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 Trial to Evaluate the Efficacy, Safety & Tolerability of Brexpiprazole in the Maintenance Treatment of Adults With Major Depressive Disorder (NCT03538691), a randomized phase 3 study. The primary outcome is Phase C: Time-to-Relapse by Any Criteria as Defined in Blinded Addendum.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT03538691 |
| Phase | Phase 3 |
| Condition | Major Depressive Disorder |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Triple |
| Enrollment | 1149 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Otsuka Pharmaceutical Development & Commercialization, Inc. |
| Results posted | Yes |
2. Clinical Question
Population
Adults with major depressive disorder entered a staged trial in which participants first received brexpiprazole with protocol-specified antidepressant therapy. The Phase C efficacy population for the primary outcome consisted of participants randomized to double-blind treatment who took at least one dose of study treatment. For the median time-to-relapse analysis, the registry describes the analyzed participants as those with impending relapse.
Intervention
In Phase C, eligible participants continued brexpiprazole, at the dose they were receiving at Week 20 of the Stabilization Phase, together with protocol-specified antidepressant therapy. Brexpiprazole was given at 2 or 3 milligrams per day in the earlier treatment phases.
Comparator
The comparison group received brexpiprazole-matching placebo with the same protocol-specified antidepressant therapy during Phase C. The primary comparison was therefore adjunctive brexpiprazole versus placebo, with antidepressant therapy continuing in both groups.
Primary question
The primary question was whether time to relapse by any of the criteria defined in a blinded addendum differed between the Phase C treatment groups. Relapse could be identified through worsening depression ratings, hospitalization, discontinuation for lack of efficacy or worsening, or specified suicidality criteria. The registry reports median times of 63 days in both groups and a hazard ratio of 1.138, with a 95% confidence interval from 0.776 to 1.669.
3. Trial Design
This was a Phase 3, multicenter, randomized, parallel-group, placebo-controlled trial of brexpiprazole as adjunctive therapy in adults with major depressive disorder. The registry classifies masking as triple and describes the study as double-blind in its official title. The record does not specify which participant, investigator, or other roles were included in the triple masking.
The study used sequential treatment phases. In Phase A, participants received brexpiprazole with protocol-specified antidepressant therapy for 6 to 8 weeks. The brexpiprazole target dose was 2 milligrams per day after an initial titration period of 2 to 4 weeks. Participants eligible after completing Phase A entered Phase B and received brexpiprazole with antidepressant therapy for 12 weeks. Eligible participants completing Phase B entered Phase C, the randomized comparison, and received either continued brexpiprazole or matching placebo, with antidepressant therapy in both groups, for up to 26 weeks.
The total enrollment was 1149. Phase C arm counts for the primary median time-to-relapse analysis were 54 for brexpiprazole plus antidepressant therapy and 51 for placebo plus antidepressant therapy. Those counts refer to participants with impending relapse in the analysis, not the full Phase C randomized groups. For other Phase C outcomes, the analyzed group counts differ; each outcome has its own analysis population.
The study status is completed. The registry lists a start date of 2018-07-13 and a primary completion date of 2022-07-08. Details of the original sample-size justification, the prespecified handling of missing data, and any interim analyses 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: Of the 1149 participants enrolled in Phase A (Acute Treatment) of the study, 766 eligible participants continued to Phase B (Stabilization). Eligible participants who completed the Phase B were randomized into Phase C (Double-blind Randomized Withdrawal) to receive brexpiprazole or placebo along with open-label antidepressant therapy (ADT) in a 1:1 ratio for up to 26 weeks.
Phase A: Acute Treatment (up to 8 Weeks)
| Stage | Phase A: Brexpiprazole + ADT | Phase B: Brexpiprazole + ADT | Phase C: Brexpiprazole + ADT | Phase C: Placebo + ADT |
|---|---|---|---|---|
| STARTED | 1149 | 0 | 0 | 0 |
| Phase A Safety Sample | 1136 | 0 | 0 | 0 |
| COMPLETED | 766 | 0 | 0 | 0 |
| NOT COMPLETED | 383 | 0 | 0 | 0 |
Reasons for not completing this period:
| Reason | Phase A: Brexpiprazole + ADT | Phase B: Brexpiprazole + ADT | Phase C: Brexpiprazole + ADT | Phase C: Placebo + ADT |
|---|---|---|---|---|
| Lost to Follow-up | 24 | 0 | 0 | 0 |
| Adverse Event | 82 | 0 | 0 | 0 |
| Subject Withdrew Consent | 54 | 0 | 0 | 0 |
| Death | 1 | 0 | 0 | 0 |
| Non-Compliance With Study Drug | 9 | 0 | 0 | 0 |
| Lack of Efficacy | 185 | 0 | 0 | 0 |
| Protocol Deviation | 12 | 0 | 0 | 0 |
| Physician Decision | 1 | 0 | 0 | 0 |
| Reason not Specified (not due to Coronavirus Disease 2019 [COVID-19] Restriction) | 15 | 0 | 0 | 0 |
Phase B: Stabilization (12 Weeks)
| Stage | Phase A: Brexpiprazole + ADT | Phase B: Brexpiprazole + ADT | Phase C: Brexpiprazole + ADT | Phase C: Placebo + ADT |
|---|---|---|---|---|
| STARTED | 0 | 766 | 0 | 0 |
| Phase B Safety Sample | 0 | 765 | 0 | 0 |
| COMPLETED | 0 | 489 | 0 | 0 |
| NOT COMPLETED | 0 | 277 | 0 | 0 |
Reasons for not completing this period:
| Reason | Phase A: Brexpiprazole + ADT | Phase B: Brexpiprazole + ADT | Phase C: Brexpiprazole + ADT | Phase C: Placebo + ADT |
|---|---|---|---|---|
| Lost to Follow-up | 0 | 5 | 0 | 0 |
| Adverse Event | 0 | 52 | 0 | 0 |
| Subject Withdrew Consent | 0 | 47 | 0 | 0 |
| Non-Compliance With Study Drug | 0 | 9 | 0 | 0 |
| Lack of Efficacy | 0 | 136 | 0 | 0 |
| Pregnancy | 0 | 1 | 0 | 0 |
| Protocol Deviation | 0 | 9 | 0 | 0 |
| Physician Decision | 0 | 6 | 0 | 0 |
| Due to COVID-19 Restriction | 0 | 1 | 0 | 0 |
| Reason not Specified (not due to COVID-19 Restriction) | 0 | 11 | 0 | 0 |
Phase C:Randomized Withdrawal (26 Weeks)
| Stage | Phase A: Brexpiprazole + ADT | Phase B: Brexpiprazole + ADT | Phase C: Brexpiprazole + ADT | Phase C: Placebo + ADT |
|---|---|---|---|---|
| STARTED | 0 | 0 | 240 | 249 |
| Phase C Safety Sample | 0 | 0 | 240 | 248 |
| COMPLETED | 0 | 0 | 120 | 131 |
| NOT COMPLETED | 0 | 0 | 120 | 118 |
Reasons for not completing this period:
| Reason | Phase A: Brexpiprazole + ADT | Phase B: Brexpiprazole + ADT | Phase C: Brexpiprazole + ADT | Phase C: Placebo + ADT |
|---|---|---|---|---|
| Lost to Follow-up | 0 | 0 | 16 | 4 |
| Adverse Event | 0 | 0 | 6 | 6 |
| Subject Withdrew Consent | 0 | 0 | 6 | 19 |
| Non-Compliance With Study Drug | 0 | 0 | 1 | 2 |
| Non-compliant Participants | 0 | 0 | 32 | 28 |
| Pregnancy | 0 | 0 | 1 | 0 |
| Lack of Efficacy (Phase C MDD Relapse) | 0 | 0 | 54 | 52 |
| Physician Decision | 0 | 0 | 0 | 1 |
| Reason not Specified (not due to COVID-19 Restriction) | 0 | 0 | 4 | 6 |
Analysis population for the primary outcome, as defined in the registry: Phase C Efficacy Sample included all participants randomized to the double-blind treatment who had taken at least one dose of investigational medicinal product (IMP) in Phase C. Overall number of participants analyzed for median time to relapse is the number of participants with impending relapse.
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: Enrolled Sample included all participants who signed the informed consent form and entered Phase A.
| Characteristic | Unit | Phase A: Brexpiprazole + ADT |
|---|---|---|
| Participants analysed | 1149 | |
| Age, Continuous | years | 42.3 (SD 13.1) |
| Sex: Female, Male: Female | Participants | 734 |
| Sex: Female, Male: Male | Participants | 415 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 110 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 968 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 71 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 5 |
| Race (NIH/OMB): Asian | Participants | 22 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 5 |
| Race (NIH/OMB): Black or African American | Participants | 159 |
| Race (NIH/OMB): White | Participants | 868 |
| Race (NIH/OMB): More than one race | Participants | 0 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 90 |
6. Primary Endpoint
The registry lists the primary outcome as Phase C: Time-to-Relapse by Any Criteria as Defined in Blinded Addendum, measured over Up to 14 days post last dose in Phase C (up to 28 weeks).
| Element | Registry entry |
|---|---|
| Result type | Median |
| Measure of spread | Full Range |
| Unit | days |
| Endpoint classification | Time-to-Event Analysis |
The primary endpoint was time to relapse by any criteria defined in a blinded addendum, assessed through up to 14 days after the last Phase C dose, for up to 28 weeks. It is a time-to-event outcome: the analysis concerns how long participants remained without a qualifying relapse event during follow-up, rather than only whether relapse occurred by one fixed visit.
The relapse definition was composite. It included a specified increase in both the Montgomery-Asberg Depression Rating Scale (MADRS) total score and the Clinical Global Impression-Severity of Illness (CGI) score at the same visit; hospitalization for depression; discontinuation for lack of efficacy or worsening of depression; and specified active-suicidality or suicidal-behavior responses on the MADRS or Columbia-Suicide Severity Rating Scale. Combining these criteria allows different forms of clinically important worsening to count as an event, but it also means the endpoint represents the composite definition rather than any single component alone.
Time-to-event methods are used because the timing of an event matters and participants may have different follow-up durations. The median is the time by which half of the analyzed event-time distribution has reached the event, when that median can be estimated. The registry reports a median of 63 days in each Phase C group, with full ranges of 8 to 185 days for brexpiprazole plus antidepressant therapy and 8 to 190 days for placebo plus antidepressant therapy. These medians are descriptive and do not, by themselves, summarize the full comparison over follow-up.
7. Results Posted in the Registry
- Phase C: Brexpiprazole + ADT vs Phase C: Placebo + ADT: hazard ratio 1.14 (95% CI 0.78–1.67), reported p = 0.510 (as reported in the registry).
Hazard ratio: Phase C: Brexpiprazole + ADT vs Phase C: Placebo + ADT
95% CI: 0.78 to 1.67
As reported in the registry
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 |
|---|---|---|---|---|
| Phase C: Change From Baseline for Randomization Phase in Sheehan Disability Scale (SDS) Mean Total Score at Week 46 | Continuous Endpoint | Mean difference | 0.24 (-0.26 to 0.74) | 2,124 per arm |
| Phase C: Time-to-functional Relapse Based on SDS Criteria | Time-to-Event Analysis | Hazard ratio | 1.18 (0.86 to 1.61) | 1,183 events |
| Phase C: Percentage of Participants Meeting Any Relapse Criteria | Binary Endpoint | Risk difference | +1.9 pts (-5.4 to 9.2) | 7,079 per arm |
Phase C: Change From Baseline for Randomization Phase in Sheehan Disability Scale (SDS) Mean Total Score at Week 46
- 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 errors.
- Result:
- Phase C: Brexpiprazole + ADT: mean 0.72 versus 0.48 on control; difference 0.24 (95% CI -0.26 to 0.74), standardized effect d = 0.09; z-test p = 0.346.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Phase C: Brexpiprazole + ADT and the control. The interval gives the range of effects that remain compatible with the data.
Phase C: Time-to-functional Relapse Based on SDS Criteria
- Endpoint type: Time to event: compared as a hazard ratio.
- Test: Hazard ratio as reported by the sponsor (Log Rank); it was not recalculated.
- Result:
- Phase C: Brexpiprazole + ADT vs Phase C: Placebo + ADT: hazard ratio 1.18 (95% CI 0.86–1.61), reported p = 0.309 (as reported in the registry).
- Interpretation:
- The 95% confidence interval includes no difference (a ratio of 1), so these data do not show a statistically significant difference between Phase C: Brexpiprazole + ADT vs Phase C: Placebo + ADT and the control. The interval gives the range of effects that remain compatible with the data.
Phase C: Percentage of Participants Meeting Any Relapse Criteria
- 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:
- Phase C: Brexpiprazole + ADT: 22.5% (54/240) versus 20.6% (51/248) on control; risk difference 1.9 percentage points (95% CI -5.4 to 9.2), risk ratio 1.09 (0.78–1.54); unadjusted two-proportion z-test p = 0.603.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Phase C: Brexpiprazole + ADT and the control. The interval gives the range of effects that remain compatible with the data.
The registry lists seven secondary outcomes, including functional relapse, meeting any relapse criterion, maintaining remission, and changes in depression, disability, and severity ratings. Results are posted for three of these outcomes: change in Sheehan Disability Scale score at Week 46, time to functional relapse, and the percentage meeting any relapse criterion. Results for the other listed secondary outcomes are not reported in the registry record.
Across the posted secondary analyses, the confidence intervals for the reported between-group comparisons include the corresponding null values, and the reported tests do not show a statistically clear difference. This broad pattern is consistent with the primary result in that these posted outcomes do not establish a clear between-group separation. It should not be taken as independent confirmation of the primary result: secondary outcomes may be correlated with one another and may assess related aspects of the same clinical course.
Secondary results generally carry less inferential weight when many outcomes are examined and no multiplicity strategy is reported. With multiple tests, the chance of at least one apparently unusual result can increase. A multiplicity procedure can control the interpretation of a family of tests, but the registry does not report whether one was prespecified or applied. The posted secondary p values should therefore be treated as exploratory evidence rather than as a collection of independent confirmatory tests.
The secondary outcomes also differ in scale and meaning. A change in a disability score is not the same quantity as time to a functional relapse, and neither is identical to a percentage meeting a relapse criterion. A lack of a clear test result across these measures does not prove that every aspect of functioning or symptoms was the same. It indicates that the posted analyses do not provide decisive evidence of a group difference for those endpoints, within their respective populations and follow-up periods.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Phase C: Change From Baseline for Randomization Phase in Sheehan Disability Scale (SDS) Mean Total Score at Week 46
- Phase C: Time-to-functional Relapse Based on SDS Criteria
- Phase C: Percentage of Participants Meeting Any Relapse Criteria
- Phase C: Percentage of Participants Maintaining Remission
- Phase C: Change From Baseline for Randomization Phase in MADRS Total Score at Week 46
- Phase C: Change From Baseline for Randomization Phase in CGI-S Score at Week 46
- Phase C: Change From Baseline for Randomization Phase in Each of the SDS Individual Item Scores at Week 46
9. Statistical Interpretation
The primary reported comparison was a hazard ratio of 1.138 for brexpiprazole plus antidepressant therapy versus placebo plus antidepressant therapy. Its 95% confidence interval was 0.776 to 1.669, and the registry reports a Log Rank p value of 0.510. The interval includes 1, the value corresponding to equal event hazards under the hazard-ratio interpretation. The data therefore do not provide a statistically clear difference between groups on the primary time-to-relapse comparison.
The direction of a hazard ratio depends on the order of the groups in the comparison. The registry labels the comparison as brexpiprazole plus antidepressant therapy versus placebo plus antidepressant therapy and reports the hazard ratio as 1.138. This estimate is above 1, but its confidence interval is wide enough to include values on either side of 1. It is not a precise indication of the size or direction of a difference. The sponsor’s reported analysis is the appropriate result to use for the trial’s primary inference.
The reported medians were both 63 days. That equality is a feature of the reported medians, not proof that the entire time-to-event distributions were identical. A median compresses the event-time information into one point; participants’ event times and censoring patterns can differ even when medians match. The full ranges also overlap substantially. Neither the medians nor the ranges replace the hazard-ratio analysis, which compares event experience across follow-up under its statistical assumptions.
The analysis population matters when interpreting the endpoint. The registry describes the primary median time-to-relapse analysis as including participants with impending relapse within the Phase C efficacy sample, which itself comprised randomized participants who took at least one dose of investigational treatment. The reported analysis counts of 54 and 51 should therefore not be read as the full number randomized to the respective Phase C groups. The reasons for the relationship between the broader randomized population and the event-time analysis population are not reported in the registry record.
In brief, the posted primary analysis does not establish a clear difference in time to relapse between the Phase C groups. It also does not establish that the treatments are equivalent or that any possible difference is absent. The confidence interval permits a range of effects, and interpretation should retain that uncertainty. The result concerns this endpoint, population, and follow-up period, not every outcome or every possible use of the treatment.
10. Statistical Methods Explained
Time-to-event data record both whether an event occurred and when it occurred. In this trial, a qualifying relapse could occur at different times during Phase C. Some participants may not have had a recorded relapse by their last observation, so they contribute follow-up up to that point without contributing a relapse event. General statistical methods for time-to-event outcomes account for this difference between event times and incomplete observation.
What does a median time describe?
The median time is a central summary of event timing: it marks the point at which half of the relevant event-time distribution has experienced the event, when estimable. It does not describe every participant, and it can conceal differences elsewhere in the distribution. The registry reports 63 days in each group for the primary outcome. The full range gives the lowest and highest reported times in the analysis, but it does not show how observations are distributed between those endpoints or how censoring was handled.
What does the hazard ratio compare?
A hazard is the instantaneous event rate among participants still under observation and not yet experiencing the event. A hazard ratio compares these rates between groups over time. A value of 1 corresponds to equal hazards under the model’s interpretation. Values on either side of 1 indicate different estimated directions, depending on the order of groups. A hazard ratio is not a ratio of the groups’ median times, and it should not be interpreted as a direct percentage change in the probability of relapse.
The registry reports a hazard ratio of 1.138, with a 95% confidence interval from 0.776 to 1.669, using a Log Rank method. The confidence interval includes 1, so the data are compatible with equal hazards as well as with differences in either direction. The reported p value is 0.510. The p value describes how unusual the test statistic would be under the null hypothesis and assumptions of the test; it is not the probability that the null hypothesis is true, nor a measure of the clinical importance of the result.
Why does the relapse definition matter?
The endpoint counts a relapse if any listed criterion is met. Its components include depression-rating changes, hospitalization, treatment discontinuation for specified reasons, and suicidality criteria. A composite endpoint can capture several forms of worsening within one analysis, but the overall result does not reveal which component contributed most. Component-specific event counts and comparisons for the primary composite are not reported in the registry record.
Why can over-dispersion matter in other analyses?
General statistical explanation: over-dispersion occurs when outcome variability exceeds what a chosen probability model expects. If it is ignored, uncertainty estimates can be too small and tests can appear more decisive than the data warrant. The primary endpoint is time-to-event, and the registry identifies a Log Rank analysis; it does not report an over-dispersion adjustment for this endpoint. The concept is more directly relevant to count outcomes modeled with distributions that impose a particular relationship between the mean and variance.
How should the analysis population be read?
The registry defines the Phase C efficacy sample as randomized participants who took at least one dose of investigational medicinal product in Phase C. It then states that the number analyzed for median time to relapse is the number with impending relapse. That endpoint-specific count is different from the number enrolled in the trial and from the full arm counts reported for some other outcomes. The precise event-time analysis procedures, censoring rules, and any sensitivity analyses are not reported in the registry record.
These methods describe distinct pieces of evidence: event-time summaries, a between-group hazard-ratio test, and its uncertainty interval. A sound interpretation uses them together without treating the median as the entire distribution or the p value as a verdict on whether an effect exists.
11. Confidence Intervals and Precision
A confidence interval expresses uncertainty in an estimate under the statistical model and analysis used. A 95% confidence interval is generated by a procedure designed, under its assumptions, to cover the underlying parameter in 95% of repeated samples. It is not a statement that there is a 95% probability that the particular interval contains the true value.
For the primary hazard ratio, the estimate is 1.138 and the 95% confidence interval is 0.776 to 1.669. The interval includes 1, the reference value for equal hazards, and extends to values on either side of it. This breadth means the estimate is not precise enough to distinguish the null value from a range of potentially different hazard ratios. The registry’s p value of 0.510 is consistent with the absence of a statistically clear difference in the reported test.
The reported medians are 63 days in both groups, but the median values do not have a confidence interval posted in the primary outcome information. The full ranges are 8 to 185 days and 8 to 190 days. A range is not a measure of precision for the group comparison: it gives endpoints of observed times and does not quantify uncertainty around the hazard ratio or median.
Precision depends on factors such as the amount of event information and the spread of the data, as well as the analysis assumptions. The registry’s primary analysis population is described as participants with impending relapse, with 54 in the brexpiprazole group and 51 in the placebo group. These endpoint-analysis counts are relevant context for the amount of information, but do not alone determine precision. A confidence interval is the more direct reported summary of uncertainty for the hazard ratio.
The interval should not be read as proof of no effect, and its inclusion of 1 should not be interpreted as proof of equivalence. Equivalence or non-inferiority conclusions require an appropriate design and prespecified margins; those details are not reported in the registry record.
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 (log scale) | Hazard ratio | Events, 80% power | Events, 90% power |
|---|---|---|---|
| 100% of the observed effect | 1.14 | 1,879 | 2,516 |
| 75% of the observed effect | 1.10 | 3,340 | 4,472 |
| 50% of the observed effect | 1.07 | 7,515 | 10,061 |
The planning figures are illustrations based on the observed effect, not the trial’s original design calculations. For time-to-event outcomes, the entries are the total number of events needed across the comparison. For other outcomes, the entries are participants per arm. The figures therefore have different units depending on the outcome; they are not all counts of people per group.
The illustration assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It considers detecting 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 represents the planned sample or event total at which the assumed effect would be detected in 80% of repeated studies under those assumptions. The 90% power column represents the corresponding planning target for 90% of repeated studies. These are design concepts: power is the long-run chance of detecting a specified effect if that effect is present and the assumptions hold. The numbers are not a statement about the chance that the trial’s finding is true.
The rows that plan for 100%, 75%, and 50% of the observed effect show how the required sample or event total changes as the target effect becomes smaller. Smaller effects need more participants or events to detect with the same power and significance level. The figures are planning illustrations, not observed power for this completed trial. They should not be read as a retrospective score of whether the study was successful or as a substitute for the reported confidence intervals.
For the primary time-to-event comparison, the posted planning values are total events, not participants per arm. A reader should keep that distinction in mind when comparing the planning illustration with the endpoint-specific analysis counts. Those counts describe analyzed participants, while the planning unit for a time-to-event outcome is the total number of events.
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
d is the total number of events needed (Schoenfeld's formula) with 1:1 allocation and proportional hazards.
Worked calculation for this trial
- Hazard ratio HR = 1.138, so ln(HR) = 0.1293.
- d = 4 × (1.96 + 0.842)2 / [ln(1.138)]2 = 1,878.7, rounded up to 1,879 events in total 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
hr <- 1.138 # observed hazard ratio
events_needed <- function(power, frac = 1) ceiling(round(4 * (z_a + qnorm(power))^2 / log(hr^frac)^2, 6)) # Schoenfeld, 1:1 allocation
for (f in c(1, 0.75, 0.5))
cat(sprintf("%3.0f%% of observed effect: events = %s (80%% power), %s (90%% power)\n", 100 * f,
format(events_needed(0.80, f), big.mark = ","), format(events_needed(0.90, f), big.mark = ",")))
# Simulation: given d total events under proportional hazards, events in the treatment arm are Binomial(d, hr / (1 + hr)).
# The score (log-rank type) statistic is (D1 - d / 2) / sqrt(d / 4).
set.seed(3538691)
d <- events_needed(0.80)
reps <- 20000
D1 <- rbinom(reps, d, hr / (1 + hr))
z <- (D1 - d / 2) / sqrt(d / 4)
cat(sprintf("Simulated power with %s events: %.3f (%d replicates)\n", format(d, big.mark = ","), mean(abs(z) > z_a), reps))
Output from running the code
100% of observed effect: events = 1,879 (80% power), 2,516 (90% power)
75% of observed effect: events = 3,340 (80% power), 4,472 (90% power)
50% of observed effect: events = 7,515 (80% power), 10,061 (90% power)
Simulated power with 1,879 events: 0.802 (20000 replicates)
The simulation uses the fact that, with d events in total and proportional hazards, the number of events in the treatment arm is binomial. It is an approximation that conditions on the total number of events, and it should land close to the target power.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Log Rank | Hazard Ratio (HR) 1.138 | 0.776 to 1.669 | 0.510 |
The registry reports the sponsor’s primary analysis as a Log Rank comparison, with a hazard ratio of 1.138, a 95% confidence interval from 0.776 to 1.669, and a p value of 0.510. That is the trial’s reported inferential analysis and takes precedence over any simple re-calculation from posted summary statistics. No discrepancy is flagged for this endpoint.
A re-calculation from summary data would not reproduce all features of a time-to-event analysis. Such a calculation may not account for the event-time pattern, censoring, or the exact analysis population and procedures. The posted median and range summaries alone cannot reconstruct the sponsor’s Log Rank analysis. Accordingly, the hazard ratio and its interval should be interpreted as reported rather than replaced by an approximate comparison of medians.
The reported confidence interval includes 1, and the reported test does not show a statistically clear difference between groups. The sponsor’s analysis therefore supports an uncertain comparison on the primary endpoint, not a conclusion of equivalence. Further details of the statistical plan and implementation are not reported in the registry record.
15. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when a study tests more than one outcome, time point, subgroup, or analysis. Each additional test creates another opportunity to observe a result that appears statistically unusual by chance. A prespecified strategy can define which outcomes are confirmatory and how error rates are controlled across them. The registry lists one primary outcome and seven secondary outcomes, but a multiplicity adjustment or testing hierarchy is not reported in the registry record.
The primary endpoint is identified as time to relapse by any criteria defined in a blinded addendum, and the posted analysis uses a Log Rank method. The record does not provide enough information to establish the full prespecified analysis plan, including all rules for model implementation, censoring, or handling deviations from the planned analysis. These unreported details limit independent assessment of how closely the posted analysis follows the original plan.
Missing-data procedures are not reported in the registry record. For a time-to-event outcome, incomplete observation can arise when a participant’s follow-up ends before a relapse is recorded. The handling of such observations can affect the analysis, so the censoring rules and assumptions matter. For the continuous secondary outcome, imputation and model procedures can also influence estimated changes. The registry’s brief results do not specify these details, and they should not be inferred.
The analysis populations differ by endpoint. The primary description defines a Phase C efficacy sample of randomized participants who took at least one dose of investigational treatment, while the number analyzed for median time to relapse is described as those with impending relapse. The secondary outcomes have their own posted arm counts. These distinctions make it important not to assume that every outcome uses the same participants or the same handling of missing observations.
Interim analyses, stopping rules, the original sample-size justification, and a complete statistical analysis plan are not reported in the registry record. Their absence from the record does not establish that such procedures were or were not used; it means their role cannot be evaluated from the posted information.
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 |
|---|---|---|---|
| Phase A: Brexpiprazole + ADT | 10 | 1136 | 0.9% |
| Phase B: Brexpiprazole + ADT | 12 | 765 | 1.6% |
| Phase C: Brexpiprazole + ADT | 1 | 240 | 0.4% |
| Phase C: Placebo + ADT | 3 | 248 | 1.2% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Phase A: Brexpiprazole + ADT | 1 of 1149 |
| Phase B: Brexpiprazole + ADT | 0 of 766 |
| Phase C: Brexpiprazole + ADT | 0 of 240 |
| Phase C: Placebo + ADT | 0 of 249 |
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 |
|---|---|
| Phase A: Brexpiprazole + ADT | 398 of 1136 |
| Phase B: Brexpiprazole + ADT | 163 of 765 |
| Phase C: Brexpiprazole + ADT | 25 of 240 |
| Phase C: Placebo + ADT | 13 of 248 |
Most frequent serious adverse event terms
| Event term | Organ system | Phase A: Brexpiprazole + ADT | Phase B: Brexpiprazole + ADT | Phase C: Brexpiprazole + ADT | Phase C: Placebo + ADT |
|---|---|---|---|---|---|
| Cataract | Eye disorders | 0 of 1136 | 0 of 765 | 0 of 240 | 1 of 248 |
| Anaphylactic shock | Immune system disorders | 0 of 1136 | 0 of 765 | 1 of 240 | 0 of 248 |
| Dislocation of vertebra | Injury, poisoning and procedural complications | 0 of 1136 | 0 of 765 | 0 of 240 | 1 of 248 |
| Epicondylitis | Injury, poisoning and procedural complications | 0 of 1136 | 0 of 765 | 0 of 240 | 1 of 248 |
| Fall | Injury, poisoning and procedural complications | 0 of 1136 | 0 of 765 | 0 of 240 | 1 of 248 |
| Bursitis | Musculoskeletal and connective tissue disorders | 0 of 1136 | 0 of 765 | 0 of 240 | 1 of 248 |
| Myocardial infarction | Cardiac disorders | 0 of 1136 | 1 of 765 | 0 of 240 | 0 of 248 |
| Abdominal pain upper | Gastrointestinal disorders | 0 of 1136 | 1 of 765 | 0 of 240 | 0 of 248 |
| Haematemesis | Gastrointestinal disorders | 0 of 1136 | 1 of 765 | 0 of 240 | 0 of 248 |
| Acute hepatic failure | Hepatobiliary disorders | 0 of 1136 | 1 of 765 | 0 of 240 | 0 of 248 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Phase A: Brexpiprazole + ADT | Phase B: Brexpiprazole + ADT | Phase C: Brexpiprazole + ADT | Phase C: Placebo + ADT |
|---|---|---|---|---|---|
| Weight increased | Investigations | 0 of 1136 | 122 of 765 | 25 of 240 | 13 of 248 |
| Headache | Nervous system disorders | 113 of 1136 | 41 of 765 | 0 of 240 | 0 of 248 |
| Akathisia | Nervous system disorders | 109 of 1136 | 0 of 765 | 0 of 240 | 0 of 248 |
| Somnolence | Nervous system disorders | 90 of 1136 | 0 of 765 | 0 of 240 | 0 of 248 |
| Insomnia | Psychiatric disorders | 72 of 1136 | 0 of 765 | 0 of 240 | 0 of 248 |
| Nausea | Gastrointestinal disorders | 64 of 1136 | 0 of 765 | 0 of 240 | 0 of 248 |
| Increased appetite | Metabolism and nutrition disorders | 60 of 1136 | 0 of 765 | 0 of 240 | 0 of 248 |
Serious events with the highest arm-level rate: anaphylactic shock (0.4%), cataract (0.4%), dislocation of vertebra (0.4%), epicondylitis (0.4%), fall (0.4%).
The serious adverse event figures are organized by treatment phase. In Phase A, 10 serious adverse events were reported among 1136 participants at risk; in Phase B, 12 among 765; in Phase C, 1 among 240 in the brexpiprazole group and 3 among 248 in the placebo group. These are counts and at-risk totals as posted for each phase. They should not be combined into a single comparative rate because the phases involve different populations and exposure periods.
The registry lists Anaphylactic shock, Cataract, Dislocation of vertebra, Epicondylitis, Fall, and Bursitis among the top serious adverse event terms, each at 0.4%. The record does not provide enough detail in this summary to attribute these terms to a particular Phase C treatment group or to infer causality. One death is reported in Phase A; no deaths are reported in Phase B or either Phase C group.
These counts describe recorded serious adverse events, not a complete assessment of comparative safety. Differences in time exposed, participant selection across phases, and event reporting affect interpretation. The registry figures alone do not establish that an event was caused by study treatment.
17. What the Result Does, and Does Not, Mean
The primary analysis describes the time to relapse by a composite set of criteria among the Phase C analysis population. The two reported median times were both 63 days, and the reported hazard ratio was 1.138 with a 95% confidence interval from 0.776 to 1.669. The interval includes the equal-hazards value, and the reported test does not show a statistically clear difference between the randomized groups.
This finding does not demonstrate that the two groups are equivalent. A non-significant test does not prove that the true effect is exactly zero, and equivalence requires a design with an appropriate margin and analysis. Those details are not reported in the registry record. The confidence interval retains uncertainty about the size and direction of the effect.
The result also does not establish what would happen for every participant or outside the study conditions. It applies to the defined Phase C comparison, to the composite relapse criteria, and to the follow-up described in the registry. Both groups received protocol-specified antidepressant therapy; the randomized contrast was brexpiprazole versus matching placebo as adjunctive treatment.
The endpoint combines several kinds of worsening, so the primary result is not a separate estimate for each criterion. Nor does the median alone summarize the full event-time distribution. Secondary outcomes add related but distinct measures, and their posted results do not replace the primary endpoint or establish a different overall conclusion.
The safety counts are similarly descriptive. They identify serious adverse event counts and selected terms but do not, by themselves, determine causation or provide a complete benefit-risk assessment. The registry record supports a bounded statistical interpretation: no clear between-group difference was demonstrated on the primary time-to-relapse analysis, while uncertainty remains about the range of effects compatible with the data.
18. Why This Trial Matters Statistically
This trial is statistically informative because it makes a randomized comparison during a maintenance phase after participants had already received brexpiprazole with antidepressant therapy in earlier phases. The Phase C contrast therefore addresses continued brexpiprazole versus matching placebo, with antidepressant therapy in both groups, among eligible participants who completed the preceding phases. It is not a comparison of starting brexpiprazole with receiving no antidepressant treatment.
The primary endpoint also illustrates why time-to-event methods matter. Relapse can occur at different times, and the analysis uses more information than a simple yes-or-no count at one visit. The hazard ratio and its confidence interval express the between-group comparison across observed follow-up, while the medians offer a compact description of event timing. Reading both together prevents the median from being mistaken for the whole analysis.
The result is a useful example of the distinction between absence of clear statistical evidence and evidence of no difference. The confidence interval includes the equal-hazards value and remains broad; the finding is inconclusive about a range of possible effects rather than a demonstration that the treatments perform identically.
The registry also presents secondary measures of symptoms, disability, and relapse. These outcomes show why multiplicity and analysis populations matter: several related questions can be asked, but a set of secondary tests is not automatically a set of confirmatory conclusions. Interpreting the trial requires attention to the prespecified hierarchy and missing-data procedures, details that are not reported in the registry record.
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 time-to-relapse analysis counts participants with impending relapse, according to the registry’s description, rather than presenting an analysis count equal to the full Phase C randomized groups. The relationship between these analysis counts and all randomized participants is not fully explained in the registry record. This makes the endpoint-specific population important to keep in view when interpreting the result.
The primary endpoint is composite. Its criteria include rating-scale changes, hospitalization, discontinuation for specified reasons, and suicidality criteria. The registry does not report component-specific results for this primary comparison, so it is not possible to determine from the posted result which criteria contributed most to the overall endpoint.
The original sample-size justification, missing-data strategy, interim analyses, detailed censoring rules, and multiplicity plan are not reported in the registry record. These omissions limit assessment of the design’s intended precision, the robustness of the analyses, and how the secondary findings should be treated. The planning illustrations based on observed effects do not fill that gap because they are not the trial’s original design calculations.
The staged design also defines the population entering Phase C: eligible participants had completed earlier treatment phases. The Phase C result therefore pertains to those who reached and entered the randomized phase, not necessarily every person enrolled at the beginning of the study. The registry figures do not establish how outcomes would compare in people who did not progress to Phase C.
Finally, the posted primary result is an estimate with a broad confidence interval, and the reported medians and full ranges are limited summaries of the event-time data. These features call for a cautious interpretation rather than a definitive claim about equivalence, absence of effect, or the result for each relapse component.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: A Trial to Evaluate the Efficacy, Safety & Tolerability of Brexpiprazole in the Maintenance Treatment of Adults With Major Depressive Disorder — NCT03538691.
- Registry record last updated 2023-10-12; status last verified 2023-10.
- Results first posted 2023-10-12.
- 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
NCT03538691 is a completed Phase 3, multicenter, randomized, parallel-group trial of brexpiprazole as adjunctive maintenance treatment for adults with major depressive disorder. Total enrollment was 1149. Eligible participants completing the earlier phases entered Phase C and received brexpiprazole plus protocol-specified antidepressant therapy or matching placebo plus the same antidepressant therapy for up to 26 weeks.
The primary endpoint was time to relapse by criteria defined in a blinded addendum. The reported median was 63 days in each group. The sponsor-reported Log Rank hazard ratio was 1.138, with a 95% confidence interval from 0.776 to 1.669 and p=0.510. The interval includes 1, so the primary analysis does not show a statistically clear difference between groups.
Several secondary outcomes and serious adverse event counts are also posted. The registry record does not report the original sample-size justification, multiplicity strategy, missing-data procedures, or detailed analysis plan. The findings should be interpreted as applying to the Phase C population, endpoints, and follow-up described in the record.