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
CROWN CORONA was a completed randomized, double-blind, parallel-group phase 3 prevention trial comparing M-M-R II vaccine with placebo in adults with repeated exposures to SARS-CoV-2. The primary endpoint was the number of participants with symptomatic COVID-19 at 60 days after receiving the trial intervention.
| Feature | CROWN CORONA |
|---|---|
| Phase | Phase 3 |
| Condition | COVID 19 |
| Primary purpose | Prevention |
| Design | Randomized, parallel-group, double-blind |
| Allocation | Randomized |
| Enrollment | 3411 |
| Arms | 2 |
| Primary endpoint type | Binary |
| Primary endpoint | Number of Participants With Symptomatic COVID-19 at 60 Days |
| Primary statistical method | Bayesian logistic regression |
| Primary effect measure | Risk difference |
| Hypothesis type | Superiority |
| Lead sponsor | Washington University School of Medicine |
| Status | Completed |
| Start | 2020-09-04 |
| Primary completion | 2021-08-10 |
2. Clinical Question
The central statistical question was whether assignment to M-M-R II vaccine was associated with a different incidence of symptomatic, laboratory test-confirmed COVID-19 at 60 days compared with placebo in adults with repeated exposures to SARS-CoV-2.
Population
Adults with repeated exposures to SARS-CoV-2 by day 60 after receiving the trial intervention, as defined for the primary endpoint.
Intervention
MR or M-M-R II ® vaccine.
Comparator
Placebo.
Primary question
Does M-M-R II vaccine change the risk of symptomatic COVID-19 by 60 days relative to placebo?
3. Trial Design
M-M-R II ®
- MR or M-M-R II ® vaccine
- Serious adverse events reported: 11 affected participants / 1722 at risk
Placebo
- Placebo
- Serious adverse events reported: 5 affected participants / 1689 at risk
The serious-adverse-event denominators shown in the registry are 1722 for M-M-R II and 1689 for placebo. Together they account for 3411 participants.
4. Endpoints
The registry identifies one primary endpoint and reports an additional secondary endpoint at 150 days. Both are binary outcomes concerning symptomatic COVID-19.
| Role | Endpoint | Time frame | Definition / statistical type |
|---|---|---|---|
| Primary | Number of Participants With Symptomatic COVID-19 at 60 Days | 60 days after receiving trial intervention | Binary. Incidence of symptomatic, laboratory test-confirmed COVID-19 in the intervention and control groups in adults with repeated exposures to SARS-CoV-2 by day 60. |
| Secondary | Number of Participants With Symptomatic COVID-19 at 150 Days | 150 days after receiving trial intervention | Binary. Symptomatic COVID-19 outcome analyzed using logistic regression with treatment, age, and a random effect for site. |
Primary endpoint definition
The registry defines symptomatic COVID-19 as laboratory test-confirmed COVID-19 accompanied by any of the following: cough, shortness of breath or difficulty breathing, fever, chills, muscle pain, sore throat, new loss of taste or smell, nausea, vomiting, or diarrhea.
The primary endpoint therefore combines a clinical symptom requirement with laboratory confirmation. Statistically, the resulting outcome is binary: each participant is classified according to whether the endpoint occurred within the specified 60-day time frame.
5. Statistical Methodology
Bayesian logistic regression
The primary endpoint was analyzed using a Bayesian logistic regression. The registry states that the model included treatment arm, age categorized as <50 versus ≥50, and a random effect for site.
Here, Y = 1 represents the binary symptomatic-COVID-19 endpoint. The model adjusts for treatment and age while accounting for site through a random effect.
Covariate adjustment
Age was incorporated into the regression as a categorical covariate using <50 versus ≥50. Treatment arm was the principal comparison, and site was represented with a random effect. This means the reported treatment comparison is model-adjusted rather than a simple unadjusted difference between two observed proportions.
Risk difference
The effect measure reported by the registry is the risk difference (RD). Conceptually, the risk difference compares the probability of the binary outcome between the two treatment groups:
An RD near zero indicates little estimated absolute difference in the modeled outcome probabilities. A positive RD indicates a higher modeled probability in the first group when the comparison is defined as M-M-R II minus placebo.
Superiority framework
The registered hypothesis type is superiority. Unlike a non-inferiority analysis, the question is not whether the vaccine is sufficiently close to placebo. The statistical question is whether the treatment comparison provides evidence of a difference in the prespecified direction under the superiority framework.
Random effect for site
The inclusion of a random effect for site recognizes that participants enrolled at different sites may have outcomes that are correlated or otherwise systematically different. Rather than treating every site contribution as completely unrelated, the model allows site-level variation to enter the analysis.
Secondary endpoint analysis
The 150-day endpoint was also analyzed with Bayesian logistic regression. The registry describes the same general covariate structure: treatment arm, age (<50 versus ≥50), and a random effect for site.
6. Primary Result: Symptomatic COVID-19 at 60 Days
The primary endpoint was the number of participants with symptomatic COVID-19 at 60 days after receiving the trial intervention.
Risk difference: M-M-R II vs placebo
95% CI: −0.5 to 1.1 · P = 0.52
Bayesian logistic regression adjusted for treatment arm, age (<50 vs ≥50), and a random effect for site.
| Primary endpoint | Estimate | 95% CI | P-value | Method |
|---|---|---|---|---|
| Symptomatic COVID-19 at 60 days | RD 0.3 | −0.5 to 1.1 | 0.52 | Bayesian logistic regression |
The reported risk difference of 0.3 is the modeled difference in the probability of symptomatic COVID-19 between the M-M-R II and placebo groups under the registry's regression analysis. Because the estimate is close to zero, the fitted comparison indicates only a small estimated absolute difference.
The 95% confidence interval from −0.5 to 1.1 spans zero. Thus, the interval includes both a small negative difference and a small positive difference. The interval is important because the point estimate alone does not communicate the uncertainty surrounding the treatment comparison.
The reported p-value of 0.52 is not a measure of the magnitude of the treatment effect. A p-value answers a hypothesis-testing question; it does not tell us whether an observed difference is clinically large, clinically small, or practically important.
The registry describes the analysis as Bayesian logistic regression while also reporting a p-value. The p-value should therefore be interpreted as the statistical quantity reported by the registry rather than as a posterior probability that the treatment is effective or ineffective.
The analysis is adjusted for age and site. Consequently, the reported RD should not be interpreted as a simple arithmetic subtraction of two unadjusted event proportions.
What the confidence interval contributes
The interval from −0.5 to 1.1 provides a range of values describing uncertainty around the estimated risk difference under the analysis framework. Because the interval crosses zero, the data represented by this analysis are compatible with either direction of a small absolute difference.
Importantly, the confidence interval does not say that there is a 95% probability that the true treatment effect lies between −0.5 and 1.1. Confidence intervals are statements about the statistical procedure used to generate the interval and its repeated-sampling properties, not probabilities assigned to a fixed parameter after observing the data.
7. Secondary Result: Symptomatic COVID-19 at 150 Days
The registry also reports the number of participants with symptomatic COVID-19 at 150 days after receiving the trial intervention.
Risk difference: M-M-R II vs placebo
95% CI: −1.4 to 1.3 · P = 0.95
Bayesian logistic regression adjusted for treatment arm, age (<50 vs ≥50), and a random effect for site.
| Secondary endpoint | Estimate | 95% CI | P-value | Method |
|---|---|---|---|---|
| Symptomatic COVID-19 at 150 days | RD 0.04 | −1.4 to 1.3 | 0.95 | Bayesian logistic regression |
The estimated risk difference of 0.04 is very close to zero. Its 95% confidence interval, −1.4 to 1.3, spans zero and is substantially wider than the point estimate itself.
The reported p-value of 0.95 does not measure the size of the treatment effect. As with the primary analysis, the magnitude of the RD and the width and location of the confidence interval provide more direct information about the estimated difference and its precision.
The wider interval relative to the point estimate illustrates an important statistical principle: an estimate close to zero can still be associated with meaningful uncertainty. The estimate alone should therefore not be treated as proof that the two groups are exactly identical.
8. Comparing the 60-Day and 150-Day Analyses
The two registry-reported analyses use the same broad statistical framework but address different follow-up windows. This distinction matters because an endpoint measured at 60 days is not statistically interchangeable with the corresponding endpoint measured at 150 days.
| Feature | 60 days | 150 days |
|---|---|---|
| Endpoint | Symptomatic COVID-19 | Symptomatic COVID-19 |
| Role | Primary | Secondary |
| Effect measure | Risk difference | Risk difference |
| Estimate | 0.3 | 0.04 |
| 95% CI | −0.5 to 1.1 | −1.4 to 1.3 |
| P-value | 0.52 | 0.95 |
| Model | Bayesian logistic regression | Bayesian logistic regression |
| Covariates | Treatment, age, random site effect | Treatment, age, random site effect |
The estimates are numerically close to zero at both time points. The 150-day confidence interval is wider, however, so the precision of the two estimates is not identical. The fact that both estimates are near zero should be distinguished from the stronger claim that the two treatment groups are proven to have exactly the same underlying risk.
9. Statistical Methods Explained
Why was logistic regression used?
The endpoints are binary: a participant either met the symptomatic-COVID-19 endpoint within the specified time frame or did not. Logistic regression is designed for binary outcomes and allows the analysis to incorporate treatment, age, and site effects simultaneously.
What does a risk difference of 0.3 mean?
The risk difference is the modeled probability in the M-M-R II group minus the modeled probability in the placebo group. An estimate of 0.3 therefore represents a small positive modeled absolute difference under the registry's analysis. The estimate should be interpreted together with its confidence interval rather than by itself.
Why is the confidence interval more informative than the point estimate alone?
A point estimate gives one numerical summary of the treatment comparison. The confidence interval shows the uncertainty surrounding that estimate. For the primary endpoint, the interval extends from −0.5 to 1.1, demonstrating that the estimate is not precise enough to exclude small differences in either direction within that interval.
Why include age as a covariate?
The registry specifies age category (<50 versus ≥50) as a covariate in the logistic regression. Including a prespecified or analytically selected covariate can account for variation associated with that characteristic and produce an adjusted treatment comparison rather than relying only on an unadjusted group comparison.
Why use a random effect for site?
Participants treated at the same site can share characteristics or care processes that make their outcomes more similar than outcomes from participants at different sites. A random site effect allows the model to account for this site-level variation while estimating the treatment comparison across the participating sites.
What does the p-value of 0.52 tell us?
The p-value is a hypothesis-testing quantity reported by the registry alongside the Bayesian logistic-regression analysis. It does not quantify the size of the risk difference, does not represent the probability that the null hypothesis is true, and should not be interpreted as a measure of clinical importance.
Why is this a superiority analysis rather than a non-inferiority analysis?
The registered hypothesis type is superiority. The objective is therefore to assess whether the treatment groups differ, rather than to demonstrate that M-M-R II remains within a prespecified acceptable loss relative to placebo. No non-inferiority margin is reported in the registry information used here.
10. Risk Difference vs Relative Measures
The choice of effect measure is central to interpreting this trial. The registry reports risk difference, not an odds ratio, risk ratio, or hazard ratio.
Unlike a relative measure, the risk difference expresses the absolute separation between the modeled probabilities of the binary outcome.
This distinction matters because absolute and relative measures answer different questions. A relative measure can appear large even when absolute risks are small, while a risk difference directly describes the absolute separation in event probability.
For CROWN CORONA, the reported primary RD of 0.3 is accompanied by a 95% CI from −0.5 to 1.1. The secondary RD of 0.04 is accompanied by a 95% CI from −1.4 to 1.3. These are the effect measures actually reported for the posted analyses.
11. Bayesian Logistic Regression in Context
The registry specifically describes the primary analysis as a Bayesian logistic regression. Bayesian regression differs from a purely likelihood-based description because inference is framed using a probability model for unknown quantities together with prior information and the observed data.
The posterior distribution combines information from the observed data with the specified prior distribution. The exact prior specifications are not reported in the information summarized here.
That distinction is important when reading the reported estimate and interval. The registry identifies the model as Bayesian, but the posted analysis also reports a conventional p-value. The p-value should therefore be treated as a reported statistical quantity rather than converted into a Bayesian probability statement.
The analysis also contains both fixed covariate information and a site-level random effect. This gives the model more structure than a simple two-group comparison of event proportions.
12. The Role of Randomization and Blinding
Randomization is the foundation for the treatment comparison. Participants were randomized to M-M-R II or placebo, creating the experimental framework for comparing the two groups.
Double blinding adds a separate layer of protection against differential behavior, assessment, or expectations associated with knowledge of treatment assignment. For a binary symptomatic outcome, blinding can be particularly relevant when symptom assessment forms part of endpoint determination.
Randomization
Creates the treatment-assignment mechanism underlying the comparative analysis.
Double blinding
Reduces the opportunity for knowledge of assignment to influence participant or study assessment processes.
These design features do not determine the numerical result by themselves. They establish the structure within which the statistical comparison can be interpreted.
13. Safety: Serious Adverse Events
The registry reports serious adverse events by treatment arm. The available figures are presented as affected participants over participants at risk.
| Treatment group | Serious adverse events | At risk |
|---|---|---|
| M-M-R II ® | 11 | 1722 |
| Placebo | 5 | 1689 |
The serious-adverse-event counts should be interpreted together with their denominators. The registry reports 11 affected participants among 1722 at risk in the M-M-R II group and 5 among 1689 at risk in the placebo group.
These counts are descriptive safety information. They are not the same endpoint as symptomatic COVID-19 and are not incorporated into the primary Bayesian logistic-regression result described above.
14. Statistical Interpretation of the Primary Analysis
The primary estimated risk difference was 0.3 for M-M-R II versus placebo. The sign of the estimate indicates the direction of the modeled comparison as reported, while the magnitude describes the estimated absolute separation between groups.
The 95% CI of −0.5 to 1.1 spans zero. This means that the uncertainty interval includes values corresponding to a small negative difference, no difference, and a small positive difference.
The reported p-value of 0.52 does not describe the size of the estimated treatment effect. A p-value and an effect estimate answer different statistical questions and should not be substituted for one another.
The reported estimate comes from a Bayesian logistic regression containing treatment arm, age category, and a random effect for site. It is therefore a model-based adjusted comparison rather than an unadjusted difference in observed event proportions.
The registry-reported analysis estimates only a small absolute difference at 60 days, with uncertainty extending on both sides of zero. Statistical interpretation should remain tied to the endpoint definition, time frame, analysis model, and uncertainty interval rather than translating the result into a broader claim about all possible effects of vaccination.
15. What the Statistical Result Does Not Mean
- The RD is not a relative risk. A risk difference describes an absolute difference between modeled probabilities.
- The p-value is not the probability that the treatment has no effect. It is a statistical quantity associated with the reported hypothesis-testing framework.
- The confidence interval is not a range containing 95% of individual treatment effects. It quantifies statistical uncertainty around the estimated treatment comparison.
- A point estimate near zero is not proof of exact equality. The interval describes what remains uncertain around the estimate.
- The 60-day and 150-day results are not interchangeable. They represent different follow-up definitions and different registered endpoint roles.
- The adjusted RD is not simply the difference between two raw percentages. The posted analysis uses treatment, age, and site information within a logistic-regression model.
16. Primary vs Secondary Endpoint Interpretation
| Feature | Primary endpoint | Secondary endpoint |
|---|---|---|
| Outcome | Symptomatic COVID-19 | Symptomatic COVID-19 |
| Time frame | 60 days | 150 days |
| Endpoint type | Binary | Binary |
| Effect measure | Risk difference | Risk difference |
| Estimate | 0.3 | 0.04 |
| 95% CI | −0.5 to 1.1 | −1.4 to 1.3 |
| P-value | 0.52 | 0.95 |
| Hypothesis type | Superiority | Superiority |
The distinction between primary and secondary endpoints is part of the statistical architecture of a clinical trial. The primary endpoint is the principal prespecified outcome around which the study's main statistical question is organized. A secondary endpoint can provide additional information but should not automatically be treated as equivalent to the primary endpoint for confirmatory interpretation.
17. Limitations
- Binary endpoint: the primary analysis reduces the clinical outcome to whether symptomatic COVID-19 occurred within the specified 60-day window.
- Time-window dependence: the 60-day and 150-day analyses answer different questions because their observation windows differ.
- Model dependence: the reported treatment effect is based on Bayesian logistic regression with age adjustment and a random effect for site.
- Site variation: the random site effect accounts for modeled site-level variation, but the registry information does not provide the magnitude of that variation.
- Confidence-interval interpretation: the primary interval crosses zero, so the point estimate should not be interpreted without its associated uncertainty.
- Safety endpoint distinction: serious adverse events are separate from the efficacy endpoint and should not be combined with the symptomatic-COVID-19 result into a single numerical conclusion.
- Bayesian model specification: the registry identifies the analysis as Bayesian logistic regression but does not provide the prior specifications in the information summarized here.
18. Why This Trial Matters Statistically
CROWN CORONA is a useful statistical teaching case because it illustrates how a binary clinical endpoint can be analyzed using a covariate-adjusted Bayesian regression model rather than only through a simple comparison of observed proportions.
| Concept | How it appears in CROWN CORONA |
|---|---|
| Randomization | Participants were randomized to M-M-R II vaccine or placebo. |
| Blinding | The trial was double-blind. |
| Binary endpoint | Symptomatic COVID-19 at 60 and 150 days was analyzed as a binary outcome. |
| Logistic regression | The posted analyses used logistic regression. |
| Bayesian analysis | The primary and secondary analyses were described as Bayesian logistic regression. |
| Covariate adjustment | Age category was included in the model. |
| Random effect | Site was included as a random effect. |
| Risk difference | The reported treatment effect was the risk difference. |
| Confidence interval | Both posted analyses included two-sided 95% confidence intervals. |
| Superiority testing | The registry identifies superiority as the hypothesis type. |
19. Reading the Primary Result as a Statistical Story
A useful way to read the primary analysis is to proceed in a fixed order rather than beginning with the p-value.
Identify what was measured
The outcome was symptomatic, laboratory test-confirmed COVID-19 at 60 days after receiving the trial intervention.
Identify how groups were formed
The trial used randomized allocation and double blinding in a parallel-group phase 3 design.
Identify how the comparison was estimated
The registry reports Bayesian logistic regression with treatment, age category, and a random effect for site.
Identify what the number means
The reported effect measure is risk difference, so the estimate represents an absolute difference in modeled probability rather than a relative hazard or odds.
Read the interval
The 95% confidence interval extends from −0.5 to 1.1 and therefore includes zero.
Read the reported p-value
The registry reports P = 0.52. This is a hypothesis-testing quantity and should not be used as a substitute for the effect estimate or its confidence interval.
20. Primary Analysis: A Compact Statistical Summary
| Component | Registry-reported information |
|---|---|
| Population | Adults with repeated exposures to SARS-CoV-2 by day 60 after receiving trial intervention |
| Intervention | MR or M-M-R II ® vaccine |
| Comparator | Placebo |
| Endpoint | Number of Participants With Symptomatic COVID-19 at 60 Days |
| Endpoint type | Binary |
| Hypothesis | Superiority |
| Model | Bayesian logistic regression |
| Covariates | Treatment arm; age (<50 vs ≥50); random effect for site |
| Effect measure | Risk difference |
| Estimate | 0.3 |
| 95% CI | −0.5 to 1.1 |
| P-value | 0.52 |
This compact representation makes the statistical structure visible: the endpoint is binary, the treatment comparison is adjusted through logistic regression, the effect is expressed on an absolute risk-difference scale, and the uncertainty interval spans zero.
21. Related Statistical Tutorials
Learn more about the methods used in this trial:
22. Related Statistical Calculators
23. Sources
- ClinicalTrials.gov: NCT04333732 — CROWN CORONA.
- PubMed: PMID 41035643.
- PubMed: PMID 37153751.
- PubMed: PMID 35713300.
- PubMed: PMID 34473343.
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24. Record Summary
CROWN CORONA was a randomized, double-blind, parallel-group phase 3 prevention trial enrolling 3411 participants and comparing M-M-R II vaccine with placebo. Its primary endpoint was symptomatic, laboratory test-confirmed COVID-19 at 60 days, analyzed as a binary outcome using Bayesian logistic regression with treatment arm, age category, and a random effect for site.
The registry-reported primary effect measure was a risk difference of 0.3, with a two-sided 95% confidence interval of −0.5 to 1.1 and a reported p-value of 0.52. The secondary 150-day analysis reported a risk difference of 0.04, with a 95% confidence interval of −1.4 to 1.3 and a reported p-value of 0.95.
Statistically, the trial provides a clear example of how randomized treatment comparisons can be analyzed for binary outcomes using a regression framework that incorporates covariate adjustment and site-level variation. The interpretation of the reported results depends on considering the endpoint definition, time frame, model, effect measure, confidence interval, and hypothesis-testing result together rather than relying on any single number.