Sleep Apnea in TIA/Stroke: Reducing Cardiovascular Risk With Positive Airway Pressure: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Sleep Apnea in TIA/Stroke: Reducing Cardiovascular Risk With Positive Airway Pressure (NCT01446913), a randomized na study. The primary outcome is HOMA IR Change From Baseline.

2. Clinical Question

The registry record describes a study intended to develop a design for a longer randomized trial examining whether effective positive airway pressure therapy might reduce cardiovascular risk among people after TIA or stroke. The posted primary outcome is not a cardiovascular event; it is change in HOMA-IR. The estimates therefore address differences in this measured risk marker, rather than directly answering whether cardiovascular events were reduced. The registry also lists several secondary measures, including inflammatory markers, blood pressure, heart rate variability, and vascular measures. Their presence places HOMA-IR within a broader set of biological and physiological outcomes, but does not change the definition of the primary question.

3. Trial Design

The registry describes NCT01446913 as a completed, randomized, single-masked, parallel-group study sponsored by Yale University. The enrollment listed is 255. The condition entries are transient ischemic attack and stroke. The study dates listed are 2011-05 for start and 2013-12 for primary completion. The phase is recorded as NA.

Three groups appear in the posted results: Standard Intervention Group, Enhanced CPAP Intervention, and Usual Care. Standard intervention included an unattended sleep study, auto titrating CPAP, and standard CPAP support. Enhanced intervention included an unattended sleep study, autotitrating CPAP, and enhanced CPAP support. Usual care was described as usual care after TIA or stroke, with a sleep study at the end of the study. The primary comparisons use the standard intervention group as the reference, with separate estimates for enhanced CPAP intervention and usual care.

Random assignment is important to the design because it is intended to make the groups comparable at the start, on average. The registry does not report the randomization procedure, how assignment was concealed, or which people were masked. It also does not report the planned allocation ratio or detailed criteria for entering the study. Those features should not be inferred from the group names or the posted numbers.

The registry reports an intention-to-treat analysis population for the primary outcome. It does not describe the statistical model, adjustments, handling of missing outcome measurements, or the original sample-size justification. The posted group summaries and recalculated comparisons can describe the observed data, but do not fill in those unreported design and analysis details.

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: Three patients withdrew prior to randomization.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Intention to treat analysis population.

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 HOMA IR Change From Baseline, measured over Baseline and up to 12 months.

The primary endpoint is change from baseline in the homeostasis model assessment-estimated insulin resistance, or HOMA-IR, measured as a HOMA-IR Index. The registry says the change was assessed from baseline to the final measurement, which could be up to 12 months. The summary parameter is the mean, with standard deviation as the measure of spread. The named population is the intention-to-treat analysis population.

HOMA-IR is calculated from fasting insulin and fasting glucose; the registry describes the index as fasting insulin multiplied by fasting glucose and divided by 22.5. It is used in the study as one measure of cardiovascular risk. This makes it a biological risk marker rather than a count of clinical cardiovascular events. A difference in its mean change describes how the measured marker varied between groups over the stated period. It does not, by itself, establish a difference in myocardial infarction, heart failure, recurrent stroke, cardiovascular death, or other clinical outcomes.

The group means are 0.9 for standard intervention, 4.0 for enhanced CPAP intervention, and 4.1 for usual care. These are reported mean changes, not baseline or final HOMA-IR values. The considerable spread in some groups is relevant to how precisely their means can be compared. The registry record does not describe a clinically important threshold for interpreting the size or direction of a HOMA-IR change.

7. Results Posted in the Registry

• Enhanced CPAP Intervention: mean 4.00 versus 0.90 on control; difference 3.10 (95% CI 0.28 to 5.92), standardized effect d = 0.34; z-test p = 0.031.
• Usual Care: mean 4.10 versus 0.90 on control; difference 3.20 (95% CI -2.14 to 8.54), standardized effect d = 0.18; z-test p = 0.240.

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.

HOMA IR Change From Baseline With CPAP Use

• 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:
  • Some CPAP Use: mean 2.40 versus -0.20 on control; difference 2.60 (95% CI -2.02 to 7.22), standardized effect d = 0.34; z-test p = 0.270.
  • Good CPAP Use: mean 3.30 versus -0.20 on control; difference 3.50 (95% CI 0.12 to 6.88), standardized effect d = 0.53; z-test p = 0.042.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Some CPAP Use and the control. The interval gives the range of effects that remain compatible with the data.
  • The 95% confidence interval excludes no difference, so the mean is statistically higher for Good CPAP Use than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

CRP Change From Baseline With CPAP Use

• 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:
  • Some CPAP Use: mean 0.90 versus 0.80 on control; difference 0.10 (95% CI -5.88 to 6.08), standardized effect d = 0.01; z-test p = 0.974.
  • Good CPAP Use: mean -3.00 versus 0.80 on control; difference -3.80 (95% CI -10.18 to 2.58), standardized effect d = -0.28; z-test p = 0.243.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Some CPAP Use 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 Good CPAP Use and the control. The interval gives the range of effects that remain compatible with the data.

IL-6 Change From Baseline With CPAP Use

• 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:
  • Some CPAP Use: mean 3.30 versus -5.30 on control; difference 8.60 (95% CI -1.04 to 18.24), standardized effect d = 0.38; z-test p = 0.080.
  • Good CPAP Use: mean 11.90 versus -5.30 on control; difference 17.20 (95% CI 0.40 to 34.00), standardized effect d = 0.50; z-test p = 0.045.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Some CPAP Use and the control. The interval gives the range of effects that remain compatible with the data.
  • The 95% confidence interval excludes no difference, so the mean is statistically higher for Good CPAP Use than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

The registry lists secondary measures spanning metabolic, inflammatory, autonomic, blood-pressure, and vascular domains. The posted summaries for CPAP-use categories show that results do not move uniformly in one direction across these different measures. Some contrasts have confidence intervals that include zero, while some reported intervals do not. The group sizes also vary by CPAP-use category. Taken together, this is a mixed pattern rather than a single consistent signal across all secondary outcomes.

These outcomes complement the primary HOMA-IR comparison by examining related biological or physiological measures. They do not replace the primary endpoint, and they do not directly answer whether cardiovascular events differed. In particular, the registry’s secondary outcome list includes measures such as CRP, IL-6, catecholamines, heart rate variability, systolic blood pressure, flow-mediated vasodilation, and carotid intima-medial thickness. Such measures provide context about possible pathways or risk markers, but a change in a marker is not itself a clinical event outcome.

The CPAP-use categories are not the same as the randomized assigned groups. Comparisons among no, some, and good CPAP use may be affected by differences between participants in those categories. The registry record does not describe adjustment for such differences, and the posted comparisons are unadjusted. They therefore carry less weight for causal interpretation than a properly analyzed randomized comparison.

Multiplicity also matters: several outcomes and contrasts create more opportunities for apparently notable results by chance. The registry record does not report a correction or a hierarchy for secondary testing. These exploratory results can help describe the observed data and motivate questions, but should not be treated as independent confirmation of the primary result. No formal secondary analyses are reported in the registry record.

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

• HOMA IR Change From Baseline With CPAP Use
• CRP Change From Baseline With CPAP Use
• IL-6 Change From Baseline With CPAP Use
• Catecholamine Change From Baseline With CPAP Use
• Heart Rate Variability Change From Baseline With CPAP Use
• 24-H Mean Systolic Blood Pressure Change From Baseline With CPAP Use
• Flow-mediated Vasodilation Mean Change From Baseline With CPAP Use
• Carotid Intima-Medial Thickness Change From Baseline With CPAP Use Change

9. Statistical Interpretation

10. Statistical Methods Explained

The primary outcome is continuous: each participant’s HOMA-IR change is summarized using a mean and standard deviation. A mean difference expresses the contrast between two group averages in the original HOMA-IR units. The posted comparisons use standard intervention as the reference. A positive mean difference therefore indicates that the other group’s reported mean change is larger than the standard group’s mean change. It does not determine whether the difference is beneficial, because the registry record does not specify a favorable direction or clinical threshold for change.

What does the confidence interval represent?

A confidence interval describes the uncertainty in an estimate using a range of values compatible with the data under the calculation’s assumptions. A narrow interval indicates greater precision than a broad interval. For the enhanced-versus-standard primary comparison, the interval is 0.279 to 5.921. For usual care versus standard, it is -2.141 to 8.541. The latter interval includes zero, which represents no mean difference. These intervals are based on unadjusted recalculations from the posted summary statistics, not a reported adjusted model.

What does the p-value add?

The unadjusted p-value is a measure of how incompatible the observed comparison is with a null model of no difference, given the calculation’s assumptions. It is not an estimate of the probability that the null model is true, nor does it describe the clinical importance of the difference. The enhanced-versus-standard comparison has p = 0.031; the usual-care-versus-standard comparison has p = 0.24. Since no multiplicity adjustment is reported, these values should be read as unadjusted evidence for each comparison, not as results corrected for the full set of outcomes or contrasts.

Why does spread matter?

The standard deviation describes how dispersed individual changes are around a group mean. When individual measurements vary widely, the mean can be estimated less precisely for a given group size. In the primary outcome, the standard deviations are 3.0 for standard intervention, 12.7 for enhanced CPAP intervention, and 24.8 for usual care. The data are therefore notably more variable in the latter two groups. Over-dispersion, in general, means that observations vary more than a model assumes; if present and ignored, it can make standard errors and confidence intervals unreliable. The registry record does not report a model-based assessment of over-dispersion, so no such diagnosis should be assumed.

What can randomization and intention to treat tell us?

Randomization is designed to balance measured and unmeasured characteristics across assigned groups on average. An intention-to-treat analysis generally compares participants according to their randomized assignment, regardless of adherence, preserving the original randomized comparison. The registry names an intention-to-treat population for the primary outcome. It does not specify how that population was defined in practice, how participants without a final measure were treated, or whether all randomized participants contributed an outcome value. The group sizes in the posted primary outcome summaries are 86, 82, and 84.

Randomization alone does not guarantee that every source of bias is removed from the reported estimate. The registry does not describe allocation concealment, masking details, adherence assessment for these assigned-group comparisons, or the statistical model. It also does not report whether baseline HOMA-IR was included as a covariate. These details matter because different analytic choices can affect estimates and uncertainty, particularly when outcomes are variable or missingness differs between groups.

How should the secondary comparisons be understood?

The additional CPAP-use comparisons group participants by no, some, or good CPAP use for HOMA-IR and other measures. Those are different from the randomized assigned-group comparisons. Use categories may reflect behavior after assignment, and the registry does not report a method for controlling factors associated with CPAP use. As a general statistical point, an observed-use comparison is not automatically a randomized causal comparison: people in different use categories may differ for reasons beyond the amount of CPAP use. The posted contrasts are descriptive and unadjusted, and should not be treated as equivalent to the trial’s assigned-group contrast.

The registry lists 18 outcome measures and reports no analyses in its analysis count. The result summaries include means, standard deviations, confidence intervals, and unadjusted p-values for selected comparisons, but a detailed statistical analysis plan is not reported in the registry record. In particular, the record does not describe a primary model, adjustment strategy, missing-data method, interim analyses, or procedures for multiple testing. Those omissions limit conclusions about whether the posted calculations match a prespecified analysis.

For continuous outcomes, the planning illustrations use the observed effect size and variability to show participant requirements under specified assumptions. Such calculations can help readers understand how sample size, variability, and target effect are related. They do not reconstruct the original trial design. The registry does not report the assumptions used when the trial was originally planned, so the planning illustrations should be kept separate from the study’s own design rationale.

11. Confidence Intervals and Precision

Precision is reflected most directly in the width of a confidence interval. The enhanced-versus-standard primary estimate is a mean difference of 3.1, with a 95% confidence interval from 0.279 to 5.921. This range is entirely above zero, but it still covers meaningfully different possible magnitudes of the mean difference. The interval describes uncertainty in the estimated group contrast, not a range containing a stated proportion of individual participants’ changes.

The usual-care-versus-standard estimate is 3.2, with a 95% confidence interval from -2.141 to 8.541. This interval is wider and includes zero. Accordingly, the observed point estimate alone gives an incomplete picture: the data are compatible with a range extending from a negative contrast to a positive one. The corresponding unadjusted p-value is 0.24.

Unequal variability across groups contributes to the uncertainty. The usual-care group has a standard deviation of 24.8, and the enhanced group has a standard deviation of 12.7, compared with 3.0 for standard intervention. The primary outcome group sizes are 86, 82, and 84, respectively. Means and standard deviations cannot show the full shape of the outcome distributions; individual-level distributions are not reported in the registry record.

These are unadjusted recalculated intervals from posted summary statistics. The registry does not report adjusted confidence intervals, an analysis model, or a multiplicity correction. Their precision should therefore be understood in the context of the calculations and assumptions used, rather than as a complete uncertainty assessment from a fully described sponsor analysis. The intervals quantify sampling uncertainty; they do not address uncertainty caused by missing measurements, measurement error, protocol deviations, or the choice of endpoint.

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 display is a planning illustration based on the observed effect, not the trial’s original design calculation. The listed planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario targets a stated fraction of the observed effect. The figures are participants per arm for the continuous outcomes in this study; the convention for time-to-event outcomes, if any, would be total events, but these comparisons are not time-to-event outcomes.

The 80% power column gives the number of participants per arm that the planning calculation estimates would be needed to have an 80% chance of detecting the assumed effect under those assumptions, if that effect and the model assumptions were correct. The 90% power column gives the corresponding planning count for a higher chance of detection. These are design targets, not guarantees about a future study’s result.

Each row uses a different fraction of the observed effect. Planning for 75% of the observed effect means targeting a smaller effect than the full observed estimate; planning for 50% means a still smaller effect. Smaller effects are harder to distinguish from random variation, so the planning calculation requires more participants. The displayed counts vary substantially by comparison because the observed effect sizes and outcome variability differ.

These figures are not observed power. They are not a retrospective judgment about whether the completed trial had enough power, and they do not change the observed estimates or confidence intervals. The registry record does not report the trial’s original sample-size assumptions or justification. The sample-size curve represents the same planning relationship between the target effect and the required sample size; it should be read as an illustration under the stated assumptions, not as another analysis of the trial outcomes.

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 = 3.100; pooled standard deviation σ = 9.127.
2. n = 2 × (1.96 + 0.842)² × 9.127² / 3.100² = 136.1, rounded up to 137 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- 3.1                      # observed difference in means
sigma <- 9.12744108295921                     # 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(1446913)
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 = 137 (80% power), 183 (90% power)
 75% of observed effect: n per arm = 242 (80% power), 324 (90% power)
 50% of observed effect: n per arm = 545 (80% power), 729 (90% power)
power.t.test: 137.1 
Simulated power at n = 137 per arm: 0.800 (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. Multiplicity, Missing Data and Analysis Populations

The registry record lists many outcome measures and several comparisons, but does not report a plan for controlling multiplicity. When multiple outcomes or contrasts are examined, the chance of obtaining at least one apparently unusual result by chance can increase. A prespecified hierarchy or adjustment procedure can address this concern; none is reported in the registry record. The unadjusted p-values should therefore be interpreted as individual comparison results, not as evidence adjusted for the full collection of tests.

The primary outcome is identified as HOMA-IR change from baseline, but details of the prespecified statistical analysis are not reported. The registry does not describe a primary model, covariate adjustment, assumptions about the outcome distribution, or whether any transformations were planned. The comparisons presented are unadjusted recalculations from group summaries. The record reports no analyses in its analysis count, so these estimates should not be confused with a detailed reported statistical analysis plan.

The primary population is described as intention to treat, but missing-data handling is not reported. The record does not say how many participants lacked a baseline or follow-up HOMA-IR measurement, whether any values were imputed, or whether a sensitivity analysis assessed the effect of missingness. Without those details, it is not possible to judge whether the posted group summaries include all randomized participants or how missing outcome measurements may affect the estimates.

The record also does not report interim analyses, stopping rules, or the sample-size assumptions used to plan the original study. These should not be inferred from the completion status or from the separate planning illustrations based on observed effects. The absence of those details does not demonstrate that particular procedures were or were not used; it means they are not reported in the registry record.

Finally, the registry does not explain how CPAP-use categories were formed or how the related secondary comparisons were adjusted, if at all. Because the use categories are not the randomized assigned groups, unmeasured differences between categories could influence their observed outcomes. This uncertainty, together with multiplicity and missing-data questions, argues for cautious interpretation of secondary findings.

15. 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 serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: recurrent stroke (7.1%), stroke (7.1%), urgent coronary revascularization (2.3%), acute mi (1.2%), unstable angina hospitalization (0.0%).

The registry reports serious adverse events among 86 participants at risk in the standard intervention group, 82 in the enhanced CPAP intervention group, and 84 in usual care. The reported counts of participants affected are 3, 6, and 7, respectively. Deaths are listed separately as 0, 4, and 2. These are group-specific counts; they should not be added together with the serious adverse event counts because the registry does not say that the categories are mutually exclusive.

The listed serious adverse event terms include recurrent stroke at 7.1%, stroke at 7.1%, urgent coronary revascularization at 2.3%, acute MI at 1.2%, and unstable angina hospitalization at 0.0%. The registry record does not provide enough detail in these summaries to determine whether event terms overlap, how events were adjudicated, or the timing of each event. The percentages should be read as the registry’s reported values rather than recalculated from the group counts.

These figures are descriptive safety summaries. Differences in counts do not, on their own, establish that an intervention caused or prevented an event. The registry record does not report a comparative statistical analysis for these safety data, and the counts do not replace review of event definitions, follow-up, and exposure.

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

The posted primary outcome compares mean HOMA-IR change from baseline through a final measurement up to 12 months. The enhanced CPAP intervention group had a mean change of 4.0 and the standard intervention group had a mean change of 0.9. Their unadjusted recalculated mean difference is 3.1, with a 95% confidence interval from 0.279 to 5.921. The usual-care group mean change was 4.1; its comparison with standard intervention is less precise and its confidence interval includes zero.

These results describe a risk marker, not cardiovascular events. The study rationale concerns whether positive airway pressure therapy might reduce cardiovascular risk, but the posted primary result is HOMA-IR change. It cannot be translated directly into an effect on stroke, myocardial infarction, heart failure, or cardiovascular death. The registry record does not report a threshold that would establish clinical importance for the observed HOMA-IR differences.

The registry names the primary population as intention to treat and identifies the trial as randomized. However, detailed analysis methods and missing-data handling are not reported. The comparison estimates are unadjusted recalculations from the summary statistics, so they should not be presented as a fully specified adjusted analysis. A confidence interval and p-value describe statistical uncertainty under the calculation’s assumptions; neither identifies the cause of a difference.

Secondary CPAP-use comparisons are also not equivalent to randomized assigned-group contrasts. Differences across use categories may reflect factors other than CPAP use, and the record does not report adjustment for such factors. The secondary outcomes span several types of risk markers, and no multiplicity procedure is reported. Their results are best treated as descriptive evidence that can inform further research questions, not as definitive confirmation of a treatment effect.

In short, the registry reports between-group differences in the primary marker, with different levels of precision for the two comparisons. It does not establish the implications of those differences for cardiovascular events or provide enough analytic detail to resolve all uncertainty about the estimates.

17. Why This Trial Matters Statistically

This trial is statistically informative because it places a continuous risk marker inside a randomized, parallel-group comparison involving standard CPAP support, enhanced support, and usual care. The distinction between assigned interventions and observed CPAP-use categories is especially important. The former preserve the randomized comparison; the latter describe participants according to use and may be affected by post-assignment differences.

The results also illustrate why point estimates should be read alongside variability and confidence intervals. The primary group means differ, but spread is much larger in the enhanced and usual-care groups than in the standard group. The confidence intervals consequently communicate different degrees of precision for the two comparisons. A nominally notable p-value for one comparison does not answer the broader questions of clinical importance, bias, or multiplicity.

The trial’s motivating question concerns cardiovascular risk after TIA or stroke, while the primary endpoint is HOMA-IR. That distinction helps clarify what the reported evidence can address and what requires direct outcome data. Biomarkers may be useful for understanding a proposed pathway, but their statistical results should not be conflated with event-based treatment effects.

Finally, the registry record makes visible important boundaries of interpretation: detailed analysis methods, missing-data procedures, multiplicity handling, and the original sample-size justification are not reported. This makes careful separation of reported summaries, recalculated unadjusted contrasts, and planning illustrations essential. It is a useful example of how statistical reading depends not only on estimates, but also on whether the design and analysis decisions are documented.

18. 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 primary outcome is a surrogate risk measure rather than a cardiovascular event. Although the registry describes HOMA-IR as one measure used to assess cardiovascular risk, it does not report a threshold for meaningful change or an analysis linking the observed changes to later cardiovascular outcomes. The result therefore has a narrower interpretation than the broader rationale for the trial.

The reported outcome variability is uneven across groups, with standard deviations of 3.0, 12.7, and 24.8. The registry summaries do not describe the shape of the distributions or provide individual-level data. The confidence intervals are recalculated from summary statistics and do not account for any unreported modeling choices.

Several details needed for a fuller appraisal are not reported in the registry record: the randomization procedure, masking details, the original sample-size justification, the primary statistical model, covariate adjustment, missing-data handling, interim analyses, and multiplicity control. The record also does not report the clinical importance threshold for HOMA-IR change. These omissions restrict assessment of how closely the posted comparisons reflect a prespecified analysis.

The secondary analyses categorized participants by CPAP use, rather than comparing only randomized groups. Such categories can be associated with differences in participant characteristics or behavior, and the registry does not describe methods to address that possibility. Multiple outcomes and contrasts also raise multiplicity concerns. These limitations are specific to interpreting the posted endpoints and summaries; they do not establish that an unreported procedure was or was not used.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Sleep Apnea in TIA/Stroke: Reducing Cardiovascular Risk With Positive Airway Pressure — NCT01446913.
• Registry record last updated 2020-11-18; status last verified 2020-10.
• Results first posted 2020-11-18.
• 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.

22. Record Summary

NCT01446913 is a completed randomized, single-masked, parallel-group study sponsored by Yale University, with 255 enrolled participants and conditions listed as transient ischemic attack and stroke. The groups were standard CPAP intervention, enhanced CPAP intervention, and usual care. The primary outcome was mean change in HOMA-IR from baseline to the final measurement, up to 12 months, in the intention-to-treat population.

The primary group means were 0.9, 4.0, and 4.1 for standard intervention, enhanced CPAP intervention, and usual care. The recalculated unadjusted mean differences versus standard intervention were 3.1 for enhanced CPAP intervention and 3.2 for usual care, with confidence intervals of 0.279 to 5.921 and -2.141 to 8.541, respectively. The registry record does not report detailed analysis methods, missing-data handling, multiplicity procedures, or original sample-size assumptions.