Dose-response regression

MinutePlot^® and R on the same data. MinutePlot version 1.0.0; R 4.5.2.

Dataset

• doseresponse_4pl (generated) — Two datasets: a generated set of 7 positive doses (0.47 to 30, doubling) × 3 replicates on a decreasing four-parameter logistic curve with noise (fixed seed), and drc’s ryegrass -- root length of ryegrass at 7 concentrations of ferulic acid (0 to 30 mM), 24 observations (Inderjit et al. 2002).
• Data file (the same format serves MinutePlot and R): doseresponse_4pl.csv and ryegrass.csv — one column per variable; paste it into the app, and keep it in the R script’s folder.
• ryegrass is R built-in (drc); doseresponse_4pl is generated.

Setup

In MinutePlot:

• Workbench → Regression → paste doseresponse_4pl.csv (dose, response) or ryegrass.csv (conc, rootl) → Preview data → Confirm → model 4PL (dose-response) → Fit model.
• Zero-dose rows stay in the fit (ryegrass: all 24 rows). No sample-name column, no groups.

In R:

• Install once: install.packages(c("drc")); then run doseresponse_drc.R top to bottom (source it, or paste it into the console) with the R data file in the same folder.
• R 4.5.2 and the package versions in the page header; each script prints the versions it runs under.

The analysis:

• Four-parameter logistic (MinutePlot: 4PL, fitted by nonlinear least squares on the dose scale; parameters lower asymptote, upper asymptote, EC50 -- the half-maximal dose, which R’s drc labels ED50 in its output -- and slope). R reference: drc::drm with fct = LL.4 -- the four-parameter log-logistic, the same curve family; the slope parameter’s sign convention differs (drc’s b is positive for a decreasing curve), so slopes are compared by magnitude.
• Fit statistics as MinutePlot reports them: R², residual standard error, residual df.
• Standard errors: the two implementations parameterise the logistic curve differently, and in a nonlinear fit the standard errors (and hence the confidence intervals) depend on the parameterisation; the point estimates, the fitted curve and the residual fit agree exactly, and the small differences in the parameter SEs are expected, not a discrepancy.
• Zero-dose (untreated control) observations are included in the fit: the curve is evaluated on the dose scale, so dose 0 lies on the upper plateau of a decreasing curve (the lower plateau of an increasing one), as in drc’s LL.4; ryegrass is fitted on all 24 observations on both sides. This needs build 196 or later -- an earlier app (including the installer built from build 186) drops the six zero-dose rows and fits 18 observations, giving EC50 2.99 instead of 3.06.

Side-by-side results

doseresponse_4pl data -- fitted parameters (slope compared by magnitude)

doseresponse_4pl data -- fit statistics

ryegrass data, all 24 observations -- fitted parameters (slope compared by magnitude)

ryegrass data, all 24 observations -- fit statistics

Verdict

MinutePlot values from the current build (zero-dose controls join the fit with build 196); the R side is unchanged and is to be re-confirmed side by side after deployment.

R script

doseresponse_drc.R — each script loads its data, prints its versions and the R-side tables shown above, in page order; no plotting.