Design standards around the intended reportable range
Choose standard levels that cover the expected unknowns and provide information where model parameters need it. Include independent QC samples where appropriate; standards used to fit the curve do not provide the same evidence as separately prepared controls.
Replicates, blank handling, matrix matching, preparation, and placement influence what the curve can support. Concentrating points at the easy middle while leaving sparse boundaries produces weak back-calculation near the ends.
Select the calibration model before routine use
A linear model may be appropriate over a bounded response range. Immunoassay standard curves often need 4PL or 5PL behavior. Weighting may be needed when variance changes across concentration.
Compare candidate models using residuals, back-calculated standards and controls, parameter stability, range behavior, and repeated runs. Do not choose the model that maximizes R² on one plate.
| Model choice | Evidence to evaluate |
|---|---|
| Linear | Residual linearity and performance across the bounded range |
| 4PL | Supported lower/upper asymptotes and symmetric sigmoid behavior |
| 5PL | Repeatable asymmetry with identifiable fifth parameter |
| Weighted fit | Variance model and recovery across low/high concentrations |
Back-calculation is inverse prediction
After fitting response as a function of concentration, unknown concentration is found by inverting the fitted relationship. Uncertainty can increase sharply near flat asymptotes because a small response change maps to a large concentration change.
Apply predilution and other preparation factors exactly once, with units. Flag values below or above the validated/reportable range according to the method rather than extrapolating an apparently precise number.
Evaluate standards, QCs, and unknowns separately
Standard back-calculation helps assess the fitted curve, but criteria should account for the role of each level and the selected model. Independent QC recovery provides different evidence. Unknown replicate agreement and dilutional consistency may also be relevant.
Document any standard exclusion with a reason and refit impact. Removing a boundary standard can change the reportable range even when the remaining curve looks excellent.
Worked example: apply the preparation factor once
Suppose inverse prediction from the fitted curve 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 concentration represented by the measured well, and 32 ng/mL is the preparation-adjusted result. Keeping the factor, operation, and units beside the result 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 |
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.