This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record.
1. Trial at a Glance
KARISMA2 was a randomized, parallel, triple-masked phase 2 trial evaluating whether lower doses of tamoxifen could achieve mammographic density reduction comparable with the 20 mg tamoxifen reference arm after 6 months of treatment. The registered primary endpoint was binary and used a non-inferiority framework.
| Feature | KARISMA2 |
|---|---|
| Phase | Phase 2 |
| Status | Completed |
| Population / condition | Risk Reduction; Mammographic Density Reduction |
| Primary purpose | Prevention |
| Design | Randomized, parallel, triple-masked |
| Enrollment | 1,440 |
| Study arms | 6 |
| Interventions | Tamoxifen Oral Tablet; Placebo Oral Tablet |
| Start | 2016-11 |
| Primary completion | 2019-10 |
| Lead sponsor | Per Hall |
| Sponsor type | OTHER |
| ClinicalTrials.gov | NCT03346200 |
2. Clinical Question
The primary statistical question was whether the lower-dose tamoxifen groups, including 1 mg, 2.5 mg, 5 mg, 10 mg, and placebo, could be considered non-inferior to the 20 mg tamoxifen reference group with respect to the proportion of women achieving a mammographic density reduction as great as or greater than the median density reduction in the 20 mg arm after 6 months.
Population
Participants enrolled in a phase 2 prevention study for risk reduction and mammographic density reduction.
Intervention
Tamoxifen oral tablets at doses of 1 mg, 2.5 mg, 5 mg, 10 mg, and 20 mg.
Comparator
Placebo oral tablet, with the 20 mg tamoxifen group serving as the reference for the registered non-inferiority comparison.
Primary question
Are the non-referent study arms non-inferior to 20 mg tamoxifen with respect to the registered mammographic-density response criterion after 6 months?
3. Trial Design
The trial used randomized allocation, a parallel design, and triple masking. Its primary purpose was prevention rather than treatment of established disease. The six-arm structure allowed the study to evaluate a dose range while retaining a placebo group and a 20 mg tamoxifen reference group.
20 mg Tamoxifen
- Reference group for the primary non-inferiority analysis
- Serious adverse events: 2 affected / 241 at risk
10 mg Tamoxifen
- Lower-dose tamoxifen comparison group
- Serious adverse events: 1 affected / 243 at risk
5 mg Tamoxifen
- Lower-dose tamoxifen comparison group
- Serious adverse events: 2 affected / 240 at risk
2.5 mg Tamoxifen
- Lower-dose tamoxifen comparison group
- Serious adverse events: 1 affected / 235 at risk
1 mg Tamoxifen
- Lower-dose tamoxifen comparison group
- Serious adverse events: 1 affected / 239 at risk
0 mg Tamoxifen
- Placebo group
- Serious adverse events: 4 affected / 242 at risk
4. Primary Endpoint
| Endpoint | Time frame | Definition | Endpoint type |
|---|---|---|---|
| Mammograpic Density Change | 6 months treatment | Change in mammography density. The trial tests non-inferiority in the proportion of women in the intervention arms (placebo, 1 mg, 2.5 mg, 5 mg, 10 mg) who have a density reduction as great as or greater after 6 months than the median density reduction in the 20 mg arm. | Binary |
The wording of the endpoint is important statistically. Although the outcome measure is reported as a percentage of change and the posted effect measure is a median difference, the inferential question is framed around a binary responder definition: whether a participant's density reduction reaches or exceeds the median density reduction observed in the 20 mg reference group.
5. Statistical Methodology
Non-inferiority framework
The primary hypothesis was non-inferiority rather than superiority. The registry states that the non-inferiority margin was based on the proportion of responders and was set to 17%. Non-inferiority was defined as the proportion of responders in a non-referent study arm being not less than one third of the responders in the 20 mg group.
The registry describes the 17% margin as arising from the responder-proportion framework: non-inferiority means that the proportion of responders in the non-referent study arm is not less than one third of the responders in the 20 mg group.
One-sided Wald tests
The posted primary analysis used one-sided Wald tests. The Wald framework evaluates an estimated effect relative to its estimated standard error, producing a standardized statistic that can be compared with the relevant hypothesis boundary.
For a non-inferiority test, the null hypothesis represents an effect sufficiently unfavorable to rule out non-inferiority. The direction of the one-sided test therefore matters: the test asks whether the observed evidence is sufficiently compatible with meeting the prespecified non-inferiority criterion.
Multiplicity adjustment
The analysis involved multiple comparisons because several non-referent study arms were evaluated against the 20 mg reference. The registry states that p-values were corrected for multiple comparisons using the Holm-Bonferroni method.
Holm-Bonferroni is a step-down procedure that controls the familywise error rate. Conceptually, the ordered p-values are compared sequentially with increasingly less stringent thresholds. This is preferable to treating several unadjusted comparisons as though they represented a single hypothesis test.
Non-inferiority significance threshold
The registry states that non-inferiority p-values were declared if less than α = 0.025. The posted analysis therefore uses a one-sided decision framework, consistent with the directionality of a non-inferiority hypothesis.
6. Primary Result: Mammographic Density Change
The registry reports a formal statistical analysis for the primary endpoint after 6 months of treatment. The analysis used one-sided Wald tests, with multiplicity adjustment by the Holm-Bonferroni method.
Posted primary effect estimate
Effect measure: Median Difference (Final Values)
97.5% two-sided CI: 41.9–100
Multiplicity-adjusted P < 0.01
Hypothesis type: Non-inferiority
| Primary endpoint | Reference | Analysis | Effect measure | Estimate | 97.5% CI | P-value |
|---|---|---|---|---|---|---|
| Mammograpic Density Change 6 months treatment |
20 mg Tamoxifen | One-sided Wald tests | Median Difference (Final Values) | 52.5 | 41.9–100 | <0.01 |
The posted estimate is 52.5, with a reported two-sided 97.5% confidence interval of 41.9 to 100. The registry identifies the effect measure as a median difference. Because the endpoint's inferential definition is based on a binary responder criterion, the estimate should be read together with the registry's endpoint definition rather than converted into an unreported percentage-point difference.
The reported P < 0.01 is evidence against the unfavorable null under the prespecified non-inferiority framework, after Holm-Bonferroni multiplicity adjustment. It does not measure the magnitude of the treatment effect. A p-value answers a hypothesis-testing question; the estimate and confidence interval provide information about effect magnitude and statistical precision.
The confidence interval indicates that the estimate is subject to statistical uncertainty. Its width is relevant when judging precision, and the upper limit reaches 100. The interval should not be interpreted as a range containing the effects for individual participants.
Non-inferiority is also not equivalent to proving that the treatments are identical. It means that the evidence supports the prespecified criterion for ruling out an unacceptable loss of efficacy relative to the reference framework. The direction of the one-sided Wald test and the 17% non-inferiority margin are therefore central to the interpretation.
7. Understanding the Non-inferiority Margin
The most important design feature of the KARISMA2 primary analysis is the distinction between a conventional superiority comparison and a non-inferiority comparison.
What the 17% margin represents
The registry defines the margin as 17% and explains it through the responder-proportion framework: 50% minus 33%, with non-inferiority corresponding to at least one third of the responder proportion in the 20 mg reference group.
Why the margin comes first
A non-inferiority result is meaningful only relative to a prespecified clinically or scientifically justified margin. The margin defines how much loss relative to the reference is considered acceptable.
A p-value below the stated threshold does not by itself explain whether an observed effect is clinically acceptable. The non-inferiority margin supplies that context. This is why non-inferiority analysis is fundamentally different from simply asking whether two treatment groups have a statistically significant difference.
8. Why a Wald Test Fits This Analysis
A Wald test is based on the estimated effect and its standard error. In large-sample settings, the standardized statistic is approximately normally distributed under the null hypothesis. This makes the method useful for testing a prespecified parameter against a non-inferiority boundary.
The Wald approach therefore links the effect estimate to its uncertainty. The resulting p-value depends not only on the estimated effect but also on the precision of that estimate.
The method is especially important to interpret correctly when the endpoint is represented as a binary responder outcome. The statistical model and coding of the responder definition determine exactly what the estimated parameter represents. The registry's posted result identifies the effect measure as a median difference, so that terminology should be retained rather than silently substituting a different effect measure.
9. Multiplicity: Why Holm-Bonferroni Matters
KARISMA2 evaluates several non-referent study arms against a 20 mg reference. If every comparison were judged independently at the same nominal significance threshold, the probability of at least one false-positive conclusion across the family of comparisons could increase.
| Component | Role in the analysis |
|---|---|
| Multiple study-arm comparisons | Several non-referent arms are evaluated relative to the 20 mg reference. |
| Multiplicity procedure | Holm-Bonferroni correction. |
| Reported p-value | <0.01. |
| Non-inferiority threshold | p < 0.025. |
The Holm-Bonferroni procedure is less restrictive than simply dividing the alpha level equally across all tests, while still controlling the familywise error rate. The practical consequence is that the reported adjusted p-value should be interpreted as part of the prespecified family of comparisons rather than as an isolated test.
Because the registry explicitly states that p-values were corrected using Holm-Bonferroni, the reported P < 0.01 should be understood as a multiplicity-adjusted result. This is important: a small p-value after adjustment carries a different inferential context from a nominal p-value obtained from one unadjusted comparison.
10. Serious Adverse Events by Study Arm
The registry reports serious adverse events by randomized study arm. These figures describe the number affected and the number at risk in each dose group.
| Study arm | Serious adverse events | Affected / at risk |
|---|---|---|
| 20 mg Tamoxifen | 2 / 241 | 2 affected among 241 at risk |
| 10 mg Tamoxifen | 1 / 243 | 1 affected among 243 at risk |
| 5 mg Tamoxifen | 2 / 240 | 2 affected among 240 at risk |
| 2.5 mg Tamoxifen | 1 / 235 | 1 affected among 235 at risk |
| 1 mg Tamoxifen | 1 / 239 | 1 affected among 239 at risk |
| 0 mg Tamoxifen | 4 / 242 | 4 affected among 242 at risk |
These counts should be interpreted as safety frequencies rather than as a formal statistical comparison. The registry reports the affected and at-risk counts by arm, but does not provide a posted comparative inferential analysis for serious adverse events in the statistical analysis record summarized here.
11. Statistical Methods Explained
Why was a non-inferiority design used?
A non-inferiority design is appropriate when the scientific objective is to determine whether an alternative retains sufficient efficacy relative to an established reference, rather than requiring evidence that it is superior. In KARISMA2, the reference was the 20 mg tamoxifen arm and the alternative groups included lower doses and placebo.
The important statistical consequence is that the null hypothesis is directional. The study is not simply asking whether there is a difference. It is asking whether the non-referent arm performs sufficiently well relative to the prespecified 17% margin.
What does the 17% non-inferiority margin mean?
The registry defines the margin as 17% through its responder-proportion framework. It states that non-inferiority means the proportion of responders in the non-referent arm is not less than one third of the responders in the 20 mg group, with the margin described as 50% minus 33%.
This illustrates a general principle of non-inferiority trials: the margin is part of the hypothesis itself. Without the margin, a non-inferiority p-value has no clinical interpretation.
Why was a Wald / z-test used?
The Wald test standardizes an estimated treatment contrast by its standard error. This produces a z statistic that can be evaluated against the null hypothesis in a large-sample framework. It is therefore a direct way to connect an estimated effect with its uncertainty.
For KARISMA2, the registry specifically reports one-sided Wald tests for the primary non-inferiority analysis. The one-sided direction is essential because the objective is to rule out an unacceptable loss rather than simply detect any difference.
Why was the Holm-Bonferroni method needed?
There are multiple non-referent study arms being compared with a common 20 mg reference. If each comparison were tested independently at the same nominal alpha level, the overall chance of a false-positive finding could increase. Holm-Bonferroni provides a step-down multiplicity adjustment that controls the familywise error rate.
Why is the confidence interval useful if the primary test is one-sided?
The confidence interval adds information about the precision of the reported effect estimate. In this registry record, the interval is explicitly reported as two-sided at 97.5% confidence, while the non-inferiority tests are one-sided. The two quantities therefore have related but distinct roles: the p-value evaluates the directional hypothesis, while the interval describes uncertainty around the estimated effect.
What does the p-value actually tell us?
The reported P < 0.01 indicates strong evidence against the null hypothesis under the specified non-inferiority framework, after the stated multiplicity correction. It does not tell us that the effect is "less than 1%" in magnitude, nor does it quantify clinical importance. Effect size and uncertainty must be read from the estimate and confidence interval.
12. Interpreting the Primary Estimate Carefully
The posted analysis reports a median difference of 52.5 with a two-sided 97.5% confidence interval of 41.9 to 100. The registry identifies this as the final-value effect measure for the primary analysis.
The estimate is the reported value of the statistical effect measure used in the registry analysis. It summarizes the observed contrast under the analysis framework rather than representing a universal treatment effect for every participant.
The value 52.5 should not be re-expressed as an unreported relative risk, odds ratio, hazard ratio, or percentage-point difference. Those are different effect measures. The endpoint is defined through a binary responder criterion, while the posted effect measure is labeled a median difference.
The 97.5% two-sided interval of 41.9–100 describes uncertainty around the reported effect estimate under the statistical framework. The relatively broad interval means that the estimate should not be treated as infinitely precise, even though the associated multiplicity-adjusted p-value is below 0.01.
A p-value depends on both the size of the estimated effect and the precision with which it is estimated. A small p-value can therefore occur with a precisely estimated effect, but it is not itself a measure of clinical magnitude. The estimate and confidence interval provide the complementary information needed for effect interpretation.
13. Design and Analysis Considerations
| Design feature | Statistical relevance |
|---|---|
| Randomization | Supports comparison of the study groups by reducing systematic allocation bias. |
| Parallel design | Participants remain assigned to their randomized study arms rather than crossing between interventions. |
| Triple masking | Masking can reduce differential expectations and assessment-related bias. |
| Six study arms | Creates multiple treatment comparisons and therefore makes multiplicity control important. |
| Prevention purpose | The clinical objective concerns risk reduction and mammographic density reduction rather than treatment of established disease. |
| Six-month assessment | The primary endpoint is explicitly defined at 6 months of treatment. |
| Non-inferiority hypothesis | Interpretation depends on the prespecified 17% margin and the direction of the one-sided test. |
The design also illustrates why a trial can have a statistically sophisticated analysis even when its primary endpoint is not a time-to-event outcome. The central issues here are binary endpoint construction, a non-inferiority hypothesis, multiple comparisons, a prespecified margin, and Wald-based inference.
14. Limitations
- Endpoint construction: the registered endpoint combines a continuous mammographic-density measurement with a binary responder criterion based on the median density reduction in the 20 mg reference group. This makes the endpoint definition especially important when interpreting the posted effect measure.
- Effect-measure terminology: the statistical analysis identifies the effect measure as a median difference, while the endpoint itself is described as binary. The two descriptions should not be silently converted into a different effect measure.
- Multiple comparisons: several study arms are evaluated relative to the 20 mg reference, making the Holm-Bonferroni adjustment an important part of the primary inference.
- Non-inferiority interpretation: statistical non-inferiority is conditional on the prespecified 17% margin. It does not mean that the compared doses are identical.
- Confidence-interval width: the reported 97.5% confidence interval extends from 41.9 to 100, so the estimate should be interpreted with attention to its uncertainty.
- Safety interpretation: serious adverse-event counts are available by arm, but the registry record summarized here does not provide a corresponding formal comparative statistical analysis.
- Generalizability: the trial was conducted for prevention and mammographic density reduction, so its findings should be interpreted within that clinical context.
15. Why This Trial Matters Statistically
KARISMA2 is a useful teaching example because it combines several fundamental clinical-trial concepts in a single primary analysis. The trial is randomized and triple-masked, uses six parallel study arms, defines a binary primary endpoint, evaluates non-inferiority, compares multiple groups against a common reference, and applies a Holm-Bonferroni correction to the resulting p-values.
| Concept | How it appears in KARISMA2 |
|---|---|
| Randomization | Participants were randomized across six parallel study arms. |
| Blinding | The trial used triple masking. |
| Binary endpoint | The primary endpoint is registered as binary and is based on a density-reduction responder criterion. |
| Non-inferiority | The lower-dose and placebo groups are evaluated using a non-inferiority framework relative to the 20 mg reference. |
| Non-inferiority margin | The registry specifies a 17% margin. |
| Wald / z-test | One-sided Wald tests were used for the primary analysis. |
| Multiplicity | Holm-Bonferroni correction was used for multiple comparisons. |
| Confidence interval | A two-sided 97.5% confidence interval accompanies the posted estimate. |
| P-value | The reported p-value is <0.01, with non-inferiority declared at p<0.025. |
| Safety by arm | Serious adverse events are reported as affected / at-risk counts for all six groups. |
The broader lesson is that a p-value cannot be interpreted independently of the hypothesis that generated it. In a non-inferiority trial, the margin determines what constitutes an unacceptable loss. With multiple arms, multiplicity adjustment determines how the family of tests is interpreted. And with a binary responder endpoint, the responder definition determines the clinical meaning of the statistical comparison.
16. Related Tutorials
Learn more about the methods used in this trial:
17. Related Calculators
18. Sources
- ClinicalTrials.gov: NCT03346200.
- PubMed: PMID 33734864.
- PubMed: PMID 42720596.
- PubMed: PMID 39593191.
- PubMed: PMID 38554131.
- PubMed: PMID 37149701.
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19. Record Summary
KARISMA2 provides a particularly useful example of non-inferiority methodology in a multi-arm randomized trial. The primary endpoint evaluated mammographic density reduction after 6 months using a binary responder definition relative to the median density reduction in the 20 mg tamoxifen reference group. The posted analysis used one-sided Wald tests, a 17% non-inferiority margin, Holm-Bonferroni multiplicity adjustment, and a non-inferiority threshold of α = 0.025. The reported effect measure was a median difference of 52.5, with a two-sided 97.5% confidence interval of 41.9–100 and a multiplicity-adjusted P < 0.01.
The statistical interpretation depends on keeping these elements together. The estimate describes the reported effect measure; the confidence interval describes uncertainty; the p-value evaluates the prespecified directional hypothesis; the non-inferiority margin defines what constitutes an acceptable loss; and Holm-Bonferroni accounts for the multiple comparisons inherent in the six-arm design. The serious adverse-event counts provide a separate safety perspective across the six study groups.