4PL calibration

What this model estimates

The known standards define lower and upper asymptotes, a location and a slope. Each eligible unknown or QC response is inverted on that calibration, returned to concentration units and corrected for dilution. The logistic shape is symmetric in its fitted coordinate; response transformation can change its appearance on the original scale.

This model is a concentration calibration. It does not impose common-shape potency relationships on the unknowns or return a test-to-reference potency ratio.

Data and design needed

Provide at least five distinct included standard concentrations with enough information to identify both plateaus and the transition. The numerical fit must converge with finite full-rank information; five levels alone do not ensure that result.

Declare positive reportable standards, optional anchors, unknown/QC dilutions and replicate treatment. Reportable range is derived from included reportable levels. Anchors can aid fitting outside it but do not automatically extend it. A zero anchor is only compatible with Untransformed concentration.

Check the settings

1. On Model, select 4PL calibration and inspect the selected increasing or decreasing Curve orientation.
2. Concentration and response each support Untransformed, Base-2, Natural or Base-10 logarithm. Choose a justified Weighting: Unweighted, Inverse expected response or Inverse squared expected response.
3. Check units, sample dilutions, the derived reportable range and applicable R²/recovery criteria. A successful fit is not a substitute for these checks.

Read concentrations and uncertainty

Review sample/QC concentration, interval, reportability and suitability in Analysis summary, then inspect the calibration curve, standard recovery, parameters and per-well evidence. The report retains the exact fitted settings and source.

Observation intervals use a two-sided 95% normal delta construction that propagates fitted-curve parameter and sample-response uncertainty through the inverse. Multiple eligible observations use a normal log-concentration delta interval for their geometric aggregate, including shared-curve and declared response-group covariance. This is not the Fieller procedure used by relative-potency 4PL.

Failures and limitations

Responses close to a plateau can carry large concentration uncertainty even when the fitted curve looks smooth. A response outside the finite inverse domain, an unidentifiable fit, invalid weight domain or an unusable interval is explicitly reported.

The application does not extrapolate a numeric sample concentration beyond the reportable interval or silently replace 4PL with another model. Follow the failure/range reason and your procedure before downstream use.

• Scientific background: Daly et al. (2005), uncertainty in inverse calibration