Improving Human Cerebrovascular Function Using Acute Intermittent Hypoxia: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Improving Human Cerebrovascular Function Using Acute Intermittent Hypoxia (NCT05164705), a randomized na study. The primary outcome is Resting Cerebral Blood Flow.

2. Clinical Question

The clinical question is about physiological measures of brain perfusion and regulation in healthy adults. It is not a question about a patient-important clinical event or treatment of a diagnosed condition. The registry summary says MRI was used to assess whether repeated exposure could improve brain blood flow or blood-flow regulation. That wording describes the study question, not a conclusion about benefit.

3. Trial Design

The registry identifies this as a randomized, single-masked, crossover study sponsored by Northwestern University. Its status is completed. The listed study dates are May 3, 2022, for the start and April 5, 2024, for primary completion. The registry enrollment is 33. The outcome-specific analysis groups list 18 participants for intermittent hypoxia and 21 for sham; these group figures should not be added together or assumed to describe separate people in a crossover study.

In a crossover design, participants are assigned to experience study conditions in a sequence, and comparisons can use information from the same participant under different conditions. That is a general description of the design type. The registry record does not report the actual treatment sequence, period structure, washout interval, or whether all participants completed both conditions. It also does not identify who was masked under the single-masking designation.

Both intervention descriptions specify visits 2-4 times per week for three weeks. The primary outcome description states that phase-contrast MRI and arterial spin labeling MRI were used to quantify whole-brain and cortical gray matter perfusion before and after the intervention. The registry gives a 4-week timeframe for the primary outcome and cerebrovascular reactivity. The relationship between this timeframe and the precise scan schedule is not further explained in the registry record.

The registry lists phase as NA. It records one primary outcome and one secondary outcome. The original sample-size justification, prespecified analysis details beyond the posted sponsor analysis, and trial-specific missing-data procedures 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: All subjects underwent a practice session, prior to assignment, to ensure they were comfortable with the study procedures and intervention. Individuals could opt out of or be excluded from further participation at this time. 8 participants chose to opt out after the practice session, hence why they are included in the Protocol Enrollment but not in the Participants Assigned.

Overall Study

Reasons for not completing this period:

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 Resting Cerebral Blood Flow, measured over 4 weeks.

The primary endpoint is resting cerebral blood flow, expressed as change in CBF in ml/100g/min. The registry describes MRI measurements of whole-brain and cortical gray matter perfusion before and after the three-week intervention. Cerebral blood flow is a continuous physiological measure: its mean describes the average change in the analyzed group, while the standard deviation describes variation among participants.

Resting perfusion is used to characterize blood flow to the brain under resting measurement conditions. Comparing its change after intermittent hypoxia with change after sham exposure addresses whether the groups' measured changes differ. It is a physiological endpoint, not a direct measure of symptoms, function, or a clinical event. The registry does not report a threshold for a clinically meaningful change or explain how such a threshold was chosen.

The posted arm means are 0.5 for intermittent hypoxia and -2.4 for sham, with standard deviations of 10.6 and 7.9, respectively. The unadjusted recalculation expresses the between-group contrast as a mean difference of 2.9, with a confidence interval from -3.049 to 8.849. These statistics describe the measured endpoint and its uncertainty; they do not by themselves establish a clinical effect.

7. Results Posted in the Registry

• Intermittent Hypoxia: mean 0.50 versus -2.40 on control; difference 2.90 (95% CI -3.05 to 8.85), standardized effect d = 0.31; z-test p = 0.339.

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.

Cerebrovascular Reactivity

• 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 deviations.
• Result:
  • Intermittent Hypoxia: mean -0.01 versus -0.03 on control; difference 0.02 (95% CI -0.13 to 0.17), standardized effect d = 0.08; z-test p = 0.797.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Intermittent Hypoxia and the control. The interval gives the range of effects that remain compatible with the data.

Cerebrovascular reactivity is the one posted secondary outcome. Its estimated contrast is close to zero relative to the uncertainty in the unadjusted calculation, and the sponsor-reported analysis also has a non-small p-value. Taken together with the primary result, the secondary outcome does not provide a clearly distinct pattern that resolves the uncertainty around resting cerebral blood flow. The outcomes measure related aspects of cerebrovascular function, but they are not the same endpoint and should not be combined as if they were one result.

Secondary outcomes can help describe whether findings across related measures are consistent, but they generally carry less confirmatory weight than a designated primary outcome. Testing multiple outcomes can increase the chance of obtaining at least one apparently notable result by chance. A prespecified multiplicity procedure can address that issue, but whether one was planned or applied is not reported in the registry record. The posted secondary p-value is unadjusted, and no adjustment strategy is described.

The secondary result should therefore be treated as supportive context rather than independent proof for or against the primary finding. The registry record does not state a hierarchy of secondary hypotheses or report whether the outcome was selected before analysis. That missing context limits how strongly the secondary evidence can be interpreted.

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

• Cerebrovascular Reactivity

9. Statistical Interpretation

10. Statistical Methods Explained

The primary outcome is continuous, and the posted group summaries are means and standard deviations. The comparison is therefore expressed as a difference in means, using intermittent hypoxia minus sham. This makes the direction of the estimate interpretable: a positive value means the posted mean change was higher in the intermittent-hypoxia group, while a negative value means it was lower. The calculated mean difference is 2.9.

What does the confidence interval describe?

A confidence interval gives a range of values compatible with the observed data under the method used to calculate it. It reflects sampling uncertainty as well as the estimated effect; it is not a range containing a specified proportion of individual participants' measurements. For the primary comparison, the 95% interval is -3.049 to 8.849. Since zero lies within that interval, the data do not distinguish a nonzero average difference from no difference at the conventional two-sided 0.05 threshold. The width also indicates that the estimate leaves substantial uncertainty about the size and direction of the difference.

What does the p-value say?

The unadjusted p-value is 0.339. In general, a p-value describes how unusual data at least as inconsistent with a specified null hypothesis would be if that null hypothesis and the analysis assumptions were true. It is not the probability that the null hypothesis is true, nor is it a measure of clinical importance. The p-value does not replace the effect estimate and confidence interval: those show the estimated scale and precision more directly.

Why distinguish the recalculation from the sponsor analysis?

The recalculation uses the posted group means and standard deviations for a simple unadjusted comparison. It is not the sponsor's mixed-model analysis and does not incorporate any participant-level pairing, sequence, or period terms. The registry reports the sponsor method as Mixed Models Analysis, with the parameter described as Slope. Its estimate is -2.86 and its p-value is 0.33. The model formula, covariates, and detailed handling of the crossover structure are not reported in the registry record. The sponsor result should therefore be read as the reported trial analysis, while the recalculation provides a transparent, summary-statistic-based comparison rather than a substitute for that model.

Why can crossover structure matter?

As a general statistical point, crossover studies can benefit from comparing conditions within the same participant, because stable characteristics of a participant may then contribute less to the contrast. However, period effects, treatment sequence, carryover, and missing measurements can matter. A model that accounts for the design may use information differently from a comparison treating the two posted groups as independent. The registry record identifies a crossover design but does not report sequence details, a washout interval, or enough model specifications to assess how those features were handled. The unadjusted calculation should not be mistaken for a paired or crossover-adjusted estimate.

What do the standard deviations add?

Standard deviation describes the spread of participant-level measurements around a group mean. It is different from the standard error, which describes uncertainty in an estimated mean. In the primary outcome, the reported standard deviations are 10.6 and 7.9. The recalculation uses these summaries to characterize the contrast and its uncertainty. In general, greater variability makes a mean difference harder to estimate precisely when other features are held constant. When data are clustered, repeated, or otherwise not independent, analyses may need to reflect that structure rather than rely on a simple independent-groups calculation.

Over-dispersion is a general concern when observed variability exceeds what a statistical model assumes. For continuous outcomes, an inaccurate variance model can affect standard errors and confidence intervals; for count outcomes, over-dispersion means counts vary more than a simple count model expects. The registry reports continuous outcomes and does not describe over-dispersion as an issue. This general concept should not be read as a claim that the trial had that problem.

Finally, p-values and intervals depend on assumptions about the data and analysis. The posted recalculation is explicitly unadjusted, and the sample-size illustrations use a normal approximation. The registry does not report the full protocol or statistical analysis plan, so details such as the primary model's covariates, missing-data approach, and prespecified decision rules cannot be verified from the registry record.

11. Confidence Intervals and Precision

The primary estimate is a mean difference of 2.9 in change in cerebral blood flow, with a 95% confidence interval from -3.049 to 8.849. The interval crosses zero and spans values on both sides of it. This means the result does not tightly determine whether the average difference favored one condition or the other, nor does it give a narrow estimate of its possible size. The endpoint's units are ml/100g/min.

Confidence intervals are useful because they display both the estimated contrast and its uncertainty. They are not proof that every value inside the interval is equally plausible, and they do not guarantee that the true effect lies within the interval. Their interpretation depends on the model and assumptions used. The registry does not state a clinically important threshold for this measure, so the interval cannot be classified against a trial-defined threshold for meaningful benefit or harm.

The sponsor's analysis reports a slope and p-value but no confidence limits in the registry record. Consequently, the precision of that reported model estimate cannot be assessed from a posted interval. The unadjusted recalculation does provide an interval, but its assumptions differ from the sponsor's mixed model and the crossover structure may be relevant. Both points should be kept in view when interpreting how precisely the treatment contrast is estimated.

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 own design calculation. For these continuous outcomes, each figure is participants per arm, not total events. The listed 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 the stated fraction of the observed effect. The trial's original sample-size assumptions and justification are not reported in the registry record.

The 80% power column gives an illustrative number of participants per arm for a design with an 80% chance of detecting the specified effect under the stated assumptions, if that effect and the model assumptions are correct. The 90% column uses a higher target probability of detection and therefore generally requires more participants per arm. Neither column describes the probability that the observed trial result is true, and these figures are not observed power.

The rows that plan for 100%, 75%, and 50% of the observed effect show how planning changes when the target effect is smaller. A smaller effect is harder to distinguish from random variation, so more participants are needed for the same target power. The resulting numbers are sensitive to the observed estimate, which can itself be uncertain. They are therefore illustrations for planning, not recommendations or evidence that a future study will attain the stated power.

For the primary outcome, the planning figures are based on the posted observed contrast. The secondary-outcome figures are based on its own observed contrast and are much larger. Those differences should be read as a consequence of the inputs used by the illustration, not as a direct comparison of the outcomes' clinical importance.

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 = 2.900; pooled standard deviation σ = 9.239.
2. n = 2 × (1.96 + 0.842)² × 9.239² / 2.900² = 159.3, rounded up to 160 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 <- 2.9                      # observed difference in means
sigma <- 9.23904756996088                     # 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(5164705)
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 = 160 (80% power), 214 (90% power)
 75% of observed effect: n per arm = 284 (80% power), 380 (90% power)
 50% of observed effect: n per arm = 638 (80% power), 854 (90% power)
power.t.test: 160.3 
Simulated power at n = 160 per arm: 0.805 (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 registry reports a Mixed Models Analysis for the primary outcome, with parameter Slope, value -2.86, and p = 0.33. It does not give a confidence interval for that estimate. The unadjusted recalculation from posted group summaries is a mean difference of 2.9, with a 95% confidence interval from -3.049 to 8.849 and p = 0.339. These are different statistical expressions and should not be treated as identical estimates. The registry does not report the model equation, arm coding, or details needed to reconcile the signs or convert the slope to the unadjusted contrast.

The reported p-values are similar in broad terms, but both analyses leave uncertainty about the treatment contrast. The sponsor's mixed model is the trial's reported analysis; the recalculation is a simple summary-statistic comparison that does not reproduce the model or account explicitly for the crossover structure. There is no flagged discrepancy in the registry record, but that does not make the two methods interchangeable. The sponsor's result should be interpreted using the information available about its method, and the missing model details limit further assessment.

15. Multiplicity, Missing Data and Analysis Populations

The registry posts one primary outcome and one secondary outcome, with analyses for both. It does not report a multiplicity adjustment or a testing hierarchy for the secondary endpoint. In general, when several hypotheses are tested, the chance of at least one apparently positive result can rise unless the analysis plan accounts for multiple testing. This concern is relevant to interpretation, but the registry record does not establish whether an adjustment was prespecified elsewhere or applied in the trial analysis. The posted secondary p-value should be read as unadjusted.

The crossover designation means that participant measurements may be related across conditions. A suitable analysis may need to account for that within-participant structure and for sequence or period effects. The registry identifies the sponsor method as a mixed model but does not report the model formula, fixed or random effects, sequence terms, period terms, or carryover assessment. The unadjusted recalculation cannot fill in those missing details.

The registry record does not report the number or pattern of missing outcome measurements, how missing data were handled, or whether any imputation was used. It also does not specify the analysis population, such as whether the sponsor analysis included all randomized participants or only participants with measurements under particular conditions. The outcome-specific group sizes are posted, but those figures alone do not explain exclusions or missingness.

The original statistical analysis plan, interim analyses, and sample-size justification are not reported in the registry record. Their absence from the record does not establish that such procedures did not exist; it means they cannot be assessed from the posted information. These reporting gaps matter because prespecified methods help readers distinguish planned confirmatory analyses from exploratory choices made after seeing data.

16. Safety Results

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

Deaths

Other (non-serious) adverse events

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

Most frequent non-serious adverse event terms

For serious adverse events, the registry reports zero affected participants in the acute intermittent hypoxia group and zero in the sham acute intermittent hypoxia group. The recorded numbers at risk for serious events are 25 in each group. Deaths are also reported as zero in each group.

For other, non-serious adverse events, one affected participant is reported in each group, with 25 at risk in each. These are participant counts as recorded, not a complete description of event types, timing, severity, or relatedness. The registry does not list serious-event terms. The record does not provide enough detail to determine whether all event categories were collected and reported in the same way, or how these safety denominators relate to the outcome-analysis groups.

Zero reported serious events in these groups is a description of the registry data, not proof that serious harms are impossible or that the two conditions have identical safety profiles. The available figures are limited to the reported event counts and at-risk denominators.

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

The posted results describe changes in two physiological measures after intermittent hypoxia and sham exposure in healthy adults. For resting cerebral blood flow, the unadjusted estimate is a mean difference of 2.9, but its confidence interval includes zero and extends in both directions. The sponsor's mixed-model result also has a non-small p-value. Together, these findings leave uncertainty about the size and direction of the contrast; they do not establish that the conditions are equivalent.

The result does not show whether an observed change would be clinically important. Resting cerebral blood flow and cerebrovascular reactivity are physiological endpoints, and the registry does not report a threshold linking their changes to a patient-important outcome. It also does not report clinical outcomes such as symptoms or functional change. The trial's stated population is healthy adults, so the results cannot be assumed to apply to people with neurological or vascular disease.

The study was randomized and crossover, but important analytic details are not available in the registry record. The posted summary-statistic recalculation is not a replacement for a design-aware model. The sponsor's analysis is reported as a mixed model, but its full specifications and confidence interval are absent. These limitations affect how precisely the results can be interpreted.

Accordingly, the record supports a cautious description: the measured outcomes did not yield a precise, clearly separated estimate of change between conditions in the posted analyses. It does not justify a treatment recommendation or a broad claim about clinical benefit or lack of benefit.

18. Why This Trial Matters Statistically

This study illustrates why a point estimate and a p-value are not enough to describe a trial result. The primary mean difference is positive, but the confidence interval includes zero and spans a substantial range in the outcome's units. Considering the interval makes the uncertainty visible and discourages interpreting a non-small p-value as proof of no effect.

The crossover design also highlights the importance of analysis matching study structure. A within-participant design can have different precision and assumptions from an independent-groups comparison. The registry provides a sponsor mixed-model result and group summaries, but not the model details needed to assess how the design was represented. A transparent unadjusted recalculation is useful context, while remaining distinct from the reported analysis.

The secondary outcome and sample-size illustrations add further statistical lessons. Multiple outcomes require attention to multiplicity, and the registry does not report an adjustment strategy. Planning calculations based on an observed effect are sensitive to uncertainty in that effect; they are illustrations rather than observed power or a substitute for a prospective design justification.

Finally, the result concerns physiological measurements in healthy adults. Distinguishing statistical evidence, precision, endpoint meaning, and population scope is essential before drawing conclusions beyond what the registry reports.

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 record leaves several trial-specific details unavailable. It does not report the crossover sequence, period structure, washout interval, or who was masked. Those details would help assess possible period, sequence, and carryover effects and clarify how the mixed-model analysis handled the design.

The sponsor's reported primary analysis has no posted confidence interval, and its model specification is not described. The simple recalculation uses group means and standard deviations and is unadjusted; it should not be interpreted as a reconstruction of the crossover model. The record also does not report missing-data procedures, the analysis population, or the pattern of missing outcome measurements.

The registry does not state a clinically important threshold for either physiological endpoint, nor does it report patient-important outcomes that would connect the measurements to symptoms or function. The study population is described as healthy adults, limiting what can be inferred about other populations. The registry enrollment is 33, while the outcome-specific analysis groups list 18 and 21; the record does not explain the relationship between these figures, and they should not be summed to infer a number of unique participants.

Finally, multiplicity handling, the original sample-size rationale, interim analyses, and detailed prespecified analysis rules are not reported in the registry record. These are reporting limitations, not evidence that the trial did not have procedures in place.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Improving Human Cerebrovascular Function Using Acute Intermittent Hypoxia — NCT05164705.
• Registry record last updated 2026-07-20; status last verified 2026-06.
• Results first posted 2026-07-20.
• 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.

23. Record Summary

NCT05164705 is a completed randomized, single-masked crossover study sponsored by Northwestern University. It evaluated acute intermittent hypoxia against sham exposure in healthy adults. Both conditions involved visits 2-4 times per week for three weeks.

The primary outcome was change in resting cerebral blood flow at a 4-week timeframe, measured using MRI. The unadjusted recalculation gives a mean difference of 2.9, with a 95% confidence interval from -3.049 to 8.849 and p = 0.339. The sponsor reports a mixed-model slope of -2.86 with p = 0.33. Cerebrovascular reactivity was the posted secondary outcome.

The registry reports no serious adverse events or deaths in either group and one other adverse event in each. Key details about the crossover analysis, missing data, multiplicity, and original sample-size rationale are not reported in the registry record.