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Generalized Anxiety Disorder Phase 3 Continuous Endpoint NCT00730691

Efficacy of Vortioxetine (Lu AA21004) in Treating Generalized Anxiety Disorder: Complete Statistical Analysis

This analysis examines the primary Week 8 anxiety-score outcome in a randomized, double-blind trial of vortioxetine, placebo and duloxetine in adults with generalized anxiety disorder. It also considers the posted secondary outcomes, safety counts, statistical precision and limitations of the registry record.

Trial start: 2008-06  ·  Enrollment: 781  ·  Sponsor: Takeda
Scope of this record

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 Vortioxetine (Lu AA21004) in Treating Generalized Anxiety Disorder (NCT00730691), a randomized phase 3 study. The primary outcome is Change From Baseline in the Hamilton Anxiety (HAM-A) Scale Total Score at Week 8.

781
Enrollment
Phase 3
5
Arms
In the primary outcome
-0.96
Mean difference
Vortioxetine 2.5 mg
-2.62–0.70
95% CI
Two-sided
FeatureRegistry value
ClinicalTrials.gov identifierNCT00730691
PhasePhase 3
ConditionGeneralized Anxiety Disorder
AllocationRandomized
Design modelParallel
MaskingDouble
Enrollment781
Arms in the primary outcome5
Lead sponsorTakeda
Results postedYes

2. Clinical Question

Population

Adults with generalized anxiety disorder were studied. The registry record reports an enrollment of 781. The primary-outcome analysis population was the full analysis set: randomized participants who received at least 1 dose of study drug and had at least 1 postbaseline primary-efficacy assessment. Further eligibility criteria and participant characteristics are not reported in the registry record.

Intervention

Participants were assigned to vortioxetine at 2.5 mg, 5 mg or 10 mg once daily. Each dose was given for 8 weeks, followed by placebo-matching capsules for 1 week. The registry describes the study as a fixed-dose comparison.

Comparator

The main comparator was placebo, given once daily for up to 9 weeks. Duloxetine 60 mg was an active reference: the regimen was 60 mg once daily for 8 weeks, followed by 30 mg once daily for 1 week. The posted primary-outcome comparisons are each against placebo.

Primary question

The primary question was whether the Week 8 change from baseline in the Hamilton Anxiety Scale total score differed between each treatment group and placebo. The registry reports adjusted least-squares means from a mixed model for repeated measurements. Lower HAM-A scores indicate less anxiety symptom burden on the scale; the statistical comparisons describe differences in change, not a complete account of treatment benefit, harms or longer-term outcomes.

3. Trial Design

This was a Phase 3, randomized, double-blind, parallel-group study with placebo control and an active reference. Takeda was the sponsor, and the registry status is completed. Enrollment was 781. The registry lists generalized anxiety disorder as the condition under study.

The five groups were placebo, vortioxetine 2.5 mg, vortioxetine 5 mg, vortioxetine 10 mg and duloxetine 60 mg. Vortioxetine groups received their assigned dose once daily for 8 weeks, then placebo-matching capsules for 1 week. The placebo group received placebo-matching capsules once daily for up to 9 weeks. The duloxetine group received 60 mg once daily for 8 weeks, then 30 mg once daily for 1 week. These descriptions establish the assigned regimens; further details about treatment adherence are not reported in the registry record.

The study start is recorded as 2008-06, and primary completion as 2009-02. The primary endpoint was change from baseline in HAM-A total score at Week 8. The primary analysis used the full analysis set, defined as randomized participants who received at least 1 dose and had at least 1 postbaseline primary-efficacy assessment. The analyzed group counts differ by treatment arm, as expected for an analysis population defined by assessment availability; the registry does not provide a full account of participant flow in the registry record reported.

Eligibility details, the original sample-size justification, planned interim analyses and the protocol’s full statistical plan are not reported in the registry record. The registry also does not report how treatment allocation was generated or concealed.

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 generalized anxiety disorder were enrolled equally in 1 of 5 treatment groups, once a day placebo, 2.5 mg, 5 mg or 10 mg vortioxetine, or 60 mg duloxetine.

Overall Study

StagePlaceboVortioxetine 2.5 mgVortioxetine 5 mgVortioxetine 10 mgDuloxetine 60 mg
STARTED157156156156156
COMPLETED121120117111106
NOT COMPLETED3636394550

Reasons for not completing this period:

ReasonPlaceboVortioxetine 2.5 mgVortioxetine 5 mgVortioxetine 10 mgDuloxetine 60 mg
Adverse Event48111123
Lack of Efficacy44211
Non-compliance with Study Drug61633
Protocol Deviations35375
Withdrawal of Consent79363
Lost to Follow-up118131513
Other11122

Analysis population for the primary outcome, as defined in the registry: The full analysis set (FAS) included all randomized patients who received at least 1 dose of study drug, and had at least 1 postbaseline value for assessment of primary efficacy. A mixed model for repeated measurements (MMRM) based on observed cases was used.

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.

CharacteristicUnitPlaceboVortioxetine 2.5 mgVortioxetine 5 mgVortioxetine 10 mgDuloxetine 60 mgTotal
Participants analysed157156156156156781
Age Continuousyears36.8 (SD 12.12)39.2 (SD 11.90)37.7 (SD 11.96)39.8 (SD 12.33)39.5 (SD 12.28)38.6 (SD 12.14)
Age, Customized: ≤55 yearsparticipants143140147137137704
Age, Customized: >55 yearsparticipants14169191977
Sex: Female, Male: FemaleParticipants102109100105113529
Sex: Female, Male: MaleParticipants5547565143252
Race/Ethnicity, Customized: Caucasian (White, including Hispanic)participants118121124120121604
Race/Ethnicity, Customized: Blackparticipants3531263331156
Race/Ethnicity, Customized: Asianparticipants4060414
Race/Ethnicity, Customized: American Indian or Alaska Nativeparticipants010203
Race/Ethnicity, Customized: Native Hawaiian/ Other Pacific Islanderparticipants010102
Region of Enrollment: United Statesparticipants157156156156156781
Weightkg84.40 (SD 25.426)79.47 (SD 19.893)80.98 (SD 20.312)80.17 (SD 21.420)79.51 (SD 20.090)80.91 (SD 21.558)
Heightcm168.74 (SD 9.605)167.87 (SD 9.139)169.25 (SD 9.282)167.61 (SD 8.378)167.94 (SD 9.300)168.28 (SD 9.147)
Body Mass Index (BMI)kg/m^229.54 (SD 8.478)28.19 (SD 6.651)28.24 (SD 6.589)28.49 (SD 7.058)28.10 (SD 6.325)28.51 (SD 7.064)
Smoking Classification: Never Smokedparticipants9285818582425
Smoking Classification: Current Smokerparticipants4143444343214
Smoking Classification: Ex-smokerparticipants2328312831141
Alcohol Consumption: Neverparticipants4049405344226
Alcohol Consumption: Once monthly or less oftenparticipants7150664964300
Alcohol Consumption: Once a weekparticipants2725312919131
Alcohol Consumption: 2 to 6 times per weekparticipants1730172222108
Alcohol Consumption: Dailyparticipants1223715
Hamilton Anxiety Scale Total Scorescores on a scale24.4 (SD 3.73)25.3 (SD 4.25)25.0 (SD 3.57)25.3 (SD 3.96)25.0 (SD 3.94)25.0 (SD 3.90)
Clinical Global Impression - Severity scale scorescores on a scale4.3 (SD 0.56)4.4 (SD 0.63)4.4 (SD 0.59)4.4 (SD 0.59)4.4 (SD 0.62)4.4 (SD 0.60)
Hospital Anxiety and Depression - Anxiety subscalescores on a scale13.9 (SD 3.23)13.8 (SD 3.40)13.8 (SD 3.70)14.0 (SD 3.02)13.4 (SD 3.70)13.8 (SD 3.41)
Hospital Anxiety and Depression - Depression subscalescores on a scale8.2 (SD 4.12)8.2 (SD 3.83)8.2 (SD 3.94)8.5 (SD 3.59)8.2 (SD 4.00)8.2 (SD 3.89)

6. Primary Endpoint

The registry lists the primary outcome as Change From Baseline in the Hamilton Anxiety (HAM-A) Scale Total Score at Week 8, measured over Baseline to Week 8.

ElementRegistry entry
Result typeLeast Squares Mean
Measure of spreadStandard Error
Unitscores on a scale
Endpoint classificationContinuous Endpoint

The primary endpoint was change from baseline in total score on the Hamilton Anxiety Scale (HAM-A) at Week 8. HAM-A is a clinician-rated scale with 14 items covering anxious mood, tension, fear, insomnia, cognitive symptoms, depressed mood and several somatic symptom areas. Each item is scored from 0 (absent) to 4 (maximum severity), and total scores range from 0 to 56. The registry describes scores below 17 as indicating mild severity, 18-24 as mild to moderate, 25-30 as moderate to severe, and scores above 30 as very severe anxiety.

The endpoint was used to quantify symptom change over the acute treatment period. A change score compares a participant’s Week 8 assessment with baseline; a negative change represents a decrease in the measured score. As a general interpretation of a symptom scale, a lower score indicates less measured symptom burden, but the change score alone does not capture every aspect of a participant’s experience or safety.

The registry reports least-squares means from a mixed model for repeated measurements, with week, baseline score-by-week and treatment-by-week interaction as factors. This approach uses measurements across visits to estimate treatment-group means while accounting for the repeated-measure structure. The reported population was the full analysis set, and the model was based on observed cases. Further details about the model specification, including covariance structure, are not reported in the registry record.

7. Results Posted in the Registry

Mean difference: Vortioxetine 2.5 mg

-0.96

95% CI: -2.62 to 0.70

Recalculated from the posted summary statistics

Primary outcome by arm, with 95% confidence intervals
Primary outcome by arm with 95% confidence intervals-15.6-14.4-13.2-12.0-10.8-9.6Placebo (n=120)Vortioxetine 2.5 mg (n=118)Vortioxetine 5 mg (n=114)Vortioxetine 10 mg (n=111)Duloxetine 60 mg (n=106)scores on a scale (95% CI)
Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Vortioxetine 2.5 mgVortioxetine 5 mgVortioxetine 10 mgDuloxetine 60 mg-4.76-3.44-2.13-0.810.501.82mean difference vs control (95% CI)

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 outcomeTypeEffect measureEstimate (95% CI)Planning size, 80% power
Change From Baseline in Hospital Anxiety and Depression (HAD) - Anxiety Subscale at Week 8Continuous EndpointMean difference0.11 (-0.89 to 1.11)20,713 per arm
Mean Clinical Global Impression Scale-Global Improvement (CGI-I) at Week 8Continuous EndpointMean difference-0.11 (-0.36 to 0.14)1,293 per arm
Change From Baseline in Sheehan Disability Scale (SDS) at Week 8Continuous EndpointMean difference0.20 (-1.57 to 1.97)15,298 per arm

Change From Baseline in Hospital Anxiety and Depression (HAD) - Anxiety Subscale at Week 8

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Vortioxetine 2.5 mgVortioxetine 5 mg-1.44-0.89-0.340.210.761.30mean difference vs control (95% CI)

Mean Clinical Global Impression Scale-Global Improvement (CGI-I) at Week 8

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Vortioxetine 2.5 mgVortioxetine 5 mg-0.41-0.28-0.16-0.040.080.21mean difference vs control (95% CI)

Change From Baseline in Sheehan Disability Scale (SDS) at Week 8

Treatment effect versus the control arm
Forest plot of mean difference vs control (95% CI)Vortioxetine 2.5 mgVortioxetine 5 mg-2.42-1.48-0.530.411.352.30mean difference vs control (95% CI)

The secondary outcomes cover anxiety symptoms, global improvement, disability and response measures. The registry lists 15 secondary outcomes, but the available numerical summaries do not cover every listed outcome or every comparison. The posted results include partial summaries for the Hospital Anxiety and Depression anxiety subscale, Clinical Global Impression-Global Improvement and Sheehan Disability Scale. Results for secondary outcomes without numerical findings are not reported in the registry record.

Across the secondary comparisons with sponsor-reported results, the posted estimates do not show a consistent pattern of clear separation from placebo. The sponsor-reported confidence intervals for the available comparisons include zero, and their p-values are not small. The secondary findings therefore do not provide a clear, consistent statistical counterpoint to the primary outcome pattern. Because these measures assess related but distinct constructs, they should not be treated as interchangeable with the primary HAM-A endpoint.

Secondary outcomes can add context by asking whether the results are reflected in other symptom or functioning measures. However, multiple outcomes and treatment comparisons create more opportunities for chance findings. Unless a multiplicity strategy is specified and applied, an unadjusted secondary p-value does not have the same evidential weight as a single prespecified primary comparison. The registry does not report the multiplicity plan or whether the posted secondary analyses were adjusted for multiple testing.

The registry identifies secondary outcomes at Week 8 and at other assessed weeks, but full numerical results are not available for all listed measures in the registry record reported. No conclusion about unreported outcomes should be inferred from the reported subset. Differences between sponsor analyses and simple recalculations also warrant caution; the sponsor’s reported model-based analyses take precedence where discrepancies are present.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

9. Statistical Interpretation

Clinical Biostats interpretation

At Week 8, the reported placebo least-squares mean change in HAM-A total score was -11.27. The corresponding reported means were -12.23 for vortioxetine 2.5 mg, -11.57 for vortioxetine 5 mg, -11.66 for vortioxetine 10 mg and -13.87 for duloxetine 60 mg. Each group’s mean change was negative, indicating a decline from baseline in the measured score. The group means alone do not establish whether between-group differences are statistically distinguishable or clinically important.

In the sponsor’s reported comparisons against placebo, the estimated least-squares mean differences were -0.96 for vortioxetine 2.5 mg, -0.30 for vortioxetine 5 mg and -0.39 for vortioxetine 10 mg. Their reported 95% confidence intervals were -2.62 to 0.69, -1.96 to 1.35 and -2.06 to 1.27, respectively; each interval includes zero. The associated p-values were 0.255, 0.719 and 0.642. These estimates are compatible with a range of differences, including little or no average separation from placebo, and do not precisely establish a direction or size of difference.

For duloxetine 60 mg versus placebo, the sponsor reported a least-squares mean difference of -2.60, with a 95% confidence interval from -4.30 to -0.89 and p = 0.003. The interval does not include zero. This is the sponsor’s reported statistical comparison; it is not a basis for extending the result to other doses, outcomes, populations or treatment periods.

The recalculated comparisons use unadjusted calculations from the posted arm summaries and are approximate. Because the registry record contains a discrepancy between some recalculated and sponsor-reported results, the sponsor’s own analysis takes precedence. The sponsor’s model-based findings should be interpreted as the primary evidence, while the simple recalculations are supplementary checks rather than replacements for the reported repeated-measures analysis.

The registry record does not report the prespecified multiplicity procedure, if any, or a clinical threshold for a meaningful HAM-A difference. The p-values should therefore be read as reported comparisons, not as a complete accounting of all uncertainty, planned testing or clinical relevance. Statistical evidence of a difference and the practical importance of a difference are separate questions.

10. Statistical Methods Explained

The primary outcome is continuous: it is a scale score, and the reported group summaries are least-squares means with standard errors. The comparisons express differences in average change from baseline between a treatment group and placebo. The estimates are based on a mixed model for repeated measurements (MMRM), rather than a simple comparison of raw participant-level change scores.

What does a least-squares mean represent?

In general, a least-squares mean is a model-based estimate of a group average, adjusted for the terms included in the model. It is not necessarily identical to the ordinary arithmetic mean of all observed scores. The registry says the HAM-A model included week, baseline score-by-week and treatment-by-week interaction as factors. It reports the Week 8 results as least-squares means and least-squares mean differences. Further model details, such as the covariance structure and any additional covariates, are not reported in the registry record.

Why use repeated-measures modeling?

In general, repeated-measures models can use outcome observations collected at multiple visits and account for the fact that measurements from the same participant are related. The registry states that an MMRM based on observed cases was used. It does not report the exact set of visits included in the primary model, the covariance structure, the estimation details or the assumptions made about missing observations. Those details matter when assessing how the model used the available data and how sensitive results might be to departures from its assumptions.

How should a mean difference be read?

The difference is reported as the treatment-group estimate relative to placebo. A negative estimate means the treatment group’s modeled change was more negative than placebo’s modeled change, using the reported score direction. For the primary outcome, the sponsor’s reported estimates for the three vortioxetine doses were close to zero relative to their confidence-interval widths, while the duloxetine estimate was more negative and its reported interval lay below zero. This is a statistical description of the posted results, not a standalone judgment about clinical importance.

What does a confidence interval add?

In general, a confidence interval describes the statistical uncertainty around an estimated effect under the analysis assumptions. A wider interval indicates less precision than a narrower interval. When an interval includes zero for a difference, the data do not exclude no average difference at the confidence level used. When it does not include zero, the interval is inconsistent with zero under that model and confidence procedure. Neither situation identifies the probability that a particular treatment effect is true.

The sponsor reports 95% confidence intervals for the primary comparisons. The MMRM estimates and intervals are the primary model-based results. The simple recalculations are based on posted arm summaries and approximate pooled standard deviations; they do not reproduce the repeated-measures model. They can therefore differ from the sponsor’s estimates, intervals and p-values. With a discrepancy recorded, the sponsor’s own analysis takes precedence.

Why can over-dispersion matter?

In general, over-dispersion means that the variability in observed data is greater than a model’s assumed variability. If a model understates variability, standard errors may be too small and intervals too narrow; if it accounts for variability poorly in another way, uncertainty estimates may also be distorted. This issue is especially relevant to count outcomes, but the general lesson is that model assumptions should match the outcome distribution. The primary outcome is continuous, and the registry does not report a specific over-dispersion assessment. It would be inappropriate to infer that such an assessment was or was not performed.

The reported standard errors describe uncertainty in the model-based group means, not the spread of individual participant outcomes. In general, a standard error becomes smaller when an estimate is more precise, while an individual-level standard deviation describes participant-to-participant variation. Keeping these quantities distinct prevents the group-level estimates from being mistaken for the distribution of individual responses.

The registry identifies the full analysis set and observed-case MMRM, but does not report the trial’s complete statistical analysis plan, model diagnostics, sensitivity analyses, interim analyses or details of handling missing observations. Those omissions limit independent assessment of model robustness and of whether the posted analysis followed the original prespecified plan.

11. Confidence Intervals and Precision

The sponsor’s 95% confidence intervals convey the precision of the Week 8 treatment-versus-placebo estimates under the reported MMRM. For vortioxetine 2.5 mg, the estimated difference was -0.96 and the interval extended from -2.62 to 0.69. For vortioxetine 5 mg, the estimate was -0.30 and the interval extended from -1.96 to 1.35. For vortioxetine 10 mg, the estimate was -0.39 and the interval extended from -2.06 to 1.27. Each interval includes zero and spans effects in both directions, so these estimates do not tightly pin down the size or direction of a difference from placebo.

For duloxetine 60 mg, the reported estimate was -2.60, with an interval from -4.30 to -0.89. That interval lies below zero, but it still spans a range of possible differences. The interval’s position and width describe statistical compatibility under the analysis; they do not determine whether a difference is important to participants. The registry record does not report a threshold for clinical importance on HAM-A.

In general, a confidence interval is a range produced by a statistical procedure that, over repeated use under its assumptions, would cover the underlying parameter at the stated rate. It is not a range containing a specified probability for the fixed effect in this individual trial. Precision depends on factors including variability, analyzed sample size and model structure. The posted primary analysis used different numbers of participants by arm, and the standard errors are reported for the least-squares means.

The recalculated intervals are approximate, unadjusted calculations from posted summaries and should not be treated as replacements for the sponsor’s model-based intervals. Because a discrepancy is recorded, the sponsor’s own results take precedence. The registry does not report intervals for every possible secondary comparison.

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 detectParticipants per arm, 80% powerParticipants per arm, 90% power
100% of the observed effect724969
75% of the observed effect1,2871,723
50% of the observed effect2,8953,875
Sample size needed versus the size of the effect to detect
Sample size needed versus size of effect to detect5001,0002,0005,00010,00040%60%80%100%80% power90% powersize of effect to detect, as % of the effect observed (log vertical scale: participants per arm)
Treat these figures cautiously. The observed difference is imprecise: its confidence interval includes no difference at all. A sample size built on a noisy estimate can be far too small or too large, so the smaller-effect rows are the more cautious guide.
Method and assumptions. Two-sided α = 0.05, 1:1 allocation, two-sample comparison of means with the pooled standard deviation. Standard deviation was approximated from model-based standard errors, so treat it as rough. Calculated for the comparison: Vortioxetine 2.5 mg.

The sample-size figures are planning illustrations based on the observed effect, not a report of the trial’s original design calculation. For this continuous primary outcome, the figures refer to participants per arm, rather than total events. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect set to the stated fraction of the observed effect. The trial’s original sample-size assumptions and justification are not reported in the registry record.

The 80% power column describes the planned number of participants per arm for a hypothetical study to have an 80% chance of detecting the specified effect under those assumptions, if that effect and the assumptions were correct. The 90% power column uses a higher target chance of detection and therefore generally calls for more participants. These are design quantities for hypothetical future studies, not probabilities that the current trial’s result is correct.

The rows that use 100%, 75% and 50% of the observed effect illustrate how the planning requirement changes with the effect size chosen to detect. Smaller effects require more participants for the same target power, because they are harder to distinguish from sampling variability. The calculation is based on the observed estimate, which itself is uncertain; it should not be read as a validated estimate of a true effect.

This is not observed power. The figures do not measure the probability that the completed trial detected an effect, and they do not establish what the original investigators planned. They are conditional illustrations under the listed assumptions. The registry does not report whether the original design used these assumptions or any similar calculation.

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 = 2 (z1−α/2 + z1−β)2 σ2 / Δ2

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

  1. Observed difference Δ = -0.960; pooled standard deviation σ = 6.518.
  2. n = 2 × (1.96 + 0.842)2 × 6.5182 / -0.9602 = 723.6, rounded up to 724 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 <- -0.960000000000001                      # observed difference in means
sigma <- 6.51778434069925                     # 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(730691)
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 = 724 (80% power), 969 (90% power)
 75% of observed effect: n per arm = 1,287 (80% power), 1,723 (90% power)
 50% of observed effect: n per arm = 2,895 (80% power), 3,875 (90% power)
power.t.test: 724.6 
Simulated power at n = 724 per arm: 0.794 (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

MethodEstimate95% CIP-value
Mixed model for repeated measurementsLS Mean Difference -0.96-2.62 to 0.690.255
Mixed model for repeated measurementsLS Mean Difference -0.30-1.96 to 1.350.719
Mixed model for repeated measurementsLS Mean Difference -0.39-2.06 to 1.270.642
Mixed model for repeated measurementsLS Mean Difference -2.60-4.30 to -0.890.003
Where the two analyses differ, rely on the sponsor's. The simple re-calculation above reaches a different conclusion from the sponsor's analysis, usually because the sponsor adjusts for covariates, stratification or repeated measures, or (for event rates) uses a negative binomial model that allows for over-dispersion and so gives wider intervals.

The sponsor’s primary results come from a mixed model for repeated measurements and are reported as least-squares mean differences with 95% confidence intervals and p-values. The recalculations are simple, unadjusted comparisons reconstructed from posted arm summaries. They use approximate pooled variability and do not reproduce the full repeated-measures model, so differences between the two sets of estimates or p-values can occur.

For the primary endpoint, the recalculated estimates are close to the sponsor’s reported estimates, but some displayed values and p-values differ. For example, the sponsor reports p = 0.255 for vortioxetine 2.5 mg versus placebo, while the recalculation reports p = 0.256. The sponsor reports p = 0.719 for vortioxetine 5 mg, compared with a recalculated p = 0.724, and p = 0.642 for vortioxetine 10 mg, compared with a recalculated p = 0.646. The duloxetine comparison has p = 0.003 in both sets of results, although the interval endpoints are not identical.

The registry record flags a discrepancy. In that situation, the sponsor’s own analysis takes precedence because it reflects the reported MMRM rather than a simplified reconstruction. Recalculated results are useful as an independent arithmetic check, but they do not overrule the sponsor’s model-based analysis. The same caution applies to secondary comparisons, where some recalculated summaries differ from the sponsor’s posted estimates.

The registry does not provide enough information to determine why every discrepancy occurs. The full analysis plan, model details and any data-handling decisions are not reported in the registry record.

15. Multiplicity, Missing Data and Analysis Populations

The registry record identifies a primary endpoint and multiple secondary outcomes, with comparisons among several treatment groups. Testing many outcomes or contrasts increases the chance that at least one result will appear notable by chance if each is considered separately. In general, multiplicity procedures can control that risk by adjusting the interpretation or testing thresholds across a family of comparisons. The registry does not report whether such a procedure was planned or used, how the family of tests was defined, or whether secondary p-values were adjusted.

The primary outcome is reported at Week 8, and the description identifies an MMRM with week, baseline score-by-week and treatment-by-week interaction as factors. The registry says the primary population was the full analysis set: randomized participants who received at least 1 dose and had at least 1 postbaseline primary-efficacy assessment. The model was based on observed cases. This describes the analysis population and broad modeling approach, but does not provide the full analysis plan.

Missing-data handling is particularly relevant to repeated assessments because not every participant necessarily contributes every planned measurement. The registry does not report the amount or pattern of missing primary-outcome data, the assumptions used for missing observations, any imputation procedure, or sensitivity analyses addressing missingness. MMRM can use observed repeated measurements under its modeling assumptions, but the record does not establish whether those assumptions are appropriate in this trial.

The registry also does not report interim analyses, stopping rules, the trial’s original sample-size justification or the full prespecified statistical plan. These omissions prevent a complete audit of whether all tests, models and analysis populations followed the original plan. They do not invalidate the posted results, but they limit how fully the choices behind those results can be evaluated.

16. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

ArmParticipants with serious adverse eventsParticipants at riskPercentage
Placebo01550.0%
Vortioxetine 2.5 mg11560.6%
Vortioxetine 5 mg01550.0%
Vortioxetine 10 mg11560.6%
Duloxetine 60 mg31541.9%
Participants with at least one serious adverse event
Serious adverse events by armPlacebo0.0%Vortioxetine 2.5 mg0.6%Vortioxetine 5 mg0.0%Vortioxetine 10 mg0.6%Duloxetine 60 mg1.9%% of participants with at least one serious adverse event

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 2% reporting threshold.

ArmParticipants affected of at risk
Placebo85 of 155
Vortioxetine 2.5 mg100 of 156
Vortioxetine 5 mg104 of 155
Vortioxetine 10 mg111 of 156
Duloxetine 60 mg116 of 154

Most frequent serious adverse event terms

Event termOrgan systemPlaceboVortioxetine 2.5 mgVortioxetine 5 mgVortioxetine 10 mgDuloxetine 60 mg
Angina pectorisCardiac disorders0 of 1550 of 1560 of 1550 of 1561 of 154
Abdominal herniaGastrointestinal disorders0 of 1550 of 1560 of 1551 of 1560 of 154
SomnolenceNervous system disorders0 of 1550 of 1560 of 1550 of 1561 of 154
Benign prostatic hyperplasiaReproductive system and breast disorders0 of 1551 of 1560 of 1550 of 1560 of 154
Sexual abuseSocial circumstances0 of 1550 of 1560 of 1550 of 1561 of 154

Most frequent non-serious adverse event terms

Event termOrgan systemPlaceboVortioxetine 2.5 mgVortioxetine 5 mgVortioxetine 10 mgDuloxetine 60 mg
NauseaGastrointestinal disorders27 of 15526 of 15645 of 15553 of 15657 of 154
HeadacheNervous system disorders20 of 15518 of 15620 of 15525 of 15626 of 154
Dry mouthGastrointestinal disorders10 of 15514 of 15617 of 15521 of 15625 of 154
DizzinessNervous system disorders5 of 15513 of 1569 of 15514 of 15617 of 154
DiarrhoeaGastrointestinal disorders9 of 1559 of 15611 of 15520 of 1566 of 154
Upper respiratory tract infectionInfections and infestations9 of 15512 of 15611 of 15512 of 1568 of 154
SomnolenceNervous system disorders6 of 1557 of 15613 of 1558 of 15618 of 154
NasopharyngitisInfections and infestations7 of 15514 of 1567 of 15512 of 1563 of 154
FatigueGeneral disorders3 of 1556 of 1568 of 1559 of 15615 of 154
ConstipationGastrointestinal disorders6 of 15510 of 1564 of 15512 of 1568 of 154

Serious events with the highest arm-level rate: angina pectoris (0.6%), somnolence (0.6%), sexual abuse (0.6%), abdominal hernia (0.6%), benign prostatic hyperplasia (0.6%).

Do not overextend the safety comparison. Serious-adverse-event counts are safety observations, not efficacy outcomes, and should not be combined with the primary result into a single benefit-risk number.

The serious adverse-event counts are reported with the number at risk in each group. The registry lists 155 participants at risk in the placebo group, with 0 affected; 156 in the vortioxetine 2.5 mg group, with 1 affected; 155 in the vortioxetine 5 mg group, with 0 affected; 156 in the vortioxetine 10 mg group, with 1 affected; and 154 in the duloxetine 60 mg group, with 3 affected. These are counts for the registry’s serious-event category, not estimates of comparative risk adjusted for exposure or other factors.

The record also lists five serious-event terms, each at 0.6%: angina pectoris, somnolence, sexual abuse, abdominal hernia and benign prostatic hyperplasia. Individual event counts for those terms are not reported in the registry record. Death figures are not reported in the registry record.

Safety counts should be read alongside the treatment period, the number at risk and the event definitions used in the registry. These figures alone do not establish whether events were caused by treatment, and they do not summarize all aspects of safety. The registry record does not provide the event-level context needed to interpret each listed serious event.

17. What the Result Does, and Does Not, Mean

The primary outcome reports average change in a clinician-rated anxiety scale through Week 8. All five groups had negative reported mean changes from baseline. The sponsor’s comparisons found that the confidence intervals for the three vortioxetine doses versus placebo included zero, while the duloxetine-versus-placebo interval did not. This describes the posted estimates and their statistical uncertainty; it is not, by itself, a complete judgment about clinical benefit or harm.

A result that is not statistically distinguishable from zero does not prove that the treatment groups are identical. It means that, under the reported analysis, the interval includes no average difference and also includes other possible differences. Conversely, an interval that excludes zero does not show that every participant experienced a change, nor does it establish that the magnitude is important in practice. Clinical importance requires interpretation against a meaningful threshold, which is not reported in the registry record.

The primary outcome concerns a particular scale, population, comparison and assessment time. It does not answer questions about longer-term outcomes, other diagnoses, different treatment regimens or individual response. The active-reference comparison is reported against placebo in the primary results; the registry does not establish a direct head-to-head comparison between duloxetine and vortioxetine.

Safety is a separate consideration. The serious adverse-event counts are small in the posted groups, but the registry information does not provide enough event-level detail to determine causality or characterize the full benefit-harm balance. Secondary outcomes offer additional perspectives, but their interpretation is limited by incomplete numerical reporting and unreported multiplicity procedures.

Accordingly, the record supports a description of the trial’s reported group estimates, confidence intervals and safety counts. It does not support a blanket conclusion about treatment effectiveness, individual outcomes or decisions for a particular person.

18. Why This Trial Matters Statistically

This trial illustrates why a mean change within a treatment group is not the same question as a treatment effect. Each group’s HAM-A mean declined from baseline, but the primary comparison asks how much the modeled change differed between each treatment and placebo. Without that contrast, within-group change alone cannot separate treatment-associated change from change that also occurred in the comparator group.

It also demonstrates the role of precision. The sponsor’s intervals for the vortioxetine comparisons include zero and cover a range of possible differences, whereas the reported duloxetine interval lies below zero. Reading estimates together with their intervals gives a fuller account than relying on point estimates or p-values alone. The distinction between statistical evidence and clinical importance remains essential because the record does not report a threshold for a meaningful HAM-A difference.

The analysis highlights the importance of matching interpretation to the method. The sponsor’s primary results come from a repeated-measures model, while the supplementary recalculations use simplified unadjusted comparisons from summary statistics. Their outputs are not interchangeable. The recorded discrepancy makes it especially important to give priority to the sponsor’s own model-based analysis while treating simple recalculations as checks.

Finally, the record shows why registry completeness matters. The analysis population and broad model are stated, but the original sample-size justification, multiplicity strategy, missing-data details and full statistical plan are not reported. Those elements affect how confidently readers can assess prespecification, robustness and the weight of secondary findings.

19. Limitations

Interpretation is limited by missing design and analysis details. The registry record does not report the original sample-size justification, detailed eligibility criteria, allocation-generation method, allocation concealment, interim analyses or full statistical analysis plan. It also does not report the planned multiplicity procedure, if any, or a clinically meaningful HAM-A threshold.

The primary analysis is described as an observed-case MMRM in the full analysis set, but the record does not report the amount or pattern of missing outcome data, the model’s covariance structure, missing-data assumptions, imputation details or sensitivity analyses. These omissions make it difficult to assess robustness to missing observations and alternative modeling choices.

The reported primary comparisons have unequal analyzed group sizes, and the registry record does not provide a complete participant-flow account in the registry record reported. The study includes a placebo group, three fixed-dose vortioxetine groups and an active reference, but the posted primary comparisons are each against placebo. They do not constitute a direct reported comparison of vortioxetine with duloxetine.

The registry records a discrepancy between sponsor results and simple recalculations from posted summaries. The recalculations are approximate and do not reproduce the MMRM; sponsor analyses therefore take precedence. The record does not explain all differences.

Numerical results are not reported for every listed secondary outcome, and the safety information is limited to aggregate counts and selected serious-event terms. The record does not provide event-level details or death figures. These limitations constrain independent assessment and make it important to avoid extending the findings beyond the reported outcome, period, population and comparisons.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

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23. Record Summary

The registry record describes a completed Phase 3, randomized, double-blind, parallel-group study of adults with generalized anxiety disorder. Enrollment was 781. Participants were assigned to placebo, vortioxetine 2.5 mg, 5 mg or 10 mg, or duloxetine 60 mg. The primary outcome was change from baseline in HAM-A total score at Week 8.

The sponsor reported MMRM-based least-squares mean comparisons against placebo. The three vortioxetine confidence intervals included zero; the duloxetine comparison had an estimate of -2.60, a 95% confidence interval from -4.30 to -0.89 and p = 0.003. Recalculated comparisons are approximate, and the sponsor’s own analyses take precedence where the record flags a discrepancy.

The record reports selected secondary outcomes and serious adverse-event counts, but does not report the full statistical plan, original sample-size justification, multiplicity procedure or detailed missing-data methods. These gaps limit independent assessment of the analysis and the broader interpretation of the results.

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