Dose-response curves
A lot of biology is a saturating S-curve, not a straight line. A drug has little effect at low doses, a steep response through the middle, and a plateau once the system is maxed out. A dose-response fit captures that shape and boils it down to a few numbers you can compare across drugs, days, and labs. This page covers the EC50 and IC50, the sigmoid models that produce them, the Hill slope, and how to compare or share fits.
What a dose-response curve is
You plot response against dose, almost always with dose on a log scale, and fit a smooth S-shaped curve through the points. The curve summarizes the whole experiment with a handful of parameters, the bottom plateau, the top plateau, the dose at the halfway point, and how steeply the response climbs.
EC50 and IC50, the halfway dose
The single most-used number is the dose that produces a half-maximal response. When the response goes up with dose, that is the EC50 (half-maximal effective concentration). When the response goes down, an inhibition, it is the IC50(half-maximal inhibitory concentration). A lower IC50 means a more potent inhibitor, it takes less drug to get halfway to full effect. This is the number you compare between compounds.
The Hill slope and the models
The Hill slope describes how steep the climb is through the middle of the curve. A slope near 1 is the standard simple case; a steeper slope means the response switches on over a narrow dose range, which can hint at cooperative binding. The Data Hub reports it as a fitted parameter with its own uncertainty.
The shape comes from a model. The 4PL (four-parameter logistic) fits the bottom plateau, the top plateau, the EC50, and the Hill slope, and is the default for a symmetric S-curve. The 5PL adds a fifth parameter for asymmetry, for curves that approach their two plateaus at different rates. The result reports each fitted parameter with its confidence interval, plus a goodness-of-fit summary (r squared and the residual spread) so you can see how well the curve tracks the points.
Comparing models
Should you use the simpler 4PL or the more flexible 5PL? A more complex model will always fit your particular points at least slightly better, just by having an extra knob to turn, so a bare improvement in fit is not a good reason to prefer it. Model comparison asks the sharper question, is the improvement big enough to justify the extra parameter, or is the simpler model good enough?
The Data Hub runs two distinct comparisons, both reported together.
- The extra-sum-of-squares F test applies when the two models are nested, that is, when the simpler model is a special case of the more complex one (for example, the 4PL is the 5PL with the asymmetry parameter fixed at 1). It asks whether the reduction in residual sum of squares justifies the added parameter, using an F statistic and a p-value. A small p (by convention, below 0.05) favors the more complex model.
- The AICc (small-sample-corrected Akaike Information Criterion) is always valid, whether or not the models are nested. It trades goodness of fit against parameter count without a null-hypothesis test. The model with the lower AICc is preferred; the Data Hub reports the delta and the Akaike weights, which express the probability each model is the better of the two.
The honest default is the simpler model unless the data clearly call for more. Read both verdicts, as they can sometimes point in different directions when the sample is small.
Global fits: sharing parameters across datasets
Often several curves should share something. Three compounds tested the same day plausibly share the same top and bottom plateau, they differ only in potency. A global fit fits all the curves at once with some parameters shared and others left free per curve. Any of the four 4PL parameters (bottom plateau, top plateau, EC50, Hill slope) or the 5PL asymmetry parameter can be designated as shared or free independently. Sharing the plateaus, for instance, pins them down using every point from every curve, which makes the per-curve EC50s more precise and lets you compare potency on a fair footing.
The result reports the shared parameters once, the free parameters per dataset, and the confidence intervals throughout. The headline is usually the ratio of EC50s between curves, with its interval, which answers "is compound A genuinely more potent than compound B?"
A worked example
You fit an inhibition curve and get an IC50 of 120 nM (95% CI 95 to 150), a Hill slope of 1.1, and r squared = 0.99. A second compound gives an IC50 of 480 nM (95% CI 410 to 560). The intervals do not overlap, so you would write "compound A was about four-fold more potent than compound B (IC50 120 nM, 95% CI 95 to 150, vs 480 nM, 95% CI 410 to 560)."
ResearchOS validates the 4PL and 5PL fits, the EC50 and IC50 estimates, and the model comparisons against scipy and R on the transparency page.