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 Roflumilast Plus Antipsychotics Proof of Mechanism Study in Schizophrenia (NCT02079844), a randomized phase 1 study. The primary outcome is Change From Baseline in Spatial Span Test Score.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02079844 |
| Phase | Phase 1 |
| Condition | Schizophrenia |
| Allocation | Randomized |
| Design model | Crossover |
| Masking | Quadruple |
| Enrollment | 20 |
| Arms in the primary outcome | 3 |
| Lead sponsor | Takeda |
| Results posted | Yes |
2. Clinical Question
Population
Participants with stable schizophrenia who were receiving second generation antipsychotics. The primary analysis population consisted of participants in the Pharmacodynamic Analysis Set who had received at least 1 dose of study drug and had post-dose pharmacodynamic results, with data at both Baseline and Day 8 for analysis.
Intervention
Add-on roflumilast at 100 μg or 250 μg, administered with second generation antipsychotics. The record describes treatment over three periods, with treatment on Days 1 through 8 in each period.
Comparator
Roflumilast placebo-matching tablets, used as an add-on to second generation antipsychotics. The study schedules placed placebo and the two roflumilast doses in different treatment-period sequences.
Primary question
Did change from Baseline in Spatial Span Test score differ between placebo and either roflumilast dose at Day 8 of treatment periods? The test measures working memory, and a positive change from Baseline is defined in the record as improvement.
The study was designed as a proof-of-mechanism evaluation, including cognitive outcomes and brain imaging and electrical activity measures. The registry record describes the purpose as determining whether cognitive impairment associated with schizophrenia is attenuated by adding roflumilast to second generation antipsychotics. The posted primary outcome concerns the Spatial Span Test; it is not a general measure of all cognitive function. The result therefore speaks to the recorded change in this particular score over the specified treatment periods, rather than establishing a broader effect on cognition or on schizophrenia.
3. Trial Design
This was a Phase 1, randomized, double-blind, placebo-controlled, three-period crossover study. The record lists quadruple masking and enrollment of 20. The study status is completed. It began in 2014-03, and primary completion was recorded as 2015-06.
The treatment schedules comprised placebo, roflumilast 100 μg, and roflumilast 250 μg in different orders. Each arm description specifies oral once-daily treatment on Days 1 through 8, followed by a 14 day washout before the next period. A crossover design allows treatment conditions to be compared within a participant over separate periods, rather than assigning each participant to just one condition. The analysis must account for the sequence and period structure, as the stated primary analysis did.
Participants had stable schizophrenia and were taking second generation antipsychotics; roflumilast was studied as an add-on. The primary endpoint was assessed at Baseline and Day 8 of Treatment Periods 1, 2 and 3. The registry also lists cognitive tests, brain activation measures, and electrophysiological measures as secondary outcomes.
The record does not report the original sample-size justification or the trial's original design assumptions. It also does not report a detailed recruitment flow in the registry record for this analysis. The posted analysis populations differ in size by treatment condition, so the enrollment figure should not be mistaken for the number contributing to each particular outcome comparison.
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 schizophrenia were enrolled equally in 1 of 3 treatment sequences which determined the order the following 3 treatments were received: placebo, once a day roflumilast 100 μg, roflumilast 250 μg.
Treatment Period 1
| Stage | Placebo + Roflumilast 100 μg + Roflumilast 250 μg | Roflumilast 100 μg + Roflumilast 250 μg + Placebo | Roflumilast 250 μg + Placebo + Roflumilast 100 μg |
|---|---|---|---|
| STARTED | 6 | 7 | 7 |
| COMPLETED | 6 | 7 | 5 |
| NOT COMPLETED | 0 | 0 | 2 |
Reasons for not completing this period:
| Reason | Placebo + Roflumilast 100 μg + Roflumilast 250 μg | Roflumilast 100 μg + Roflumilast 250 μg + Placebo | Roflumilast 250 μg + Placebo + Roflumilast 100 μg |
|---|---|---|---|
| Voluntary Withdrawal | 0 | 0 | 2 |
Treatment Period 2
| Stage | Placebo + Roflumilast 100 μg + Roflumilast 250 μg | Roflumilast 100 μg + Roflumilast 250 μg + Placebo | Roflumilast 250 μg + Placebo + Roflumilast 100 μg |
|---|---|---|---|
| STARTED | 5 | 7 | 5 |
| COMPLETED | 5 | 6 | 5 |
| NOT COMPLETED | 0 | 1 | 0 |
Reasons for not completing this period:
| Reason | Placebo + Roflumilast 100 μg + Roflumilast 250 μg | Roflumilast 100 μg + Roflumilast 250 μg + Placebo | Roflumilast 250 μg + Placebo + Roflumilast 100 μg |
|---|---|---|---|
| Voluntary Withdrawal | 0 | 1 | 0 |
Treatment Period 3
| Stage | Placebo + Roflumilast 100 μg + Roflumilast 250 μg | Roflumilast 100 μg + Roflumilast 250 μg + Placebo | Roflumilast 250 μg + Placebo + Roflumilast 100 μg |
|---|---|---|---|
| STARTED | 5 | 5 | 5 |
| COMPLETED | 5 | 5 | 5 |
| NOT COMPLETED | 0 | 0 | 0 |
Analysis population for the primary outcome, as defined in the registry: Participants from the Pharmacodynamic Analysis Set, all randomized participants who received at least 1 dose of study drug and had at least 1 pharmacodynamic result post-dose, with data available at both Baseline and Day 8 for analysis.
5. Baseline Characteristics
The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.
Population: All randomized participants.
| Characteristic | Unit | Placebo + Roflumilast 100 μg + Roflumilast 250 μg | Roflumilast 100 μg + Roflumilast 250 μg + Placebo | Roflumilast 250 μg + Placebo + Roflumilast 100 μg | Total |
|---|---|---|---|---|---|
| Participants analysed | 6 | 7 | 7 | 20 | |
| Age, Continuous | years | 34.8 (SD 10.13) | 36.9 (SD 10.38) | 48.1 (SD 10.93) | 40.2 (SD 11.63) |
| Sex: Female, Male: Female | Participants | 2 | 2 | 3 | 7 |
| Sex: Female, Male: Male | Participants | 4 | 5 | 4 | 13 |
| Race/Ethnicity, Customized: Asian | participants | 0 | 1 | 1 | 2 |
| Race/Ethnicity, Customized: Black or African American | participants | 5 | 5 | 4 | 14 |
| Race/Ethnicity, Customized: White | participants | 1 | 1 | 2 | 4 |
| Region of Enrollment: United Kingdom | participants | 6 | 7 | 7 | 20 |
| Height | cm | 169.8 (SD 8.68) | 175.0 (SD 7.64) | 169.1 (SD 10.96) | 171.4 (SD 9.14) |
| Weight | kg | 79.38 (SD 4.804) | 85.09 (SD 17.406) | 81.41 (SD 15.470) | 82.09 (SD 13.532) |
| Body Mass Index (BMI) | kg/m^2 | 27.75 (SD 3.871) | 27.56 (SD 3.823) | 28.20 (SD 3.158) | 27.84 (SD 3.433) |
| Tobacco Classification: Never used tobacco | participants | 1 | 1 | 3 | 5 |
| Tobacco Classification: Current tobacco user | participants | 2 | 4 | 3 | 9 |
| Tobacco Classification: Ex-tobacco user | participants | 3 | 2 | 1 | 6 |
| Caffeine Classification: Consumes caffeine | participants | 4 | 5 | 5 | 14 |
| Caffeine Classification: Does not consume caffeine | participants | 2 | 2 | 2 | 6 |
6. Primary Endpoint
The registry lists the primary outcome as Change From Baseline in Spatial Span Test Score, measured over Baseline and Day 8 of Treatment Periods 1, 2 and 3.
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | score on a scale |
| Endpoint classification | Continuous Endpoint |
The primary endpoint was change from Baseline in Spatial Span Test score, assessed at Baseline and Day 8 of Treatment Periods 1, 2 and 3. The test evaluates working memory. Participants reproduce a pattern of blue blocks tapped by a rater, and then reproduce the reverse pattern. The score ranges from 0 (worst) to 32 (best); the registry defines a positive change from Baseline as improvement.
Working memory is one component of cognition, making this measure relevant to the study's stated question about cognitive impairment in schizophrenia. It provides a scored performance measure rather than relying only on a broad clinical impression. However, a change in Spatial Span score represents performance on this task, not cognition in every domain. Other cognitive tests and brain activity measures were listed as secondary outcomes.
The primary outcome is reported as a least-squares mean with standard error. The analysis population required a participant to have received at least 1 dose, to have at least 1 post-dose pharmacodynamic result, and to have data at both Baseline and Day 8 for analysis. Thus the reported means concern participants meeting those outcome-specific data requirements, not necessarily everyone enrolled.
7. Results Posted in the Registry
- Roflumilast 100 μg: mean 0.03 versus -0.20 on control; difference 0.23 (95% CI -1.20 to 1.67), standardized effect d = 0.11; z-test p = 0.751.
- Roflumilast 250 μg: mean -0.07 versus -0.20 on control; difference 0.13 (95% CI -1.32 to 1.59), standardized effect d = 0.06; z-test p = 0.858.
Mean difference: Roflumilast 100 μg
95% CI: -1.20 to 1.67
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 in the Continuous Performance Test (CPT) | Continuous Endpoint | Mean difference | -0.01 (-0.29 to 0.28) | 74,999 per arm |
| Change From Baseline in Brief Assessment of Cognition in Schizophrenia: Symbol-Coding | Continuous Endpoint | Mean difference | 0.15 (-4.81 to 5.12) | 35,475 per arm |
| Change From Baseline in Category Fluency Animal Naming Scores | Continuous Endpoint | Mean difference | 1.75 (-0.49 to 3.99) | 56 per arm |
Change From Baseline in the Continuous Performance Test (CPT)
- 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:
- Roflumilast 100 μg: mean 0.07 versus 0.08 on control; difference -0.01 (95% CI -0.29 to 0.28), standardized effect d = -0.01; z-test p = 0.967.
- Roflumilast 250 μg: mean 0.23 versus 0.08 on control; difference 0.15 (95% CI -0.13 to 0.44), standardized effect d = 0.37; z-test p = 0.300.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Roflumilast 100 μg 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 Roflumilast 250 μg and the control. The interval gives the range of effects that remain compatible with the data.
Change From Baseline in Brief Assessment of Cognition in Schizophrenia: Symbol-Coding
- 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:
- Roflumilast 100 μg: mean 0.89 versus 0.73 on control; difference 0.15 (95% CI -4.81 to 5.12), standardized effect d = 0.02; z-test p = 0.952.
- Roflumilast 250 μg: mean 2.15 versus 0.73 on control; difference 1.42 (95% CI -3.60 to 6.44), standardized effect d = 0.20; z-test p = 0.579.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Roflumilast 100 μg 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 Roflumilast 250 μg and the control. The interval gives the range of effects that remain compatible with the data.
Change From Baseline in Category Fluency Animal Naming Scores
- 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:
- Roflumilast 100 μg: mean 1.04 versus -0.71 on control; difference 1.75 (95% CI -0.49 to 3.99), standardized effect d = 0.53; z-test p = 0.126.
- Roflumilast 250 μg: mean -1.47 versus -0.71 on control; difference -0.76 (95% CI -3.03 to 1.51), standardized effect d = -0.23; z-test p = 0.513.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Roflumilast 100 μg 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 Roflumilast 250 μg and the control. The interval gives the range of effects that remain compatible with the data.
The registry lists secondary cognitive measures, including the Continuous Performance Test, Symbol-Coding, and Category Fluency, as well as brain activation and electrical activity measures. These outcomes broaden the proof-of-mechanism assessment beyond working memory, but each measures a different task or physiological response. They should not be treated as interchangeable indicators of a single cognitive effect.
Among the secondary cognitive comparisons with posted summary statistics, estimated contrasts vary in direction and size. The recalculated confidence intervals for those comparisons include zero. The pattern is therefore not a consistent, precise signal across the displayed cognitive measures. This does not establish that every secondary outcome was unchanged; the registry lists 14 secondary outcomes as posted, while only some outcomes have detailed results in the registry record.
The secondary results are supportive context rather than a substitute for the prespecified primary endpoint. The primary outcome directly addresses the Spatial Span Test question, while secondary measures explore other aspects of cognition and neural activity. A pattern across secondary measures can motivate further research, but it cannot resolve uncertainty in the primary comparison by itself.
Unadjusted secondary comparisons carry less weight because multiple outcomes and contrasts create more opportunities for apparently notable results to occur by chance. The registry record does not report a multiplicity adjustment for these secondary analyses. Their estimates and intervals should therefore be read as exploratory unless a fuller analysis plan establishes otherwise. No single secondary comparison should be elevated as definitive on the basis of its point estimate alone.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Change From Baseline in the Continuous Performance Test (CPT)
- Change From Baseline in Brief Assessment of Cognition in Schizophrenia: Symbol-Coding
- Change From Baseline in Category Fluency Animal Naming Scores
- Ventrolateral Prefrontal (VLPF) Cortex and Orbitofrontal (OFX) Cortex Activation During the Shift Trials
- Ventral Striatum Activation During the Reward Trials
- Change From Baseline in P300 Amplitude at the Midline Parietal Electrode (Pz)
- Change From Baseline in Mismatch Negativity (MMN) Amplitude at the Midline Frontal Electrode (Fz)
- Change From Baseline in Amplitude of the C1 Component of the Visual Evoked Potentials at the Midline Occipital Electrode (Oz)
9. Statistical Interpretation
The posted primary estimates are close to zero relative to their uncertainty. The placebo least-squares mean change was -0.199. The corresponding values were 0.033 for roflumilast 100 μg and -0.066 for roflumilast 250 μg. The posted comparisons against placebo were 0.232 for 100 μg and 0.133 for 250 μg. The sponsor's ANOVA results report 95% confidence intervals of -1.269 to 1.733 and -1.389 to 1.655, respectively, with p-values of 0.753 and 0.859.
Both intervals include zero and also include changes in either direction. The data therefore do not give a precise estimate of the difference between each roflumilast dose and placebo on this endpoint. The p-values are not evidence that the treatments are equivalent, nor do they establish that any difference is absent. A non-significant result can arise when the estimated difference is small, when uncertainty is substantial, or both; the interval is important for understanding which values remain compatible with the analysis.
The posted re-calculations give mean differences of 0.232 for roflumilast 100 μg and 0.133 for roflumilast 250 μg. Their unadjusted p-values are 0.751 and 0.858, and their intervals are -1.203 to 1.667 and -1.319 to 1.585. These calculations are simple re-calculations from posted summary statistics, not replacements for the study's crossover ANOVA. The sponsor's own analysis is the relevant reported analysis for the trial.
The score is defined so that a positive within-condition change indicates improvement, but the between-condition contrast is the key question for the randomized comparison. The small positive estimated contrasts do not, by themselves, establish a meaningful advantage. No threshold for a clinically important difference is reported in the registry record, and the posted intervals are broad relative to the point estimates. Interpretation should therefore focus on the uncertainty, the endpoint's specific scope, and the analysis design rather than on the direction of a point estimate alone.
These findings concern a proof-of-mechanism study with a short treatment-period endpoint. They cannot establish durable changes, effects on other cognitive domains, or the overall clinical effect of treatment. The record lists several other cognitive and neurophysiological outcomes, but those measures do not change the primary endpoint's result or resolve its uncertainty.
10. Statistical Methods Explained
The primary analysis is described as an analysis of variance (ANOVA) with treatment sequence, study period, and treatment as fixed effects, and participant nested within treatment sequence as a random effect. That structure reflects the crossover design: participants receive conditions in a sequence, outcomes are recorded in separate periods, and observations from the same participant are related rather than independent.
Why account for sequence and period?
Treatment sequence identifies the order in which the conditions were assigned. Study period identifies when an outcome was measured within the crossover. Including both allows the treatment comparison to be made while accounting for systematic differences associated with order or period. The record does not state whether additional terms or sensitivity analyses were used, so none should be assumed.
The participant-within-sequence random effect accounts for repeated observations from the same participant. In general, repeated measurements on one person tend to be more alike than measurements from unrelated people. Treating them as independent could misstate uncertainty. A random participant effect represents this within-person clustering in the analysis model.
What does a least-squares mean represent?
A least-squares mean is a model-based mean, adjusted for the terms included in the analysis. It is not necessarily identical to a raw arithmetic average. The primary result reports such means for each condition and least-squares mean differences for comparisons with placebo. The reported ANOVA confidence intervals and p-values belong to that model-based analysis.
The posted re-calculations are different in purpose. They use the available summary statistics to produce simple, unadjusted comparisons. Their standard deviations are approximate, derived from the reported standard errors, and the calculations do not reproduce the full crossover model. They are useful as a transparent check on the scale of the estimates, but they do not account for the study's sequence, period, or participant structure in the way the reported ANOVA does.
How should a p-value be read?
A p-value describes how compatible the observed data are with a specified null model, under the assumptions of the analysis. It is not the probability that the null hypothesis is true, and it does not measure the probability that a treatment effect is clinically important. A large p-value does not prove no difference. In this study, the reported primary p-values accompany intervals that include zero and span values in both directions, so the results remain uncertain about the size and direction of the treatment contrasts.
The p-values in the re-calculations are explicitly unadjusted. They are not the sponsor's ANOVA p-values and should not be substituted for them. The registry record does not report a multiple-comparison adjustment for the primary comparisons; that aspect of the statistical plan is not reported in the registry record.
Why can over-dispersion matter?
In general, over-dispersion means that observations vary more than a model's assumed variance structure allows. If that extra variability is ignored, standard errors can be too small and confidence intervals too narrow, making results appear more precise than warranted. The primary endpoint is continuous and the stated analysis is ANOVA; the registry record does not identify over-dispersion as an issue or describe an alternative variance model. It should therefore be treated as a general statistical consideration, not as a reported problem in this trial.
The analysis population is also part of the method. For the primary outcome, the record specifies the Pharmacodynamic Analysis Set and requires data at both Baseline and Day 8 for analysis. The registry record does not report how missing outcome observations were handled beyond that population definition, or whether other analysis populations were used for sensitivity checks.
11. Confidence Intervals and Precision
A confidence interval describes a range of effect values compatible with the data and the statistical model at the stated confidence level. It is not a guarantee that the true effect lies within the particular interval, and it does not show the probability that an individual participant will improve. Its width conveys precision: narrower intervals indicate a more precise estimate, while wider intervals leave a broader range of plausible effects.
For the primary comparisons, the sponsor's reported 95% confidence intervals are -1.269 to 1.733 for roflumilast 100 μg versus placebo and -1.389 to 1.655 for roflumilast 250 μg versus placebo. Each contains zero and includes both negative and positive values. This means the posted analysis does not pin down whether the between-condition difference is positive or negative, or how large it might be within the interval.
The re-calculated intervals are -1.203 to 1.667 and -1.319 to 1.585. These are simple unadjusted intervals based on posted summary statistics, not the crossover ANOVA intervals. They should be read separately from the sponsor's estimates, because the underlying calculation and assumptions differ. The registry record's reported ANOVA results are the principal trial results.
The standard errors attached to the condition means also indicate uncertainty around those estimates; they are not ranges of observed participant scores. Neither standard errors nor confidence intervals describe the full spread of individual outcomes. The registry record does not report a clinically important difference threshold for the Spatial Span Test, so the interval cannot be classified against such a threshold from these registry entries alone.
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 | 1,290 | 1,726 |
| 75% of the observed effect | 2,293 | 3,069 |
| 50% of the observed effect | 5,158 | 6,904 |
The sample-size estimates are planning illustrations based on observed effects, not the trial's original design assumptions. For these continuous outcomes, the figures are participants per arm, not total events. The stated calculation assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect: 100%, 75%, or 50%.
The 80% power column gives the number of participants per arm that the planning calculation associates with an 80% chance of detecting the specified effect under those assumptions. The 90% power column gives the corresponding number per arm for a 90% chance. These are design probabilities under a hypothetical planning model, not probabilities that the observed result is correct. This is not observed power.
Rows for a smaller fraction of the observed effect require more participants because smaller differences are harder to distinguish from random variation. The very small estimated effects in some comparisons can therefore produce very large planning figures. Those values are sensitive to the observed effect used as the planning target, and the estimates can be unstable when the underlying trial is small and the effect estimate is uncertain.
The registry record does not report the original sample-size justification, its target effect, or the design assumptions used to set enrollment. These illustrations should not be interpreted as evidence that the completed study was designed to detect the displayed effects or that it had a particular observed power.
13. How the Sample Size Is Derived
Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).
Formula
n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.
Worked calculation for this trial
- Observed difference Δ = 0.232; pooled standard deviation σ = 2.103.
- n = 2 × (1.96 + 0.842)2 × 2.1032 / 0.2322 = 1,289.3, rounded up to 1,290 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 <- 0.232 # observed difference in means
sigma <- 2.10251049937925 # 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(2079844)
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 = 1,290 (80% power), 1,726 (90% power)
75% of observed effect: n per arm = 2,293 (80% power), 3,069 (90% power)
50% of observed effect: n per arm = 5,158 (80% power), 6,904 (90% power)
power.t.test: 1290.2
Simulated power at n = 1,290 per arm: 0.804 (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 | LS Mean Difference 0.232 | -1.269 to 1.733 | 0.753 |
| ANOVA | LS Mean Difference 0.133 | -1.389 to 1.655 | 0.859 |
The sponsor's own primary analysis is the crossover ANOVA described in the registry record. It reports least-squares mean differences of 0.232 for roflumilast 100 μg versus placebo and 0.133 for roflumilast 250 μg versus placebo, with 95% confidence intervals of -1.269 to 1.733 and -1.389 to 1.655. The corresponding reported p-values are 0.753 and 0.859.
The re-calculated comparisons are unadjusted calculations from the posted summary statistics. They produce the same displayed point estimates, but their intervals and p-values differ slightly from the sponsor's ANOVA results. That is expected when a simple summary-statistic calculation does not reproduce the model terms and covariance structure of a crossover analysis. The record does not flag a discrepancy, but the sponsor's model-based analysis remains the trial's reported analysis and should take precedence over a simplified recalculation when describing the trial result.
The recalculated figures can help readers understand the scale of a contrast without implying that they are a second independent study result. They should not be combined with the ANOVA outputs or treated as corroborating evidence. The interpretation should center on the sponsor's reported confidence intervals and their substantial uncertainty.
15. Multiplicity, Missing Data and Analysis Populations
The registry record describes the primary ANOVA structure and lists multiple secondary outcomes, but a comprehensive multiplicity strategy is not reported in the registry record. In particular, the record does not state whether the primary treatment comparisons were adjusted for multiple testing, whether secondary outcomes formed a prespecified hierarchy, or whether any family-wise error or false-discovery procedure was used.
Multiplicity matters because every additional outcome or contrast creates another opportunity for a result that looks unusual under a no-effect model. A collection of unadjusted p-values should not be interpreted as though each were the only analysis conducted. The posted secondary results are therefore best viewed as exploratory evidence, especially when considered alongside the primary result.
The primary outcome's analysis population is defined as the Pharmacodynamic Analysis Set: randomized participants who received at least 1 dose, had at least 1 post-dose pharmacodynamic result, and had Baseline and Day 8 data for analysis. This specifies who contributed to that outcome, but it does not describe all missing-data procedures. The registry record does not report the number or reasons for missing observations by outcome, imputation methods, or sensitivity analyses for missing data.
The record also does not report whether an intention-to-treat analysis, a per-protocol analysis, or other analysis populations were used for the primary endpoint. Nor does it report interim analyses or stopping rules. These omissions prevent a full assessment of how analysis choices may have affected the results. They should not be filled in by assuming common practice; details not stated remain not reported in the registry record.
Because this is a crossover trial, the treatment sequence, period, and repeated observations are relevant to analysis. The stated ANOVA includes sequence and period as fixed effects and participant nested within sequence as a random effect. The record does not explain how potential carryover was evaluated or whether additional analyses addressed it. The described 14 day washout periods are part of the schedule, but they do not by themselves document a statistical carryover assessment.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Placebo | 1 | 16 | 6.2% |
| Roflumilast 100 μg | 0 | 17 | 0.0% |
| Roflumilast 250 μg | 0 | 19 | 0.0% |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Placebo | 8 of 16 |
| Roflumilast 100 μg | 7 of 17 |
| Roflumilast 250 μg | 9 of 19 |
Most frequent serious adverse event terms
| Event term | Organ system | Placebo | Roflumilast 100 μg | Roflumilast 250 μg |
|---|---|---|---|---|
| Suicide attempt | Psychiatric disorders | 1 of 16 | 0 of 17 | 0 of 19 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Placebo | Roflumilast 100 μg | Roflumilast 250 μg |
|---|---|---|---|---|
| Nasopharyngitis | Infections and infestations | 1 of 16 | 2 of 17 | 1 of 19 |
| Headache | Nervous system disorders | 1 of 16 | 1 of 17 | 2 of 19 |
| Toothache | Gastrointestinal disorders | 1 of 16 | 1 of 17 | 1 of 19 |
| Palpitations | Cardiac disorders | 1 of 16 | 0 of 17 | 0 of 19 |
| Abdominal pain lower | Gastrointestinal disorders | 0 of 16 | 0 of 17 | 1 of 19 |
| Diarrhoea | Gastrointestinal disorders | 0 of 16 | 0 of 17 | 1 of 19 |
| Gingival swelling | Gastrointestinal disorders | 0 of 16 | 1 of 17 | 0 of 19 |
| Nausea | Gastrointestinal disorders | 0 of 16 | 1 of 17 | 0 of 19 |
| Vomiting | Gastrointestinal disorders | 0 of 16 | 0 of 17 | 1 of 19 |
| Catheter site bruise | General disorders | 1 of 16 | 0 of 17 | 0 of 19 |
Serious events with the highest arm-level rate: suicide attempt (6.2%).
The registry lists serious adverse events affecting 1 participant in the placebo group and 0 in each roflumilast dose group. The corresponding numbers listed at risk are 16 for placebo, 17 for roflumilast 100 μg, and 19 for roflumilast 250 μg. These are the posted group figures; they should not be added to produce a total because the study used a crossover design and the record does not establish that the group counts represent non-overlapping people.
The record also lists other adverse events affecting 8 participants in the placebo group, 7 in the 100 μg group, and 9 in the 250 μg group, with the respective numbers at risk of 16, 17, and 19. These figures describe the posted event categories and are not a comparison adjusted for exposure time or participant characteristics.
The serious adverse event term listed among the top terms is “Suicide attempt” at 6.2%. The registry record does not provide enough detail to interpret that term's relationship to treatment or to establish causality. Death counts are not reported in the registry record. The small group figures and crossover design make these data descriptive; they do not establish comparative safety.
17. What the Result Does, and Does Not, Mean
The posted result describes change in a specific working-memory task after treatment periods, in participants meeting the primary analysis population requirements. It does not show a precise difference between placebo and either roflumilast dose on the Spatial Span Test. The sponsor's confidence intervals include zero and a range of values in both directions, so the direction and magnitude of any difference remain uncertain.
This is not proof of equivalence or proof that there is no effect. Equivalence requires a defined margin and an analysis designed to test whether differences fall within that margin; the registry record does not report such a margin or an equivalence analysis. Likewise, the p-values do not indicate the probability that a treatment works or that the null hypothesis is true.
The primary endpoint is not a direct measure of every cognitive domain, daily functioning, symptoms, or long-term outcomes. The study is described as a proof-of-mechanism study and uses treatment periods of 8 days with washouts. Its posted results do not establish persistence beyond those assessed periods. Brain imaging, electrical activity, and other cognitive outcomes may inform separate mechanistic questions, but they do not change the scope of the primary measure.
The findings also should not be generalized beyond the population and conditions described in the record without additional evidence. Participants had stable schizophrenia and were receiving second generation antipsychotics. The registry does not report enough information to determine how representative the analyzed participants were of a broader clinical population.
In statistical terms, the principal conclusion is uncertainty: the model-based estimates are close to zero and imprecise, and the reported intervals remain compatible with effects on either side of zero. The record does not establish a clinically important threshold for this score, so statistical estimates cannot be translated into a judgment about clinical importance from these registry entries alone.
18. Why This Trial Matters Statistically
This trial is statistically informative because it illustrates the distinction between a point estimate and the precision of an estimate. The primary comparisons are positive numerically, but the confidence intervals are broad and include values in both directions. Reading only the direction of the estimate would omit the main feature of the evidence: considerable uncertainty about the treatment contrast.
The crossover structure also makes the analysis model important. Participants contribute measurements across treatment periods, so the analysis accounts for sequence, period, and participant. A simple comparison of summary means cannot reproduce all of that structure. The difference between the sponsor's ANOVA and the unadjusted recalculation is a practical reminder that estimates depend not only on the reported averages but also on the design and covariance assumptions.
The study is also a useful example of why sample-size illustrations derived from observed effects need careful interpretation. A small, uncertain observed effect can imply very large planning estimates, but those figures are not the original trial rationale and do not tell whether the completed trial had adequate power. The original design assumptions are not reported in the registry record.
Finally, the record spans cognitive performance, imaging, and electrophysiology. Such breadth can support mechanistic exploration, but it increases the importance of prespecification and multiplicity control. The registry record does not report a complete multiplicity strategy, which limits how strongly secondary patterns can be interpreted. These considerations make transparent reporting of model structure, uncertainty, and analysis choices central to understanding the trial.
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 available primary comparison is imprecise: both sponsor-reported intervals include zero and extend to values in either direction. The registry record does not report a threshold for a clinically important change in Spatial Span score, which limits interpretation of the estimates in practical terms.
The study enrolled 20, while outcome-specific analysis counts vary by treatment condition. The primary population requires Baseline and Day 8 data, and the registry record does not report detailed missing-data handling, reasons for missingness, or sensitivity analyses. The enrollment figure should not be treated as the number analyzed for each result.
The crossover design allows within-participant comparisons but also makes period and sequence effects relevant. The stated model accounts for treatment sequence, study period, and participant nested within sequence. The registry record does not report how carryover was evaluated, whether the washout duration was supported by a specific analysis, or whether alternative models were tested.
Multiple cognitive, imaging, and electrical activity outcomes were listed. A comprehensive multiplicity strategy is not reported in the registry record, so secondary results should be treated cautiously. The original sample-size justification and design assumptions are also not reported, and the observed-effect planning illustrations cannot fill that gap.
Finally, the primary endpoint measures one working-memory task at Day 8 of treatment periods. It does not establish sustained effects, broad cognitive change, or clinical outcomes beyond the specific measures and timeframes recorded. The posted adverse-event summaries are descriptive and do not establish comparative safety or causation.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Roflumilast Plus Antipsychotics Proof of Mechanism Study in Schizophrenia — NCT02079844.
- Registry record last updated 2016-10-03; status last verified 2016-08.
- Results first posted 2016-10-03.
- 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
NCT02079844 is a completed Phase 1 randomized, double-blind, placebo-controlled, three-period crossover proof-of-mechanism study sponsored by Takeda. It evaluated add-on roflumilast at 100 μg and 250 μg against placebo in participants with stable schizophrenia receiving second generation antipsychotics.
The primary endpoint was change from Baseline in Spatial Span Test score at Day 8 of treatment periods. The sponsor's ANOVA reported mean differences of 0.232 and 0.133 versus placebo, with 95% confidence intervals that included zero. The estimates are imprecise, and the record does not establish a clinically important threshold, equivalence, or an effect beyond the measured task and timeframe.