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 Brexpiprazole as Adjunctive Treatment in Patients With Major Depressive Disorder With an Inadequate Response to Antidepressant Treatment (NCT01838681), a randomized phase 3 study. The primary outcome is Full Remission During the Randomised Treatment Period.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01838681 |
| Phase | Phase 3 |
| Condition | Major Depressive Disorder |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 1986 |
| Arms in the primary outcome | 2 |
| Lead sponsor | H. Lundbeck A/S |
| Results posted | Yes |
2. Clinical Question
Population
Adults with major depressive disorder and an inadequate response to antidepressant treatment. The primary outcome population was randomised patients who took at least one dose of the randomised treatment in Period B.
Intervention
Brexpiprazole added to open-label treatment with a commercially available antidepressant, with a flexible dose of 1 to 3 mg/day in the study title.
Comparator
Placebo added to open-label treatment with a commercially available antidepressant.
Primary question
During the 24-week randomised treatment period, how did the number of participants meeting the registry definition of full remission compare between the brexpiprazole-plus-antidepressant group and the placebo-plus-antidepressant group?
The primary outcome was a participant count, not a continuous symptom score or a time-to-remission estimate. Full remission required both a MADRS total score of 10 or less and a decrease of at least 50% from randomisation, maintained for at least 8 consecutive weeks during randomised treatment. The registry reports 95 participants meeting this definition in the brexpiprazole group and 110 in the placebo group. The analysis therefore describes the observed remission counts in the primary outcome population and the estimated between-group difference. It does not, by itself, establish why participants did or did not meet the definition, or describe outcomes beyond the stated treatment period.
3. Trial Design
This was a Phase 3, randomised, double-blind, parallel-group, placebo-controlled study sponsored by H. Lundbeck A/S. The registry lists an overall enrolment of 1986 and marks the study completed. The recorded study start is 2013-06 and the primary completion is 2016-06.
The comparison analysed is from Period B, described as 24 weeks of randomised treatment. Participants received either brexpiprazole or placebo as an adjunct to open-label treatment with a commercially available antidepressant. The official title describes flexible dosing of brexpiprazole at 1 to 3 mg/day. The antidepressant treatment was open-label, while the study as a whole is recorded as double-blind; the registry record does not further explain masking procedures for each treatment component.
For the primary outcome, the registry defines the population as all randomised patients who took at least one dose of randomised treatment in Period B. There were 441 participants in the placebo-plus-antidepressant group and 444 in the brexpiprazole-plus-antidepressant group for this outcome. These outcome denominators are smaller than the overall enrolment, and the registry record does not explain the full flow from enrolment to these analysis groups in the information.
The study description states that it evaluated long-term efficacy and safety, while the primary remission outcome has a specified timeframe of randomisation to the end of Period B, 24 weeks. The record lists 18 outcome measures and one reported analysis. Further details about the original sample-size rationale, allocation procedures, or other protocol features 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.
Period A
| Stage | Period A Placebo and ADT (8 Weeks) | Period B Placebo and ADT (24 Weeks Randomised Treatment) | Period B Brexpiprazole and ADT (24 Weeks Randomised Treatment) | Period A+ Placebo and ADT (Non-randomised Patients) |
|---|---|---|---|---|
| STARTED | 1986 | 0 | 0 | 0 |
| COMPLETED | 1661 | 0 | 0 | 0 |
| NOT COMPLETED | 325 | 0 | 0 | 0 |
Reasons for not completing this period:
| Reason | Period A Placebo and ADT (8 Weeks) | Period B Placebo and ADT (24 Weeks Randomised Treatment) | Period B Brexpiprazole and ADT (24 Weeks Randomised Treatment) | Period A+ Placebo and ADT (Non-randomised Patients) |
|---|---|---|---|---|
| Adverse Event | 39 | 0 | 0 | 0 |
| Lack of Efficacy | 21 | 0 | 0 | 0 |
| Early response | 148 | 0 | 0 | 0 |
| Withdrawal by Subject | 70 | 0 | 0 | 0 |
| Protocol Violation | 16 | 0 | 0 | 0 |
| Non-compliance with IMP | 6 | 0 | 0 | 0 |
| Lost to Follow-up | 4 | 0 | 0 | 0 |
| Withdrawal before treatment | 4 | 0 | 0 | 0 |
| Administrative or other reasons | 17 | 0 | 0 | 0 |
Period B/A+
| Stage | Period A Placebo and ADT (8 Weeks) | Period B Placebo and ADT (24 Weeks Randomised Treatment) | Period B Brexpiprazole and ADT (24 Weeks Randomised Treatment) | Period A+ Placebo and ADT (Non-randomised Patients) |
|---|---|---|---|---|
| STARTED | 0 | 442 | 444 | 770 |
| COMPLETED | 0 | 380 | 349 | 653 |
| NOT COMPLETED | 0 | 62 | 95 | 117 |
Reasons for not completing this period:
| Reason | Period A Placebo and ADT (8 Weeks) | Period B Placebo and ADT (24 Weeks Randomised Treatment) | Period B Brexpiprazole and ADT (24 Weeks Randomised Treatment) | Period A+ Placebo and ADT (Non-randomised Patients) |
|---|---|---|---|---|
| Adverse Event | 0 | 13 | 27 | 16 |
| Lack of Efficacy | 0 | 9 | 11 | 6 |
| Withdrawal by Subject | 0 | 28 | 35 | 47 |
| Protocol Violation | 0 | 1 | 4 | 6 |
| Non-compliance with IMP | 0 | 2 | 3 | 3 |
| Lost to Follow-up | 0 | 2 | 5 | 11 |
| Withdrawal before treatment | 0 | 1 | 0 | 0 |
| Administrative or other reasons | 0 | 6 | 10 | 28 |
Analysis population for the primary outcome, as defined in the registry: All randomised patients who took at least one dose of randomised treatment (brexpiprazole or placebo) in Period B.
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 | All Enrolled Patients |
|---|---|---|
| Participants analysed | 1986 | |
| Age, Continuous | years | 47.3 (SD 12.0) |
| Sex: Female, Male: Female | Participants | 1402 |
| Sex: Female, Male: Male | Participants | 584 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 |
| Race (NIH/OMB): Asian | Participants | 3 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 |
| Race (NIH/OMB): Black or African American | Participants | 19 |
| Race (NIH/OMB): White | Participants | 1918 |
| Race (NIH/OMB): More than one race | Participants | 0 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 46 |
| Region of Enrollment: Russian Federation | participants | 121 |
| Region of Enrollment: Romania | participants | 15 |
| Region of Enrollment: United States | participants | 78 |
| Region of Enrollment: Ukraine | participants | 189 |
| Region of Enrollment: United Kingdom | participants | 168 |
| Region of Enrollment: Canada | participants | 30 |
| Region of Enrollment: Latvia | participants | 84 |
| Region of Enrollment: Sweden | participants | 85 |
| Region of Enrollment: Finland | participants | 136 |
| Region of Enrollment: Poland | participants | 325 |
6. Primary Endpoint
The registry lists the primary outcome as Full Remission During the Randomised Treatment Period, measured over From randomisation to end of Period B (24 weeks).
| Element | Registry entry |
|---|---|
| Result type | Number |
| Measure of spread | not applicable |
| Unit | participants |
| Endpoint classification | Binary Endpoint |
The primary endpoint is the number of participants achieving full remission during the randomised treatment period, from randomisation to the end of Period B at 24 weeks. A participant counted as being in full remission had to meet both parts of the registry definition: a MADRS total score of 10 or less and a decrease of at least 50% from the randomisation score, maintained for at least 8 consecutive weeks during randomised treatment.
MADRS is a 10-item depression rating scale. Each item is rated from 0 to 6; the total score ranges from 0, meaning symptoms absent, to 60, meaning severe depression. The registry describes the items as representing core symptoms of depressive illness.
This endpoint is useful for interpreting a threshold-based outcome that combines a symptom level with a sustained change from baseline. Requiring both conditions makes the outcome more specific than relying on a single score at one assessment. As a binary endpoint, it classifies each participant as meeting or not meeting the full-remission definition over the stated period. It does not show the exact symptom trajectory, the time at which remission began, or how participants who did not meet the full definition may have changed. Those questions require other outcomes or analyses. The registry record does not report further details about how missing or incomplete measurements were handled for this endpoint.
7. Results Posted in the Registry
- Period B Brexpiprazole and ADT (24 Weeks Randomised Treatment): 21.4% (95/444) versus 24.9% (110/441) on control; risk difference -3.5 percentage points (95% CI -9.1 to 2.0), risk ratio 0.86 (0.67–1.09); unadjusted two-proportion z-test p = 0.211.
Risk difference: Period B Brexpiprazole and ADT (24 Weeks Randomised Treatment)
95% CI: -9.1 to 2.0 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 |
|---|---|---|---|---|
| Full Functional Remission During the Randomised Treatment Period | Binary Endpoint | Risk difference | -1.2 pts (-6.1 to 3.6) | 13,720 per arm |
| Full Global Score Remission During the Randomised Treatment Period | Binary Endpoint | Risk difference | -5.2 pts (-11.2 to 0.8) | 1,227 per arm |
| Total Time in Remission During the Randomised Treatment Period | Continuous Endpoint | Mean difference | -3.50 (-9.46 to 2.46) | 2,619 per arm |
Full Functional Remission During the Randomised Treatment Period
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Period B Brexpiprazole and ADT (24 Weeks Randomised Treatment): 15.3% (68/444) versus 16.6% (73/441) on control; risk difference -1.2 percentage points (95% CI -6.1 to 3.6), risk ratio 0.93 (0.68–1.25); unadjusted two-proportion z-test p = 0.615.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Period B Brexpiprazole and ADT (24 Weeks Randomised Treatment) and the control. The interval gives the range of effects that remain compatible with the data.
Full Global Score Remission During the Randomised Treatment Period
- Endpoint type: Binary: the number of participants with the event, compared as proportions.
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Period B Brexpiprazole and ADT (24 Weeks Randomised Treatment): 27.3% (121/444) versus 32.4% (143/441) on control; risk difference -5.2 percentage points (95% CI -11.2 to 0.8), risk ratio 0.84 (0.69–1.03); unadjusted two-proportion z-test p = 0.093.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Period B Brexpiprazole and ADT (24 Weeks Randomised Treatment) and the control. The interval gives the range of effects that remain compatible with the data.
Total Time in Remission During the Randomised Treatment Period
- 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:
- Period B Brexpiprazole and ADT (24 Weeks Randomised Treatment): mean 30.00 versus 33.50 on control; difference -3.50 (95% CI -9.46 to 2.46), standardized effect d = -0.08; z-test p = 0.250.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Period B Brexpiprazole and ADT (24 Weeks Randomised Treatment) and the control. The interval gives the range of effects that remain compatible with the data.
The registry lists 17 posted secondary outcomes. The numerical comparisons described in the accompanying tables include functional remission, global-score remission, and total time in remission. Across these displayed comparisons, the point estimates are in the direction of lower outcomes in the brexpiprazole-plus-antidepressant group, while the confidence intervals include the no-difference value. This is a broad description of their pattern, not a claim that every secondary outcome in the registry has the same result.
These measures relate to the primary endpoint by examining other aspects of remission: a functional measure, a global-score measure, and time spent in remission. They can add context because full remission under the primary definition is a threshold-based outcome. However, they do not replace the primary endpoint or remove its uncertainty. The registry also lists other secondary outcomes, including symptom-score changes and response at Week 6, but those outcome titles alone do not establish their results.
Unadjusted secondary comparisons carry less weight when many outcomes are examined. General explanation: with multiple statistical tests, the chance of at least one apparently notable result arising by chance can increase unless the analysis plan accounts for multiplicity. The registry record does not report a multiplicity adjustment or a testing hierarchy in the information. Secondary findings are therefore best treated as supporting or exploratory context, not as independent confirmation of the primary comparison.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Full Functional Remission During the Randomised Treatment Period
- Full Global Score Remission During the Randomised Treatment Period
- Total Time in Remission During the Randomised Treatment Period
- Time to Full Remission During the Randomised Treatment Period
- Full Remission Sustained During the Randomised Treatment Period
- Change From Randomisation to Week 6 in MADRS Total Score During the Randomised Treatment Period
- Change From Randomisation to Week 24 in MADRS Total Score During the Randomised Treatment Period
- Response at Week 6 During the Randomised Treatment Period
9. Statistical Interpretation
The posted primary results are 110 participants meeting full remission in the placebo-plus-antidepressant group and 95 in the brexpiprazole-plus-antidepressant group. The corresponding denominators are 441 and 444. The recalculated unadjusted risk difference, defined as brexpiprazole plus antidepressant minus placebo plus antidepressant, is -0.035, with a 95% confidence interval from -0.091 to 0.020 and an unadjusted p-value of 0.211.
The point estimate is negative, so the observed difference in the posted counts is in the direction of fewer participants meeting the full-remission definition in the brexpiprazole group. The confidence interval includes zero and extends in both directions. Thus, the recalculation is compatible with a range of differences that includes no difference as well as differences in either direction. It should not be read as a precise estimate establishing the direction or size of an underlying effect.
The registry also reports a logistic-regression odds ratio of 0.83, with a 95% confidence interval from 0.60 to 1.15 and p = 0.264. This is the sponsor-reported analysis and uses a different effect measure from the unadjusted risk difference. The reported interval includes 1, the no-association value for an odds ratio. The registry record does not describe covariates or other details of this logistic-regression model in the information.
These results concern the defined analysis population and the 24-week randomised treatment period. They do not establish that the groups were identical, nor do they establish a difference. The uncertainty is material: the posted estimate alone cannot resolve whether the underlying between-group difference is small, absent, or in another direction. The endpoint also requires at least 8 consecutive weeks meeting the remission definition, so a participant who improved without meeting that sustained threshold would not count as having full remission.
Related secondary outcomes provide additional views of remission and symptom change, but they should be interpreted in context rather than used to overturn the primary result. The record lists multiple secondary measures, and the statistical information does not establish a multiplicity-adjusted conclusion across them. The outcome values and comparison estimates are displayed in the tables; this discussion explains their scope and uncertainty rather than treating any single numerical estimate as a standalone conclusion.
10. Statistical Methods Explained
The primary outcome is binary at the participant level: each person either met the full-remission definition during the stated period or did not. The posted arm results give the number meeting the definition and the number in the outcome population. A risk difference expresses the difference between the two groups’ proportions meeting the outcome. Here it is reported as brexpiprazole plus antidepressant minus placebo plus antidepressant, so a negative estimate indicates a lower observed proportion in the brexpiprazole group. The recalculated estimate uses the posted summary counts and is unadjusted.
What does the confidence interval describe?
General explanation: a confidence interval describes the uncertainty around an estimate under the assumptions of the method used. A 95% interval is not a guarantee that the true effect lies inside this particular interval. For a risk difference, zero represents no difference between groups. If the interval spans zero, the posted data do not rule out no difference at that confidence level. The interval also communicates which positive and negative differences remain compatible with the data and method. Its width matters: estimates with wider intervals are less precise than estimates with narrower intervals.
Why are there two effect measures?
The recalculation reports a risk difference, while the sponsor’s reported analysis uses an odds ratio from logistic regression. A risk difference describes an absolute contrast between outcome proportions. An odds ratio compares the odds of the outcome between groups. General explanation: these measures answer related but distinct questions and are not numerically interchangeable. An odds ratio of 1 represents equal odds; a risk difference of zero represents equal proportions. The registry record reports the sponsor’s odds ratio and its interval and p-value, but the model’s covariates and further implementation details are not reported in the registry record.
What does an unadjusted recalculation mean?
The recalculated comparison is a simple analysis of the posted summary statistics, without adjustment for additional variables. It provides a transparent comparison of the recorded counts and denominators. It is not a replacement for the sponsor’s prespecified or otherwise reported analysis. In this record, the discrepancy indicator is false, so there is no flagged conflict between the recalculated result and the sponsor-reported result. The sponsor’s own analysis remains the analysis reported by the study.
Why can the analysis population differ from overall enrolment?
The primary endpoint population is defined as randomised patients who took at least one dose of randomised treatment in Period B. The displayed denominators therefore refer to that outcome population, not to the overall enrolment. General explanation: using a defined analysis population affects what a result describes. It is important to know whether participants without an endpoint measurement, or participants who did not take treatment, are included and how they are handled. The population definition is reported, but a full participant flow and the handling of missing endpoint data are not reported in the registry record.
Why can over-dispersion matter?
General explanation: over-dispersion arises when observed variability is greater than a statistical model expects. It can make standard errors too small if the model does not account for that extra variability, which in turn can make intervals appear too narrow. This primary endpoint is a binary participant count, and no dispersion statistic is reported for it. The registry record does not report a separate over-dispersion assessment. The concept is relevant to statistical methods generally, but it should not be assumed to have affected this analysis.
What does a p-value contribute?
General explanation: a p-value measures how unusual data at least as discrepant as those observed would be under a specified null hypothesis and model. It is not the probability that the null hypothesis is true, nor is it a measure of clinical importance. A p-value does not replace the effect estimate or its confidence interval. For the primary outcome, the unadjusted recalculation and the sponsor-reported model each have their own p-value because they use different methods and effect measures.
11. Confidence Intervals and Precision
The primary risk-difference estimate is -0.035, with a 95% confidence interval from -0.091 to 0.020. The interval includes zero, so the posted data do not distinguish the estimated difference from no difference at the 95% confidence level using this recalculation. It also spans values on both sides of zero, meaning the data are compatible with a negative or positive difference under the stated measure. The interval is the main guide to precision; the point estimate alone does not convey how uncertain the comparison is.
The sponsor-reported odds ratio is 0.83, with a 95% confidence interval from 0.60 to 1.15. This interval includes 1, the no-difference value for an odds ratio. Because the sponsor’s analysis reports an odds ratio and the recalculation reports a risk difference, their intervals are on different scales and should not be compared as if they were the same quantity.
The primary outcome denominators are 441 in the placebo-plus-antidepressant group and 444 in the brexpiprazole-plus-antidepressant group. These numbers describe the analysed outcome population. They do not remove uncertainty about the comparison: precision depends on the observed outcome information and the statistical method, not simply on the fact that the group sizes are similar.
General explanation: an interval can be compatible with both a modest benefit and a modest disadvantage while still leaving the estimate uncertain. The interval does not give the probability of each possible effect, and it does not settle questions about clinical importance. The registry record does not report a threshold for a clinically important difference, so this page cannot classify the interval against such a threshold.
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 | 2,221 | 2,972 |
| 75% of the observed effect | 4,000 | 5,355 |
| 50% of the observed effect | 9,118 | 12,205 |
The sample-size table and curve are planning illustrations based on the observed effect, rather than a record of the trial’s original design calculation. For the binary outcomes, the figures are participants per arm, not total participants. The planning assumptions listed for the illustration are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. The original trial’s own sample-size assumptions and justification are not reported in the registry record.
The 80% power column describes the number of participants per arm the illustration estimates would be needed for an 80% chance of detecting the chosen effect under those assumptions, if that effect were the true one. The 90% power column describes the corresponding planning target for a 90% chance. These are design probabilities under assumptions, not probabilities that the study result is correct and not measures of the chance that a treatment works.
Rows planning for a smaller fraction of the observed effect require more participants per arm than rows planning for the full observed effect. This reflects a general statistical principle: smaller differences are harder to distinguish from random variation, so they usually require more information. The table should therefore be read as a sensitivity illustration showing how sample-size requirements change when the target effect changes. These figures are not observed power.
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 = 0.249; treatment proportion p1 = 0.214; average p̄ = 0.232.
- First term: z1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5967 = 1.1695.
- Second term: z1−β × √[p0(1−p0) + p1(1−p1)] = 0.842 × 0.5962 = 0.5017.
- n = (1.1695 + 0.5017)2 / (-0.0355)2 = 2,220.0, rounded up to 2,221 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 <- 0.249433106575964 # control proportion
p1 <- 0.213963963963964 # 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(1838681)
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 = 2,221 (80% power), 2,972 (90% power)
75% of observed effect: n per arm = 4,000 (80% power), 5,355 (90% power)
50% of observed effect: n per arm = 9,118 (80% power), 12,205 (90% power)
power.prop.test: 2220
Simulated power at n = 2,221 per arm: 0.801 (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) 0.83 | 0.60 to 1.15 | 0.264 |
The registry reports the sponsor’s primary comparison as a logistic-regression odds ratio of 0.83, with a 95% confidence interval from 0.60 to 1.15 and p = 0.264. The recalculation from the posted counts gives an unadjusted risk difference of -0.035, with a 95% confidence interval from -0.091 to 0.020 and an unadjusted p-value of 0.211. The results use different measures and methods, so the numerical estimates should not be compared directly.
Both intervals include their respective no-difference values: 1 for the odds ratio and zero for the risk difference. The sponsor-reported model is the study’s reported analysis; the recalculation is an unadjusted check based on the posted summary counts. The registry record does not provide the model covariates or further details needed to reproduce the logistic regression. The record flags no discrepancy between the reported and recalculated results. The recalculation should therefore be treated as a complementary summary, not as a substitute for the sponsor’s analysis.
15. Multiplicity, Missing Data and Analysis Populations
The registry record lists 18 outcome measures, including the primary outcome and 17 posted secondary outcomes. It also lists one reported analysis. The statistical information does not report a multiplicity adjustment, a hierarchy for testing outcomes, or a plan for controlling the overall type I error across the primary and secondary comparisons. These details are not reported in the registry record.
General explanation: when investigators test many outcomes, the chance of obtaining one or more small p-values by chance can rise. A prespecified hierarchy, adjustment procedure, or clearly defined primary endpoint can help readers understand how the family of tests was handled. In the absence of reported details, secondary p-values should not be interpreted as if they were necessarily adjusted or as a single confirmatory set of tests.
The primary outcome population is described as all randomised patients who took at least one dose of randomised treatment in Period B. The record does not provide, in the information, a full account of participant disposition, the number of missing primary measurements, or the method used to handle missing data. It also does not report whether sensitivity analyses were conducted to assess the effect of missing observations. These omissions limit assessment of how robust the estimate is to incomplete outcome data.
The registry identifies the primary outcome comparison as a logistic-regression analysis, but the model details beyond that description are not reported. The information does not state which covariates, if any, were included, nor does it give the assumptions used for any missing-data model. The recalculation is unadjusted and cannot resolve these uncertainties. Readers can interpret the posted counts, effect estimates, and intervals as reported, while recognising that the record does not document all analysis choices needed for a full audit.
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 and ADT | 13 | 441 | 2.9% |
| Brexpiprazole and ADT | 9 | 444 | 2.0% |
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 and ADT | 97 of 441 |
| Brexpiprazole and ADT | 108 of 444 |
Most frequent serious adverse event terms
| Event term | Organ system | Placebo and ADT | Brexpiprazole and ADT |
|---|---|---|---|
| Suicidal ideation | Psychiatric disorders | 3 of 441 | 2 of 444 |
| Intentional overdose | Injury, poisoning and procedural complications | 2 of 441 | 0 of 444 |
| Major depression | Psychiatric disorders | 1 of 441 | 1 of 444 |
| Pancreatitis | Gastrointestinal disorders | 0 of 441 | 1 of 444 |
| Influenza | Infections and infestations | 1 of 441 | 0 of 444 |
| Forearm fracture | Injury, poisoning and procedural complications | 1 of 441 | 0 of 444 |
| Radius fracture | Injury, poisoning and procedural complications | 0 of 441 | 1 of 444 |
| False positive investigation result | Investigations | 1 of 441 | 0 of 444 |
| Obesity | Metabolism and nutrition disorders | 0 of 441 | 1 of 444 |
| Dizziness | Nervous system disorders | 0 of 441 | 1 of 444 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Placebo and ADT | Brexpiprazole and ADT |
|---|---|---|---|
| Headache | Nervous system disorders | 31 of 441 | 34 of 444 |
| Weight increased | Investigations | 22 of 441 | 42 of 444 |
| Nasopharyngitis | Infections and infestations | 34 of 441 | 28 of 444 |
| Accidental overdose | Injury, poisoning and procedural complications | 25 of 441 | 27 of 444 |
Serious events with the highest arm-level rate: suicidal ideation (0.7%), intentional overdose (0.5%), ovarian cyst (0.3%), influenza (0.2%), forearm fracture (0.2%).
The registry reports serious adverse events in 13 of 441 participants in the placebo-plus-antidepressant group and 9 of 444 participants in the brexpiprazole-plus-antidepressant group. It also reports other adverse events in 97 of 441 and 108 of 444 participants, respectively. These are group counts and denominators as posted; the figures should be read alongside the definitions and collection procedures, which are not described in detail.
The record lists the following serious adverse event terms with percentages: suicidal ideation, 0.7%; intentional overdose, 0.5%; ovarian cyst, 0.3%; influenza, 0.2%; forearm fracture, 0.2%; and false positive investigation result, 0.2%. The information presented does not assign these listed percentages to a specific treatment group, so they should not be used as arm-specific comparisons.
Deaths are recorded as null for both groups, which means death counts are not reported in the registry record; it should not be interpreted as a reported count of zero. Safety counts are descriptive and do not, on their own, establish that an event was caused by a study treatment or that two groups differ in risk. No safety advice or treatment conclusion follows from these figures alone.
17. What the Result Does, and Does Not, Mean
The posted primary outcome data show that fewer participants in the brexpiprazole-plus-antidepressant group than in the placebo-plus-antidepressant group met the registry definition of full remission during the 24-week randomised treatment period. The recalculated risk difference is negative, but its confidence interval includes zero and reaches values on both sides of zero. The sponsor-reported odds-ratio interval likewise includes its no-difference value. The estimates are therefore uncertain and do not establish a clear between-group difference.
This result is specific to the outcome definition, analysis population, and period reported. Full remission required a MADRS score of 10 or less together with a decrease of at least 50% from randomisation, sustained for at least 8 consecutive weeks. Participants who changed symptomatically but did not meet both criteria would not be counted as fully remitted under this endpoint. The comparison also concerns brexpiprazole or placebo added to open-label antidepressant treatment, not either study drug in isolation.
The result does not establish whether either treatment is effective or ineffective, and it does not provide medical advice. It does not describe outcomes outside the specified randomised period, nor does it resolve the role of missing data or all analysis choices that are not reported in the registry record. The safety counts are also descriptive and should not be interpreted as proof of causation or as a comprehensive assessment of risk.
General explanation: statistical uncertainty and clinical importance are different questions. A confidence interval describes uncertainty in an estimated comparison, while judging importance requires a relevant clinical threshold and context. The registry record does not report a threshold for a clinically important difference. The most defensible reading is therefore limited to the posted estimates, their uncertainty, and the stated study population and timeframe.
18. Why This Trial Matters Statistically
This trial illustrates why a binary clinical endpoint should be read together with its definition, denominators, effect estimate, and confidence interval. A remission count can be easy to understand, but its interpretation depends on the threshold and duration required to qualify. Here, full remission requires both a low MADRS score and a sustained decrease from randomisation, rather than a single low score at one visit.
The example also shows why the analysis population matters. The primary outcome uses randomised participants who took at least one dose in Period B, while overall enrolment is a different figure. Readers should keep the outcome denominators in view rather than treating overall enrolment as the number contributing to every result.
Finally, the registry presents both a sponsor-reported logistic-regression odds ratio and a simple unadjusted recalculation using a risk difference. These are different summaries of the comparison. Looking at the effect estimate and interval, rather than relying on a p-value alone, makes the uncertainty more visible. The limited reporting on multiplicity, missing data, and model details also demonstrates how registry results can be informative while leaving important questions about analysis choices unresolved.
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 primary endpoint is a threshold-based remission outcome. It does not show the full course of symptoms or the timing of remission, and a participant must meet both score criteria for at least 8 consecutive weeks to count. Other outcomes may address some of these dimensions, but they do not change what the primary endpoint measures.
The primary outcome population is restricted to randomised patients who took at least one dose of randomised treatment in Period B. The registry record does not give a full participant flow or explain how people outside this population were handled. Missing-data methods and sensitivity analyses are not reported in the registry information, limiting assessment of the impact of incomplete outcome data.
The study title describes a long-term evaluation, but the primary outcome timeframe in the posted results is the 24-week randomised treatment period. The result should not be extended to timeframes beyond that period. Treatment was adjunctive: both groups received open-label antidepressant treatment, with brexpiprazole or placebo added. The comparison is not a test of brexpiprazole without antidepressant treatment.
The sponsor’s logistic-regression model is identified, but its covariates and further details are not reported in the registry record. Multiplicity handling for the many listed outcomes is also not reported. The secondary findings therefore warrant caution, especially when considered apart from the primary outcome. Finally, the registry safety section reports group counts and selected serious-event terms, but the information does not fully describe event ascertainment, attribution, or all safety analyses.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Brexpiprazole as Adjunctive Treatment in Patients With Major Depressive Disorder With an Inadequate Response to Antidepressant Treatment — NCT01838681.
- Registry record last updated 2017-08-09; status last verified 2017-07.
- Results first posted 2017-08-09.
- 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
NCT01838681 is a completed Phase 3 randomised, double-blind, parallel-group, placebo-controlled study sponsored by H. Lundbeck A/S. It evaluated brexpiprazole as an adjunct to open-label antidepressant treatment in adults with major depressive disorder and an inadequate response to antidepressant treatment. Overall enrolment was 1986.
The primary outcome was full remission during the 24-week randomised treatment period, defined by MADRS score and sustained improvement criteria. The primary outcome population included participants who took at least one dose of randomised treatment in Period B. The posted results and the sponsor’s logistic-regression analysis are shown in the accompanying tables; the estimates have confidence intervals that include their respective no-difference values. The registry record does not report several analysis details, including the original sample-size justification, multiplicity handling, and missing-data methods.