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 A Randomized Controlled Trial of Eculizumab in AQP4 Antibody-positive Participants With NMO (PREVENT Study) (NCT01892345), a randomized phase 3 study. The primary outcome is Participants With An Adjudicated On-trial Relapse.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01892345 |
| Phase | Phase 3 |
| Condition | Neuromyelitis Optica, Neuromyelitis Optica Spectrum Disorder |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Quadruple |
| Enrollment | 143 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Alexion Pharmaceuticals, Inc. |
| Results posted | Yes |
2. Clinical Question
Population
Participants with neuromyelitis optica spectrum disorder who were anti-aquaporin-4 (AQP4) antibody-positive and had relapsing disease. The primary analysis population was the Full Analysis Set: randomized participants who received at least one dose of study drug.
Intervention
Eculizumab, administered by intravenous infusion. The registry describes an induction period with weekly doses followed by a maintenance period, but the complete maintenance regimen is not reported in the registry record.
Comparator
Matching placebo, administered by intravenous infusion. It contained the same buffer components without the active ingredient.
Primary question
How did the occurrence and timing of protocol-defined, positively adjudicated on-trial relapses compare between participants assigned to eculizumab and those assigned to placebo during follow-up?
The primary endpoint counted participants with an adjudicated on-trial relapse. The registry also reports a sponsor analysis using time to relapse, so the event-count comparison and the time-to-event comparison answer related but distinct statistical questions. The former compares whether participants experienced an event during the recorded period; the latter incorporates when events occurred and uses a stratified log-rank test.
The trial was randomized, quadruple-masked, parallel-group, and placebo-controlled. These design features support a structured comparison between assigned groups, but the registry record does not give enough detail to assess every aspect of implementation, such as the randomization procedure or the exact roles covered by quadruple masking. Nor does it report the original sample-size justification or all details of the prespecified statistical plan. The results therefore need to be read as posted, with attention to the endpoint definitions, analysis population, follow-up, and distinction between sponsor-reported and unadjusted recalculated analyses.
3. Trial Design
This was a phase 3 randomized, double-blind, placebo-controlled, multicenter, parallel-group trial of eculizumab in participants with relapsing neuromyelitis optica who were AQP4 antibody-positive. The registry describes the masking as quadruple. Enrollment was 143. The trial status is terminated; the start date was 2014-04-11 and primary completion was 2018-07-17.
Participants were assigned to eculizumab or matching placebo. The primary analysis population was the Full Analysis Set, defined in the registry as all participants randomized to treatment who received at least one dose of study drug. The endpoint timeframe was baseline through up to 211 weeks, at end of study. The published endpoint description specifies that an on-trial relapse required new or worsening neurologic symptoms, an objective change on neurologic examination, and persistence for more than 24 hours, with confirmation by the treating physician. For the primary endpoint, the relapse also had to meet the protocol definition and be positively adjudicated by the relapse adjudication committee.
The registry describes an induction schedule for each group. Eculizumab participants received 900 milligrams by intravenous infusion weekly for 4 weeks and a 1200 mg fifth dose at Week 4; matching placebo followed the corresponding schedule. The remainder of the maintenance-period descriptions is incomplete in the registry record, so the full dosing schedule cannot be established from that record alone.
The original sample-size justification, planned allocation ratio, and trial-specific assumptions for power and significance are not reported in the registry record. Details of the randomization sequence, stratification factors, handling of protocol deviations, and exact responsibilities encompassed by quadruple masking are also not reported in the registry record. The registry identifies a stratified log-rank test for the sponsor’s primary time-to-event analysis, but further details of its stratification and model implementation are not reported in the registry record.
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.
Before assignment: Main inclusion criteria were: participants aged ≥ 18 years old with NMO/NMOSD, AQP4 antibody-positive, historical relapse of at least 2 in last 12 months or 3 in last 24 months with at least 1 in 12 months prior to screening, Expanded Disability Status Scale score ≤ 7. If receiving immunosuppressive therapies, must be on a stable maintenance dose.
Overall Study
| Stage | Eculizumab | Placebo |
|---|---|---|
| STARTED | 96 | 47 |
| Received At Least 1 Dose Of Study Drug | 96 | 47 |
| COMPLETED | 80 | 44 |
| NOT COMPLETED | 16 | 3 |
Reasons for not completing this period:
| Reason | Eculizumab | Placebo |
|---|---|---|
| Adverse Event | 0 | 2 |
| Death | 1 | 0 |
| Lost to Follow-up | 3 | 0 |
| Withdrawal by Subject | 12 | 1 |
Analysis population for the primary outcome, as defined in the registry: Full Analysis Set (FAS): all participants who were randomized to treatment, received at least 1 dose of study drug.
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.
Population: Full Analysis Set (FAS): all participants who were randomized to treatment and who received at least 1 dose of study drug.
| Characteristic | Unit | Eculizumab | Placebo | Total |
|---|---|---|---|---|
| Participants analysed | 96 | 47 | 143 | |
| Age, Continuous | years | 43.9 (SD 13.32) | 45.0 (SD 13.29) | 44.3 (SD 13.27) |
| Sex: Female, Male: Female | Participants | 88 | 42 | 130 |
| Sex: Female, Male: Male | Participants | 8 | 5 | 13 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 13 | 3 | 16 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 78 | 41 | 119 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 5 | 3 | 8 |
| Race/Ethnicity, Customized: Asian | Participants | 37 | 15 | 52 |
| Race/Ethnicity, Customized: Black or African American | Participants | 9 | 8 | 17 |
| Race/Ethnicity, Customized: White | Participants | 46 | 24 | 70 |
| Race/Ethnicity, Customized: Other or Unknown | Participants | 4 | 0 | 4 |
| Overall Stratification Groupings (4 strata) at Randomization: Low EDSS (≤ 2.0) | Participants | 11 | 5 | 16 |
| Overall Stratification Groupings (4 strata) at Randomization: High EDSS (≥ 2.5 to ≤ 7) and Treatment Naive | Participants | 12 | 5 | 17 |
| Overall Stratification Groupings (4 strata) at Randomization: High EDSS (≥ 2.5 to ≤ 7): Same IST | Participants | 44 | 22 | 66 |
| Overall Stratification Groupings (4 strata) at Randomization: High EDSS (≥ 2.5 to ≤ 7): Change in IST | Participants | 29 | 15 | 44 |
6. Primary Endpoint
The registry lists the primary outcome as Participants With An Adjudicated On-trial Relapse, measured over Baseline, Up To 211 Weeks (End of Study).
| Element | Registry entry |
|---|---|
| Result type | Count Of Participants |
| Measure of spread | not applicable |
| Unit | Participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint was the number of participants with an adjudicated on-trial relapse, measured from baseline through up to 211 weeks, at end of study. An on-trial relapse was defined as new neurologic symptoms or worsening of existing symptoms together with an objective change on neurologic examination, persisting for more than 24 hours and confirmed by the treating physician. An event counted as adjudicated only when it met the protocol definition and was positively adjudicated by the relapse adjudication committee.
This endpoint focuses on clinically identified relapse events rather than a laboratory measurement or a change in a continuous scale. A count-based summary describes how many participants experienced at least one qualifying event during the recorded follow-up. It does not, by itself, describe how soon events occurred, how many events each participant experienced, or the length of time each participant was observed. Those are different questions, which is why the registry also reports a sponsor time-to-event analysis.
Adjudication applies a defined review process to event classification and can help distinguish qualifying relapses from other symptom changes. However, the registry record does not report the adjudication procedures in enough detail to assess reviewer agreement or other operational features. The endpoint’s clinical definition and its application are therefore important context when interpreting the posted counts and the sponsor’s separate analysis of event timing.
7. Results Posted in the Registry
- Eculizumab: 3.1% (3/96) versus 42.6% (20/47) on control; risk difference -39.4 percentage points (95% CI -54.0 to -24.9), risk ratio 0.07 (0.02–0.23); unadjusted two-proportion z-test p = <0.001.
Risk difference: Eculizumab
95% CI: -54.0 to -24.9 percentage points
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Change From Baseline In EDSS At End Of Study | Continuous Endpoint | Mean difference | -0.30 (-0.62 to 0.02) | 129 per arm |
| Change From Baseline In Modified Rankin Scale (mRS) Score At End Of Study | Continuous Endpoint | Mean difference | -0.30 (-0.56 to -0.04) | 93 per arm |
| Change From Baseline In Hauser Ambulation Index (HAI) Score At End of Study | Continuous Endpoint | Mean difference | -0.90 (-1.41 to -0.39) | 32 per arm |
Change From Baseline In EDSS At End Of Study
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
- Result:
- Eculizumab: mean -0.18 versus 0.12 on control; difference -0.30 (95% CI -0.62 to 0.02), standardized effect d = -0.35; z-test p = 0.062.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Eculizumab and the control. The interval gives the range of effects that remain compatible with the data.
Change From Baseline In Modified Rankin Scale (mRS) Score At End Of Study
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
- Result:
- Eculizumab: mean -0.20 versus 0.10 on control; difference -0.30 (95% CI -0.56 to -0.04), standardized effect d = -0.41; z-test p = 0.023.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Eculizumab than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Change From Baseline In Hauser Ambulation Index (HAI) Score At End of Study
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
- Result:
- Eculizumab: mean -0.40 versus 0.50 on control; difference -0.90 (95% CI -1.41 to -0.39), standardized effect d = -0.70; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Eculizumab than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The secondary outcomes extend the assessment beyond adjudicated relapse to include disability, ambulation, and quality-of-life measures. The registry lists six secondary outcome measures, including EDSS, modified Rankin Scale, Hauser Ambulation Index, and EQ-5D measures. Numerical group summaries and unadjusted recalculations are available for EDSS, modified Rankin Scale, and Hauser Ambulation Index. Numerical results for the other listed measures are not reported in the registry record.
Across the three outcomes with posted numerical results, the recalculated mean differences are negative. Their confidence intervals do not all have the same relation to zero: the EDSS interval includes zero, while the intervals for modified Rankin Scale and Hauser Ambulation Index are below zero. This is a broad pattern in the posted summaries, not a single combined outcome or a substitute for the primary relapse analysis. The scales measure different aspects of disability or function, and their estimates should be interpreted on their own terms.
Secondary outcomes can complement a primary endpoint by showing whether results extend to other measured domains. They do not automatically confirm or explain the primary result. The registry record does not report whether the secondary analyses were prespecified as confirmatory, whether multiplicity was controlled, or how missing measurements were handled. When many outcomes are assessed, the chance of at least one apparently notable result can increase if no adjustment is made. For that reason, unadjusted secondary results carry less confirmatory weight than a prespecified primary analysis with a clearly documented testing strategy.
The absence of numerical results for some listed secondary measures also limits any overall assessment of consistency across the planned outcome set. The registry record does not report a complete inferential analysis across all secondary endpoints. The posted secondary summaries should therefore be treated as supportive descriptive evidence rather than as a definitive collection of independent tests.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Adjudicated On-trial Annualized Relapse Rate (ARR)
- Change From Baseline In EDSS At End Of Study
- Change From Baseline In Modified Rankin Scale (mRS) Score At End Of Study
- Change From Baseline In Hauser Ambulation Index (HAI) Score At End of Study
- Change From Baseline In European Quality Of Life (EuroQoL) Health 5-Dimension Questionnaire (EQ-5D) Visual Analogue Scale At End Of Study
- Change From Baseline In EuroQoL EQ-5D Index Score At End Of Study
9. Statistical Interpretation
For the primary endpoint, the posted counts were 3 participants with an adjudicated relapse among those assigned to eculizumab and 20 among those assigned to placebo. The unadjusted recalculation expresses the difference in participant-level risks as -0.394, with a 95% confidence interval from -0.540 to -0.249 and p < 0.001. The negative direction reflects a lower observed event proportion in the eculizumab group in this comparison. This count-based summary does not incorporate when relapses occurred.
The sponsor-reported analysis used time to relapse and a stratified log-rank test. Its hazard ratio was 0.058, with a 95% confidence interval from 0.017 to 0.197 and p < 0.001. A hazard ratio compares event rates over follow-up under the analysis model; it is not the same quantity as a risk difference. The registry does not include enough methodological detail to reconstruct the sponsor’s analysis fully, and the reported hazard ratio should not be read as a direct conversion of the participant counts.
The confidence intervals for the primary count-based difference and the sponsor’s hazard ratio both indicate statistical uncertainty, even though each interval lies on one side of its respective null value. The interval for the recalculated risk difference describes plausible values for that unadjusted group contrast under its assumptions. The interval for the sponsor’s hazard ratio describes uncertainty in the time-to-event estimate under its analysis. Neither interval captures every source of uncertainty, including uncertainty from endpoint classification, follow-up, missing observations, or model choices.
The secondary outcomes add a broader view of disability and function, but they are not interchangeable with the primary relapse endpoint. Numerical results are posted for changes in EDSS, modified Rankin Scale, and Hauser Ambulation Index. The registry also lists six secondary outcome measures; numerical summaries for the remaining listed measures are not reported in the registry record. Secondary findings should be considered alongside the primary result and with caution because the record does not report whether or how multiplicity was controlled.
These data describe the randomized groups and the analyses recorded in the registry. They do not establish why the group results differed, whether the estimates would be reproduced in another study, or how well the findings apply beyond the registered population and trial conditions. The trial’s status is terminated, but the reason for termination is not reported in the registry record. No inference about that reason should be drawn from the status label alone.
10. Statistical Methods Explained
Several statistical summaries address different aspects of the primary endpoint. The registry posts participant counts by group, an unadjusted recalculation of the risk difference, and a sponsor-reported time-to-event analysis. They should be kept distinct: each uses a different summary of the observed outcome and, in the sponsor analysis, a different method.
What does a risk difference describe?
A risk difference subtracts the event proportion in the comparator group from the event proportion in the intervention group. A negative value means the observed event proportion was lower in the intervention group for the comparison as defined. The recalculated risk difference is -0.394, with a 95% confidence interval from -0.540 to -0.249. This is an unadjusted calculation based on posted group-level counts. It is not an adjusted estimate from the sponsor’s time-to-event analysis.
For a binary endpoint such as whether a participant had an adjudicated relapse, the risk difference retains the outcome in an intuitive form: a difference in the proportion of participants experiencing an event. It does not use the timing of events or account for differing lengths of observation in the way a time-to-event analysis can. Interpretation also depends on the defined follow-up window and on which participants contribute to the analysis.
What does the hazard ratio describe?
The sponsor reported a hazard ratio of 0.058, with a 95% confidence interval from 0.017 to 0.197, using a stratified log-rank test. In general, a hazard ratio compares event rates over time between groups, conditional on the analysis framework. It is not a ratio of the total number of participants with events, nor does it directly state the probability that an individual participant will relapse. A value below the null value of one indicates a lower estimated event rate over time in the eculizumab group under the sponsor’s analysis.
Time-to-event methods can use information about when events occur and can account for participants whose event status is not observed through the same duration, subject to the method’s assumptions and data handling. The registry record does not report the detailed censoring rules, the stratification variables, or the full implementation of the sponsor’s analysis. Those details matter when assessing whether the method is appropriate and how its estimate should be interpreted.
How should the p-values be read?
The unadjusted recalculation reports p < 0.001 for the risk difference. The sponsor reports p < 0.001 for the stratified log-rank analysis. A p-value describes how incompatible the observed data are with a specified null hypothesis under the assumptions of the test; it is not the probability that the null hypothesis is true, and it does not measure the size or importance of an effect. The two p-values arise from different analyses, so their numerical magnitudes should not be treated as a direct comparison of methods or evidence strength.
The sponsor’s method is the reported primary time-to-event analysis. The count-based recalculation is a simple unadjusted comparison and does not replace that analysis. The registry record does not report additional details needed to verify whether the sponsor’s analysis included covariate adjustment beyond stratification or how any departures from the analysis plan were handled.
How do continuous secondary outcomes differ?
EDSS, modified Rankin Scale, and Hauser Ambulation Index results are posted as mean changes from baseline at end of study. A mean difference contrasts the group averages; its sign indicates which group had the numerically lower average change under the registry’s coding. The standard deviation describes variability among participants, whereas the confidence interval for the mean difference describes uncertainty about the group contrast. They are not the same quantity.
The posted unadjusted recalculations give a mean difference and confidence interval for each of these outcomes. Such comparisons do not account for multiplicity unless a correction or other prespecified strategy is applied. The registry record does not report whether the sponsor used multiplicity adjustment for secondary outcomes, nor does it provide reported analyses for these continuous outcomes. The recalculations therefore describe simple group contrasts and should not be treated as a complete confirmatory analysis.
What are the limits of summary-statistic recalculation?
Unadjusted recalculations use the posted group sizes and summary statistics rather than participant-level data. They cannot reproduce analyses that depend on individual event times, covariates, missingness patterns, repeated measurements, or stratification. Small differences between a simple recalculation and a sponsor analysis can arise because the methods target different estimands or use different information. In this record, the sponsor’s time-to-event estimate and the recalculated risk difference are not the same statistical quantity, and there is no discrepancy flag indicating a conflict between a sponsor result and a corresponding recalculation.
11. Confidence Intervals and Precision
A confidence interval describes a range of values compatible with the observed data under a statistical method and its assumptions. It conveys precision: narrower intervals indicate less sampling uncertainty for that estimate, while wider intervals indicate more. It does not include every possible source of uncertainty, such as uncertainty about endpoint assessment, incomplete follow-up, or whether the analysis assumptions are appropriate.
For the primary unadjusted risk difference, the estimate is -0.394 and the 95% confidence interval runs from -0.540 to -0.249. The entire interval is below zero, the null value for a difference. This indicates that the posted count-based estimate is statistically distinguishable from no difference under the recalculation’s assumptions. The interval still spans a range of possible group contrasts; the point estimate alone should not be treated as exact.
The sponsor’s time-to-event estimate is a hazard ratio of 0.058, with a 95% confidence interval from 0.017 to 0.197. The interval lies below one, the null value for a ratio. It reflects uncertainty in the sponsor’s time-to-event analysis, not uncertainty in the risk difference. Because the analyses summarize outcomes differently, their intervals cannot be substituted for one another or compared as though they bound the same effect.
For the continuous secondary outcomes, the recalculated confidence interval for EDSS includes zero, while those for modified Rankin Scale and Hauser Ambulation Index lie below zero. These intervals concern unadjusted mean differences, and their interpretation is limited by the absence of reported multiplicity handling and full sponsor analyses. A confidence interval that excludes its null value does not by itself establish clinical importance, and one that includes the null does not prove that the groups are identical.
All intervals are conditional on the data, endpoint definitions, and methods used. The registry record does not report enough detail to evaluate every analysis assumption or the handling of missing data. Precision should therefore be considered together with the design and reporting limitations, rather than as a complete measure of certainty.
12. Planning a Similar Trial: Sample Size
This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 17 | 22 |
| 75% of the observed effect | 35 | 47 |
| 50% of the observed effect | 88 | 117 |
The planning figures for the posted comparisons are expressed as participants per arm. They are not total event counts. The registry’s general planning illustration assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It uses the observed effect as a starting point and considers detecting the stated fraction of that effect. The original trial’s own sample-size assumptions and justification are not reported in the registry record.
The 80% power column gives the illustrative number of participants per arm for a design that would have an 80% chance of detecting the specified effect under the planning assumptions, if that effect and those assumptions were correct. The 90% power column gives the corresponding illustration for a 90% chance. These are design-planning concepts, not guarantees about a future study’s result.
The figures are shown for planning at 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. The smaller the effect a study aims to detect, the more participants it generally needs, all else equal. These calculations use the observed effect as an input, which can make them optimistic if that effect is larger than the effect a future study would encounter. This is not observed power; it is a planning illustration, not a measure of the probability that the completed trial detected an effect.
The primary count-based comparison and the continuous secondary comparisons use participants per arm in their planning figures. The general registry note says time-to-event planning tables use total events under a Schoenfeld approach, but the planning figures attached to the posted recalculated comparisons are per-arm figures. The sponsor’s hazard-ratio analysis should not be confused with those per-arm illustrations.
13. How the Sample Size Is Derived
Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).
Formula
n is the number of participants in each arm, p0 and p1 are the control and treatment proportions, and p̄ is their average.
Worked calculation for this trial
- Control proportion p0 = 0.426; treatment proportion p1 = 0.031; average p̄ = 0.228.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5937 = 1.1636.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5241 = 0.4411.
- n = (1.1636 + 0.4411)2 / (-0.3943)2 = 16.6, rounded up to 17 participants per arm for 80% power.
The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).
R code
alpha <- 0.05
z_a <- qnorm(1 - alpha / 2) # two-sided
p0 <- 0.425531914893617 # control proportion
p1 <- 0.03125 # treatment proportion
n_per_arm <- function(power, frac = 1) {
q1 <- p0 + (p1 - p0) * frac # smaller effect = fraction of the observed difference
pbar <- (p0 + q1) / 2
z_b <- qnorm(power)
ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^2, 6))
}
for (f in c(1, 0.75, 0.5))
cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))
# Check against R's built-in function (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")
# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(1892345)
n <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))
Output from running the code
100% of observed effect: n per arm = 17 (80% power), 22 (90% power)
75% of observed effect: n per arm = 35 (80% power), 47 (90% power)
50% of observed effect: n per arm = 88 (80% power), 117 (90% power)
power.prop.test: 16.6
Simulated power at n = 17 per arm: 0.861 (20000 replicates)
The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Stratified Log-Rank Test | Hazard Ratio (HR) 0.058 | 0.017 to 0.197 | < 0.001 |
The sponsor’s reported primary analysis is a stratified log-rank test of time to event, with a hazard ratio of 0.058, a 95% confidence interval from 0.017 to 0.197, and p < 0.001. This is the registry’s reported time-to-event result. The recalculated analysis uses the posted participant counts to estimate an unadjusted risk difference of -0.394, with a 95% confidence interval from -0.540 to -0.249 and p < 0.001.
These estimates are not competing versions of the same statistic. The risk difference compares the participant-level event proportions during the recorded endpoint period. The hazard ratio summarizes the relative event rate over time using the sponsor’s method. Different methods can yield different numerical summaries while addressing related questions, particularly when event timing and follow-up contribute to the analysis.
The registry record does not report enough detail to reproduce the stratified log-rank analysis from summary data. The recalculation is therefore best read as a transparent, unadjusted contrast of the posted counts, not as a replacement for the sponsor’s primary analysis. The record does not flag a discrepancy between sponsor and recalculated results. Where a discrepancy is flagged, the sponsor’s own analysis takes precedence; that condition is not indicated for this trial.
15. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when a study tests several outcomes, comparisons, time points, or subgroups. Without a prespecified strategy to control the overall chance of false-positive findings, interpreting each p-value as though it were the only test can overstate the strength of the evidence. The registry lists six secondary outcome measures in addition to the primary endpoint. Whether the study used a multiplicity adjustment, hierarchical testing procedure, or another approach is not reported in the registry record.
The primary endpoint has a sponsor-reported time-to-event analysis and an unadjusted count-based recalculation. These analyses target related but distinct summaries; the registry does not report whether the relationship between them was specified in a formal testing hierarchy. The registry also does not report whether interim analyses were planned or conducted, or whether any such analyses affected the final inference. Those details should not be inferred from the p-values or the trial status.
The Full Analysis Set is defined as randomized participants who received at least one dose of study drug. That definition excludes randomized participants who did not receive a dose, if any, but the registry record does not report whether there were such participants or how they were handled in other analyses. The registry does not provide a detailed account of missing outcome data, censoring, reasons for withdrawal, or sensitivity analyses. For continuous secondary outcomes, the number contributing to each end-of-study summary and the missing-data method are not reported in the registry record.
These omissions matter because missingness and analysis-population choices can affect estimates and their uncertainty. In a time-to-event analysis, the way follow-up ends for participants without an observed event is also relevant; the registry record does not report the detailed censoring rules. The available information supports describing the posted results, but it does not permit a full audit of the analysis plan, multiplicity control, or missing-data assumptions.
16. 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 |
|---|---|---|---|
| Eculizumab | 30 | 96 | 31.2% |
| Placebo | 26 | 47 | 55.3% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Eculizumab | 1 of 96 |
| Placebo | 0 of 47 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Eculizumab | 86 of 96 |
| Placebo | 43 of 47 |
Most frequent serious adverse event terms
| Event term | Organ system | Eculizumab | Placebo |
|---|---|---|---|
| Neuromyelitis optica spectrum disorder | Nervous system disorders | 7 of 96 | 16 of 47 |
| Pneumonia | Infections and infestations | 3 of 96 | 1 of 47 |
| Cholecystitis acute | Hepatobiliary disorders | 1 of 96 | 1 of 47 |
| Bronchitis | Infections and infestations | 1 of 96 | 1 of 47 |
| Cellulitis | Infections and infestations | 2 of 96 | 0 of 47 |
| Influenza | Infections and infestations | 1 of 96 | 1 of 47 |
| Sepsis | Infections and infestations | 2 of 96 | 0 of 47 |
| Urinary tract infection | Infections and infestations | 2 of 96 | 0 of 47 |
| Leukocytosis | Blood and lymphatic system disorders | 1 of 96 | 0 of 47 |
| Pancytopenia | Blood and lymphatic system disorders | 0 of 96 | 1 of 47 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Eculizumab | Placebo |
|---|---|---|---|
| Upper respiratory tract infection | Infections and infestations | 28 of 96 | 6 of 47 |
| Headache | Nervous system disorders | 22 of 96 | 11 of 47 |
| Nasopharyngitis | Infections and infestations | 20 of 96 | 9 of 47 |
| Nausea | Gastrointestinal disorders | 16 of 96 | 12 of 47 |
| Diarrhoea | Gastrointestinal disorders | 15 of 96 | 7 of 47 |
| Urinary tract infection | Infections and infestations | 11 of 96 | 10 of 47 |
| Back pain | Musculoskeletal and connective tissue disorders | 14 of 96 | 6 of 47 |
| Pain in extremity | Musculoskeletal and connective tissue disorders | 10 of 96 | 10 of 47 |
| Dizziness | Nervous system disorders | 14 of 96 | 6 of 47 |
| Vomiting | Gastrointestinal disorders | 9 of 96 | 8 of 47 |
Serious events with the highest arm-level rate: neuromyelitis optica spectrum disorder (34.0%), pneumonia (3.1%), pancytopenia (2.1%), thrombocytopenia (2.1%), myocardial ischaemia (2.1%).
The registry reports serious adverse events affecting 30 participants in the eculizumab group and 26 in the placebo group. The groups at risk were 96 and 47 participants, respectively. Other adverse events affected 86 participants assigned to eculizumab and 43 assigned to placebo. Deaths were reported for 1 participant in the eculizumab group and 0 in the placebo group.
These are counts of participants affected, not a complete account of event frequency, severity, duration, or causal attribution. The registry record does not report enough detail to determine whether participants could contribute more than one event to a category or how exposure time was incorporated. The group sizes also differ, so raw counts alone do not provide a standardized comparison.
The listed serious-event terms include neuromyelitis optica spectrum disorder at 34.0%, pneumonia at 3.1%, and pancytopenia, thrombocytopenia, myocardial ischaemia, and vertigo at 2.1% each. The registry record does not specify the denominator or full coding and attribution details for these listed percentages. These safety summaries are descriptive and should not be interpreted as establishing that a treatment caused or prevented an event.
17. What the Result Does, and Does Not, Mean
The primary results show a numerical difference in adjudicated relapse occurrence between the randomized groups: 3 participants in the eculizumab group and 20 in the placebo group had a qualifying event. The unadjusted risk-difference estimate is -0.394, with a 95% confidence interval from -0.540 to -0.249. Separately, the sponsor’s stratified log-rank analysis reports a hazard ratio of 0.058, with a 95% confidence interval from 0.017 to 0.197. Together, these are statistical descriptions of the recorded trial outcomes, using different methods.
The result does not, by itself, establish the size of an effect in every population or setting. The trial concerned AQP4 antibody-positive participants with relapsing disease, and the endpoint depended on a defined clinical event and committee adjudication. Generalization beyond these participants, endpoint procedures, and follow-up conditions requires evidence beyond this registry record.
The results also do not resolve every question about durability, repeated relapses, functional outcomes, quality of life, or safety. The primary participant-count endpoint does not show how many events occurred per participant or when each occurred. The sponsor’s time-to-event analysis addresses timing, but complete details of its implementation are not reported in the registry record. Numerical results for some listed secondary measures are also not reported in the registry record.
Statistical evidence and clinical importance are not the same. A p-value does not quantify the probability that a finding is true, and a confidence interval does not establish that every value in its range is equally plausible in a practical sense. The registry results should be understood with the limits of the reporting, including missing information about multiplicity, missing data, and the original design assumptions. The terminated status alone does not explain why the trial ended; the reason is not reported in the registry record.
18. Why This Trial Matters Statistically
This trial illustrates why endpoint type matters. A participant-level relapse count gives an accessible comparison of whether participants experienced an adjudicated event, while a time-to-event analysis uses information about when events occurred. The registry reports both kinds of summaries, making it important to distinguish the unadjusted risk difference from the sponsor’s hazard ratio rather than treating them as interchangeable estimates.
It also shows the value of reading confidence intervals alongside point estimates. The primary count-based interval and the sponsor’s hazard-ratio interval both lie on the side of their respective null values indicating a lower observed event measure in the eculizumab group. Their widths still express uncertainty, and their different estimands mean that one interval cannot be used to validate or replace the other.
The registry’s secondary results illustrate another common issue: findings across multiple outcomes can vary, and the interpretation of individual unadjusted tests depends on the study’s multiplicity strategy. That strategy, along with the original sample-size justification and important missing-data details, is not reported in the registry record. Recognizing what is absent is part of sound statistical interpretation, not a reason to fill gaps by assumption.
Finally, the posted safety counts show why raw numbers require context. Group sizes differ, and event counts alone do not establish comparative rates, causation, or the overall balance of benefits and harms. A careful statistical reading separates descriptive data, sponsor analyses, recalculations, and unanswered methodological questions.
19. 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.
The registry record does not report the reason the trial was terminated. The status label should therefore not be used to infer whether termination reflected efficacy, safety, recruitment, operational, or other considerations. The record reports primary completion as 2018-07-17, but does not explain the relationship between completion and termination.
Although the primary endpoint timeframe extends from baseline through up to 211 weeks, the registry does not provide participant-level follow-up durations, event times, detailed censoring rules, or a complete account of withdrawals. These details limit independent assessment of the sponsor’s time-to-event result. The stratification factors and further implementation details for the log-rank analysis are also not reported in the registry record.
The endpoint depended on clinical signs, treating-physician confirmation, protocol criteria, and adjudication. The registry provides the event definition but does not report operational details such as the adjudication process, reviewer agreement, or how ambiguous events were handled. Such information would help assess the reliability and consistency of event classification.
The original sample-size justification and trial-specific assumptions are not reported in the registry record. The planning illustrations based on observed effects are not a substitute for the trial’s original design rationale. The record also does not report whether interim analyses occurred, whether multiplicity was controlled, or how missing observations were handled across primary and secondary analyses.
Finally, the registry lists six secondary outcomes, while numerical summaries are available for only some of them in the results. The missing numerical results and lack of full sponsor analyses for the continuous secondary outcomes restrict assessment of the entire outcome set. These limitations do not erase the posted findings, but they narrow what can be concluded from the registry record alone.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: A Randomized Controlled Trial of Eculizumab in AQP4 Antibody-positive Participants With NMO (PREVENT Study) — NCT01892345.
- Registry record last updated 2019-06-26; status last verified 2019-06.
- Results first posted 2019-06-26.
- 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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23. Record Summary
The record describes a phase 3 randomized, quadruple-masked, parallel-group, placebo-controlled trial in AQP4 antibody-positive participants with relapsing neuromyelitis optica spectrum disorder. Enrollment was 143, and the trial is listed as terminated. The primary endpoint was the number of participants with a protocol-defined, positively adjudicated on-trial relapse through up to 211 weeks.
The posted counts were 3 participants with relapse in the eculizumab group and 20 in the placebo group. The unadjusted recalculated risk difference was -0.394, with a 95% confidence interval from -0.540 to -0.249. The sponsor’s stratified log-rank analysis reported a hazard ratio of 0.058, with a 95% confidence interval from 0.017 to 0.197.
Numerical results are also posted for three continuous secondary outcomes. Important details—including the original sample-size justification, multiplicity plan, missing-data handling, and the reason for termination—are not reported in the registry record.