1. Use 4PL as the simpler sigmoid question

A 4PL estimates lower and upper asymptotes, a location or midpoint parameter, and slope under a symmetric-transition convention. Begin by asking whether representative data support those four quantities and whether the residual behavior is adequate for the intended result.

Do not add a fifth parameter merely because one curve looks asymmetric. First check concentration coverage, plate effects, normalization, variance, outliers, and whether either asymptote is weakly observed.

2. Ask whether asymmetry is repeatable

A 5PL adds a parameter that allows different curvature on the two sides of the transition. The visual below isolates that conceptual difference; it does not show current Provenarium output.

The extra flexibility is useful only when relevant concentrations inform it across representative runs. Sparse plateaus or a narrow transition can make the asymmetry parameter unstable or confounded with slope and location.

Conceptual model comparison

A fifth parameter changes transition symmetry

4PL: symmetric transition5PL: asymmetric transition
Conceptual four- and five-parameter logistic curvesA solid symmetric four-parameter curve and a dashed asymmetric five-parameter curve share illustrative lower and upper responses. The curves differ through the transition, showing the behavior added by the fifth parameter.Concentration (log scale)Response (%)
4PL question
Does one symmetric transition describe representative runs adequately?
5PL question
Is asymmetry repeatable, identifiable, and useful enough to justify another parameter?
Conceptual curves explain the model difference; they are not fitted Provenarium output. Provenarium supports exact supplier-verified common-shape 4PL and common-shape 5PL contracts; this illustration does not represent their fitted output.

3. Compare the models on decision-relevant evidence

Fit prespecified candidates during development and retain both results. Compare convergence, parameter uncertainty and bounds, residual structure, standard or QC recovery, prediction behavior, and repeated-run stability—not only R² or the best-looking line.

A useful improvement should persist on independent or later runs and matter to the reported result. A small fit-statistic gain with unstable parameters does not establish that 5PL earns its place.

EvidenceQuestion
CoverageDo concentrations support both plateaus and both sides of the transition?
ResidualsDoes asymmetry remove a repeated structure rather than one isolated point?
ParametersIs the fifth parameter finite, stable, and away from arbitrary bounds?
PerformanceDo recovery, prediction, or reportable results improve on independent runs?

4. Lock the selected model before routine analysis

Approve one exact equation, parameter convention, transformation, weighting, starting-value and bounds policy, convergence rule, and uncertainty method. Routine runs apply that version without searching across models after observing the data.

Preserve the development comparison and rationale. A later model change creates a new method version and requires impact assessment rather than silently rewriting retained results.

Limits and software conventions

Packages may reverse curve direction, change slope sign, fit log concentration directly, or define the 5PL asymmetry term differently. Names such as “4PL” and “5PL” do not make outputs interchangeable.

Provenarium supports three exact supplier-verified quantitative relative-potency contracts: parallel-line log-log, common-shape 4PL, and common-shape 5PL. This conceptual comparison does not imply support for a generic logistic model builder or a different 5PL convention.

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.

Primary references