The fifth parameter models asymmetry
A 4PL describes lower and upper asymptotes, a midpoint, and a slope. A 5PL adds an asymmetry parameter so curvature can differ around the inflection region.
That flexibility is valuable only when the concentration design informs it. Sparse asymptotes or a narrow transition region can make a 5PL appear precise while individual parameters remain unstable.
| Model | Useful starting point | Primary caution |
|---|---|---|
| 4PL | Approximately symmetric sigmoid | Symmetry may be too restrictive |
| 5PL | Repeatable asymmetric response | Extra parameter can be weakly identified |
| Restricted fit | Shared or fixed parameters justified by the method | Restriction must be explicit and tested |
Parameter names do not guarantee the same equation
Software packages can reverse curve direction, define slope sign differently, parameterize concentration on a log scale, or use different forms of the 5PL asymmetry term. Two outputs labeled “4PL” are not necessarily interchangeable.
Store the model identifier and version, exact equation or convention, units, transformation, starting-value logic, bounds, restrictions, weighting, optimization status, and uncertainty method.
Review fit behavior as a collection of evidence
Inspect observed-versus-fitted plots and residuals at the well or summarized level used by the analysis. Review whether the midpoint is bracketed, asymptotes are supported, parameter estimates are plausible, and the optimizer converged without pressing against arbitrary bounds.
For routine use, model decisions should be defined in the method rather than selected anew because one run looks better under an alternative. Development comparisons should preserve every candidate and rationale.
Frequently asked questions
When should I use a 5PL instead of a 4PL?
When asymmetry is scientifically plausible, repeatedly evident, and supported by enough concentrations and replicates to estimate the fifth parameter reliably. Compare diagnostics and repeated-run performance rather than one fit statistic.
What does a restricted relative-potency fit do?
It estimates selected parameters jointly or fixes them according to the method, often to encode a common curve shape. The exact restrictions differ by model and should be named in the result.