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 Efficacy of Lu AA21004 on Cognitive Dysfunction in Major Depressive Disorder (NCT01564862), a randomized phase 2 study. The primary outcome is Change From Baseline to Week 8 in the Digit Symbol Substitution Test (DSST).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01564862 |
| Phase | Phase 2 |
| Condition | Depressive Disorder, Major |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Quadruple |
| Enrollment | 602 |
| Arms in the primary outcome | 3 |
| Lead sponsor | Takeda |
| Results posted | Yes |
2. Clinical Question
Population
Adults with major depressive disorder were enrolled. The primary analysis used a Full Analysis Set: randomized participants who received at least one dose of study drug and had at least one valid post-baseline assessment for the primary efficacy measure. Participants with baseline Digit Symbol Substitution Test scores > 70 were excluded from that analysis.
Intervention
Vortioxetine, identified in the record as Lu AA21004, was given once daily. The described regimen began with 10 mg for one week, followed by dose adjustment to a maximum of 20 mg for up to 7 weeks.
Comparator
The study included matching placebo capsules once daily and an active-reference duloxetine group. Duloxetine was given at 60 mg for up to 8 weeks, with a 30 mg taper-down period for one week. The placebo regimen included a one-week taper-down period.
Primary question
The primary question was whether change from baseline to Week 8 in the Digit Symbol Substitution Test differed between each active-treatment group and placebo. The reported endpoint is the adjusted least-squares mean change, measured in correct symbols. The record also reports a direct comparison between the two active-treatment groups.
3. Trial Design
This was a phase 2, randomized, double-blind, parallel-group, placebo-controlled, active-referenced study of Lu AA21004 for cognitive dysfunction in adults with major depressive disorder. The registry records quadruple masking, but it does not specify which people or roles were masked. Enrollment was 602, and the study status is completed. The record lists a start in 2012-04 and primary completion in 2014-02.
Participants were assigned to vortioxetine, duloxetine, or matching placebo. Vortioxetine was administered orally once daily, starting at 10 mg for one week, with dose adjustment up to 20 mg for up to 7 weeks. Duloxetine was administered at 60 mg for up to 8 weeks, followed by a 30 mg once-daily taper-down for one week. The placebo description specifies matching capsules once daily for up to 9 weeks, including a one-week taper-down period.
The primary outcome was change from baseline to Week 8 in the Digit Symbol Substitution Test. The primary analysis used an ANCOVA model with treatment and center as fixed factors and baseline score as a covariate. The Full Analysis Set required randomization, at least one dose, and at least one valid post-baseline primary efficacy assessment; participants with baseline scores > 70 were excluded. These analysis-set criteria mean the primary outcome counts need not match enrollment. The original allocation details, trial-specific sample-size justification, and complete statistical analysis plan 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: Participants with a diagnosis of major depressive disorder were enrolled equally in 1 of 3 treatment groups, once a day placebo, 10 to 20 mg flexible dose of vortioxetine, or 60 mg duloxetine.
Overall Study
| Stage | Vortioxetine (Lu AA21004) | Duloxetine | Placebo |
|---|---|---|---|
| STARTED | 198 | 210 | 194 |
| Received Treatment | 196 | 207 | 191 |
| COMPLETED | 168 | 176 | 164 |
| NOT COMPLETED | 30 | 34 | 30 |
Reasons for not completing this period:
| Reason | Vortioxetine (Lu AA21004) | Duloxetine | Placebo |
|---|---|---|---|
| Pretreatment Event or Adverse Event | 6 | 12 | 6 |
| Major Protocol Deviation | 3 | 3 | 4 |
| Lost to Follow-up | 10 | 8 | 6 |
| Voluntary Withdrawal | 9 | 6 | 8 |
| Lack of Efficacy | 1 | 5 | 6 |
| Other reason(s) | 1 | 0 | 0 |
Analysis population for the primary outcome, as defined in the registry: Full Analysis Set included all randomized participants who received at least one dose of study drug and had at least 1 valid post-baseline value for assessment of primary efficacy. Participants with scores of \> 70 at Baseline were excluded.
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 | Vortioxetine (Lu AA21004) | Duloxetine | Placebo | Total |
|---|---|---|---|---|---|
| Participants analysed | 198 | 210 | 194 | 602 | |
| Age, Continuous | years | 44.2 (SD 12.21) | 45.7 (SD 11.46) | 45.0 (SD 12.07) | 45.0 (SD 11.90) |
| Age, Customized: ≤ 55 years | participants | 158 | 164 | 152 | 474 |
| Age, Customized: > 55 years | participants | 40 | 46 | 42 | 128 |
| Sex: Female, Male: Female | Participants | 135 | 138 | 119 | 392 |
| Sex: Female, Male: Male | Participants | 63 | 72 | 75 | 210 |
| Race/Ethnicity, Customized: Hispanic or Latino | participants | 8 | 7 | 15 | 30 |
| Race/Ethnicity, Customized: Non-Hispanic and Non- Latino | participants | 90 | 104 | 82 | 276 |
| Race/Ethnicity, Customized: Not-Specified | participants | 100 | 99 | 97 | 296 |
| Race/Ethnicity, Customized: Caucasian (or White, including Hispanic) | participants | 169 | 176 | 171 | 516 |
| Race/Ethnicity, Customized: Black | participants | 28 | 27 | 20 | 75 |
| Race/Ethnicity, Customized: Asian | participants | 1 | 6 | 1 | 8 |
| Race/Ethnicity, Customized: American Indian or Alaska Native | participants | 0 | 1 | 2 | 3 |
| Height | cm | 168.2 (SD 9.17) | 169.7 (SD 9.14) | 169.0 (SD 9.43) | 169.0 (SD 9.25) |
| Weight | kg | 81.84 (SD 22.068) | 81.68 (SD 20.965) | 80.96 (SD 20.316) | 81.50 (SD 21.099) |
| Body Mass Index (BMI) | kg/m^2 | 28.86 (SD 7.334) | 28.39 (SD 7.312) | 28.27 (SD 6.354) | 28.51 (SD 7.018) |
| Smoking Classification: Never Smoked | participants | 95 | 109 | 105 | 309 |
| Smoking Classification: Current Smoker | participants | 73 | 68 | 56 | 197 |
| Smoking Classification: Past Smoker | participants | 30 | 33 | 33 | 96 |
| Alcohol Consumption: Never | participants | 89 | 84 | 87 | 260 |
| Alcohol Consumption: Once Monthly or Less Often | participants | 67 | 73 | 51 | 191 |
| Alcohol Consumption: Once a Week | participants | 23 | 31 | 29 | 83 |
| Alcohol Consumption: 2 to 6 Times per Week | participants | 15 | 19 | 24 | 58 |
| Alcohol Consumption: Daily | participants | 4 | 3 | 3 | 10 |
6. Primary Endpoint
The registry lists the primary outcome as Change From Baseline to Week 8 in the Digit Symbol Substitution Test (DSST), measured over Baseline and Week 8.
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | Correct symbols |
| Endpoint classification | Continuous Endpoint |
The primary endpoint was change from baseline to Week 8 in the Digit Symbol Substitution Test (DSST), expressed as the number of correct symbols. The test asks participants to copy symbols paired with simple geometric shapes or numbers within a specified time. Its possible score ranges from 0 to 133. As described in the record, a higher number of correct symbols reflects greater objective cognitive functioning, and an increase in score represents improvement in an integrated measure of cognitive function.
The DSST is used to capture performance that draws on several abilities rather than a single narrow task. The registry description identifies speed, memory, executive function, and visual scanning as relevant contributions. That breadth makes the test a measure of task performance across several cognitive demands, but it does not make the score a direct measure of every aspect of cognition or daily functioning.
The reported arm values are least-squares means, adjusted using the ANCOVA model described in the record, with standard errors as the dispersion measure. The primary comparison concerns adjusted change in correct symbols, not simply the raw score at Week 8. An increase is the favorable direction according to the endpoint description, but statistical evidence for a difference should be read alongside the estimate’s confidence interval and the sponsor’s reported analysis.
7. Results Posted in the Registry
- Vortioxetine (Lu AA21004): mean 4.60 versus 2.85 on control; difference 1.75 (95% CI 0.26 to 3.24), standardized effect d = 0.25; z-test p = 0.021.
- Duloxetine: mean 4.06 versus 2.85 on control; difference 1.21 (95% CI -0.25 to 2.67), standardized effect d = 0.17; z-test p = 0.104.
Mean difference: Vortioxetine (Lu AA21004)
95% CI: 0.26 to 3.24
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Change From Baseline to Week 8 in the Perceived Deficits Questionnaire (PDQ) Attention/Concentration and Planning/Organization Subscore | Continuous Endpoint | Mean difference | -2.60 (-4.15 to -1.05) | 120 per arm |
| Clinical Global Impressions-Improvement (CGI-I) Score at Week 8 | Continuous Endpoint | Mean difference | -0.29 (-0.53 to -0.05) | 229 per arm |
| Change From Baseline to Week 8 in the Trail Making Test (TMT-A) | Continuous Endpoint | Mean difference | -1.05 (-3.81 to 1.71) | 2,358 per arm |
Change From Baseline to Week 8 in the Perceived Deficits Questionnaire (PDQ) Attention/Concentration and Planning/Organization Subscore
- 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:
- Vortioxetine (Lu AA21004): mean -8.90 versus -6.30 on control; difference -2.60 (95% CI -4.15 to -1.05), standardized effect d = -0.36; z-test p = 0.001.
- Duloxetine: mean -9.30 versus -6.30 on control; difference -3.00 (95% CI -4.53 to -1.47), standardized effect d = -0.42; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Vortioxetine (Lu AA21004) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Duloxetine than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Clinical Global Impressions-Improvement (CGI-I) Score at Week 8
- 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:
- Vortioxetine (Lu AA21004): mean 2.35 versus 2.64 on control; difference -0.29 (95% CI -0.53 to -0.05), standardized effect d = -0.26; z-test p = 0.017.
- Duloxetine: mean 2.23 versus 2.64 on control; difference -0.40 (95% CI -0.64 to -0.17), standardized effect d = -0.37; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Vortioxetine (Lu AA21004) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Duloxetine than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Change From Baseline to Week 8 in the Trail Making Test (TMT-A)
- 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:
- Vortioxetine (Lu AA21004): mean -7.70 versus -6.65 on control; difference -1.05 (95% CI -3.81 to 1.71), standardized effect d = -0.08; z-test p = 0.455.
- Duloxetine: mean -8.06 versus -6.65 on control; difference -1.41 (95% CI -4.13 to 1.31), standardized effect d = -0.11; z-test p = 0.310.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Vortioxetine (Lu AA21004) 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 Duloxetine and the control. The interval gives the range of effects that remain compatible with the data.
The record lists secondary outcomes spanning perceived cognitive difficulties, clinician-rated improvement, and several cognitive tasks. These include the Perceived Deficits Questionnaire (PDQ), Clinical Global Impressions-Improvement (CGI-I), Trail Making Tests, Stroop, Groton Maze Learning, Detection, and Identification tasks. The available posted results cover a subset of those measures in detail. Taken as a group, they add context about different facets of performance and assessment, but they do not all measure the same outcome as the DSST.
The sponsor reports differences versus placebo for the PDQ subscore and CGI-I, while the posted comparison for TMT-A does not have a corresponding sponsor analysis in the registry record. The approximate TMT-A comparisons have confidence intervals that include zero. These patterns should not be collapsed into one overall claim about cognitive benefit: measures differ in content, scale, direction, and analysis, and the sponsor-reported findings are not interchangeable with the primary endpoint result.
Secondary outcomes are generally less decisive when many endpoints are examined and the multiplicity procedure is not reported. Without knowing whether and how the analysis accounted for the set of tests, an unadjusted p-value can overstate the strength of evidence across the complete outcome family. The registry record does not report a multiplicity adjustment or identify which secondary outcomes, if any, were designated as key confirmatory tests. The secondary results are therefore most useful as supporting or exploratory context, interpreted in relation to their estimates and uncertainty rather than as independent confirmation of the primary finding.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Change From Baseline to Week 8 in the Perceived Deficits Questionnaire (PDQ) Attention/Concentration and Planning/Organization Subscore
- Clinical Global Impressions-Improvement (CGI-I) Score at Week 8
- Change From Baseline to Week 8 in the Trail Making Test (TMT-A)
- Change From Baseline to Week 8 in the Trail Making Test B (TMT-B)
- Change in Time From Baseline to Week 8 in the Stroop Test
- Change From Baseline to Week 8 in the Groton Maze Learning Test (GMLT)
- Change From Baseline to Week 8 in the Detection Task (DT)
- Change From Baseline to Week 8 in the Identification Task (IT)
9. Statistical Interpretation
In the primary endpoint results, the adjusted mean change was 4.6 correct symbols for vortioxetine, 4.06 for duloxetine, and 2.85 for placebo. The sponsor’s ANCOVA result for vortioxetine versus placebo was a least-squares mean difference of 1.75, with a 95% confidence interval from 0.28 to 3.21 and p = 0.019. The interval is above zero, so the posted sponsor analysis indicates a positive adjusted difference for that comparison. This describes the observed trial result; it does not establish how large or important the difference would be in other settings.
For duloxetine versus placebo, the sponsor reported a least-squares mean difference of 1.21, with a 95% confidence interval from -0.23 to 2.65 and p = 0.099. That interval includes zero, so the estimate is compatible with both a positive difference and little or no difference under the analysis. The active-treatment comparison was 0.54, with a 95% confidence interval from -0.89 to 1.96 and p = 0.460. The record therefore does not show a clear separation between the active groups on this endpoint.
These are adjusted estimates from the sponsor’s ANCOVA, while the posted recalculation is an unadjusted approximation based on summary statistics. The recalculated p-values are 0.021 for vortioxetine versus placebo and 0.104 for duloxetine versus placebo. Because the record indicates a discrepancy between the sponsor analysis and the recalculation, the sponsor’s own analysis takes precedence. The recalculation can be read as a check based on available summaries, not as a replacement analysis.
The results are specific to the recorded endpoint, analysis set, and Week 8 time point. They do not answer every question about cognitive performance, depression symptoms, functioning, or longer-term outcomes. The record does not report whether the primary comparison was adjusted for multiple testing or describe the original sample-size assumptions, so neither should be inferred from these results.
10. Statistical Methods Explained
The primary endpoint is continuous: it is a score measuring the number of correct symbols, and the analysis focuses on change from baseline. For a continuous outcome, an arm mean summarizes the center of the group’s measured results. The registry reports least-squares means rather than only unadjusted arithmetic averages. Least-squares means are model-based estimates that account for the factors and covariates included in the stated model.
The primary analysis used analysis of covariance, or ANCOVA. In general, ANCOVA compares outcome values across treatment groups while accounting for baseline values and specified factors. In this trial, the record says treatment and center were fixed factors and the baseline value was a covariate. Including baseline score can help account for starting-score differences in the model; including center accounts for the trial center factor as specified. The record does not give further details about model diagnostics, missing-data handling, or the exact implementation.
A least-squares mean difference is the model-based contrast between two groups. For the primary outcome, a positive difference favors the group with the higher adjusted change because the endpoint description says an increase in correct symbols represents improvement. The estimate alone does not show its precision; the confidence interval supplies a range of values compatible with the data and analysis. A p-value addresses how inconsistent the observed result is with a specified null hypothesis under the analysis assumptions, but it does not measure the probability that the null hypothesis is true or the probability that the result will replicate.
Why compare adjusted and unadjusted results?
The recalculated comparisons use posted arm summaries and approximate standard deviations derived from the standard errors. They are simple, unadjusted re-calculations rather than the trial’s ANCOVA. The sponsor’s analysis incorporates the stated baseline and center adjustments, so the two approaches can produce slightly different confidence limits and p-values. The record flags a discrepancy; accordingly, the sponsor’s own result is the principal reported analysis and takes precedence over the approximate recalculation. A difference between the two does not by itself identify an error or explain its cause.
The registry also reports a standard error for each arm’s least-squares mean. A standard error describes the uncertainty in an estimated mean, not the spread of individual participant scores. It should not be interpreted as a standard deviation. The comparison’s confidence interval is more directly useful for considering the range of plausible group differences under the fitted analysis.
What does the Full Analysis Set mean?
The primary analysis set included randomized participants who received at least one dose and had at least one valid post-baseline primary efficacy value. The registry further states that people with baseline DSST scores > 70 were excluded. Thus, the analysis population is defined by post-randomization treatment exposure and outcome availability, as well as the baseline-score exclusion. The primary endpoint counts represent that analysis population, not necessarily everyone randomized or enrolled.
The record does not report a detailed missing-data method for the primary endpoint. Requiring a valid post-baseline measure defines who was included, but it does not explain how missing follow-up values were handled in the model or whether sensitivity analyses were conducted. It also does not report the trial-specific multiplicity procedure. Those gaps matter when interpreting a collection of primary and secondary tests, because the chance of at least one apparently notable finding can increase when many hypotheses are examined.
Other reported secondary outcomes use different measures, including patient-reported cognitive difficulties, clinician ratings, and cognitive task performance. Their scales and directions are not necessarily interchangeable with the DSST. Each outcome should be interpreted according to its own definition and analysis, rather than treating all score changes as equivalent evidence about the same construct.
11. Confidence Intervals and Precision
A confidence interval expresses uncertainty around an estimated treatment contrast. In general, a wider interval indicates less precision, while a narrower interval indicates greater precision. The interval is not a guarantee that the true effect lies inside it, and it does not describe the range of individual participant responses. Its interpretation depends on the analysis and its assumptions.
For the sponsor’s primary comparison of vortioxetine with placebo, the estimated difference was 1.75 correct symbols, with a 95% confidence interval from 0.28 to 3.21. The interval is entirely above zero, but it spans a range of effect sizes rather than identifying one exact value. Its lower end is relatively close to zero compared with its upper end, so the magnitude remains uncertain even though the reported interval excludes zero.
For duloxetine versus placebo, the 95% confidence interval ranged from -0.23 to 2.65 around the estimate of 1.21. Because the interval includes zero, the data do not sharply distinguish a positive difference from no difference under the sponsor’s analysis. The active-treatment comparison’s interval, from -0.89 to 1.96, also includes zero and allows differences in either direction.
The confidence intervals in the registry are based on the sponsor’s ANCOVA. The re-calculated intervals are approximate and differ somewhat, so the sponsor analysis is the appropriate reference for the reported trial inference. Precision also depends on the analysis population, endpoint measurement, and handling of unavailable values. Details about missing-data sensitivity analyses 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 | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 252 | 337 |
| 75% of the observed effect | 448 | 600 |
| 50% of the observed effect | 1,007 | 1,348 |
The sample-size figures are planning illustrations based on the observed effect, not the original design assumptions for this trial. The listed assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each row considers detecting the stated fraction of the observed effect. For these continuous outcomes, the figures are participants per arm; the registry’s note about total event counts applies to time-to-event calculations, not these displayed comparisons.
The 80% power column indicates the number of participants per arm estimated to give an 80% chance of rejecting the null hypothesis under the planning assumptions if the effect used for planning were the true effect. The 90% power column uses a higher target chance of detecting that assumed effect, and therefore generally requires more participants per arm. These are planning quantities, not a statement about the probability that the trial result is correct. This is not observed power.
The rows reduce the effect used for planning from 100% of the observed effect to 75% and 50%. Smaller assumed effects require more participants per arm to achieve the same target power, because a smaller group difference is harder to distinguish from random variation. For example, the primary vortioxetine comparison’s planning figures rise from 252 participants per arm for 80% power at 100% of the observed effect to 448 at 75% and 1,007 at 50%. These figures should not be treated as a recommended design without considering the intended endpoint, analysis, allocation, and other design choices.
The original trial sample-size justification and design assumptions are not reported in the registry record. The displayed calculations are therefore retrospective illustrations using the observed effect, not evidence that the trial was planned around these values.
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, Δ is the difference in means to detect and σ is the common standard deviation.
Worked calculation for this trial
- Observed difference Δ = 1.750; pooled standard deviation σ = 7.008.
- n = 2 × (1.96 + 0.842)2 × 7.0082 / 1.7502 = 251.7, rounded up to 252 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
delta <- 1.75 # observed difference in means
sigma <- 7.00779620641099 # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^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 (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")
# Simulation: exact two-sample t-test using simulated means and variances
set.seed(1564862)
n <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n)) # difference in sample means
s2 <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1)) # pooled sample variance
tstat <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))
Output from running the code
100% of observed effect: n per arm = 252 (80% power), 337 (90% power)
75% of observed effect: n per arm = 448 (80% power), 600 (90% power)
50% of observed effect: n per arm = 1,007 (80% power), 1,348 (90% power)
power.t.test: 252.7
Simulated power at n = 252 per arm: 0.800 (20000 replicates)
The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-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 |
|---|---|---|---|
| ANCOVA | LS mean difference 1.75 | 0.28 to 3.21 | 0.019 |
| ANCOVA | LS mean difference 1.21 | -0.23 to 2.65 | 0.099 |
| ANCOVA | LS mean difference 0.54 | -0.89 to 1.96 | 0.460 |
The registry reports the sponsor’s primary ANCOVA comparisons as least-squares mean differences. For vortioxetine versus placebo, the sponsor reported 1.75, a 95% confidence interval from 0.28 to 3.21, and p = 0.019. For duloxetine versus placebo, the reported difference was 1.21, a 95% confidence interval from -0.23 to 2.65, and p = 0.099. The direct active-treatment comparison was 0.54, with a 95% confidence interval from -0.89 to 1.96 and p = 0.460.
The simple recalculations from arm summaries produce similar estimated differences but not identical inferential results. Their unadjusted p-values are 0.021 for vortioxetine versus placebo and 0.104 for duloxetine versus placebo. The recalculated confidence limits also differ slightly from the sponsor’s intervals. The discrepancy flag reflects that the calculation methods and posted results do not match exactly.
The recalculations do not reproduce the sponsor’s adjustment for baseline score and center. They use summary statistics and an approximate standard deviation, so they are not a substitute for the trial model. The sponsor’s own analysis takes precedence. The recalculations are best read as an independent, limited check on the scale and direction of the reported contrasts, not as a competing primary result.
15. Multiplicity, Missing Data and Analysis Populations
The trial has a primary endpoint and a broad set of secondary outcomes. When several comparisons and outcomes are tested, the chance of obtaining at least one small p-value by chance can increase. Statistical procedures can address this multiplicity, for example by adjusting the threshold for interpreting a family of tests or by specifying a sequence of hypotheses in advance. The registry record does not report whether such a procedure was used, which comparisons formed any testing family, or whether the secondary analyses were intended to be confirmatory.
This reporting gap affects how strongly secondary p-values can be interpreted as evidence across the whole study. A nominally small p-value for an individual secondary outcome does not, by itself, establish that the overall collection of findings is robust to multiple testing. The same issue does not erase the reported endpoint estimates; it limits how much weight should be placed on isolated significance labels without a stated testing plan.
The primary Full Analysis Set required randomization, receipt of at least one dose, and a valid post-baseline primary efficacy assessment. Participants with baseline DSST scores > 70 were excluded. The registry does not report a detailed account of missing outcome values, the method used to handle missingness, or sensitivity analyses assessing the impact of missing data. It therefore is not possible to determine from the registry record whether the analysis results are sensitive to different assumptions about unavailable measurements.
The record names the ANCOVA factors and covariate for the primary endpoint, but does not provide a full statistical analysis plan, the original sample-size justification, or details of interim analyses. Those items are not reported in the registry record. Their absence should not be filled by assumptions about the study protocol.
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 |
|---|---|---|---|
| Vortioxetine (Lu AA21004) | 1 | 196 | 0.5% |
| Duloxetine | 1 | 207 | 0.5% |
| Placebo | 2 | 191 | 1.0% |
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 |
|---|---|
| Vortioxetine (Lu AA21004) | 73 of 196 |
| Duloxetine | 84 of 207 |
| Placebo | 41 of 191 |
Most frequent serious adverse event terms
| Event term | Organ system | Vortioxetine (Lu AA21004) | Duloxetine | Placebo |
|---|---|---|---|---|
| Acute myocardial infarction | Cardiac disorders | 0 of 196 | 0 of 207 | 1 of 191 |
| Craniocerebral injury | Injury, poisoning and procedural complications | 0 of 196 | 1 of 207 | 0 of 191 |
| Subdural haematoma | Injury, poisoning and procedural complications | 0 of 196 | 1 of 207 | 0 of 191 |
| Depression | Psychiatric disorders | 0 of 196 | 0 of 207 | 1 of 191 |
| Suicide attempt | Psychiatric disorders | 1 of 196 | 0 of 207 | 0 of 191 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Vortioxetine (Lu AA21004) | Duloxetine | Placebo |
|---|---|---|---|---|
| Nausea | Gastrointestinal disorders | 40 of 196 | 43 of 207 | 8 of 191 |
| Headache | Nervous system disorders | 20 of 196 | 24 of 207 | 16 of 191 |
| Dry mouth | Gastrointestinal disorders | 6 of 196 | 16 of 207 | 9 of 191 |
| Nasopharyngitis | Infections and infestations | 7 of 196 | 8 of 207 | 11 of 191 |
| Diarrhoea | Gastrointestinal disorders | 11 of 196 | 6 of 207 | 5 of 191 |
| Dizziness | Nervous system disorders | 6 of 196 | 11 of 207 | 5 of 191 |
| Decreased appetite | Metabolism and nutrition disorders | 3 of 196 | 12 of 207 | 1 of 191 |
Serious events with the highest arm-level rate: acute myocardial infarction (0.5%), depression (0.5%), suicide attempt (0.5%), craniocerebral injury (0.5%), subdural haematoma (0.5%).
The registry reports serious adverse events affecting 1 participant in the vortioxetine group, 1 in the duloxetine group, and 2 in the placebo group. The corresponding numbers at risk were 196, 207, and 191. These are arm-level counts as recorded for the serious-adverse-event summary. They should be read as descriptive trial safety information, not as a formal comparison establishing a difference between groups.
The record lists acute myocardial infarction, depression, suicide attempt, craniocerebral injury, and subdural haematoma among the serious-event terms, each with a reported percentage of 0.5%. The listed terms do not identify an arm for each event in the registry record, so no group attribution should be inferred from that list. The registry also reports other adverse events affecting 73 participants in the vortioxetine group, 84 in the duloxetine group, and 41 in the placebo group; those are separate from the serious-event counts.
Deaths are not reported in the registry record. These counts do not describe event timing, duration, causal attribution, or the full clinical context. They are not sufficient on their own to establish comparative safety.
17. What the Result Does, and Does Not, Mean
The primary endpoint measures a specific performance task: the number of correct symbols completed on the DSST, with an increase described as improvement in an integrated measure of cognitive function. The sponsor’s adjusted analysis found a positive difference for vortioxetine versus placebo at Week 8, with a confidence interval excluding zero. The duloxetine-versus-placebo interval included zero, as did the direct comparison between the active groups. These statements describe the posted results and their uncertainty; they do not determine whether an observed score difference is important to participants in daily life.
The endpoint is not a complete measure of major depressive disorder or of every aspect of cognition. A test score can reflect several abilities at once, and the record does not establish that a difference on this task translates into broader functioning or persists beyond the assessed time point. Secondary outcomes may provide additional perspectives, but they have their own measurement properties and are subject to uncertainty and multiplicity concerns.
The record describes a phase 2 study with a specific analysis population, treatment regimens, and Week 8 assessment. Its findings should be understood within those conditions. The results alone do not establish what would occur in other populations, under different regimens, or over longer follow-up. Nor does a p-value state the probability that a treatment effect is real. The estimates, confidence intervals, study methods, and missing reporting details all contribute to interpretation.
No medical advice or treatment recommendation follows from these registry results. The statistical conclusion is narrower: the sponsor’s analysis reports a positive adjusted DSST contrast between vortioxetine and placebo, while the precision and meaning of the effect remain bounded by the reported interval, endpoint, design, and analysis information.
18. Why This Trial Matters Statistically
This trial illustrates why a treatment comparison should be read through its endpoint, analysis population, and model rather than through a single p-value. The DSST is a continuous measure with a defined favorable direction, and the sponsor used ANCOVA to account for baseline score and center. The resulting least-squares mean difference is therefore a model-based contrast, not merely a subtraction of raw group averages.
It also demonstrates the importance of distinguishing an adjusted sponsor analysis from a summary-statistic recalculation. The recalculated estimates are close in direction, but the reported p-values and confidence intervals differ. Because the record flags a discrepancy, the sponsor’s own analysis is the primary reference. This distinction helps prevent an approximate audit from being mistaken for the trial’s prespecified analysis.
The presence of an active-reference group and multiple secondary measures broadens the questions that can be explored, but it also makes multiplicity and reporting transparency important. The registry does not report the multiplicity strategy or full statistical plan. Without those details, secondary findings should be treated as contextual evidence rather than a collection of separate definitive conclusions.
Finally, the study shows why statistical significance and practical meaning are different considerations. Confidence intervals communicate uncertainty in the estimated contrast, while the endpoint’s interpretation and the study context determine what the score difference can reasonably represent. The registry result is informative about one measured outcome at one follow-up time; it is not a universal statement about cognition or clinical outcomes.
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 analysis population was narrower than enrollment: it required receipt of study drug and a valid post-baseline primary assessment, and excluded participants with baseline DSST scores > 70. The registry record does not provide enough information to evaluate the effect of missing assessments or the baseline-score exclusion on the estimates. Details of missing-data methods and sensitivity analyses are not reported in the registry record.
The primary inference is based on an ANCOVA described only by its treatment and center fixed factors and baseline covariate. Further model details, diagnostics, and the original statistical analysis plan are not reported. The registry also does not report a multiplicity procedure, despite the range of secondary outcomes and comparisons. This limits interpretation of the secondary p-values as a coordinated body of evidence.
The approximate recalculation is based on arm summary values and standard errors, not participant-level data or the sponsor’s full adjusted model. It produces slightly different results from the sponsor analysis. The discrepancy means the recalculated result should not replace the sponsor’s ANCOVA; the sponsor’s own analysis takes precedence.
The primary endpoint is a test score assessed at Week 8. The record does not establish how the observed score contrast relates to everyday functioning or longer-term outcomes. The listed secondary results cover only some of the measures described in the study, and their scales and directions vary. The record also does not provide the trial’s original sample-size justification, interim-analysis details, or a full account of serious-event context. These omissions constrain assessment of design rationale, robustness, and safety patterns.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Efficacy of Lu AA21004 on Cognitive Dysfunction in Major Depressive Disorder — NCT01564862.
- Registry record last updated 2015-02-05; status last verified 2015-02.
- Results first posted 2015-02-05.
- 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.
Continue through the Clinical Biostats statistical pathway
Use this trial's endpoint as a starting point for deeper study of effect measures, confidence intervals, and sample-size planning.
23. Record Summary
NCT01564862 is a completed phase 2 randomized, double-blind, parallel-group study of vortioxetine (Lu AA21004), duloxetine, and placebo in adults with major depressive disorder. Enrollment was 602. The primary endpoint was change from baseline to Week 8 in correct symbols on the Digit Symbol Substitution Test, analyzed using ANCOVA with treatment and center as fixed factors and baseline value as a covariate.
The sponsor reported a positive adjusted DSST difference for vortioxetine versus placebo, while the duloxetine-versus-placebo and active-treatment comparisons had confidence intervals that included zero. Summary-statistic recalculations differ somewhat from the sponsor’s results; the sponsor analysis takes precedence. The registry does not report the multiplicity strategy, original sample-size justification, or detailed missing-data methods.