Atomoxetine and Huntington's Disease: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Atomoxetine and Huntington's Disease (NCT00368849), a randomized phase 2 study. The primary outcome is Conners' Adult Attention Rating Scale (CAARS).

2. Clinical Question

3. Trial Design

The registry describes a phase 2, randomized, quadruple-masked, placebo-controlled crossover study of atomoxetine for attention deficits in adults with mild Huntington's disease. The listed enrollment was 20, and the study status is completed. Its start is recorded as 2005-11 and primary completion as 2008-02. The sponsor was the University of Iowa.

A crossover design differs from a parallel-group design because treatment conditions are evaluated within a study organized around treatment periods rather than assigning participants permanently to only one treatment condition. In general, this can make within-person comparisons informative. The registry identifies this study as crossover, but the treatment sequence, period structure, washout arrangements, and how possible carryover effects were addressed are not reported in the registry record. The detailed randomization procedure is also not reported in the registry record.

The treatment descriptions state that participants received atomoxetine 40 milligram twice a day for 4 weeks or matching placebo twice a day for 4 weeks. The primary outcome comparison uses 18 participants for atomoxetine and 20 for placebo, and its description says the analysis was based on completers. The reason the arm counts differ is not reported in the registry record.

CAARS was the primary outcome. The two secondary outcomes were the Symptom Checklist-90-Revised (SCL-90-R) and the Unified Huntington Disease Rating Scale (UHDRS) Total Motor Score. The registry lists five outcome measures and five analyses, with two secondary outcomes posted. The original sample-size rationale, planned enrollment assumptions, and whether the trial had interim analyses are not reported in the registry record.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Before assignment: Participants were screened before baseline for the presence of attentional problems through interview, medical status (including safety laboratories and electrocardiogram), and history for inclusion/exclusion criteria.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Analysis was based on number of completers

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.

6. Primary Endpoint

The registry lists the primary outcome as Conners' Adult Attention Rating Scale (CAARS), measured over There are two time points for this measure: baseline and after 4 weeks of treatment.

The primary endpoint was change from baseline in the Conners' Adult Attention Rating Scale (CAARS), a self-report measure of attention. The registry describes it as a frequently used self-rating measure for adult Attention Deficit Hyperactivity Disorder. It contains 66 items, each scored from 0 to 3 points, and higher total scores represent greater impairment. The reported outcome is the change in score for each treatment condition, not a final score alone.

Attention and focus were among the study's stated interests, making a self-report attention scale relevant to the question being examined. A change score expresses how the recorded score differed from baseline during a treatment condition. A negative mean change indicates a decrease in the scale score; because higher scores indicate greater impairment, direction is interpretable in relation to that scale definition. It does not, by itself, establish why a score changed or whether a difference is clinically important.

The registry describes two time points for this measure: baseline and after 4 weeks of treatment. The outcome is reported as a mean with a standard error. The registry record does not report a threshold for a clinically important CAARS change, so the size of a score difference cannot be classified as clinically important from the posted information alone.

7. Results Posted in the Registry

• Atomoxetine: mean -2.88 versus -2.24 on control; difference -0.64 (95% CI -3.69 to 2.41), standardized effect d = -0.13; z-test p = 0.681.

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.

Symptom Checklist-90-Revised (SCL-90-R)

• 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:
  • Atomoxetine: mean -4.20 versus -4.64 on control; difference 0.44 (95% CI -4.69 to 5.57), standardized effect d = 0.05; z-test p = 0.866.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Atomoxetine and the control. The interval gives the range of effects that remain compatible with the data.

Unified Huntington Disease Rating Scale (UHDRS) Total Motor Score

• 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:
  • Atomoxetine: mean 0.42 versus -0.35 on control; difference 0.77 (95% CI -4.08 to 5.62), standardized effect d = 0.10; z-test p = 0.756.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Atomoxetine and the control. The interval gives the range of effects that remain compatible with the data.

The two posted secondary outcomes add information about symptom ratings and motor score, but their overall pattern does not create a consistent direction across the domains studied. The unadjusted re-calculated intervals for both include zero, and the sponsor-reported tests do not provide a clear separation between treatment conditions. These results are best treated as exploratory context alongside the primary attention outcome, rather than as a separate basis for a firm conclusion.

The secondary measures are related to the study's broader interests in symptoms and daily functioning, but they are not interchangeable with CAARS. The SCL-90-R and UHDRS Total Motor Score measure different constructs, so their numerical changes cannot be read as replications of an attention-scale result. Their role is to describe additional outcomes recorded during the study, not to establish the primary question by themselves.

Unadjusted secondary results carry less weight when several outcomes are examined because each additional test creates another opportunity for an apparently notable finding by chance. In general, a multiplicity plan can address that issue by defining how inference is controlled across outcomes. The registry record does not report whether such a plan was used, nor does it report a hierarchy for the secondary outcomes. The reported secondary p-values should therefore not be treated as multiplicity-adjusted evidence.

The record lists five outcome measures and five analyses, while two secondary outcomes are posted. The relationship between all listed measures and the posted analyses is not described in enough detail to reconstruct a complete testing strategy. This uncertainty is an additional reason to interpret secondary findings cautiously and to avoid elevating any single result beyond its stated exploratory role.

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

• Symptom Checklist-90-Revised (SCL-90-R)
• Unified Huntington Disease Rating Scale (UHDRS) Total Motor Score

9. Statistical Interpretation

10. Statistical Methods Explained

The posted results include arm-level means and standard errors, a sponsor-reported ANCOVA, and simple unadjusted re-calculations based on the posted summary statistics. These are different forms of analysis and should not be treated as interchangeable. The registry identifies the primary analysis population as completers. It does not report a detailed statistical analysis plan, the planned handling of missing observations, or the specific assumptions used for the sponsor's ANCOVA.

What does a mean change describe?

For a continuous outcome such as CAARS, the mean is the arithmetic average of the observed score changes in a treatment condition. A mean change of -2.88 describes the average change among the participants included in that arm's reported result. It does not mean every participant changed by that amount. The standard error describes the uncertainty in an estimated mean, rather than the spread of individual participants' scores. In general, a standard error becomes smaller when an estimate is based on more information, though its interpretation depends on the design and analysis.

What is the treatment contrast?

The re-calculated primary contrast is the atomoxetine mean change minus the placebo mean change. The reported estimate is -0.64. This summarizes the difference between the two posted means on the CAARS change scale. It is an unadjusted calculation from summary statistics, not the sponsor's ANCOVA result. The value is a point estimate: it gives one central estimate of the contrast, but not the uncertainty surrounding that estimate.

How should the confidence interval be read?

A confidence interval describes uncertainty around an estimated contrast under the method used to calculate it. In general, a wider interval indicates less precision, while a narrower interval indicates greater precision. The re-calculated interval for the primary contrast runs from -3.689 to 2.409. Since zero lies within this interval, the posted summary data are compatible with no difference as well as with contrasts in either direction. The confidence level and the interval-construction method are not reported in the registry record, so they should not be inferred from the interval alone.

What does the p-value add?

The unadjusted p-value for the re-calculated primary contrast is 0.681. In general, a p-value assesses how compatible observed data are with a specified null hypothesis under the analysis model; it is not a measure of the size or clinical importance of an effect. It is also not the probability that the null hypothesis is true. The sponsor's ANCOVA reports p = 0.63. These p-values refer to their respective analyses, and the registry does not report further details about the sponsor model or its assumptions.

Why distinguish ANCOVA from an unadjusted calculation?

ANCOVA is a model-based method that compares groups while accounting for one or more covariates. The registry names ANCOVA and reports a mean difference in final values, but does not identify the covariates or describe the model specification. The re-calculation instead uses the posted treatment-condition summary statistics and does not reproduce an ANCOVA model. In general, results from adjusted and unadjusted analyses can differ because they use information and assumptions differently. Here, the numerical estimates are close, but their methods and outcome descriptions are not the same.

What does crossover add to the interpretation?

In general, a crossover design can use within-participant information because participants receive treatment conditions during different periods. Such designs require attention to treatment sequence, period effects, and possible carryover from an earlier condition. The registry labels this trial crossover but does not report sequence details, washout arrangements, or an analysis of period or carryover effects. The posted primary sponsor method is called ANCOVA, but the specific model details are not reported. It is therefore not possible to determine from the registry record how crossover features entered that analysis.

Why can over-dispersion matter?

For some outcomes, observed variability can exceed what a simple model assumes. In general, over-dispersion can make standard errors too small if a model fails to account for the extra variability, leading to intervals that appear more precise than warranted. The posted primary endpoint is continuous and reported with standard errors; the registry does not describe an over-dispersion assessment or identify such a problem. This concept is relevant when evaluating model assumptions generally, not as a reported finding in this trial.

Finally, the registry does not report multiplicity procedures, a protocol-defined significance threshold, a detailed sample-size justification, or interim analyses. Those omissions matter for interpreting a collection of outcomes and the planning context, but they do not alter the arithmetic of the posted summaries.

11. Confidence Intervals and Precision

The re-calculated primary estimate is -0.64, and its confidence interval extends from -3.689 to 2.409. The interval includes zero and spans contrasts in both directions. This means the estimate is not precise enough to pin down whether the contrast favors a lower mean change with atomoxetine, a higher mean change, or little difference. It also does not establish that the conditions are equivalent.

The arm-level standard errors are 1.1 for atomoxetine and 1.1 for placebo. Standard error reflects uncertainty in an estimated mean, not the range of individual scores. The confidence interval expresses uncertainty about the contrast, and its width is a useful indication of precision. The confidence level and exact interval method are not reported in the registry record.

The posted sample is small, with the primary analysis based on completers and different numbers reported for the two treatment conditions. These features limit the information available for estimating the contrast. The registry does not report enough about missing observations or the crossover analysis to assess how those issues affect uncertainty. The sponsor reports a point estimate and p-value but no confidence interval, so precision for that analysis cannot be evaluated from a posted sponsor interval.

Statistical uncertainty is not the only limitation: the registry does not report a threshold for a clinically important CAARS difference. Consequently, even a more precise estimate would need a meaningful clinical benchmark for interpreting practical importance. The interval should be read as uncertainty around this study's estimate, not as a prediction interval for individual participants or as a guarantee about future studies.

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.

The sample-size figures are planning illustrations based on the observed effect, not the trial's original design assumptions. For these continuous outcomes, the figures refer to participants per arm, not total events. The listed assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation; the target effect is the stated fraction of the observed effect. The trial's own sample-size justification and original planning assumptions are not reported in the registry record.

The 80% power column describes the number of participants per arm that the planning calculation estimates would be needed to have an 80% chance of detecting the specified effect under the stated assumptions, if that effect and the assumptions were correct. The 90% power column uses a higher target chance of detecting that effect, and therefore generally calls for more participants per arm. Power is a design property under assumptions, not a guarantee that a particular study will produce a statistically clear result.

The rows consider planning for 100%, 75%, and 50% of the observed effect. A smaller target effect requires more participants to distinguish it from random variation, all else equal. The displayed values should be treated as illustrations rather than a recommendation for a future trial: the observed effect in a small study may be an imprecise basis for planning, and the assumptions may not capture a crossover design. The calculations are not observed power.

These calculations do not reconstruct the original design. The registry record does not report why the trial enrolled 20 participants, what effect size was anticipated, or what design-specific considerations informed its planned size. The illustrations also do not include a stated allowance for incomplete observations or crossover-specific features beyond the assumptions listed.

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 z_1−α/2 = 1.960) and the desired power (z_1−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

1. Observed difference Δ = -0.640; pooled standard deviation σ = 4.802.
2. n = 2 × (1.96 + 0.842)² × 4.802² / -0.640² = 883.7, rounded up to 884 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 <- -0.64                      # observed difference in means
sigma <- 4.80179364635989                     # 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(368849)
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 = 884 (80% power), 1,183 (90% power)
 75% of observed effect: n per arm = 1,571 (80% power), 2,104 (90% power)
 50% of observed effect: n per arm = 3,535 (80% power), 4,732 (90% power)
power.t.test: 884.6 
Simulated power at n = 884 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

The sponsor's primary analysis is reported as ANCOVA, with a mean difference in final values of -0.65 and p = 0.63. The unadjusted re-calculation from the posted change summaries gives a mean difference of -0.64, a confidence interval from -3.689 to 2.409, and p = 0.681. The estimates are numerically close, but they arise from differently described analyses: one is an ANCOVA of final values, while the re-calculation contrasts posted mean changes.

The registry does not report the ANCOVA covariates, model specification, or a confidence interval for the sponsor result. It is therefore not possible to reproduce the sponsor's analysis or assess its precision from the posted information. The re-calculated interval is not a substitute for an interval from the sponsor's model. Because the registry does not flag a discrepancy, the two estimates can be described as broadly similar in their central values, while retaining the distinction between methods.

The sponsor's reported p-value should be read as a result of its own analysis, not as a direct restatement of the unadjusted calculation. Neither p-value alone establishes clinical importance or equivalence. The posted primary evidence remains imprecise, and the registry's missing detail limits evaluation of the model assumptions and crossover-specific analysis.

15. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when several outcomes, time points, or statistical comparisons are examined. In general, the more tests performed, the greater the chance that at least one result appears unusual even when there is no underlying difference. Statistical plans can address this by defining a primary outcome, a testing hierarchy, or an adjustment approach. The registry identifies CAARS as the primary outcome and lists two secondary outcomes, but multiplicity procedures and the planned order of testing are not reported in the registry record.

The record reports five outcome measures and five analyses, while only two secondary outcomes are posted in the results information. The complete relationship between the listed outcomes and analyses is not reported. It is therefore not possible to determine whether the posted p-values were selected from a larger set of planned tests or whether adjustments were made elsewhere. The secondary p-values should be read as unadjusted unless the registry states otherwise; no such adjustment is reported.

The primary outcome description says the analysis was based on completers. The arm-level primary summaries include 18 for atomoxetine and 20 for placebo. The registry does not explain the difference in counts, identify the reasons for incomplete observations, or describe an intention-to-treat analysis. Methods for imputation, handling missing outcome values, or sensitivity analyses are not reported in the registry record. This leaves uncertainty about how incomplete data may have affected the estimates.

The study is labeled crossover, but sequence, period, and washout details are not reported. The registry also does not describe how the analysis accounted for those design features or whether carryover was considered. The ANCOVA model specification is not posted, and no interim analyses or stopping rules are reported. These are limitations in the available record; they do not establish that a particular procedure was absent, only that its use is not reported.

The original sample-size calculation and its assumptions are also not reported. The separate planning illustrations based on the observed effect do not fill that gap and should not be confused with the trial's own design rationale.

16. Safety Results

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

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: inpatient hospitalization (5.0%), an important medical event (5.0%).

The registry lists serious adverse events affecting 0 of 20 participants at risk in the atomoxetine group and 3 of 20 in the matching-placebo group. It lists other adverse events affecting 10 of 18 participants at risk for atomoxetine and 7 of 20 for matching placebo. These are counts of participants with reported events, not estimates of comparative risk adjusted for study design.

The serious-event terms listed include Inpatient Hospitalization and An Important Medical Event, each recorded as 5.0%. The registry does not provide event-level narratives in the information summarized for these results, so the terms should not be used to infer cause, severity beyond their serious-event classification, or relationship to treatment. The listed term percentages should be read as registry entries, not as a basis for reconstructing additional totals.

Deaths are not reported in the registry record. The different at-risk counts for other adverse events and the absence of further detail about event timing, recurrence, or analysis mean these figures are descriptive. They should not be treated as a definitive comparison of safety between treatment conditions.

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

The posted primary result is an estimate of the difference between mean CAARS changes under atomoxetine and placebo in this completed crossover study. The re-calculated contrast is -0.64, and the interval from -3.689 to 2.409 includes zero. The sponsor's ANCOVA estimate is -0.65 with p = 0.63. Together, these results describe an uncertain comparison in this study; they do not establish equivalence, prove that a difference exists, or determine a clinically meaningful effect.

Statistical uncertainty should not be confused with evidence that no effect is possible. An interval that includes zero can also include nonzero values in either direction. Conversely, a point estimate on one side of zero does not by itself establish a reliable or important difference. The registry does not report a clinically important threshold for CAARS, so the practical significance of the estimate cannot be determined from the score difference alone.

The study is small and its primary analysis is described as based on completers. Details about missing data and the crossover analysis are limited in the registry record. Those limitations constrain the interpretation of both the point estimate and its uncertainty. The results also concern the measured outcomes and participants described in this record; they cannot automatically be generalized to other populations, durations, or treatment schedules.

The secondary results describe additional symptom and motor measures, but do not resolve the uncertainty in the primary comparison. Multiplicity handling is not reported, which further counsels against treating isolated secondary results as confirmatory. Adverse-event counts are descriptive and do not independently establish comparative safety.

These findings are a statistical account of what the registry reports. They are not medical advice, and they do not by themselves support a treatment decision. The registry does not report enough detail to resolve all design, analysis, or clinical-importance questions.

18. Why This Trial Matters Statistically

This study is statistically informative because it brings together a randomized, masked, placebo-controlled comparison and a crossover design for outcomes related to attention and Huntington's disease. Its primary measure is explicitly described as a self-report attention scale, and the results include both a sponsor-reported ANCOVA and a re-calculation from posted summaries. That makes it possible to distinguish a model-based sponsor result from a simpler comparison of reported means.

The close central estimates are useful context, but precision remains crucial. The re-calculated interval spans zero and includes values in both directions. This illustrates why an estimated difference should be read with its uncertainty rather than judged from the point estimate or p-value alone. The sample-size illustrations also show how strongly planning requirements depend on the effect size one aims to detect, without serving as observed evidence about power in this completed study.

The record also demonstrates why design details matter. Crossover trials can use within-participant information, but sequence, period, and carryover handling are essential for understanding the analysis. Those details are not reported. Similarly, the completer-based primary analysis and absent missing-data description constrain evaluation of how participants contributed to the results.

Finally, several outcomes were measured, but multiplicity handling is not reported. This makes the distinction between a primary result and secondary exploratory evidence especially important. The study offers a focused statistical example of interpreting uncertainty, analysis populations, and reporting gaps without treating a non-small p-value as proof of no effect or a point estimate as proof of an important effect.

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 registry identifies the study as crossover but does not report the treatment sequence, period structure, washout arrangements, or how period and carryover effects were handled. Without those details, readers cannot evaluate whether the posted analysis fully reflects the design. The sponsor's method is labeled ANCOVA, but its model specification and covariates are not reported.

The primary endpoint analysis is described as based on completers. The reported treatment-condition counts differ, and the registry does not explain why or describe how missing observations were handled. No intention-to-treat analysis or sensitivity analysis is reported in the record. These omissions limit assessment of the influence of incomplete data.

The posted sponsor result has no confidence interval, and the confidence level and calculation method for the re-calculated interval are not reported. The registry also does not provide a clinically important difference threshold for CAARS, making it difficult to judge practical importance from the numerical contrast alone.

The registry does not report the original sample-size justification, multiplicity procedures, interim analyses, or a detailed statistical analysis plan. The planning illustrations based on the observed effect cannot substitute for the original design rationale. Secondary findings are consequently difficult to place within a prespecified testing strategy.

Enrollment was 20, and the primary summaries are based on completers. The information therefore provides limited precision, as reflected in the interval spanning both sides of zero. The record does not provide enough detail to determine how representative the enrolled participants were of other people with Huntington's disease or how the results might apply beyond the treatment periods described.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Atomoxetine and Huntington's Disease — NCT00368849.
• Registry record last updated 2012-12-20; status last verified 2012-12.
• Results first posted 2012-11-27.
• 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.

23. Record Summary

NCT00368849 is a completed phase 2 randomized, quadruple-masked, placebo-controlled crossover study sponsored by the University of Iowa. Enrollment was 20. It examined atomoxetine versus matching placebo for attention deficits in adults with mild Huntington's disease, with treatment descriptions specifying 4 weeks for each condition.

The primary outcome was change in CAARS score, analyzed among completers. The re-calculated mean difference was -0.64, with a confidence interval from -3.689 to 2.409 and p = 0.681. The sponsor reported an ANCOVA mean difference in final values of -0.65 and p = 0.63. Two secondary outcomes were posted; multiplicity handling, missing-data methods, crossover analysis details, and the original sample-size justification are not reported in the registry record.