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Sigmoidal dose-response (5PL, asymmetric)

The five-parameter logistic adds an asymmetry parameter S to the 4PL curve, y = Bottom + (Top − Bottom) / (1 + 10^((LogEC50 − x) · HillSlope))^S, reducing to 4PL when S = 1.

What is Sigmoidal dose-response (5PL, asymmetric)?

Real-world dose-response curves are often asymmetric — the approach to Top isn't a mirror image of the departure from Bottom. The 5PL adds a single extra parameter S that captures this asymmetry: S < 1 ⇒ flatter approach to Bottom; S > 1 ⇒ flatter approach to Top.

Trade-off: 5PL fits better when asymmetry is real but is less identifiable than 4PL when S ≈ 1 — the extra parameter sits on a flat likelihood ridge and convergence can be slow. If S CI includes 1 with wide bounds, 4PL is the better-conditioned fit.

When should I use Sigmoidal dose-response (5PL, asymmetric)?

Immunoassay calibration curves with visible asymmetry in the residuals of a 4PL fit.

What data does it need?

Numeric X (dose / log-dose) + Y (response).

What does it report?

Five-parameter fit table + CI/PI bands.

How do I interpret the result?

Compare 4PL vs 5PL via nonlinear_compare to test whether the asymmetry is statistically supported.