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 Armodafinil Treatment as Adjunctive Therapy in Adults With Major Depression Associated With Bipolar I Disorder (NCT00481195), a randomized phase 2 study. The primary outcome is The Mean Change From Baseline to Endpoint (Week 8 or Last Observation After Baseline) in the 30 Item Inventory of Depressive Symptomatology Clinician Rated (IDS C30).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT00481195 |
| Phase | Phase 2 |
| Condition | Bipolar I Depression |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 257 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Cephalon |
| Results posted | Yes |
2. Clinical Question
The clinical question was whether armodafinil, used as adjunctive therapy, produced a different change in depressive symptom severity from placebo among adults experiencing a major depressive episode associated with Bipolar I disorder. The registry describes participants as inadequately responsive to their current treatment for the current major depressive episode. The study compared armodafinil 150 mg/day with placebo over an 8-week treatment period.
Population
Adults with major depression associated with Bipolar I disorder who were inadequately responsive to their current treatment for the current major depressive episode. The primary endpoint population was the full analysis set: participants assessed with the IDS-C30 at baseline and at least one post-baseline time point.
Intervention
Armodafinil 150 mg/day, administered as adjunctive therapy. The registry describes the study as fixed dosage and lists armodafinil as a drug intervention.
Comparator
Placebo, used as the adjunctive comparison. The trial was double blind, randomized, and parallel group.
Primary question
Whether mean change from baseline to endpoint in the clinician-rated IDS-C30 differed between the armodafinil and placebo groups. Endpoint was Week 8 or the last observation after baseline.
The IDS-C30 measures depressive symptom severity, with higher scores indicating more severe symptoms. The endpoint therefore focuses on change in a continuous symptom score, rather than a binary classification such as remission or response. A more negative change represents a larger reduction in the score from baseline. The registry record does not report a separate clinical threshold for interpreting the size of a score change.
3. Trial Design
This was a Phase 2, randomized, double-blind, parallel-group study with placebo control. It evaluated armodafinil 150 mg/day as adjunctive therapy in adults with Bipolar I depression. The official title describes an 8-week, fixed-dosage study. The registry lists enrollment of 257, a start date of 2007-06, primary completion in 2008-12, and a completed status. Cephalon is listed as the sponsor.
The two intervention groups were armodafinil 150 mg/day and placebo. The primary endpoint results include 124 participants in the armodafinil group and 123 in the placebo group. These endpoint counts need not represent every person enrolled: the primary analysis population required an IDS-C30 assessment at baseline and at least one time point after baseline. The registry record does not report the reasons that endpoint counts differ from enrollment.
The primary outcome was a least-squares mean change in IDS-C30 total score from baseline to endpoint, with endpoint defined as Week 8 or the last observation after baseline. The listed full analysis set included participants meeting the assessment requirement. The registry describes the IDS-C30 as a standardized, clinician-rated, 30-item scale based on the nine symptom domains of DSM-IV criteria. Scores range from 0 to 84, and higher scores indicate more severe depressive symptoms.
The registry lists additional symptom-score changes at several follow-up weeks, as well as remission and response outcomes. It records 40 outcome measures and 40 analyses, and identifies 39 secondary outcomes as posted. Further details of the randomization procedure, concealment, treatment adherence, concomitant-treatment rules, and the trial’s original sample-size justification are not reported in the registry record. The recorded design features establish the broad comparison, but they do not by themselves specify every operational detail or the statistical plan used by the sponsor.
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: The study consisted of a 1 to 2 week screening period, an 8 week double blind treatment period, and a 1 week follow up period.
Overall Study
| Stage | Armodafinil 150 mg/Day | Placebo |
|---|---|---|
| STARTED | 128 | 129 |
| COMPLETED | 89 | 90 |
| NOT COMPLETED | 39 | 39 |
Reasons for not completing this period:
| Reason | Armodafinil 150 mg/Day | Placebo |
|---|---|---|
| Adverse Event | 16 | 11 |
| Lack of Efficacy | 1 | 3 |
| Lost to Follow-up | 4 | 6 |
| Physician Decision | 3 | 1 |
| Protocol Violation | 10 | 7 |
| Withdrawal by Subject | 3 | 9 |
| Miscellaneous | 2 | 2 |
Analysis population for the primary outcome, as defined in the registry: Full analysis set defined as subjects who were assessed with the IDS-C30 at both baseline and at least one time point after baseline
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 | Armodafinil 150 mg/Day | Placebo | Total |
|---|---|---|---|---|
| Participants analysed | 128 | 129 | 257 | |
| Age, Categorical: <=18 years | Participants | 0 | 0 | 0 |
| Age, Categorical: Between 18 and 65 years | Participants | 128 | 129 | 257 |
| Age, Categorical: >=65 years | Participants | 0 | 0 | 0 |
| Age Continuous | years | 42.6 (SD 11.34) | 44.9 (SD 11.53) | 43.7 (SD 11.47) |
| Sex: Female, Male: Female | Participants | 64 | 76 | 140 |
| Sex: Female, Male: Male | Participants | 64 | 53 | 117 |
| Region of Enrollment: United States | participants | 115 | 105 | 220 |
| Region of Enrollment: Hungary | participants | 0 | 2 | 2 |
| Region of Enrollment: Romania | participants | 5 | 7 | 12 |
| Region of Enrollment: Bulgaria | participants | 8 | 15 | 23 |
6. Primary Endpoint
The registry lists the primary outcome as The Mean Change From Baseline to Endpoint (Week 8 or Last Observation After Baseline) in the 30 Item Inventory of Depressive Symptomatology Clinician Rated (IDS C30), measured over Baseline and 8 weeks from start of study drug administration (or last observation after baseline).
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | Units on a scale |
| Endpoint classification | Continuous Endpoint |
The primary endpoint was mean change from baseline to endpoint in the 30-item Inventory of Depressive Symptomatology, Clinician Rated (IDS-C30). Endpoint was Week 8 or the last observation after baseline. The registry defines the analyzed population as participants assessed with the IDS-C30 at baseline and at least one time point after baseline.
The IDS-C30 is a standardized clinician-rated measure of depressive symptom severity. Its 30 items cover the nine symptom domains of DSM-IV criteria. The total score ranges from 0 to 84, with higher scores indicating more severe symptoms. Because the score is continuous, the analysis can compare average changes between groups rather than only classifying participants into categories.
Change from baseline gives the comparison a common starting reference: negative values indicate that the measured score decreased over follow-up. The reported least-squares means are adjusted model estimates, but the registry record does not report the model’s covariates or other details needed to reconstruct that adjustment. The score is one measure of symptom severity; the registry record does not provide a separate threshold for judging whether a particular change is clinically important. The primary endpoint therefore answers a specific statistical question about average score change, not every question about symptoms, functioning, or longer-term outcomes.
7. Results Posted in the Registry
- Armodafinil 150 mg/Day: mean -15.60 versus -12.50 on control; difference -3.10 (95% CI -6.79 to 0.59), standardized effect d = -0.21; z-test p = 0.099.
Mean difference: Armodafinil 150 mg/Day
95% CI: -6.79 to 0.59
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| The Mean Change From Baseline to Week 1 in the 30 Item Inventory of Depressive Symptomatology Clinician Rated (IDS C30) | Continuous Endpoint | Mean difference | -1.70 (-4.04 to 0.64) | 462 per arm |
| The Mean Change From Baseline to Week 2 in the 30 Item Inventory of Depressive Symptomatology Clinician Rated (IDS C30) | Continuous Endpoint | Mean difference | -2.70 (-5.60 to 0.20) | 259 per arm |
| The Mean Change From Baseline to Week 3 in the 30 Item Inventory of Depressive Symptomatology Clinician Rated (IDS C30) | Continuous Endpoint | Mean difference | -2.40 (-5.67 to 0.87) | 384 per arm |
The Mean Change From Baseline to Week 1 in the 30 Item Inventory of Depressive Symptomatology Clinician Rated (IDS C30)
- 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:
- Armodafinil 150 mg/Day: mean -6.50 versus -4.80 on control; difference -1.70 (95% CI -4.04 to 0.64), standardized effect d = -0.18; z-test p = 0.155.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Armodafinil 150 mg/Day and the control. The interval gives the range of effects that remain compatible with the data.
The Mean Change From Baseline to Week 2 in the 30 Item Inventory of Depressive Symptomatology Clinician Rated (IDS C30)
- 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:
- Armodafinil 150 mg/Day: mean -10.00 versus -7.30 on control; difference -2.70 (95% CI -5.60 to 0.20), standardized effect d = -0.25; z-test p = 0.068.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Armodafinil 150 mg/Day and the control. The interval gives the range of effects that remain compatible with the data.
The Mean Change From Baseline to Week 3 in the 30 Item Inventory of Depressive Symptomatology Clinician Rated (IDS C30)
- 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:
- Armodafinil 150 mg/Day: mean -13.10 versus -10.70 on control; difference -2.40 (95% CI -5.67 to 0.87), standardized effect d = -0.20; z-test p = 0.150.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Armodafinil 150 mg/Day and the control. The interval gives the range of effects that remain compatible with the data.
The listed secondary outcomes include IDS-C30 change from baseline at several follow-up weeks, as well as remission and response at endpoint. The registry reports additional early-week changes at Week 1, Week 2, and Week 3. Across those early follow-up summaries, the group means move in the same direction as the endpoint means: both groups have negative average changes, and the armodafinil group’s reported mean decrease is larger at each of these listed times. This broad pattern is descriptive and does not establish a consistent treatment effect across all outcomes.
The sponsor’s reported analyses for the early-week comparisons differ in their p-values. The Week 1 analysis is reported as p = 0.080, the Week 2 analysis as p = 0.027, and the Week 3 analysis as p = 0.080. These results should be read in the context of the primary endpoint and the many listed outcomes, rather than as independent confirmation. The registry record does not report a multiplicity adjustment for the secondary analyses.
When many outcomes or time points are analyzed, the chance of obtaining at least one apparently unusual result by chance can increase. This is a general statistical concern, not a claim about the cause of any particular result in this trial. Without a reported multiplicity strategy, individual unadjusted secondary p-values carry less weight than a prespecified primary analysis. The registry record does not report the full statistical plan needed to establish which secondary analyses were confirmatory or how they were intended to support the primary question.
The record names remission and response outcomes, but their results are not reported in the registry record. Nor does it provide numerical secondary results in the information available for later listed time points. Accordingly, the early-week pattern can inform description of the observed score changes, but it cannot be used to infer unreported categorical outcomes or a complete trajectory across all scheduled assessments.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- The Mean Change From Baseline to Week 1 in the 30 Item Inventory of Depressive Symptomatology Clinician Rated (IDS C30)
- The Mean Change From Baseline to Week 2 in the 30 Item Inventory of Depressive Symptomatology Clinician Rated (IDS C30)
- The Mean Change From Baseline to Week 3 in the 30 Item Inventory of Depressive Symptomatology Clinician Rated (IDS C30)
- The Mean Change From Baseline to Week 4 in the 30 Item Inventory of Depressive Symptomatology Clinician Rated (IDS C30)
- The Mean Change From Baseline to Week 6 in the 30 Item Inventory of Depressive Symptomatology Clinician Rated (IDS C30)
- The Mean Change From Baseline to Week 8 in the 30 Item Inventory of Depressive Symptomatology Clinician Rated (IDS C30)
- Number of Patients Achieving Remission at Endpoint According to the 30-item Inventory of Depressive Symptomatology-Clinician-Rated (IDS-C30)
- Number of Patients Achieving "Response" at Endpoint According to the 30-item Inventory of Depressive Symptomatology-Clinician-Rated (IDS-C30)
9. Statistical Interpretation
At endpoint, the reported least-squares mean change was -15.6 in the armodafinil 150 mg/day group and -12.5 in the placebo group. Since lower IDS-C30 scores indicate less severe symptoms, both group means represent decreases from baseline, and the armodafinil group’s reported mean decrease was larger. The unadjusted recalculation of the difference, expressed as armodafinil minus placebo, is -3.1 score units. This recalculation is based on posted group summary statistics and is not a replacement for the sponsor’s analysis.
The registry reports a sponsor analysis using ANOVA with p = 0.044, which rounds to p = 0.044 at three decimal places. The simple unadjusted recalculation gives p = 0.099. Those values are not interchangeable: the recalculation uses posted summaries and an approximate standard deviation, while the sponsor reports its own ANOVA result. Because the registry record marks a discrepancy, the sponsor’s own analysis takes precedence. The different results show why an unadjusted reconstruction should be read as a check on the posted summaries, not as a correction to the trial’s reported inference.
The recalculated difference is accompanied by a confidence interval that extends from -6.787 to approximately 0.587 score units. It includes zero, so the recalculation is compatible with a range of possible group differences, including no difference. The reported point estimate favors a greater mean decrease in the armodafinil group, but the interval and unadjusted p-value indicate uncertainty around that estimate. The interval’s upper limit is rounded to three decimal places.
The sponsor’s p-value is below the conventional 0.05 threshold, but that fact alone does not establish the magnitude or clinical importance of the difference. The registry record does not state the multiplicity strategy for the primary and secondary analyses, and does not provide the sponsor’s estimated treatment difference or its confidence interval. Those omissions limit how fully the sponsor’s result can be interpreted from the record alone. The primary outcome is also a mean score change; it does not directly report how many participants achieved remission or response.
Randomization and double blinding are relevant design protections against systematic differences in treatment assignment and outcome assessment. They do not eliminate uncertainty from sampling, missing observations, or analytical choices. The endpoint population is defined by having IDS-C30 assessments, and the registry uses a last-observation endpoint rule for participants without a Week 8 value. The record does not report enough detail to assess how missing outcomes were handled in all analyses or whether that approach could affect the estimate.
10. Statistical Methods Explained
The primary outcome is continuous: it is a score on the IDS-C30, and the analysis compares changes in average scores. A continuous outcome preserves information across the scale, rather than reducing each participant’s result to a yes-or-no category. A group mean is useful for describing average change, although it does not show the full spread of individual outcomes or how many participants improved by a particular amount.
What does a least-squares mean represent?
A least-squares mean is a model-based estimate of a group mean. Such estimates can account for variables included in the statistical model, rather than simply averaging the observed scores. The registry labels the primary group results as least-squares means and reports standard errors. However, the model specification, any covariates, and the handling of baseline values are not reported in the registry record. The reported least-squares means should therefore be read as the sponsor’s model-based summaries, without assuming details that are absent from the record.
The armodafinil group’s endpoint least-squares mean change was -15.6, and the placebo group’s was -12.5. A negative change means the follow-up score was lower than baseline on average. Since higher IDS-C30 scores mean more severe symptoms, a decline indicates a lower average score. This interpretation describes the direction of the measured scale; it does not by itself establish the clinical importance of the change.
What does the difference compare?
The recalculated mean difference is -3.1, with armodafinil minus placebo as the direction of comparison. A negative difference means the armodafinil group’s average change was more negative than the placebo group’s average change. It is a difference in changes, not a statement that every participant in one group had a larger reduction than every participant in the other. Group averages can coexist with substantial variation among individual participants.
The recalculated comparison is an unadjusted calculation from the posted summary statistics. It is distinct from the sponsor’s reported ANOVA analysis. The record reports the sponsor’s p-value as 0.044 and the recalculated p-value as 0.099. Because the registry record flags a discrepancy, the sponsor’s own analysis takes precedence. The recalculation can help readers understand the relation between the posted averages and a simple comparison, but it does not reproduce the sponsor’s model.
What do standard errors and confidence intervals tell the reader?
A standard error describes the statistical uncertainty around an estimated mean; it is not the spread of individual participant scores. The primary standard errors are 1.32 for armodafinil and 1.34 for placebo. A confidence interval expresses uncertainty around an estimate as a range of values compatible with the data and the method used to calculate it. It should be interpreted as a range, not as a guarantee that the true value lies within it.
The recalculated confidence interval is based on an approximate pooled standard deviation derived from the posted standard errors. The record identifies that approximation, so the interval is a reconstruction rather than a sponsor-reported interval. The interval spans zero, which means the recalculated results do not rule out no group difference. The sponsor’s analysis has its own reported p-value but no estimate or confidence limits in the registry record, so the two inferential summaries cannot be aligned through a direct comparison of sponsor-reported intervals.
Why can analyses differ?
Different analyses can produce different estimates or p-values when they use different model specifications, adjustment variables, analysis populations, or variance estimates. These are general statistical considerations, not confirmed explanations for the discrepancy in this trial. The registry record does not report the details needed to identify why the sponsor’s ANOVA result differs from the simple unadjusted recalculation. No explanation should be inferred solely from the difference between the reported p-values.
The sponsor’s reported analysis is the trial’s own inferential result and should be given priority. The unadjusted recalculation is useful for checking what follows from the posted means and their uncertainty, but it cannot recover unreported design or analysis details. In particular, the registry record does not report the original statistical analysis plan, the model covariates, or the sponsor’s confidence interval for the treatment comparison.
What is the role of the outcome population?
The primary analysis population is defined as participants assessed with the IDS-C30 at baseline and at least one post-baseline time point. This definition identifies who could contribute to the endpoint analysis, but it does not disclose whether every included participant had a Week 8 measurement. The endpoint is defined as Week 8 or the last observation after baseline, so the time point used may vary for participants without a Week 8 observation. The registry record does not report the number of participants whose endpoint came from an earlier observation or provide further missing-data sensitivity analyses.
In general, missing data matter because a result based on observed measurements can be affected if the availability of measurements is related to outcomes. That general concern does not establish that the trial’s result is biased. Assessment of its impact would require information about missingness, analysis rules, and sensitivity analyses that are not reported in the registry record.
11. Confidence Intervals and Precision
Precision concerns how much uncertainty surrounds an estimated group difference. The recalculated endpoint difference is -3.1 score units. Its confidence interval runs from -6.787 to approximately 0.587, rounded to three decimal places. The interval crosses zero, so the range of values compatible with this reconstruction includes a difference in either direction as well as no difference. The point estimate alone does not convey that uncertainty.
A confidence interval is not a statement that every value in the range is equally likely, nor does it guarantee that the true effect lies within the interval. It summarizes uncertainty under the assumptions of the method used. In this case, the interval is recalculated from posted summary statistics and an approximate pooled standard deviation. It is not a confidence interval reported for the sponsor’s ANOVA result. The registry record does not report the sponsor’s treatment-effect estimate or confidence limits.
The interval’s breadth relative to the point estimate indicates that the recalculated comparison is not highly precise. It remains compatible with a more substantial negative difference as well as a small positive difference. This is one reason to avoid treating a single p-value as a complete description of the evidence. The p-value of 0.099 from the unadjusted recalculation and the confidence interval address related uncertainty, while the sponsor’s reported p-value of 0.044 comes from its own analysis. The discrepancy means these summaries should not be merged into one conclusion.
Standard errors reported for the group means quantify uncertainty in those mean estimates, not variability among individual IDS-C30 scores. The registry does not report the individual-level score distribution or the sponsor’s confidence interval, which limits a fuller assessment of precision. The confidence interval is therefore best treated as an approximate, unadjusted reconstruction.
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 | 357 | 478 |
| 75% of the observed effect | 635 | 850 |
| 50% of the observed effect | 1,428 | 1,911 |
The planning figures are participants per arm, not total events. The illustrations use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each row considers an effect to detect expressed as a fraction of the observed effect. These are planning assumptions for the illustration; the trial’s own original design assumptions are not reported in the registry record.
The 80% power column gives the number of participants per arm that the illustration estimates would be needed to have an 80% chance of detecting the stated effect under those assumptions, if that effect were the true effect and the planning model applied. The 90% power column uses a higher target chance of detection and therefore requires more participants per arm for the same assumed effect. These are prospective planning concepts, not descriptions of the completed trial’s probability of obtaining a significant result.
The rows scale the assumed effect to 100%, 75%, or 50% of the observed effect. Smaller effects are harder to distinguish from random variation, so the planning illustration requires more participants per arm when the target effect is smaller. The figures are based on the observed effect in this trial, which may be an uncertain estimate and may not represent the effect expected in a future study. They are not observed power.
The illustration is not the original enrollment calculation for this study. The registry record does not report the sponsor’s original assumptions or sample-size justification, so these figures should not be read as evidence about how the trial’s enrollment target was chosen. They are conditional planning references tied to the stated assumptions and observed effect, rather than a recommendation about the design of another study.
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 = -3.100; pooled standard deviation σ = 14.780.
- n = 2 × (1.96 + 0.842)2 × 14.7802 / -3.1002 = 356.8, rounded up to 357 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 <- -3.1 # observed difference in means
sigma <- 14.7800000552318 # 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(481195)
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 = 357 (80% power), 478 (90% power)
75% of observed effect: n per arm = 635 (80% power), 850 (90% power)
50% of observed effect: n per arm = 1,428 (80% power), 1,911 (90% power)
power.t.test: 357.8
Simulated power at n = 357 per arm: 0.803 (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 |
|---|---|---|---|
| ANOVA | not reported | 0.044 |
The registry reports the sponsor’s primary comparison as an ANOVA analysis with p = 0.044, which is 0.044 when rounded to three decimal places. The simple unadjusted recalculation from the posted least-squares means and standard errors gives a mean difference of -3.1 and p = 0.099. The registry record flags a discrepancy between these results.
The two analyses should not be treated as if they were the same calculation. The recalculation uses posted summary statistics and an approximate pooled standard deviation, while the sponsor’s result is the reported trial analysis. The registry record does not provide enough information about the sponsor’s model to reproduce its ANOVA result or explain why the p-values differ. It also does not provide the sponsor’s treatment-effect estimate or confidence interval.
For that reason, the sponsor’s own analysis takes precedence. The recalculation remains useful as a transparent, unadjusted reading of the posted group summaries, but it does not overturn the sponsor’s result. The discrepancy is important because conclusions about statistical evidence can depend on the analysis used; it is not appropriate to select whichever p-value appears more favorable. Interpretation should keep the two results distinct and recognize that the record lacks the details needed to reconcile them.
15. Multiplicity, Missing Data and Analysis Populations
The registry records 40 outcome measures and 40 analyses, with 39 secondary outcomes identified as posted. The listed outcomes include repeated IDS-C30 change assessments at different follow-up times and endpoint remission and response measures. Testing multiple outcomes or time points raises a general multiplicity issue: without adjustment or a clearly prespecified hierarchy, the chance of at least one nominally small p-value can increase. The registry record does not report whether the sponsor adjusted for multiplicity, specified a hierarchy, or treated particular secondary analyses as confirmatory.
This absence matters when interpreting secondary p-values, including results at individual follow-up weeks. A nominal p-value describes evidence under the model and comparison used for that analysis; it does not account automatically for the number of other tests performed. No adjusted secondary p-values or multiplicity procedure are reported in the registry record. The primary analysis should therefore remain the main inferential focus, while secondary findings are interpreted cautiously as supportive or exploratory only if their role is otherwise established. Their formal role is not reported.
The primary population is defined as participants assessed with IDS-C30 at baseline and at least one post-baseline time point. The endpoint uses Week 8 or the last observation after baseline. This identifies the broad assessment rule, but the registry record does not report the number of missing endpoint measurements, reasons for missingness, or a detailed missing-data method. It also does not report sensitivity analyses testing alternative assumptions about missing outcomes. The impact of missing data therefore cannot be evaluated from the record alone.
Missingness can affect interpretation if the likelihood of having an observed score is related to symptom outcomes. This is a general consideration, not evidence that missingness caused bias in this study. The record does not provide enough detail to determine whether the last-observation endpoint rule affected the estimate or whether results would differ under another approach.
The sponsor reports an ANOVA analysis for the primary outcome, but the detailed statistical analysis plan, model specification, and analysis covariates are not reported in the registry record. The full analysis set is described by its assessment requirements, but further population definitions and their use across analyses are not given. Thus, it is possible to describe the stated primary population and endpoint rule, but not to reconstruct all analytic decisions or assess the robustness of the findings to alternative populations and missing-data assumptions.
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 |
|---|---|---|---|
| Armodafinil 150 mg/Day | 3 | 126 | 2.4% |
| Placebo | 3 | 125 | 2.4% |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 3% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Armodafinil 150 mg/Day | 56 of 126 |
| Placebo | 54 of 125 |
Most frequent serious adverse event terms
| Event term | Organ system | Armodafinil 150 mg/Day | Placebo |
|---|---|---|---|
| Depression | Psychiatric disorders | 1 of 126 | 1 of 125 |
| Mania | Psychiatric disorders | 0 of 126 | 2 of 125 |
| Small intestinal obstruction | Gastrointestinal disorders | 1 of 126 | 0 of 125 |
| Epididymal cyst | Reproductive system and breast disorders | 1 of 126 | 0 of 125 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Armodafinil 150 mg/Day | Placebo |
|---|---|---|---|
| Headache | Nervous system disorders | 14 of 126 | 12 of 125 |
| Insomnia | Psychiatric disorders | 13 of 126 | 10 of 125 |
| Diarrhoea | Gastrointestinal disorders | 12 of 126 | 8 of 125 |
| Nausea | Gastrointestinal disorders | 9 of 126 | 6 of 125 |
| Upper respiratory tract infection | Infections and infestations | 6 of 126 | 9 of 125 |
| Dry Mouth | Gastrointestinal disorders | 8 of 126 | 5 of 125 |
| Vomiting | Gastrointestinal disorders | 5 of 126 | 4 of 125 |
| Somnolence | Nervous system disorders | 6 of 126 | 2 of 125 |
| Restlessness | Psychiatric disorders | 7 of 126 | 1 of 125 |
| Weight increased | Investigations | 1 of 126 | 6 of 125 |
Serious events with the highest arm-level rate: mania (1.6%), depression (0.8%), small intestinal obstruction (0.8%), epididymal cyst (0.8%).
The safety record lists 3 participants affected by serious adverse events in the armodafinil group and 3 in the placebo group. The corresponding groups at risk are listed as 126 and 125. These counts describe participants recorded as affected; they do not by themselves describe event severity beyond the registry’s serious-event classification, timing, relatedness to treatment, or whether an individual experienced more than one event.
The registry also lists serious adverse event terms with percentages: Mania, 1.6%; Depression, 0.8%; Small intestinal obstruction, 0.8%; and Epididymal cyst, 0.8%. The record does not provide further detail about these events or their relationship to study treatment. Deaths are not reported in the registry record.
These safety counts should be read as descriptive registry results, not as a complete comparison of risk. The record does not provide confidence intervals or a statistical comparison for serious adverse events. Similar counts alone cannot establish that the groups had equivalent safety, and the registry information does not support conclusions about uncommon or longer-term events.
17. What the Result Does, and Does Not, Mean
The results describe average IDS-C30 score changes in a randomized, double-blind comparison of adjunctive armodafinil 150 mg/day with placebo. At endpoint, both groups had negative mean changes, with a larger mean decrease reported for armodafinil. The simple unadjusted recalculation estimates a difference of -3.1 score units, while the sponsor reports an ANOVA p-value of 0.044. The recalculated p-value is 0.099 and the recalculated confidence interval includes zero. Because the registry record flags a discrepancy, the sponsor’s own analysis takes precedence, while the reconstruction should remain clearly distinguished from it.
These findings do not establish how an individual participant would respond. Group averages do not describe the full distribution of scores, and the registry record does not give the proportion of participants reaching a particular degree of improvement. Although remission and response appear among the listed outcomes, their results are not reported in the registry record. The endpoint also does not establish change in functioning, quality of life, or outcomes beyond the study’s follow-up period.
The statistical result should not be reduced to whether a p-value lies on one side of a conventional threshold. Effect size, precision, analysis choices, and the status of the endpoint within the analysis plan all matter. In this trial, the sponsor’s reported analysis and the unadjusted reconstruction do not yield the same p-value, and the record does not include sufficient model details to reconcile them. The secondary outcomes add descriptive context, but multiple testing and the unreported multiplicity approach limit the weight placed on individual secondary p-values.
The endpoint population was defined by observed IDS-C30 assessments, and the endpoint could use the last observation after baseline rather than a Week 8 assessment. Details about missing measurements and sensitivity analyses are not reported. These limitations prevent a complete assessment of how analysis choices and incomplete follow-up may have affected the estimate. The record supports a description of the posted results and their uncertainty, but it does not settle every question about the magnitude, clinical importance, or robustness of the comparison.
18. Why This Trial Matters Statistically
This trial illustrates why a registry result should be read through both its design and its analysis. Randomization, double blinding, and placebo control describe important features of the comparison, while the endpoint definition identifies what the primary analysis measured. Here, the primary outcome was a continuous clinician-rated symptom score, and the reported group means indicate decreases in both arms.
It also demonstrates the difference between a sponsor-reported analysis and a simple recalculation from summary statistics. The recalculated mean difference and p-value do not match the sponsor’s reported p-value. The registry flags the discrepancy, and the sponsor’s own analysis takes precedence. Without model details, the reconstruction cannot explain the difference or serve as a substitute for the trial analysis. Keeping the two results separate is a practical lesson in reproducible interpretation.
Precision is another central issue. The recalculated interval includes zero and spans values in either direction around the estimate. A point estimate and a p-value alone do not communicate that uncertainty, and a nominally notable secondary result must be considered alongside other tests. The registry’s multiplicity approach is not reported, limiting the strength of conclusions from individual secondary analyses.
Finally, the record shows why analysis populations and missing-data rules matter. The primary population requires baseline and post-baseline assessments, and endpoint may be Week 8 or the last observation after baseline. Further information about missing outcomes and sensitivity analyses is not reported. These details shape what can be learned from the posted result and what remains uncertain. The trial is therefore useful as an example of interpreting a clinical endpoint without overstating what registry-level summaries can establish.
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.
Several trial-specific limitations affect interpretation of the registry results. The endpoint is defined as Week 8 or the last observation after baseline, so it may not represent the same follow-up time for every participant. The record does not report how many endpoint values were taken at Week 8 versus an earlier observation, why observations were missing, or whether sensitivity analyses assessed the effect of missing data.
The registry defines the full analysis set by IDS-C30 assessments at baseline and at least one post-baseline time point. It does not provide further detail on the analysis population for every outcome, nor does it explain exclusions or missing assessments. The endpoint group counts are 124 for armodafinil and 123 for placebo, while the safety groups at risk are listed separately as 126 and 125. The record does not explain the differences between these analysis counts.
The reported primary sponsor analysis is an ANOVA with p = 0.044, while the unadjusted recalculation gives p = 0.099. The registry flags the discrepancy but does not report the model specification, adjustment variables, sponsor estimate, or sponsor confidence interval needed to reconcile the results. The recalculated standard deviation is approximate, adding uncertainty to the reconstruction.
The record does not report the original sample-size justification, a detailed statistical analysis plan, or the approach to multiplicity across the numerous outcomes and analyses. Results for listed remission and response endpoints are not reported in the registry record. Safety information is also limited: serious-event counts and selected terms are listed, but detailed event narratives, treatment relatedness, and a statistical comparison are not reported. These limitations do not invalidate the recorded results, but they restrict the conclusions that can be drawn from the registry record alone.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Armodafinil Treatment as Adjunctive Therapy in Adults With Major Depression Associated With Bipolar I Disorder — NCT00481195.
- Registry record last updated 2013-07-19; status last verified 2013-07.
- Results first posted 2010-12-20.
- 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
NCT00481195 is a completed Phase 2 randomized, double-blind, parallel-group, placebo-controlled study sponsored by Cephalon. It evaluated armodafinil 150 mg/day as adjunctive therapy for adults with major depression associated with Bipolar I disorder. The registry lists enrollment of 257 and an 8-week fixed-dosage design.
The primary endpoint was mean IDS-C30 change from baseline to Week 8 or the last observation after baseline. The registry reports least-squares mean changes of -15.6 for armodafinil and -12.5 for placebo. The sponsor reports an ANOVA p-value of 0.044; an unadjusted recalculation gives a difference of -3.1 and p = 0.099. The registry flags this discrepancy, so the sponsor’s own analysis takes precedence.
The record lists secondary symptom outcomes and serious adverse event counts, but multiplicity handling, detailed missing-data methods, and the original sample-size justification are not reported in the registry record. Interpretation is therefore limited to the posted outcomes and analysis details.