1. Design standards around the reportable range
Choose known levels that span expected unknowns and inform the parts of the curve used for inverse prediction. Include separately prepared QCs where appropriate; standards used to fit the curve do not provide the same evidence as independent controls.
Retain standard identity, assigned concentration and unit, preparation, replicate, plate position, raw response, blank correction, and inclusion state. Sparse range boundaries make back-calculation weakest exactly where reportability changes.
2. Apply the predefined fit to the standards
Fit response as a function of known concentration using the approved equation, transformations, weighting, bounds, replicate handling, and convergence rule. Plot every standard observation and review residuals, parameter state, and back-calculated standard performance.
The illustrative standards below follow response = 0.100 + 0.400 × concentration exactly. An ordinary unweighted linear fit therefore returns intercept 0.100 response units and slope 0.400 response units per ng/mL. Real calibration data require residual, recovery, variance, and independent-QC evidence; the model is not selected by R² alone.
Worked linear fit: response = 0.100 + 0.400 × concentration| Standard (ng/mL) | Observed response | Back-calculated concentration |
|---|---|---|
| 0 | 0.100 | 0.00 ng/mL |
| 1 | 0.500 | 1.00 ng/mL |
| 2 | 0.900 | 2.00 ng/mL |
| 4 | 1.700 | 4.00 ng/mL |
| 8 | 3.300 | 8.00 ng/mL |
3. Invert the fitted curve for the unknown
Find the concentration whose fitted response matches the unknown response. For an observed response of 2.660 in the worked linear fit, concentration = (2.660 − 0.100) ÷ 0.400 = 6.4 ng/mL. That value represents the measured well or plate dilution before any off-plate preparation adjustment.
Inverse uncertainty grows near flat regions because a small response change maps to a large concentration change. A numerical answer outside the supported range is not automatically reportable.
(2.660 − 0.100) ÷ 0.400 = 6.4 ng/mL4. Apply the preparation factor once
Suppose inverse prediction returns 6.4 ng/mL for an unknown that was prediluted 1:5 before it reached the plate. The final sample concentration is 6.4 × 5 = 32 ng/mL.
Store both values: 6.4 ng/mL is the plate concentration and 32 ng/mL is the preparation-adjusted result. Keeping the factor, operation, and units beside both values prevents a reviewer or downstream system from applying the dilution twice.
6.4 ng/mL × 5 = 32 ng/mL| Record | Value |
|---|---|
| Inverse-predicted plate concentration | 6.4 ng/mL |
| Sample predilution | 1:5 |
| Applied preparation factor | 5 |
| Final sample concentration | 32 ng/mL |
5. Decide whether the result is reportable
Evaluate standard fit and recovery, independent QC performance, unknown replicate agreement, dilutional consistency, and the validated plate and final-sample ranges defined by the method.
Document every standard exclusion and its effect on fit and range. Flag values outside the supported range rather than extrapolating an apparently precise concentration.
6. Preserve the source-to-result path
Report the source wells, standards and QCs, exact model and settings, exclusions, diagnostics, inverse prediction, preparation factor, both concentrations and units, range status, software version, and controlled configuration.
A reviewer should be able to trace 32 ng/mL back through the factor of 5 and the 6.4 ng/mL inverse prediction to the unknown response and retained calibration data.
Limits and model alternatives
A linear model may suit a justified bounded range; a supported sigmoid may require 4PL or 5PL behavior; changing variance may justify weighting. Each alternative changes the assumptions behind inverse prediction.
Provenarium supports linear, 4PL, and 5PL calibration for standard-curve analysis. Compare candidates during development using residuals, back-calculated standards, independent QCs, parameter stability, range behavior, and repeated runs. Do not choose whichever model maximizes R² on one routine plate.
Frequently asked questions
Is a straight line appropriate for every calibration curve?
No. Use it only over a range where the response and error structure support it. Many immunoassays show sigmoidal behavior requiring a nonlinear model.
Can an unknown outside the standards be extrapolated?
Software can calculate an extrapolation, but reportability should follow validated range and method rules. Dilute or concentrate and remeasure when the procedure requires it.
Why use weighting?
Weighting can account for changing variance across the range. Its form should be justified using representative data and controlled as part of the method.