Exposure–response modeling
Set up, run, and review this analysis in Lifescio.
Supported analysis
The Emax model adds a concentration-dependent effect to baseline; the sigmoid option estimates a Hill coefficient controlling steepness. Nonlinear least squares fits parameters and provides residual and identifiability diagnostics.
Supported scope: The model assumes a direct response with independent additive constant-variance errors. Delayed responses, hysteresis, tolerance and indirect turnover are not represented. Extrapolating an asymptote from only low concentrations is particularly uncertain.
Prepare data and configure the analysis
Provide Concentration and Response in exactly two columns. Concentrations must be nonnegative, with at least four distinct values. Choose emax for a fixed Hill coefficient of one or sigmoid to estimate it. More observations than fitted parameters are required; the sigmoid form has four parameters.
Responses may increase or decrease because Emax is fitted with either sign. The workflow fits a direct exposure–response curve with additive constant-variance error. It does not accept time, subject, delay, or repeated-measure structure.
Input reference (2 fields)
Enter your data and prespecified choices. Ranges include both limits. For table fields, use cell editing, Paste data, or Import CSV / TSV. Review whether the first imported row contains headings and map the source columns before applying the import. Empty numeric cells are not treated as zero. Open file is for an exported Lifescio analysis JSON file, not a spreadsheet.
| Input | Format | Allowed range | Guidance |
|---|---|---|---|
| Exposure–response observations | Table | — | Columns in order: Concentration; Response. |
| PD model | Selection | — | Choices: emax, sigmoid. |
Run and review
- Give the analysis a descriptive name and review every example value. Record units, data preparation, and planning assumptions in Reproducibility & notes. For simulations, record the seed and replication or sampling settings.
- Choose Run analysis. Resolve input errors before interpreting output. In the connected app, a run uses a saved input revision; local preview runs need the page to stay open.
- Review Diagnostics for method limitations, warnings, and available numerical checks. A completed run means computation finished; it does not establish that the assumptions fit your study.
- Use the Result table selector to inspect each output. Editing inputs does not recalculate existing results: an earlier-input notice means you need to run again to obtain matching results.
Understand the outputs
PD parameters contains baseline, Emax, EC50, and the Hill coefficient for the sigmoid model. Add baseline and Emax to obtain the modeled asymptote; Emax alone is not the maximum absolute response.
Fit diagnostics and Residuals help assess precision and fit. Approximate parameter limits use a local linear approximation, with positive-scale parameters transformed back. The fit curve is drawn over the observed concentration range and does not validate extrapolated clinical dosing.
Troubleshooting and common mistakes
If the model is unidentifiable or the intervals are huge, inspect concentration coverage rather than adding duplicate rows. Data with no clear transition or plateau may not distinguish Emax from EC50.
If residuals suggest two responses at the same concentration, investigate delayed effects or mixed populations. A sigmoid option cannot repair every direct-effect violation. Verify that concentrations, rather than dose values with a different interpretation, were entered in the first column.
After correcting inputs, run again and check that the results belong to the new input snapshot. Increasing simulation draws improves numerical precision only; it does not repair invalid data or an unsuitable model.
Save, compare, and export
In the connected app, Save analysis retains the inputs in your account. Run history lets you inspect earlier runs, each with the input revision it used. In local preview, Save analysis downloads an input file instead; download results before leaving the page.
Use Result + inputs for a JSON archive containing the completed result and its inputs, Download CSV for the selected result table, PDF report for a report, and a chart's SVG button for its figure. Table displays round to three decimals; CSV and JSON exports retain calculation precision. Use those values when assessing a result near a decision boundary.
To reopen an archive, select the matching analysis method and choose Open file. Imported inputs start a new draft; a result archive can also display its retained result. It does not attach itself to an existing account analysis or recompute the result. Save or run the imported draft when you want a new account record.