This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for Study of Allogeneic Umbilical Cord Blood Infusion for Adults With Ischemic Stroke (NCT03004976), a randomized phase 2 study. The primary outcome is Shift in Modified Rankin Scale (mRS).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT03004976 |
| Phase | Phase 2 |
| Condition | Stroke, Stroke, Acute, Brain Injury, Acute |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Triple |
| Enrollment | 79 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Joanne Kurtzberg, MD |
| Results posted | Yes |
2. Clinical Question
Population
Adults with ischemic stroke were eligible for the study. The registry describes the primary analysis population as the Modified Intention To Treat population: participants with both a baseline and a 90-day modified Rankin Scale score. The total enrollment was 79, while the primary endpoint summaries include 47 participants in the umbilical cord blood group and 26 in the placebo group. The registry record does not explain the difference between enrollment and those endpoint denominators.
Intervention
The intervention was a single intravenous infusion of unrelated donor umbilical cord blood, given 3-10 days following stroke. The study description says participants did not receive immunosuppressive or myeloablative medications before infusion. Follow-up was planned for one year after infusion.
Comparator
The comparison group received a single intravenous infusion of diluent intended to have the same appearance and odor as a cord blood unit, also within 3-10 days following stroke. The study used a randomized, parallel-group design with triple masking.
Primary question
The primary endpoint was the shift in modified Rankin Scale score from baseline to three months after infusion. The scale records disability from 0 to 6, with 6 representing death. The registry defines a downward shift as a clinical improvement and describes the shift coding so that larger shift values represent more desirable outcomes for hypothesis testing. The statistical question is whether the distribution of these shifts differed between the assigned groups.
3. Trial Design
CoBIS 2 was a phase 2, randomized, triple-masked, parallel-group study comparing a single umbilical cord blood infusion with placebo in adults with ischemic stroke. The registry reports enrollment of 79 and a completed status. The study began on 2017-03-14, and primary completion was recorded as 2020-07-17. The sponsor is listed as Joanne Kurtzberg, MD.
The intervention was administered intravenously within 3-10 days following stroke. The placebo was a diluent with the same appearance and odor as a cord blood unit. The study description states that participants did not receive immunosuppressive or myeloablative medications before infusion. Follow-up was for one year after infusion, with assessments at 24 hours and at 30, 90, 180 and 365 days after infusion. These assessments covered safety and tolerability as well as neurological symptoms, quality of life, emotional status and cognitive status.
The primary endpoint population was narrower than enrollment: it included participants with both baseline and 90-day modified Rankin Scale scores. Its arm summaries report 47 participants for umbilical cord blood and 26 for placebo. Other posted outcomes use their own denominators, which vary by endpoint. The registry record does not report why denominators differ or how missing outcome data were handled.
The record lists 24 outcome measures and 23 posted secondary outcomes. These include safety events, mortality, functional independence and another modified Rankin Scale assessment. The registry record does not report the sample-size justification, a detailed statistical analysis plan, or whether interim analyses were conducted. The study’s completed status describes its recorded status, not a conclusion about the efficacy of the intervention.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Overall Study
| Stage | Umbilical Cord Blood | Placebo |
|---|---|---|
| STARTED | 52 | 27 |
| COMPLETED | 39 | 21 |
| NOT COMPLETED | 13 | 6 |
Reasons for not completing this period:
| Reason | Umbilical Cord Blood | Placebo |
|---|---|---|
| Lost to Follow-up | 7 | 5 |
| Physician Decision | 1 | 0 |
| Withdrawal by Subject | 1 | 0 |
| Death | 4 | 1 |
Analysis population for the primary outcome, as defined in the registry: Modified Intention To Treat population (participants who have a baseline and 90 day mRS score)
5. Baseline Characteristics
The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.
| Characteristic | Unit | Umbilical Cord Blood | Placebo | Total |
|---|---|---|---|---|
| Participants analysed | 52 | 27 | 79 | |
| Age, Continuous | years | 61.3 (SD 13.0) | 64.0 (SD 11.1) | 62.2 (SD 12.4) |
| Sex: Female, Male: Female | Participants | 21 | 10 | 31 |
| Sex: Female, Male: Male | Participants | 31 | 17 | 48 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 6 | 2 | 8 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 46 | 25 | 71 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 1 | 1 | 2 |
| Race (NIH/OMB): Asian | Participants | 3 | 1 | 4 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Black or African American | Participants | 13 | 6 | 19 |
| Race (NIH/OMB): White | Participants | 35 | 19 | 54 |
| Race (NIH/OMB): More than one race | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 |
| Region of Enrollment: United States | Participants | 52 | 27 | 79 |
6. Primary Endpoint
The registry lists the primary outcome as Shift in Modified Rankin Scale (mRS), measured over baseline to 3 months post infusion.
| Element | Registry entry |
|---|---|
| Result type | Median |
| Measure of spread | Inter-Quartile Range |
| Unit | score on a scale |
| Endpoint classification | not reduced to a single comparison |
The primary endpoint is the shift in modified Rankin Scale score from baseline to three months after infusion. The modified Rankin Scale is an ordinal disability scale, with scores from 0 to 6 and 6 representing death. The registry states that a downward shift is considered an improvement and that shifts were coded so larger values represent more desirable outcomes for hypothesis testing.
Using a change from baseline focuses the endpoint on how a participant’s recorded disability score changed over the follow-up period, rather than on the follow-up score alone. The ordinal scale retains ordered categories: a higher category represents a different level of disability, but the distances between adjacent categories are not necessarily equal. A rank-based comparison or an ordinal regression model can therefore analyze the ordering without treating the score as a continuous measurement with equal spacing. This is a general statistical rationale, not a reported explanation of the investigators’ choice.
The registry reports a median shift of 1 in each group, with an inter-quartile range from 0 to 2 in each group. The endpoint population is defined as participants with both a baseline and 90-day score. That definition makes the observed endpoint summaries specific to participants with those measurements; the registry record does not report how missing scores were handled or whether other analysis populations were used for the primary endpoint.
7. Why No Re-analysis Is Shown
8. Statistical Interpretation
For the primary endpoint, both groups had a reported median modified Rankin Scale shift of 1, with an inter-quartile range of 0 to 2. Equal medians do not establish that the full distributions were identical; they describe the middle of each group’s observed distribution. The posted analyses also compare the groups using a Wilcoxon Mann-Whitney method and a cumulative logit proportional odds model.
The Wilcoxon Mann-Whitney odds estimate was 0.9, with a 95% confidence interval from 0.53 to 1.55 and p = 0.71. The cumulative logit model reported an odds ratio of 0.9, with a 95% confidence interval from 0.4 to 2.3 and p = 0.87. Both confidence intervals include 1, the value corresponding to no difference on an odds-ratio scale. The p-values are not small under conventional thresholds, but neither a p-value nor a confidence interval proves that the groups are equivalent. The intervals show that the estimates remain compatible with a range of effects in either direction, including no difference.
The posted secondary recalculations likewise do not give precise evidence of a group difference: their confidence intervals include the no-difference value, and the reported unadjusted p-values are not small under conventional thresholds. Those calculations are simple, unadjusted comparisons based on posted summary counts. They should not be treated as substitutes for a prespecified sponsor analysis, and the registry record does not report sponsor analyses for these secondary outcomes.
These results describe the recorded outcomes for the analyzed participants and the methods named in the registry. They do not establish that the treatments are equivalent, nor do they establish that a clinically important difference is absent. The endpoint summaries and confidence intervals leave uncertainty about the size and direction of any difference. The registry record does not report a clinically meaningful threshold for the primary endpoint, so the estimates cannot be judged against such a threshold from the registry information alone.
The safety results are descriptive counts and should be interpreted separately from the efficacy comparisons. The numbers at risk differ across safety listings and endpoint analyses. The record does not report an adjusted safety comparison or explain the denominator differences. These findings therefore characterize the reported events, rather than providing a definitive comparative assessment of risk.
9. Statistical Methods Explained
The registry reports two analyses of the primary modified Rankin Scale shift: a Wilcoxon Mann-Whitney analysis and a cumulative logit proportional odds model. It reports an estimate, a 95% confidence interval and a p-value for each. The explanations below describe these methods generally; the registry record does not provide the complete analysis specifications.
Why use a rank-based test?
The modified Rankin Scale is ordinal: its categories have an order, but the spacing between categories need not be equal. A Wilcoxon Mann-Whitney test uses the ordering of observations to compare the groups, rather than assuming that each one-step change has the same numerical meaning. In general, this type of test assesses whether values from one group tend to rank differently from values in the other group. The registry labels its reported effect measure as Wilcoxon Mann-Whitney odds. The record does not give a more detailed definition of that estimate or describe any adjustments.
What does the proportional odds model add?
A cumulative logit proportional odds model is a general method for ordinal outcomes. It uses the ordered categories and models cumulative probabilities across category thresholds. The proportional-odds assumption means that the modeled group contrast is treated as consistent across those thresholds. The registry reports an odds ratio from this model, but it does not report diagnostics or tests of the proportional-odds assumption, covariates, or other model details. The result should therefore be read as the model-based estimate named in the record, not as evidence that every modeling assumption was verified.
How should estimates and confidence intervals be read?
An estimate gives the effect size on the scale used by a method. A confidence interval describes the statistical uncertainty around that estimate under the method’s assumptions. In general, an interval that includes the no-difference value means that the data do not clearly distinguish the estimate from no difference at the stated confidence level. It does not show that the true effect is exactly zero. The p-value measures how unusual results at least as extreme as the observed result would be under a specified null hypothesis and model; it is not the probability that the null hypothesis is true. These general explanations do not change the registry’s reported estimates.
The two primary analyses use different methods and effect measures, but both estimates are 0.9. Their confidence intervals are broad enough to include the no-difference value and values on either side. The medians and inter-quartile ranges provide a separate descriptive view of the outcome: each group’s median shift was 1, and each group’s inter-quartile range was 0 to 2. A median and inter-quartile range do not describe every feature of an ordinal distribution, which is why the registry also reports group-comparison analyses.
What do the secondary recalculations represent?
For mortality and functional independence, the posted recalculations include risk differences, confidence intervals, unadjusted p-values, and relative measures. A risk difference expresses a contrast between the observed proportions in the two groups. A relative risk compares those proportions as a ratio; an odds ratio compares the odds. These are general definitions. The recalculations are unadjusted and use the posted summary counts; they are not reported sponsor analyses. The record does not supply a sponsor analysis for these secondary outcomes.
Confidence intervals for binary outcomes can be wide when the observed counts are limited. Wide intervals indicate uncertainty in the estimated contrast. They should not be summarized only by whether an interval crosses the no-difference value: the range of compatible effects is also important. The posted secondary comparisons do not adjust for multiple testing, and the registry record does not report whether a multiplicity procedure was used elsewhere.
What do the sample-size illustrations mean?
The planning illustrations are calculations based on observed effects, not the trial’s original design or observed power. The stated assumptions are a two-sided significance level of 0.05, equal allocation between groups, a normal approximation, and detection of the stated fraction of the observed effect. They describe hypothetical participants per arm needed under those assumptions. They do not show how many participants were actually analyzed, and they do not establish the probability that this completed study detected an effect. The registry record does not report the trial’s own sample-size justification or design assumptions.
10. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Wilcoxon (Mann-Whitney) | Wilcoxon Mann-Whitney Odds 0.9 | 0.53 to 1.55 | 0.710 |
| Cumulative Logit Proportional Odds Model | Odds Ratio (OR) 0.9 | 0.4 to 2.3 | 0.870 |
The registry reports two sponsor analyses for the primary endpoint. The first is a Wilcoxon Mann-Whitney analysis, with a Wilcoxon Mann-Whitney odds estimate of 0.9, a 95% confidence interval from 0.53 to 1.55, and p = 0.71. The second is a cumulative logit proportional odds model, with an odds ratio of 0.9, a 95% confidence interval from 0.4 to 2.3, and p = 0.87. These are the registry’s reported primary analyses and should be distinguished from simple unadjusted recalculations based on posted summary statistics for selected secondary outcomes.
The registry record does not flag a discrepancy between the sponsor analyses and a recalculation of the primary endpoint. The secondary recalculations do not replace the sponsor’s primary analyses: they concern different outcomes and do not use the same reported analysis methods. No sponsor analyses are listed for the posted secondary outcomes. The record does not report further details about adjustments, model diagnostics, or a complete statistical analysis plan, so the relationship between the reported primary analyses and any broader analysis plan cannot be assessed from the registry record.
The primary analyses give estimates close to 1 and confidence intervals that include 1. They do not establish equivalence or rule out potentially meaningful differences. The sponsor’s results are best read as the reported primary statistical comparisons, with their uncertainty and the limitations of the available analysis details kept in view.
11. Multiplicity, Missing Data and Analysis Populations
The registry reports a primary endpoint and multiple secondary outcomes, but it does not report whether the statistical plan adjusted for multiple comparisons, specified a hierarchy among outcomes, or reserved particular secondary analyses for confirmatory testing. With many outcomes, testing each one at an unadjusted threshold can increase the chance of at least one false-positive result. That is a general statistical concern, not evidence that any particular posted finding is false. The secondary recalculations are explicitly unadjusted and should be interpreted as exploratory unless another analysis plan, not reported in the registry record, establishes otherwise.
The primary endpoint population is defined as participants with both baseline and 90-day modified Rankin Scale scores. The reported endpoint summaries use 47 participants in the umbilical cord blood group and 26 in the placebo group. Enrollment was 79. Other outcomes have different denominators. The registry record does not report the reasons for missing scores, the methods used to handle missing data, whether any imputation was performed, or whether sensitivity analyses assessed the effect of missing observations. Without those details, the possible influence of missing data on the estimates cannot be evaluated from the registry record.
The record also does not report a detailed analysis plan, covariate adjustments for the primary comparison, model diagnostics, or whether interim analyses were conducted. It does not provide a sample-size justification for the trial’s original design. The planning illustrations based on observed effects are not a substitute for that information and should not be interpreted as observed power.
These absences limit assessment of how fully the reported analyses followed prespecified methods and whether the findings are robust to alternative missing-data or multiplicity approaches. They do not establish that the analyses were inappropriate; they mean that the registry record does not contain enough information to assess those issues.
12. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Umbilical Cord Blood | 14 | 52 | 26.9% |
| Placebo | 11 | 27 | 40.7% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Umbilical Cord Blood | 4 of 52 |
| Placebo | 1 of 27 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 0% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Umbilical Cord Blood | 36 of 52 |
| Placebo | 17 of 27 |
Most frequent serious adverse event terms
| Event term | Organ system | Umbilical Cord Blood | Placebo |
|---|---|---|---|
| FALL | Injury, poisoning and procedural complications | 2 of 52 | 2 of 27 |
| SEIZURE | Nervous system disorders | 2 of 52 | 2 of 27 |
| ISCHEMIA CEREBROVASCULAR | Nervous system disorders | 2 of 52 | 1 of 27 |
| STROKE | Nervous system disorders | 1 of 52 | 2 of 27 |
| COGNITIVE DISTURBANCE | Nervous system disorders | 1 of 52 | 1 of 27 |
| DEATH NOS | General disorders | 2 of 52 | 0 of 27 |
| DEHYDRATION | Metabolism and nutrition disorders | 1 of 52 | 1 of 27 |
| FRACTURE | Injury, poisoning and procedural complications | 1 of 52 | 1 of 27 |
| HYPERTENSION | Vascular disorders | 2 of 52 | 0 of 27 |
| MYOCARDIAL INFARCTION | Cardiac disorders | 1 of 52 | 1 of 27 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Umbilical Cord Blood | Placebo |
|---|---|---|---|
| PAIN IN EXTREMITY | Musculoskeletal and connective tissue disorders | 12 of 52 | 4 of 27 |
| DEPRESSION | Psychiatric disorders | 5 of 52 | 5 of 27 |
| URINARY TRACT INFECTION | Infections and infestations | 5 of 52 | 5 of 27 |
| FALL | Injury, poisoning and procedural complications | 6 of 52 | 3 of 27 |
| HEADACHE | Nervous system disorders | 5 of 52 | 4 of 27 |
| HYPOKALEMIA | Metabolism and nutrition disorders | 3 of 52 | 5 of 27 |
| LEUKOCYTOSIS | Blood and lymphatic system disorders | 7 of 52 | 1 of 27 |
| ANEMIA | Blood and lymphatic system disorders | 3 of 52 | 4 of 27 |
| EDEMA LIMBS | General disorders | 6 of 52 | 1 of 27 |
| HYPOTENSION | Vascular disorders | 5 of 52 | 2 of 27 |
Serious events with the highest arm-level rate: fall (7.4%), seizure (7.4%), stroke (7.4%), death nos (3.8%), hypertension (3.8%).
The safety listings report serious adverse events and other adverse events separately. In the serious adverse event listing, 14 of 52 participants at risk in the umbilical cord blood group were affected, compared with 11 of 27 participants at risk in the placebo group. For other adverse events, the corresponding counts are 36 of 52 and 17 of 27. The listing also reports 4 deaths in the umbilical cord blood group and 1 in the placebo group. These are descriptive counts, not adjusted comparisons.
The most frequent serious event terms listed include FALL, SEIZURE and STROKE, each reported as 7.4%; DEATH NOS, HYPERTENSION and ISCHEMIA CEREBROVASCULAR are each reported as 3.8%. The registry record does not provide further context about event timing, severity grading, attribution, or whether participants could contribute more than one event. The percentages should therefore be read as reported event-term figures, not as a complete account of participant-level risk.
The safety listing’s numbers at risk differ from the denominators used for the mortality and primary endpoint results. The registry record does not explain the denominator differences or reconcile the death counts across listings. These figures do not, on their own, establish a comparative safety effect or explain the causes of events.
13. What the Result Does, and Does Not, Mean
The primary result describes the observed modified Rankin Scale shifts among participants included in the registry-defined endpoint population. Both groups had the same reported median shift, and the two sponsor analyses produced estimates with confidence intervals spanning the no-difference value. The results do not show a clearly separated group difference in those analyses, but that is not the same as proving that the groups were equivalent.
Uncertainty matters. The confidence intervals allow for effects in either direction, and the registry record does not give a threshold for what size of shift would be clinically important. A non-significant p-value does not establish that an effect is absent; it indicates that the data did not provide strong evidence against the null hypothesis under the specified analysis. The record also does not report enough information to assess how missing data, multiplicity or alternative model assumptions might affect interpretation.
The secondary outcomes provide additional descriptive information, but their unadjusted recalculations are not replacements for the primary analysis. They address distinct outcomes and time points, use varying denominators, and are subject to multiplicity concerns. Safety counts likewise describe reported events and should not be interpreted as a definitive comparison of risks.
Overall, the registry results can be used to understand what was measured, how the primary endpoint was analyzed, and the uncertainty around the reported estimates. They do not establish equivalence, exclude all potentially important differences, or provide a basis for medical advice. Further details about the full analysis plan and missing-data handling are not reported in the registry record.
14. Why This Trial Matters Statistically
This trial illustrates a common statistical challenge in clinical research: an ordinal outcome can be clinically interpretable while resisting simple treatment as a continuous score. The modified Rankin Scale has ordered categories, and the registry’s shift definition makes the direction of improvement explicit for hypothesis testing. Reporting both a rank-based comparison and an ordinal regression gives two statistical views of the primary outcome, although the registry record does not report the full assumptions and diagnostics for either analysis.
It also shows why estimates and intervals matter alongside p-values. The primary analyses do not clearly separate the groups, but their confidence intervals span a range that includes the no-difference value and effects on either side. That uncertainty cannot be reduced to a yes-or-no conclusion. The reported medians are useful descriptive summaries, yet they do not capture every aspect of the outcome distribution.
The different denominators across endpoint and safety listings are another important consideration. A result is tied to its analysis population, and the registry-defined primary population requires both baseline and 90-day measurements. The registry record does not explain the denominator differences or the handling of missing data, which limits assessment of the analyses’ reach and robustness.
Finally, multiple secondary outcomes create a need for transparent multiplicity planning. Unadjusted comparisons can be informative as exploratory evidence, but should not be given the same confirmatory weight as the primary analysis. The record’s missing details about multiplicity and the original sample-size justification demonstrate why clear statistical reporting is essential to interpreting a completed trial.
15. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
Several limitations specific to this record affect interpretation. The primary endpoint analysis is restricted to the Modified Intention To Treat population, defined as participants with baseline and 90-day modified Rankin Scale scores. The record does not report how many participants lacked those measurements, why they were missing, or how missing data were handled. It also does not explain why the primary endpoint and safety listings use different numbers at risk.
The record names two primary analyses but does not provide a detailed statistical analysis plan, covariate details, model diagnostics, or an account of interim analyses. The proportional odds assumption is not discussed. The record does not state a clinically meaningful threshold for the primary endpoint, which limits interpretation of the possible importance of the effects compatible with the confidence intervals.
There are many listed outcomes, while the registry record does not report whether a multiplicity adjustment or outcome hierarchy was used. The secondary recalculations are unadjusted and should not be read as confirmatory evidence. The record also does not report the original sample-size justification. Planning illustrations based on observed effects do not fill that gap and are not observed power.
Safety information is presented as counts and event-term percentages, without a reported adjusted comparison or details sufficient to assess timing, attribution or participant-level recurrence. The registry record also does not explain the relationship between death counts in the safety listing and mortality endpoint analysis. These are limitations of the information available in the record, not evidence that any unreported method was or was not used.
16. Related Tutorials
17. Related Statistical Calculators
18. Sources
- ClinicalTrials.gov: Study of Allogeneic Umbilical Cord Blood Infusion for Adults With Ischemic Stroke — NCT03004976.
- Registry record last updated 2022-12-06; status last verified 2022-11.
- Results first posted 2022-09-23.
- Data retrieved from ClinicalTrials.gov on 2026-11-09.
- Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.
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19. Record Summary
NCT03004976, CoBIS 2, was a completed phase 2 randomized, triple-masked, parallel-group study of umbilical cord blood infusion versus placebo in adults with ischemic stroke. The registry reports enrollment of 79 and a primary endpoint of modified Rankin Scale shift from baseline to three months after infusion.
The median shift was 1 in each group, with an inter-quartile range of 0 to 2. The sponsor-reported Wilcoxon Mann-Whitney and cumulative logit analyses both gave estimates of 0.9, with confidence intervals that included the no-difference value. These results do not establish equivalence and leave uncertainty about the size and direction of any difference.
Secondary outcomes and safety listings add descriptive information, but their denominators vary and the secondary recalculations are unadjusted. The registry record does not report the sample-size justification, missing-data methods, multiplicity strategy, or a detailed statistical analysis plan.