not prove either claim. Independent low-level samples test whether the method performs as intended there.
| Input or estimate | Value |
|---|---|
| Response SD, σ | 0.006 response units |
| Calibration slope, S | 0.020 response units per ng/mL |
| Proposed DL | 0.99 ng/mL |
| Proposed QL | 3.0 ng/mL |
4. Verify the proposed limits with samples
Prepare independent samples at and around the proposed levels. At 0.99 ng/mL, test the defined detection or classification claim. At 3.0 ng/mL, test the required accuracy, precision, recovery, or total-error claim.
Include matrix, instruments, analysts, days, reagent lots, preparation, and other routine sources needed for intended use. Predefine acceptance, handling below the limit, and what happens when a level fails.
5. Approve and report the supported limit
State the term, analyte, matrix, unit, estimation method and inputs, study design, raw and derived data, model and software version, proposed value, verification results, criteria, and final approved limit.
Keep qualifiers such as <LLOQ separate from the stored numerical estimate and status. Downstream exports should transmit the qualifier, value where appropriate, and unit as distinct fields.
Limits and alternative approaches
Signal-to-noise, blank and low-level variability, empirical low-level performance, and other applicable frameworks may define different estimates and constants. Select the approach that matches the procedure and intended claim.
For nonlinear curves, local sensitivity and variance can change across the range. Applying one global linear slope mechanically near an asymptote may misrepresent inverse-prediction performance. This page explains an educational example, not a current Provenarium LOD/LOQ calculation capability.
Frequently asked questions
Is LOQ always 10 times standard deviation divided by slope?
No. That is one conventional relationship under specific assumptions. Use the approach appropriate to the procedure and applicable framework, then verify performance.
Can the lowest calibration standard automatically be called LLOQ?
Only if its role and performance are established under the method. A nominal level is not made reportable by its position in the plate layout.
Are LOD and LOQ required for every potency assay?
Not necessarily. Select performance characteristics based on intended use and applicable guidance, documenting the rationale.