Noninferiority & equivalence
Set up, run, and review this analysis in Lifescio.
Supported analysis
Select means or proportions, the expected treatment-minus-control difference, a positive margin, allocation ratio, power and alpha. Normal approximations estimate analyzable sample sizes, then dropout inflates recruitment.
Supported scope: Independent groups and a prespecified variance are assumed. The app defines noninferiority for higher outcomes being better. Small binary cell counts can invalidate the normal approximation; exact, constrained-score and specialized regulatory designs may give different sample sizes.
Prepare data and configure the analysis
Choose the endpoint and hypothesis
Select means for a continuous endpoint or proportions for a binary response. The noninferiority option evaluates treatment minus control against the negative margin; equivalence evaluates both margins. This calculator defines higher outcomes as better. Re-express an adverse endpoint consistently before using it; changing only the sign of the expected difference is insufficient if the baseline probability or interpretation also changes.
Enter Expected treatment minus control in outcome units for means, or as an absolute probability difference for proportions. Enter Positive margin on that same scale. For noninferiority the expected difference must exceed the negative margin; for equivalence its absolute value must be smaller than the margin. Choose the margin from the study rationale, not by adjusting it to obtain a convenient sample size.
Supply planning assumptions
For means, Common standard deviation is the anticipated individual-outcome standard deviation, not a standard error. For proportions, Control proportion plus the expected difference gives the treatment probability; both must be strictly between zero and one. The standard-deviation field is used only for means, and the control-proportion field only for proportions.
Target power, One-sided alpha, and Expected dropout proportion are decimals: 0.80, 0.025, and 0.10 are common example formats, not study recommendations. Treatment/control allocation ratio of 2 requests about twice as many treatment participants. Dropout inflation is applied separately after analyzable group sizes are rounded up. For a transparent first check, use means, difference 0, margin 3, standard deviation 10, power 0.80, alpha 0.025, ratio 1, and dropout 0.10; then replace every assumption with your study values.
Input reference (10 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 |
|---|---|---|---|
| Endpoint | Selection | — | Choices: means, proportions. |
| Hypothesis | Selection | — | Choices: noninferiority, equivalence. |
| Expected treatment minus control | Number | -100–100 | — |
| Positive margin | Number | 0.0001–100 | — |
| Common standard deviation (means) | Number | 0.001–1000 | — |
| Control proportion | Number | 0.001–0.999 | — |
| Target power | Number | 0.5–0.999 | — |
| One-sided alpha | Number | 0.0001–0.1 | — |
| Treatment/control allocation ratio | Number | 0.1–10 | — |
| Expected dropout proportion | Number | 0–0.8 | — |
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
Read Required sample size
Control analyzable and Treatment analyzable are the group sizes required by the normal-approximation calculation. Total analyzable is their sum. Control recruit and Treatment recruit include the specified dropout allowance; recruit their sum when describing the enrollment target. Integer rounding can make the final allocation ratio slightly different from the input.
Achieved power is recalculated at the rounded analyzable sizes. It is a planning quantity under your assumed effect, not power estimated from observed trial results. The Power by sample size chart varies total analyzable participants; it does not show dropout-adjusted recruitment.
The illustrative means setup above gives 175 analyzable participants per group and 195 to recruit per group. This is an independent check of the setup, not a recommended design. The calculator does not analyze a completed trial or produce its treatment-effect confidence interval.
Troubleshooting and common mistakes
Resolve invalid or surprising results
If equivalence is rejected at setup, check that the assumed effect lies inside both margins. For noninferiority, an expected effect at or below the negative margin cannot meet a power target above one half with this design. For proportions, check the implied treatment probability as well as the baseline; an absolute difference of 5 is invalid when you meant five percentage points (0.05).
A large sample size commonly reflects a small distance to the boundary, large variability, stringent alpha, or high power. Check those inputs before treating the answer as a software problem. A sparse-binary warning means the normal approximation may be unreliable; changing the data merely to silence it is inappropriate. Compare with a method suited to the endpoint and protocol. The workspace cannot select or justify a clinical margin for you.
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.