Dose-response regression: the EC50 from a sigmoid curve

Root growth falling with the concentration of an inhibitor, a signal rising with the concentration of an analyte: responses to a dose series are usually sigmoid on a log-dose axis, with a lower and an upper plateau and a steep middle. The four-parameter logistic (4PL) describes that curve with the two plateaus, the slope, and the EC50 — the dose giving the half-way response — which is normally the number you are after.

The data

Root length (cm) of ryegrass at seven concentrations of ferulic acid (mM), including untreated controls at 0 (the ryegrass data of the drc package):

r = replicate: r1 is replicate 1, r2 replicate 2, and so on.

Dose-response layout: one row per dose, replicates across. Zero-dose controls are included in the fit.

In MinutePlot

Choose Regression, model 4PL (dose-response), paste the table, run. The curve is fitted on the dose scale (so dose 0 sits on the upper plateau of a falling curve), and the table reports the lower and upper asymptotes, the slope and the EC50, each with a standard error and confidence interval.

The result

EC50 = 3.06 mM (95 % CI 2.67–3.45); upper plateau 7.79 cm, lower plateau 0.48 cm, slope 2.98 — the same fit R’s drc package gives on this data. Half the growth is lost at about 3 mM.

The figure MinutePlot produces: the data on a log-dose axis, the fitted four-parameter curve, and the EC50 marked with R² in the corner.

Styling and exporting this figure: see Figure styling and Exporting & downloading.

Report it like this

“Root length followed a four-parameter logistic dose-response (EC50 = 3.06 mM, 95 % CI 2.67–3.45; upper plateau 7.79 cm, lower plateau 0.48 cm).”