LOD / LOQ
Analytical context
LOD and LOQ are key validation parameters. They define the concentration level where an analyte can be reliably detected (LOD) and quantified with acceptable precision (LOQ).
\[ \mathrm{LOD} = 3.3\,\frac{\sigma}{S}, \qquad \mathrm{LOQ} = 10\,\frac{\sigma}{S} \]
With a blank mean, corresponding signal thresholds are:
\[ y_{\mathrm{LOD}} = y_{\mathrm{blank}} + 3.3\sigma, \qquad y_{\mathrm{LOQ}} = y_{\mathrm{blank}} + 10\sigma \]
Crosslink: For slope \(S\) and regression modeling, use Calibration Line (Linear Regression).
Formulas (MathJax)
\[ \mathrm{LOD} = 3.3\,\frac{\sigma}{S} \]
\[ \mathrm{LOQ} = 10\,\frac{\sigma}{S} \]
\[ \sigma = \frac{\mathrm{LOD}\cdot S}{3.3} \]
\[ \sigma = \frac{\mathrm{LOQ}\cdot S}{10} \]
\[ y_{\mathrm{LOD}} = y_{\mathrm{blank}} + 3.3\sigma,\quad y_{\mathrm{LOQ}} = y_{\mathrm{blank}} + 10\sigma \]
Symbol legend
- \(\sigma\): signal standard deviation (blank or low-level replicates)
- \(S\): calibration slope (signal/concentration)
- \(\mathrm{LOD}\): limit of detection
- \(\mathrm{LOQ}\): limit of quantification
- \(y_{\mathrm{blank}}\): mean blank signal
- \(y_{\mathrm{LOD}}, y_{\mathrm{LOQ}}\): signal thresholds for detection/quantification
Detailed examples
Example 1 (standard computation):
\(\sigma=0.004\), \(S=0.108\).
\(\mathrm{LOD}=3.3\cdot0.004/0.108\approx0.122\).
\(\mathrm{LOQ}=10\cdot0.004/0.108\approx0.370\).
\(\sigma=0.004\), \(S=0.108\).
\(\mathrm{LOD}=3.3\cdot0.004/0.108\approx0.122\).
\(\mathrm{LOQ}=10\cdot0.004/0.108\approx0.370\).
Example 2 (signal thresholds):
With \(y_{blank}=0.012\):
\(y_{LOD}\approx0.0252\), \(y_{LOQ}\approx0.0520\).
This shows where transition from detection to reliable quantification begins.
With \(y_{blank}=0.012\):
\(y_{LOD}\approx0.0252\), \(y_{LOQ}\approx0.0520\).
This shows where transition from detection to reliable quantification begins.
Example 3 (reverse from LOD):
Given \(\mathrm{LOD}=0.122\), \(S=0.108\).
\(\sigma=\mathrm{LOD}\cdot S/3.3\approx0.0040\).
Given \(\mathrm{LOD}=0.122\), \(S=0.108\).
\(\sigma=\mathrm{LOD}\cdot S/3.3\approx0.0040\).
Example 4 (method optimization):
Reducing \(\sigma\) (better repeatability) or increasing \(S\) (higher sensitivity) directly improves LOD/LOQ. The calculator helps quantify which lever has stronger impact.
Reducing \(\sigma\) (better repeatability) or increasing \(S\) (higher sensitivity) directly improves LOD/LOQ. The calculator helps quantify which lever has stronger impact.
Deeper insight
Choosing the right σ
In practice, \(\sigma\) often comes from replicate blank measurements or low-level standards. The dataset must reflect real method behavior to avoid optimistic LOD/LOQ claims.
Regulatory note
Guidelines (ICH/DIN/ISO) may differ in details, but the \(3.3\sigma/S\) and \(10\sigma/S\) approach is widely used for transparent estimation and method comparisons.
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