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 Epratuzumab Versus Placebo in Subjects With Moderate to Severe General Systemic Lupus Erythematosus (SLE) (NCT01261793), a randomized phase 3 study. The primary outcome is The Percent of Subjects Meeting Treatment Response Criteria at Week 48 According to a Combined Response Index.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01261793 |
| Phase | Phase 3 |
| Condition | Systemic Lupus Erythematosus |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Quadruple |
| Enrollment | 791 |
| Arms in the primary outcome | 3 |
| Lead sponsor | UCB Pharma |
| Results posted | Yes |
2. Clinical Question
Population
Participants with moderate to severe systemic lupus erythematosus (SLE). The primary-outcome population was the Full Analysis Set: randomized participants who received at least 1 partial dose of study drug.
Intervention
Epratuzumab was given in two schedules: 600 mg weekly or 1200 mg every other week. Both schedules delivered infusions over four 12-week treatment cycles, for 48 weeks total.
Comparator
Weekly placebo infusions over four 12-week treatment cycles. Participants in the 1200 mg every-other-week schedule also received placebo infusions every other week, maintaining that schedule’s infusion pattern.
Primary question
At Week 48, what percentage of participants in each group met the combined response index criteria, and how did each epratuzumab schedule compare with placebo?
The combined index drew on disease-activity assessments and concomitant medication criteria. It required improvement or no worsening across specified organ-system assessments, no worsening on the systemic lupus disease activity and physician global assessments, and no changes in concomitant medications. The registry record identifies this response percentage at Week 48 as the primary outcome.
The comparisons concern the proportion of participants meeting a defined response threshold, not the size of change in an individual participant’s symptoms or disease activity. The registry record also lists response outcomes at earlier weeks and changes in daily corticosteroid dose, but results for the corticosteroid outcomes are not reported in the registry record.
3. Trial Design
This was a phase 3, randomized, quadruple-masked, parallel-group study of epratuzumab and placebo in participants with moderate to severe SLE. The registry record lists an enrollment of 791 and a completed study. The recorded start was 2010-12, and primary completion was 2015-05.
Three treatment groups were described: weekly placebo; epratuzumab 600 mg weekly; and epratuzumab 1200 mg every other week. The treatment cycles were 12 weeks long, with four cycles over 48 weeks. In the every-other-week epratuzumab group, placebo infusions were also administered every other week. This maintained the infusion schedule described for that arm.
Randomization and masking are listed in the registry record, but details such as the allocation sequence, concealment procedures, and which roles were included in the quadruple masking are not reported in the registry record. The sample-size justification and the trial’s original design assumptions are also not reported in the registry record. Those details cannot be reconstructed from the final enrollment or the observed outcome results.
The primary outcome was analyzed in the Full Analysis Set, defined as randomized participants who received at least 1 partial dose of study drug. The displayed group denominators were 263 for placebo, 261 for epratuzumab 1200 mg every other week, and 264 for epratuzumab 600 mg weekly. These are the denominators for the primary outcome population, not a substitute for the record’s overall enrollment figure.
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: Participant Flow refers to the Randomized Set (RS).
Overall Study
| Stage | Placebo Weekly (RS) | Epratuzumab 1200 mg Every Other Week (RS) | Epratuzumab 600 mg Weekly (RS) |
|---|---|---|---|
| STARTED | 263 | 262 | 266 |
| COMPLETED | 178 | 171 | 184 |
| NOT COMPLETED | 85 | 91 | 82 |
Reasons for not completing this period:
| Reason | Placebo Weekly (RS) | Epratuzumab 1200 mg Every Other Week (RS) | Epratuzumab 600 mg Weekly (RS) |
|---|---|---|---|
| Lack of Efficacy | 44 | 37 | 32 |
| Protocol Violation | 3 | 5 | 6 |
| Lost to Follow-up | 10 | 3 | 7 |
| Withdrawal by Subject | 12 | 14 | 14 |
| Death | 3 | 1 | 0 |
| Adverse Event | 9 | 24 | 19 |
| Patient non-availability | 1 | 1 | 1 |
| Suspected pregnancy | 1 | 1 | 0 |
| Patient non-compliance | 1 | 0 | 1 |
| Patient pregnant | 1 | 0 | 0 |
| Outside the study area | 0 | 2 | 1 |
| Lack of efficacy & patient not available | 0 | 1 | 0 |
Analysis population for the primary outcome, as defined in the registry: The Full Analysis Set (FAS) consisted of all subjects in the Randomized Set (RS) who had received at least 1 partial dose of the 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: Baseline Characteristics refers to the Safety Set (SS).
| Characteristic | Unit | Placebo Weekly (SS) | Epratuzumab 1200 mg Every Other Week (SS) | Epratuzumab 600 mg Weekly (SS) | Total Title |
|---|---|---|---|---|---|
| Participants analysed | 263 | 261 | 264 | 788 | |
| Age, Categorical: <=18 years | Participants | 0 | 0 | 0 | 0 |
| Age, Categorical: Between 18 and 65 years | Participants | 254 | 257 | 254 | 765 |
| Age, Categorical: >=65 years | Participants | 9 | 4 | 10 | 23 |
| Age, Continuous | years | 41.1 (SD 11.8) | 40.8 (SD 11.5) | 41.2 (SD 12.7) | 41.0 (SD 12.0) |
| Sex: Female, Male: Female | Participants | 245 | 247 | 245 | 737 |
| Sex: Female, Male: Male | Participants | 18 | 14 | 19 | 51 |
6. Primary Endpoint
The registry lists the primary outcome as The Percent of Subjects Meeting Treatment Response Criteria at Week 48 According to a Combined Response Index, measured over At Week 48.
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | not applicable |
| Unit | Percentage of responders |
| Endpoint classification | Binary Endpoint |
The primary endpoint was the percentage of participants meeting treatment-response criteria at Week 48 according to a combined response index. It is a binary outcome at the participant level: each participant is classified as meeting or not meeting the specified response criteria, and the group result is expressed as a percentage of responders.
The index combined several components. The British Isles Lupus Assessment Group Index (BILAG-2004) component required improvement from study entry or no worsening in other organ systems. The SLEDAI-2K and physician’s global assessment components required no worsening compared with study entry. The concomitant-medication component required no changes. The registry record states that the percentages use the number of participants in the relevant group within the Full Analysis Set.
Using a combined index can capture multiple aspects of disease activity and medication use in one defined response classification. It also means that the endpoint is shaped by every component’s rule: a participant’s classification depends on the index as a whole, rather than on any single assessment. A responder percentage does not describe the magnitude of improvement among responders, nor does it show how each component contributed to the overall classification.
The endpoint therefore addresses the frequency of meeting the registry-defined criteria at the specified time point. It should be interpreted as a group-level proportion, with uncertainty around the comparison between each epratuzumab group and placebo.
7. Results Posted in the Registry
- Epratuzumab 1200 mg Every Other Week (FAS): 34.1% (89/261) versus 33.5% (88/263) on control; risk difference 0.6 percentage points (95% CI -7.5 to 8.7), risk ratio 1.02 (0.80–1.30); unadjusted two-proportion z-test p = 0.877.
- Epratuzumab 600 mg Weekly (FAS): 35.2% (93/264) versus 33.5% (88/263) on control; risk difference 1.8 percentage points (95% CI -6.3 to 9.9), risk ratio 1.05 (0.83–1.33); unadjusted two-proportion z-test p = 0.669.
Risk difference: Epratuzumab 1200 mg Every Other Week (FAS)
95% CI: -7.5 to 8.7 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 |
|---|---|---|---|---|
| The Percent of Subjects Meeting Treatment Response Criteria at Week 24 According to a Combined Response Index | Binary Endpoint | Risk difference | +0.6 pts (-7.4 to 8.7) | 86,730 per arm |
| The Percent of Subjects Meeting Treatment Response Criteria at Week 12 According to a Combined Response Index | Binary Endpoint | Risk difference | +2.1 pts (-5.8 to 10.1) | 7,305 per arm |
| The Percent of Subjects Meeting Treatment Response Criteria at Week 36 According to a Combined Response Index | Binary Endpoint | Risk difference | +0.3 pts (-7.8 to 8.3) | 551,296 per arm |
The Percent of Subjects Meeting Treatment Response Criteria at Week 24 According to a Combined Response Index
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Epratuzumab 1200 mg Every Other Week (FAS): 33.0% (86/261) versus 32.3% (85/263) on control; risk difference 0.6 percentage points (95% CI -7.4 to 8.7), risk ratio 1.02 (0.80–1.30); unadjusted two-proportion z-test p = 0.878.
- Epratuzumab 600 mg Weekly (FAS): 43.6% (115/264) versus 32.3% (85/263) on control; risk difference 11.2 percentage points (95% CI 3.0 to 19.5), risk ratio 1.35 (1.08–1.68); unadjusted two-proportion z-test p = 0.008.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Epratuzumab 1200 mg Every Other Week (FAS) and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Epratuzumab 600 mg Weekly (FAS) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The Percent of Subjects Meeting Treatment Response Criteria at Week 12 According to a Combined Response Index
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Epratuzumab 1200 mg Every Other Week (FAS): 32.2% (84/261) versus 30.0% (79/263) on control; risk difference 2.1 percentage points (95% CI -5.8 to 10.1), risk ratio 1.07 (0.83–1.38); unadjusted two-proportion z-test p = 0.596.
- Epratuzumab 600 mg Weekly (FAS): 40.9% (108/264) versus 30.0% (79/263) on control; risk difference 10.9 percentage points (95% CI 2.8 to 19.0), risk ratio 1.36 (1.08–1.72); unadjusted two-proportion z-test p = 0.009.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Epratuzumab 1200 mg Every Other Week (FAS) and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Epratuzumab 600 mg Weekly (FAS) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The Percent of Subjects Meeting Treatment Response Criteria at Week 36 According to a Combined Response Index
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Epratuzumab 1200 mg Every Other Week (FAS): 33.0% (86/261) versus 32.7% (86/263) on control; risk difference 0.3 percentage points (95% CI -7.8 to 8.3), risk ratio 1.01 (0.79–1.29); unadjusted two-proportion z-test p = 0.951.
- Epratuzumab 600 mg Weekly (FAS): 36.7% (97/264) versus 32.7% (86/263) on control; risk difference 4.0 percentage points (95% CI -4.1 to 12.2), risk ratio 1.12 (0.89–1.42); unadjusted two-proportion z-test p = 0.330.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Epratuzumab 1200 mg Every Other Week (FAS) and the control. The interval gives the range of effects that remain compatible with the data.
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Epratuzumab 600 mg Weekly (FAS) and the control. The interval gives the range of effects that remain compatible with the data.
The secondary response outcomes at Weeks 12, 24, and 36 provide context on how the pattern varied over time. Across these assessments, the epratuzumab 1200 mg every-other-week group remained close to placebo. The 600 mg weekly group had a more noticeable numerical separation from placebo at the earlier assessments, while the separation was less pronounced at Week 36. This broad pattern does not replace the primary Week 48 comparison, which is the study’s stated primary endpoint.
These secondary outcomes are related to the primary outcome because they use the same combined response index at earlier time points. They can show whether the response pattern at Week 48 is consistent with observations at other scheduled assessments, but they do not change the definition or status of the primary result. Results at different time points are also not independent evidence in the same way as entirely separate trials, because they concern the same study groups and participants.
The registry record lists changes from baseline in daily corticosteroid dose at Week 24 and Week 48 as secondary outcomes, but those results are not reported in the registry record. The absence of posted results means those outcomes cannot be used to support or qualify the response findings in this account.
Multiple secondary comparisons create more opportunities for apparently notable findings. The registry record does not report a multiplicity adjustment or a prespecified testing hierarchy for these outcomes. Without such information, the unadjusted secondary results carry less weight than a result from a clearly defined primary test: their p-values do not account for the full set of outcomes and comparisons. They are best treated as descriptive signals requiring cautious interpretation, rather than conclusive evidence of a treatment difference.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- The Percent of Subjects Meeting Treatment Response Criteria at Week 24 According to a Combined Response Index
- The Percent of Subjects Meeting Treatment Response Criteria at Week 12 According to a Combined Response Index
- The Percent of Subjects Meeting Treatment Response Criteria at Week 36 According to a Combined Response Index
- Change From Baseline in Daily Corticosteroid Dose at Week 24
- Change From Baseline in Daily Corticosteroid Dose at Week 48
9. Statistical Interpretation
At Week 48, the recorded response percentages were 33.5% in the placebo group, 34.1% with epratuzumab 1200 mg every other week, and 35.2% with epratuzumab 600 mg weekly. The recalculated unadjusted comparisons give small positive risk-difference estimates for both epratuzumab schedules relative to placebo. The corresponding confidence intervals include no difference, and the unadjusted p-values are 0.877 and 0.669, respectively.
These results do not establish a clear difference between either epratuzumab schedule and placebo on the primary response outcome. At the same time, a non-significant test does not establish that the groups are equivalent. The intervals allow for a range of possible group differences, so both the estimated contrasts and their uncertainty matter. The registry record’s primary endpoint is a binary response classification at one time point; it does not by itself describe each participant’s disease course or the magnitude of any change.
The two schedules should be considered separately in relation to placebo. The estimated response percentages are close across the three groups, and the recalculated evidence does not distinguish either active schedule from placebo at the conventional statistical threshold. That is a statement about the posted comparison and its precision, not a claim that the treatments have identical effects or that an effect has been ruled out.
The earlier response outcomes show a more noticeable numerical separation between the 600 mg weekly group and placebo at Weeks 12 and 24 than is evident at later assessments. The Week 36 and Week 48 patterns are closer. These secondary results are exploratory in interpretation: they cover several time points and comparisons, and no multiplicity adjustment is reported in the registry record. The Week 48 primary result remains the main planned outcome identified by the record.
The sponsor’s posted primary analyses use logistic regression and report odds ratios, whereas the recalculations use unadjusted risk differences from the posted summary counts. Those measures are on different scales and are not expected to have the same numerical values. Both descriptions should be kept in view: the sponsor’s analyses do not report a statistically significant primary comparison, and the unadjusted recalculations also have confidence intervals that include the null value.
10. Statistical Methods Explained
The registry record reports logistic regression for the sponsor’s primary analyses. The recalculations use unadjusted comparisons of the posted responder counts and denominators. These approaches address the same broad question—whether response differs between a treatment group and placebo—but summarize the difference on different scales.
What does a response percentage represent?
For a binary outcome, each participant falls into one of two categories for the analysis: meeting the response criteria or not meeting them. The response percentage describes the share classified as responders in a group. The primary endpoint uses the Full Analysis Set, which the registry record defines as randomized participants who received at least 1 partial dose of study drug. Percentages alone do not show the number of events, the detail of each participant’s assessment, or the components that led to the classification.
In general, binary outcomes can be compared using measures such as a risk difference, risk ratio, or odds ratio. A risk difference expresses the absolute contrast between group proportions. A risk ratio compares those proportions as a ratio. An odds ratio compares the odds of response. These measures answer related but not identical questions, and their numerical sizes are not interchangeable. In particular, an odds ratio should not be read as a percentage-point difference.
Why report both the sponsor analysis and a recalculation?
The sponsor-reported analyses are described as logistic regression and give odds ratios with 95% confidence intervals and p-values. The recalculated results are unadjusted risk differences based on the posted summary statistics. The recalculation does not reproduce the sponsor’s model: it does not account for any covariates or other modeling choices unless those are explicitly part of the posted summary calculation. The registry record does not give enough detail to infer additional features of the sponsor’s model beyond the reported method.
Because the measures differ, comparison should focus on the substantive conclusion and uncertainty, not on exact agreement between the effect estimates. The sponsor’s odds-ratio intervals include the no-association value of 1. The recalculated risk-difference intervals include 0, the corresponding null value for an absolute difference. The reported p-values and recalculated p-values are also from different analyses, so they should not be treated as duplicate calculations of one identical model.
How should confidence intervals and p-values be understood?
In general, a confidence interval gives a range of effect estimates compatible with the data and the method used, at the stated confidence level. A narrow interval indicates greater precision than a wide interval, though precision alone does not determine whether the result is important. When an interval for a risk difference includes 0, the data are compatible with no absolute difference as well as with effects in either direction across the range. For an odds ratio, the corresponding no-association value is 1.
A p-value measures how incompatible the observed data are with a specified null hypothesis under the analysis assumptions. It is not the probability that the null hypothesis is true, and it does not measure the probability that the result occurred by chance in a general sense. A p-value above a conventional threshold does not prove equality. A p-value below a threshold does not establish clinical importance or remove concerns about multiple testing, bias, or outcome measurement.
What are the analysis populations and missing-data issues?
The primary result is reported for the Full Analysis Set, with the population definition stated in the registry record. The serious-adverse-event results identify groups as the safety set, but a separate definition of that set is not reported in the registry record. The registry record does not report the missing-data method for the primary or secondary outcomes, how participants with incomplete assessments were classified, or whether sensitivity analyses were conducted. Those omissions limit evaluation of how incomplete follow-up might affect the response percentages.
Similarly, the registry record does not report the full statistical analysis plan, details of model covariates, interim analyses, or the trial’s own sample-size justification. The posted analysis methods and estimates can be described, but unreported design or analysis choices should not be inferred from them.
11. Confidence Intervals and Precision
The Week 48 recalculations show small positive risk-difference estimates for both epratuzumab schedules compared with placebo. For each comparison, the confidence interval includes zero. This means the interval does not rule out no absolute difference, and it also permits differences in either direction within the interval’s limits. The intervals are therefore important context for the point estimates: the observed data do not pin down a precise treatment-placebo contrast.
The sponsor-reported logistic-regression odds ratios also have 95% confidence intervals that include 1, the null value for an odds ratio. The sponsor’s results and the recalculations use different effect measures, so their interval limits cannot be compared as if they were on one shared scale. Their general implication is consistent: the posted primary analyses do not provide a clearly separated estimate from the relevant null value.
Confidence intervals describe statistical uncertainty under the analysis method; they do not cover every possible source of uncertainty. They do not account automatically for concerns such as unreported missing-data handling or multiplicity. Nor do they show whether a difference would be meaningful to participants. The registry record does not report a threshold for a clinically important difference, so the interval cannot be judged against such a threshold.
Failure to exclude the null should not be read as proof that the groups are identical. The results indicate limited precision for distinguishing these groups on the Week 48 binary response endpoint. The estimates, interval ranges, analysis scale, and endpoint definition all matter when interpreting how much the posted data can establish.
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 | 85,851 | 114,930 |
| 75% of the observed effect | 152,447 | 204,083 |
| 50% of the observed effect | 342,606 | 458,652 |
The planning figures are illustrations based on the observed effect, not the trial’s original design justification. For these binary response outcomes, the figures are participants per arm. The calculation assumptions stated in the registry record are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to be detected is set to the stated fraction of the observed effect. The trial’s original sample-size assumptions are not reported in the registry record.
The 80% power column describes the number of participants per arm that the planning calculation estimates would be needed to have an 80% chance of detecting the specified effect under those assumptions, if that effect were real. The 90% power column gives the analogous planning number for a 90% chance. These are design illustrations, not evidence about the probability that the trial’s result is correct. This is not observed power.
The rows vary the effect used in the calculation: the observed effect, 75% of the observed effect, and 50% of the observed effect. The general pattern is that smaller effects need more participants to detect with the same target power. Because the Week 48 recalculated contrasts are small, the corresponding planning figures are large, particularly for the every-other-week comparison. The 600 mg weekly comparison has different planning figures because its observed contrast is different.
These figures should not be read as a recommendation for a future trial without further design work. They rely on the listed assumptions and the observed effect, which itself is uncertain. A planning illustration based on one observed estimate can change substantially if the true effect differs. The figures also do not establish what sample size the original investigators expected or used to plan the completed trial.
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 = 0.335; treatment proportion p1 = 0.341; average p̄ = 0.338.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6689 = 1.3110.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.6689 = 0.5629.
- n = (1.3110 + 0.5629)2 / (0.0064)2 = 85,850.5, rounded up to 85,851 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 <- 0.334600760456274 # control proportion
p1 <- 0.340996168582375 # 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(1261793)
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 = 85,851 (80% power), 114,930 (90% power)
75% of observed effect: n per arm = 152,447 (80% power), 204,083 (90% power)
50% of observed effect: n per arm = 342,606 (80% power), 458,652 (90% power)
power.prop.test: 85850.5
Simulated power at n = 85,851 per arm: 0.802 (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 |
|---|---|---|---|
| Regression, Logistic | Odds Ratio (OR) 1.024 | 0.710 to 1.477 | =0.899 |
| Regression, Logistic | Odds Ratio (OR) 1.070 | 0.743 to 1.539 | =0.716 |
The registry record reports the sponsor’s primary analyses as logistic regression, with odds ratios, 95% confidence intervals, and p-values. For epratuzumab 1200 mg every other week versus placebo, the reported odds ratio is 1.024, with a 95% confidence interval from 0.710 to 1.477 and p = 0.899. For epratuzumab 600 mg weekly versus placebo, the reported odds ratio is 1.070, with a 95% confidence interval from 0.743 to 1.539 and p = 0.716.
The recalculated comparisons use unadjusted risk differences derived from the posted responder counts and denominators. Odds ratios and risk differences describe contrasts on different scales, so their estimates are not expected to match numerically. The sponsor analysis is the registry-reported analysis; the recalculation offers a separate, simple comparison based on posted summary statistics. The registry record does not provide enough information to reconstruct all details of the logistic-regression models.
Both analyses convey substantial uncertainty around the Week 48 comparisons: the sponsor’s odds-ratio intervals include 1, while the recalculated risk-difference intervals include 0. The registry record does not flag a discrepancy between its posted analyses and the recalculations. Neither analysis should be presented as proving that the groups are equivalent.
15. Multiplicity, Missing Data and Analysis Populations
The registry record identifies one primary outcome at Week 48 and lists several secondary outcomes: response at Weeks 12, 24, and 36, and changes in daily corticosteroid dose at Weeks 24 and 48. There are also two epratuzumab schedules compared with placebo. Testing multiple outcomes, time points, and treatment comparisons raises a multiplicity issue: the more hypotheses examined, the greater the chance that some results may appear statistically notable even when there is no underlying difference.
A multiplicity strategy might specify a hierarchy of tests or adjust the threshold for interpreting multiple comparisons. The registry record does not report whether such a strategy was planned or used. It also does not report a statistical analysis plan describing the order of testing or how the secondary outcomes were intended to support the primary result. Therefore, unadjusted secondary p-values should not be interpreted as if they were the only tests conducted.
The primary outcome population is defined as randomized participants who received at least 1 partial dose of study drug. The record does not report how missing Week 48 response assessments were handled, whether missing observations were imputed, or what sensitivity analyses were used to assess missing-data assumptions. It is therefore not possible to assess from the registry record whether the reported percentages depend on a particular missing-data rule.
The record does not report interim analyses, stopping rules, the original sample-size justification, or the full analysis plan. It also does not describe details of the randomization procedure or the roles included in quadruple masking. These items are not evidence of a flaw; they are limits on what can be evaluated from the registry record. The reported results can be interpreted according to their stated populations and methods, while these unreported details remain unresolved.
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 |
|---|---|---|---|
| Placebo Weekly (SS) | 45 | 263 | 17.1% |
| Epratuzumab 1200 mg Every Other Week (SS) | 45 | 261 | 17.2% |
| Epratuzumab 600 mg Weekly (SS) | 50 | 264 | 18.9% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Placebo Weekly (SS) | 3 of 263 |
| Epratuzumab 1200 mg Every Other Week (SS) | 1 of 261 |
| Epratuzumab 600 mg Weekly (SS) | 0 of 264 |
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 |
|---|---|
| Placebo Weekly (SS) | 151 of 263 |
| Epratuzumab 1200 mg Every Other Week (SS) | 145 of 261 |
| Epratuzumab 600 mg Weekly (SS) | 158 of 264 |
Most frequent serious adverse event terms
| Event term | Organ system | Placebo Weekly (SS) | Epratuzumab 1200 mg Every Other Week (SS) | Epratuzumab 600 mg Weekly (SS) |
|---|---|---|---|---|
| Systemic lupus erythematosus | Musculoskeletal and connective tissue disorders | 7 of 263 | 6 of 261 | 6 of 264 |
| Chest pain | General disorders | 2 of 263 | 4 of 261 | 3 of 264 |
| Pneumonia | Infections and infestations | 3 of 263 | 2 of 261 | 4 of 264 |
| Urinary tract infection | Infections and infestations | 2 of 263 | 0 of 261 | 3 of 264 |
| Gastroenteritis | Infections and infestations | 3 of 263 | 0 of 261 | 1 of 264 |
| Headache | Nervous system disorders | 3 of 263 | 0 of 261 | 1 of 264 |
| Dyspnoea | Respiratory, thoracic and mediastinal disorders | 0 of 263 | 0 of 261 | 4 of 264 |
| Anaemia | Blood and lymphatic system disorders | 1 of 263 | 2 of 261 | 0 of 264 |
| Leukopenia | Blood and lymphatic system disorders | 1 of 263 | 0 of 261 | 2 of 264 |
| Abdominal pain | Gastrointestinal disorders | 2 of 263 | 0 of 261 | 1 of 264 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Placebo Weekly (SS) | Epratuzumab 1200 mg Every Other Week (SS) | Epratuzumab 600 mg Weekly (SS) |
|---|---|---|---|---|
| Urinary tract infection | Infections and infestations | 44 of 263 | 37 of 261 | 38 of 264 |
| Upper respiratory tract infection | Infections and infestations | 37 of 263 | 38 of 261 | 37 of 264 |
| Headache | Nervous system disorders | 42 of 263 | 29 of 261 | 33 of 264 |
| Nausea | Gastrointestinal disorders | 36 of 263 | 32 of 261 | 25 of 264 |
| Nasopharyngitis | Infections and infestations | 21 of 263 | 15 of 261 | 24 of 264 |
| Diarrhoea | Gastrointestinal disorders | 19 of 263 | 15 of 261 | 25 of 264 |
| Sinusitis | Infections and infestations | 19 of 263 | 12 of 261 | 20 of 264 |
| Bronchitis | Infections and infestations | 23 of 263 | 13 of 261 | 11 of 264 |
| Back pain | Musculoskeletal and connective tissue disorders | 19 of 263 | 14 of 261 | 14 of 264 |
| Vomiting | Gastrointestinal disorders | 16 of 263 | 12 of 261 | 16 of 264 |
Serious events with the highest arm-level rate: systemic lupus erythematosus (2.7%), chest pain (1.5%), pneumonia (1.5%), dyspnoea (1.5%), cholelithiasis (1.1%).
The safety results list serious adverse events by study group and give the number at risk and the number affected. The placebo group had 45 participants affected among 263 at risk; the epratuzumab 1200 mg every-other-week group had 45 among 261; and the epratuzumab 600 mg weekly group had 50 among 264. These are counts reported for the safety set. They describe participants affected, not the total number of serious-event episodes.
The death counts were 3 in the placebo group, 1 in the 1200 mg every-other-week group, and 0 in the 600 mg weekly group. Other adverse events were reported for 151 participants in the placebo group, 145 in the 1200 mg every-other-week group, and 158 in the 600 mg weekly group. The registry record does not provide enough detail in these summary figures to determine the causes or timing of the events, or whether events were considered related to study treatment.
Among the listed serious-event terms, systemic lupus erythematosus was reported at 2.7%, and chest pain, pneumonia, and dyspnoea at 1.5% each. Cholelithiasis and gastroenteritis were each listed at 1.1%. Such event summaries should be read as descriptive safety information, not as proof that a treatment caused or prevented an event. Interpretation also depends on event definitions, duration of observation, and group-level clinical context, which are not fully detailed in these figures.
17. What the Result Does, and Does Not, Mean
The Week 48 results describe the proportion of participants who met a combined response definition in each study group. The response percentages were similar across the three groups, and neither the sponsor-reported analyses nor the unadjusted recalculations show a statistically clear primary comparison with placebo. The interval estimates remain compatible with no difference as well as with effects in either direction.
This does not establish that epratuzumab and placebo have identical effects. A failure to distinguish groups statistically can reflect uncertainty, and the confidence intervals indicate that the estimates are not precise enough to rule out every potentially relevant difference. Conversely, a numerical difference between percentages does not by itself establish a treatment effect. The magnitude, precision, endpoint definition, and analysis method all contribute to interpretation.
The combined index reflects a specific set of disease-activity and medication criteria at a particular time point. It does not describe every aspect of SLE, the experience of each participant, or the size of change among those meeting the response threshold. The posted primary result also does not answer the secondary question about corticosteroid-dose change, because those results are not reported in the registry record.
The registry record supplies no threshold for a clinically important response difference, so these statistical estimates cannot be translated into a judgment about clinical importance from the record alone. The safety counts are descriptive and do not establish causation. Taken together, the findings should be understood as an account of the recorded outcomes and their uncertainty—not as individualized medical guidance or a definitive statement about treatment for any person.
18. Why This Trial Matters Statistically
This trial illustrates why a clinical outcome needs a precise definition before its group percentages can be interpreted. The primary result is not a general measure of all SLE activity; it is the fraction meeting a combined index with specified rules for organ-system assessments, disease-activity scores, physician assessment, and concomitant medication changes. A different response definition could classify participants differently.
It also demonstrates the importance of separating effect size from statistical evidence. The Week 48 percentages are close, while the recalculated risk-difference intervals include zero and the sponsor’s odds-ratio intervals include one. The point estimates alone do not convey the uncertainty, and the p-values alone do not show the range of plausible effects.
The comparison of sponsor-reported logistic-regression odds ratios with unadjusted risk differences is a useful reminder that analyses can express related group contrasts on different scales. Interpretation should identify which measure is being discussed and avoid treating odds ratios as percentage-point changes. The registry record’s lack of a flagged discrepancy does not make the analyses identical; it indicates that the listed results do not trigger a discrepancy flag in the posted record.
Finally, the trial’s multiple time points and secondary outcomes highlight the role of multiplicity and transparent analysis plans. The primary endpoint has a designated status, while secondary findings require more caution when adjustment and testing hierarchy are not reported. Registry records make outcomes and analyses accessible, but unreported design and analysis details remain important limits when judging precision and strength of evidence.
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.
- Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.
Several trial-specific details needed for a fuller statistical assessment are not reported in the registry record. These include the original sample-size justification, the analysis plan in full, the handling of missing endpoint data, and any sensitivity analyses. Without this information, the robustness of the Week 48 response percentages to incomplete assessments cannot be evaluated from the record.
The record does not report whether multiplicity was addressed across the two epratuzumab comparisons and the several secondary outcomes. This is especially relevant to interpreting secondary response findings at multiple time points. The sponsor’s primary method is identified as logistic regression, but details such as model covariates are not reported in the registry record. Consequently, the reported odds ratios cannot be fully reproduced from the information available.
The posted primary comparisons use the Full Analysis Set, defined by receipt of at least 1 partial dose after randomization. The record does not provide details about participants excluded from that set or how their outcomes were handled. The safety results identify a safety-set population, but its definition is not reported in the registry record.
The study used a combined response index. The overall percentages do not show the contribution of each component, how many participants failed each criterion, or the extent of improvement among responders. The registry record lists corticosteroid-dose outcomes but does not report their results. These limitations constrain interpretation to the posted response summaries, analyses, and safety counts, rather than allowing a complete assessment of all clinical outcomes or analysis decisions.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Study of Epratuzumab Versus Placebo in Subjects With Moderate to Severe General Systemic Lupus Erythematosus (SLE) — NCT01261793.
- Registry record last updated 2020-12-04; status last verified 2020-11.
- Results first posted 2018-06-29.
- 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
This completed phase 3 randomized, quadruple-masked, parallel-group study compared weekly placebo with epratuzumab 600 mg weekly and epratuzumab 1200 mg every other week in participants with moderate to severe SLE. Four 12-week treatment cycles were described, for 48 weeks total.
The primary outcome was the percentage meeting the combined response index at Week 48 in the Full Analysis Set. Response percentages were 33.5% for placebo, 34.1% for epratuzumab 1200 mg every other week, and 35.2% for epratuzumab 600 mg weekly. The sponsor reported logistic-regression odds ratios with confidence intervals that include 1; unadjusted risk-difference recalculations have intervals that include 0.
Results for secondary corticosteroid-dose outcomes and several design or analysis details are not reported in the registry record. Serious-adverse-event counts are descriptive and do not establish causation.