Stroke and CPAP Outcome Study: A Sham-controlled Trial of CPAP Among Stroke Rehabilitation Patients: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Stroke and CPAP Outcome Study: A Sham-controlled Trial of CPAP Among Stroke Rehabilitation Patients (NCT02551757), a randomized phase 1, phase 2 study. The primary outcome is Feasibility of Enrolling Eligible Stroke Patients Admitted to Inpatient Rehabilitation for an Acute Ischemic or Hemorrhagic Stroke Into a Pilot, Randomized Clinical Trial of Active Versus Sham CPAP..

2. Clinical Question

The clinical question is framed as a feasibility question, rather than as a definitive test of functional benefit. The posted primary outcome counts are 13 among 20 participants assigned to active CPAP and 17 among 20 assigned to sham-CPAP. The accompanying risk difference is -0.2 for active relative to sham, with a confidence interval from -0.461 to 0.061.

The trial also considered CPAP use and functional change as secondary outcomes. These address related but distinct questions: whether CPAP was used during rehabilitation and whether functional independence changed between admission and discharge. The registry record does not report a result for the listed functional change outcome. The primary result should therefore be read as a narrow feasibility finding, with the secondary endpoints offering only partial context about treatment exposure and function.

3. Trial Design

This completed study, NCT02551757, was a randomized, parallel-group, sham-controlled pilot trial conducted during inpatient rehabilitation after acute stroke. The registry lists PHASE1 and PHASE2, an enrollment of 40, and a quadruple masking classification. The brief summary also describes the study as double-blind. The record does not explain how those masking labels relate to one another or provide enough operational detail to reconcile them.

Participants were randomly assigned to auto-titrating CPAP or sham-CPAP during their rehabilitation stay. The posted primary outcome groups each contain 20 participants. The active intervention used auto-titrating CPAP, with pressure adjusted between 4 to 20 cm of water and a goal apnea-hypopnea index less than or equal to 5. The sham device is described as an auto-titrating CPAP modified to provide a high level of blinding. The registry’s sham-device description is incomplete, so further technical details are not reported in the registry record.

The registry lists the study start as 2013-06 and primary completion as 2014-11, and marks the status as completed. Its primary outcome timeframe is 18 months. Secondary outcomes include hours of CPAP per night, with a timeframe of up to 28 days, and median change in the Functional Independence Measure between rehabilitation admission and discharge. The record does not report the original sample-size justification, the detailed allocation procedure, or the trial’s original statistical analysis plan. Those omissions limit how fully the design can be assessed from the registry record alone.

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.

Overall Study

Analysis population for the primary outcome, as defined in the registry: Eligible recruited participants included those randomized to sham or active CPAP during inpatient rehabilitation.

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 Feasibility of Enrolling Eligible Stroke Patients Admitted to Inpatient Rehabilitation for an Acute Ischemic or Hemorrhagic Stroke Into a Pilot, Randomized Clinical Trial of Active Versus Sham CPAP., measured over 18 months.

The primary endpoint is described as feasibility of enrolling eligible stroke patients admitted to inpatient rehabilitation into a pilot randomized trial of active versus sham CPAP. Its stated measure is the number of stroke patients willing to participate during inpatient rehabilitation over 18 months and be randomized. This kind of endpoint addresses whether recruitment and randomization can be carried out in the intended clinical setting; it is not a direct measure of functional recovery or CPAP efficacy.

The posted outcome data give counts of 13 among 20 participants in the active-CPAP group and 17 among 20 in the sham-CPAP group. The registry presents the comparison as a risk difference of -0.2 for active relative to sham. Because the outcome is framed around willingness and randomization, but the record does not give a screening log or the number of eligible patients approached, these arm counts cannot describe the recruitment rate among all potentially eligible patients. They describe the posted results within the randomized groups.

Feasibility endpoints are useful in pilot studies because they can inform whether a larger study might be practicable. The registry record does not report a formal feasibility threshold or a prespecified rule for judging success. Therefore, the counts can be described, but the record does not establish a threshold-based conclusion about whether the recruitment target was met.

7. Results Posted in the Registry

• Eligible Recruited Participants: Active-CPAP: 65.0% (13/20) versus 85.0% (17/20) on control; risk difference -20.0 percentage points (95% CI -46.1 to 6.1), risk ratio 0.76 (0.53–1.11); unadjusted two-proportion z-test p = 0.144.

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.

Hours of CPAP Per Night

• 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:
  • Active-CPAP: mean 3.90 versus 3.60 on control; difference 0.30 (95% CI -1.40 to 2.00), standardized effect d = 0.13; z-test p = 0.729.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Active-CPAP and the control. The interval gives the range of effects that remain compatible with the data.

The posted secondary information is incomplete. CPAP use per night has group means, variability estimates, a mean difference, and an unadjusted comparison. The other listed secondary outcome is median change in the Functional Independence Measure between rehabilitation admission and discharge, but its result is not reported in the registry record. The available secondary evidence therefore covers treatment use but does not provide a posted numerical account of functional change.

CPAP use can help describe exposure to the assigned devices during rehabilitation, while functional change addresses a clinical outcome distinct from the primary feasibility question. Neither should be treated as a substitute for the primary endpoint. The primary result concerns counts in the randomized groups; the secondary use result describes hours of device use, and the functional-change result is absent. These endpoints answer different questions and cannot be combined into a single conclusion from the registry record.

The unadjusted comparison for CPAP use has a confidence interval that includes zero. This means the posted estimate does not precisely distinguish a positive mean difference from no difference or a difference in the opposite direction. The record does not provide a result for the functional endpoint that could be assessed alongside it.

In general, secondary analyses carry less weight when their prespecification, multiplicity handling, and analysis populations are not documented. Testing several outcomes can increase the chance of apparently notable findings arising by chance, and selective availability of results can complicate interpretation. The registry record reports no registered analyses and does not state how multiplicity was handled. These limitations make secondary findings more appropriately descriptive and exploratory than confirmatory. They should be considered as context for the pilot, without repeating or extending the primary conclusion.

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

• Hours of CPAP Per Night
• Median Change in the Functional Independence Measure (FIM) Between Admission and Discharge From the Rehabilitation Unit Comparing Active-CPAP Versus Sham-CPAP.

9. Statistical Interpretation

10. Statistical Methods Explained

The registry reports group counts for the primary outcome and means with standard deviations for CPAP use. The statistical summaries compare active-CPAP with sham-CPAP. The basic interpretation depends on distinguishing the observed group values from the estimated contrast and from the uncertainty around that contrast.

What does the risk difference represent?

A risk difference expresses the difference between the proportions with an event in the two groups. Here the comparison is active relative to sham, and the estimate is -0.2. A negative value means the observed proportion was lower in active than sham. The posted arm counts are 13 among 20 and 17 among 20, respectively. The risk difference gives the contrast on an absolute scale, rather than describing a relative change. The registry also reports a risk ratio and odds ratio, which express the same comparison using relative scales.

How should the p-value be read?

The unadjusted p-value for the primary comparison is 0.144. In general, a p-value describes how compatible the data are with a specified null model under the assumptions of the analysis. It is not the probability that the null hypothesis is true, nor a measure of the size or clinical importance of an effect. A p-value should be interpreted together with the estimated effect and its confidence interval. The registry record does not identify the test used to produce this p-value or describe adjustments for other analyses.

What do confidence intervals add?

In general, a confidence interval communicates the uncertainty of an estimate under a statistical procedure. For the primary risk difference, the interval runs from -0.461 to 0.061. Since it includes zero, it is compatible with no difference as well as with effects on either side of zero. The risk-ratio and odds-ratio intervals also include 1, the no-association value for those measures. These intervals do not prove that there is no effect; they show that the available data do not pin down the contrast precisely.

How are continuous outcomes summarized?

CPAP use is summarized by a mean and standard deviation in each group. The means are 3.9 hours per night for active-CPAP and 3.6 for sham-CPAP. The standard deviations are 2.7 and 1.8, respectively. In general, the mean describes the group’s average, while the standard deviation describes variability among observations around that average. The estimated mean difference is 0.3, with a confidence interval from -1.399 to 1.999. This interval includes zero, so the estimate is imprecise about the direction and magnitude of a difference.

Standard deviations are not confidence intervals for the group means. They describe spread in individual observations, whereas the interval for a mean difference describes uncertainty in the estimated contrast. General statistical interpretation also depends on the distribution and independence assumptions of the analysis. The registry record does not report diagnostics or a detailed model for the continuous endpoint, so those assumptions cannot be assessed from the posted summaries alone.

Why does uncertainty matter in a pilot trial?

A pilot study often has a feasibility focus and may yield estimates that are uncertain. Small group sizes can make estimates sensitive to the outcomes of individual participants, and broad intervals can include quite different possible effects. This general point does not establish why this particular trial enrolled its recorded number of participants: the trial’s original sample-size rationale is not reported in the registry record.

The displayed planning illustrations use the observed effect as a reference and then consider smaller fractions of that effect. These are planning calculations under stated assumptions, not evidence that the trial had a particular probability of detecting an effect. General planning work should be based on a justified target effect and assumptions appropriate to a future study, rather than simply adopting a pilot estimate. The registry record does not report the trial’s original target effect or design calculations.

What remains unspecified?

The registry record reports no registered analyses in the posted analysis listing. It does not describe the statistical test for the primary outcome, covariate adjustment, handling of missing observations, or whether all randomized participants were included in each analysis. It also does not report a multiplicity strategy. These details matter because they clarify which comparisons were planned, how incomplete data were treated, and how results from several outcomes should be interpreted. Without them, the posted estimates can be described, but not fully audited against a prespecified analysis plan.

In general, an unadjusted comparison is a direct comparison of groups without statistical adjustment for other variables. It can be informative as a transparent summary, but it may not match an analysis that was prespecified to account for baseline differences or other design features. The registry record does not identify whether the posted comparisons were intended as the definitive analyses. Accordingly, the estimates and p-values should be treated as the registry’s reported summaries rather than as a complete statistical account of the trial.

11. Confidence Intervals and Precision

Precision concerns how tightly the data locate an estimated effect. The primary risk difference is -0.2, with a confidence interval from -0.461 to 0.061. That interval spans zero and includes estimates on both sides of no difference. Thus, the point estimate gives a direction, but the interval shows that the data do not precisely determine the direction or size of the underlying contrast.

The relative measures convey similar uncertainty. The risk ratio is 0.765, with an interval from 0.528 to 1.108, and the odds ratio is 0.328, with an interval from 0.071 to 1.518. Both intervals include 1, the value corresponding to no association. The different point estimates reflect the distinct scales of these measures; they should not be read as interchangeable quantities.

For CPAP use, the mean difference is 0.3 hours per night, with an interval from -1.399 to 1.999. This interval includes zero and accommodates values in either direction. It indicates that the observed means alone do not tightly establish the magnitude of a group difference. The registry record does not report a confidence interval for the functional-change outcome because no result for that outcome is posted.

In general, a confidence interval is not a guarantee that the true effect lies within its particular limits. It is an uncertainty summary produced by a statistical procedure under its assumptions. Those assumptions and the precise procedures used are not detailed for the posted analyses. The small randomized groups and the absence of fuller analysis details further counsel against treating the point estimates as precise or definitive.

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 illustrations are planning calculations based on the observed effect, not the trial’s original design rationale. The 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. For these non-time-to-event outcomes, the figures are participants per arm, not total events. The record’s note that time-to-event planning tables would give total events does not apply to these outcomes.

The 80% power column describes the planned number of participants per arm under which the calculation has an 80% chance of detecting the stated effect, assuming the planning model and assumptions hold. The 90% column describes the corresponding calculation for 90% power. These are design targets for a future study, not descriptions of what happened in the trial. This is not observed power.

The primary-outcome illustration lists 73 participants per arm for planning for 100% of the observed effect, 121 for 75% of the observed effect, and 250 for 50% of the observed effect at 80% power. The corresponding 90% planning figures are 97, 161, and 335 participants per arm. The CPAP-use illustration lists 868, 1,543, and 3,472 participants per arm at 80% power for those effect fractions, and 1,162, 2,066, and 4,648 at 90% power.

The pattern reflects a general planning principle: smaller effects require more participants to detect under otherwise unchanged assumptions. These values are illustrations tied to the observed effects and should not be treated as definitive targets. The original sample-size assumptions are not reported in the registry record.

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, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.850; treatment proportion p₁ = 0.650; average p̄ = 0.750.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.6124 = 1.2002.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.5958 = 0.5015.
4. n = (1.2002 + 0.5015)² / (-0.2000)² = 72.4, rounded up to 73 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
p0 <- 0.85                          # control proportion
p1 <- 0.65                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^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 (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(2551757)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 73 (80% power), 97 (90% power)
 75% of observed effect: n per arm = 121 (80% power), 161 (90% power)
 50% of observed effect: n per arm = 250 (80% power), 335 (90% power)
power.prop.test: 72.4 
Simulated power at n = 73 per arm: 0.807 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-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 a primary feasibility outcome and secondary outcomes concerning CPAP use and functional change. It does not report a statistical analysis plan or a strategy for handling multiplicity across outcomes. In general, when several outcomes or comparisons are examined, the chance of at least one apparently unusual result can increase. A prespecified approach helps readers distinguish confirmatory tests from exploratory analyses. Without that information, unadjusted p-values should be interpreted cautiously, particularly for secondary outcomes.

The record’s analysis listing contains no reported analyses. It does not specify which analysis populations were intended, such as whether the primary analysis was to include every randomized participant, or how participants with missing outcome data were to be handled. Missing-data methods are not reported in the registry record. The posted counts and means are therefore not accompanied by enough information to determine how incomplete observations, if any, affected the estimates.

The registry record also does not report whether analyses were adjusted for baseline characteristics, whether there were interim analyses, or the statistical procedures planned for the primary endpoint. The trial’s original sample-size justification and detailed protocol-level analysis decisions are not reported in the registry record. These are absences of reporting, not evidence that such procedures were or were not used.

These gaps limit reproducibility and make it harder to judge whether the posted analyses follow prespecified decisions. They do not invalidate the descriptive values, but they constrain the strength of conclusions that can be drawn from them. A complete interpretation would need clear definitions of analysis populations, missing-data handling, the primary statistical procedure, and the intended role of secondary outcomes.

15. 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.

The registry reports zero serious adverse events among the 20 participants in the active-CPAP group and zero among the 20 participants in the sham-CPAP group. It also reports zero other adverse events in each group among the same listed group sizes. These are the adverse-event figures recorded for the trial.

Such counts describe what was reported in the registry; they do not establish that an intervention is free of risk. In general, the ability to detect uncommon events depends on the amount of safety information and the duration and completeness of follow-up. The registry does not provide event terms for serious adverse events, and deaths are not reported in the record. The adverse-event summaries should therefore be read as limited reporting for this pilot study, not as a comprehensive safety assessment.

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

The result describes a randomized comparison in a pilot study of CPAP during inpatient rehabilitation after acute stroke. For the primary feasibility outcome, the posted counts are 13 among 20 in the active group and 17 among 20 in the sham group. The estimated risk difference is -0.2, with a confidence interval from -0.461 to 0.061 and an unadjusted p-value of 0.144. This is an uncertain estimate that does not establish a clear difference between groups.

The primary endpoint concerns willingness to participate and be randomized, not functional improvement. Because the registry does not provide counts of eligible patients approached or a prespecified feasibility threshold, the result cannot establish the recruitment rate among all eligible patients or whether a formal feasibility target was achieved. It also cannot by itself answer whether CPAP changes functional outcomes.

The CPAP-use result gives a mean difference of 0.3 hours per night, with a confidence interval from -1.399 to 1.999. The registry record does not report a numerical result for the listed functional-change outcome. These registry entries do not support a complete assessment of the relation between assignment, device use, and functional change.

The findings do not establish that active CPAP works or does not work. They also do not establish equivalence between active and sham treatment: an interval that includes no difference is not proof that effects are identical. The results are best understood as descriptive pilot evidence with considerable uncertainty and incomplete reporting of analyses and outcomes. Wider conclusions would require evidence beyond the registry summaries and a more complete account of the study’s analysis and follow-up.

17. Why This Trial Matters Statistically

This trial is statistically informative because it illustrates the difference between a feasibility outcome and an efficacy outcome. The primary endpoint asks whether eligible patients were willing to participate and be randomized during inpatient rehabilitation. That question is relevant to whether research can be conducted in a specific care setting, but it is not the same as asking whether treatment changes function.

The posted comparison also illustrates why effect estimates and uncertainty should be read together. The primary point estimate is a risk difference of -0.2, while its confidence interval includes zero and extends across both directions. The counts alone may invite a simple directional comparison, but the interval shows that the data leave considerable uncertainty about the contrast.

The registry also provides planning illustrations based on observed effects. These demonstrate how planned sample sizes can increase as the effect used for planning becomes smaller, and how design assumptions shape those illustrations. They are not a replacement for an original protocol or a justified sample-size calculation. The registry record does not report the trial’s original design rationale.

Finally, the gaps in analysis reporting are themselves important for statistical interpretation. The record does not report multiplicity handling, missing-data methods, analysis populations, or registered analyses. Such information helps readers assess whether results were prespecified and how robust they may be to analytic choices. The trial therefore offers useful pilot estimates while also showing why clear reporting is needed before a small randomized study can support strong conclusions.

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 randomized groups are small, and the confidence intervals for the primary comparison and CPAP-use comparison are broad enough to include values on either side of no difference. This limits precision. The primary outcome is a feasibility count, and the registry does not report the number of eligible patients approached, so the posted group counts do not provide a recruitment rate for all eligible patients.

The functional-change outcome is listed, but its result is not reported in the registry record. This leaves the posted secondary evidence incomplete. The registry also does not report a detailed analysis plan, analysis populations, missing-data methods, multiplicity handling, or the original sample-size rationale. The number and nature of any interim analyses are not reported in the registry record.

Masking is classified as quadruple, while the brief summary describes a double-blind pilot trial. The record does not explain this difference. The sham-device description is also incomplete. These reporting limitations make it difficult to evaluate masking procedures from the registry record alone.

The trial was a pilot study in the setting of inpatient rehabilitation after acute stroke. Its results should not be assumed to describe other populations or settings. The registry’s adverse-event summaries report zero events in the listed categories, but deaths are not reported and the record does not give detailed event terms. These considerations limit how much can be concluded about safety from the posted summaries.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Stroke and CPAP Outcome Study: A Sham-controlled Trial of CPAP Among Stroke Rehabilitation Patients — NCT02551757.
• Registry record last updated 2021-01-13; status last verified 2020-12.
• Results first posted 2020-11-25.
• 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

NCT02551757 is a completed randomized, parallel-group, sham-controlled pilot trial of auto-titrating CPAP during inpatient rehabilitation after acute stroke. The registry lists PHASE1 and PHASE2, enrollment of 40, and quadruple masking; the brief summary describes double-blinding. The primary outcome concerns feasibility of enrolling eligible patients willing to participate and be randomized over 18 months.

The primary result reports counts of 13 among 20 in active-CPAP and 17 among 20 in sham-CPAP, with a risk difference of -0.2 and a confidence interval from -0.461 to 0.061. The secondary CPAP-use outcome reports a mean difference of 0.3 hours per night; the listed functional-change result is not reported in the registry record. The record does not report the original sample-size rationale, detailed analysis plan, multiplicity approach, or missing-data methods.