Synthetic data · independently computed
A subgroup benefit hidden by the overall average.
This calculation record accompanies a simulated treatment-response illustration. It contains no real patient data and is not an OptiMod-generated analysis.
Within this prespecified baseline group, treatment improves the hypothetical symptom score. Group B responds in the opposite direction, so the pooled average is close to zero. The direct interaction test supports this difference between groups.
Study design
600 simulated participants, two baseline biomarker groups defined before outcomes, and 1:1 randomization within each group. Each of the four group-by-arm cells contains 150 observations. The outcome is change in a hypothetical symptom score: lower values indicate improvement.
| Baseline group · arm | n | Mean change | SD |
|---|---|---|---|
| A · control | 150 | -0.0367 | 3.4390 |
| A · treatment | 150 | -8.0823 | 3.2932 |
| B · control | 150 | +0.2448 | 3.8159 |
| B · treatment | 150 | +7.9868 | 3.1937 |
Effects and uncertainty
| Comparison | Difference | Individual 95% CI | Two-sided p | Holm p (A/B) |
|---|---|---|---|---|
| Pooled treatment − control | -0.1518 | -1.2191 to +0.9155 | 0.7799 | — |
| Group A: treatment − control | -8.0457 | -8.8107 to -7.2806 | 1.473e-59 | 2.947e-59 |
| Group B: treatment − control | +7.7420 | +6.9423 to +8.5417 | 5.324e-53 | 5.324e-53 |
| Interaction: B effect − A effect | +15.7877 | +14.6832 to +16.8921 | 1.877e-110 | — |
Negative treatment-minus-control differences indicate benefit. The interaction is the group B effect minus the group A effect. Holm adjustment covers the two prespecified subgroup tests; confidence intervals are individual 95% intervals, not simultaneous intervals.
Statistical method
Unadjusted pooled and within-group comparisons use two-sided Welch tests and Welch–Satterthwaite confidence intervals. The interaction uses a four-independent-cell contrast, with the sum of the four sample-mean variances and Satterthwaite degrees of freedom. This directly tests whether the two treatment effects differ. See the NIST two-sample t-test reference.
The pooled comparison intentionally shows the unstratified mean. Its nonsignificant result does not establish equivalence. The subgroup and interaction analyses use the baseline group information built into the simulation; no groups are discovered after inspecting the outcome.
Distribution display
Every curve is a Gaussian kernel density estimate of the exported observations, using the same bandwidth of 1.2 score points and a grid from −24 to +24. The pooled treatment density has two local maxima. Curves describe the observed distribution; the treatment-effect conclusions come from comparisons with control and the interaction test.
Reproduce and inspect
Data (CSV) · Full statistics and curves (JSON) · Reproduction script · Methodology and display notes
Seed: 20261106. Runtime: CPython 3.9.6, standard library only. Run python3 generate_example.py to regenerate the CSV, statistics and this report.
CSV SHA-256: 53d7b4d771e4320a012e29ab6e915136691da2375e54101859781165ce52232f
The effect structure is deliberately specified for illustration. The statistically supported benefit in this synthetic group is not evidence about a real medicine, clinical practice or regulatory efficacy, and does not establish that OptiMod supports a particular analysis feature.