This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for The Effectiveness of SensAwake™ for Continue Positive Airway Pressure Treatment of Obstructive Sleep Apnea Patients (NCT03294629), a randomized na study. The primary outcome is Compliance of Auto-CPAP Therapy.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT03294629 |
| Phase | NA |
| Condition | Obstructive Sleep Apnea |
| Allocation | Randomized |
| Design model | Crossover |
| Masking | Double |
| Enrollment | 35 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Chang Gung Memorial Hospital |
| Results posted | Yes |
2. Clinical Question
Population
Participants with obstructive sleep apnea who remove the mask for unknown reasons during automatic continuous positive airway pressure (Auto-CPAP) therapy were the focus of the study. The study description refers to moderate-to-severe obstructive sleep apnea. The registry enrollment is 35; the posted primary outcome lists 25 observations in each condition.
Intervention
Auto-CPAP with the SensAwake modification activated. The study describes SensAwake as a device modification and compares its use with standard Auto-CPAP.
Comparator
Auto-CPAP without SensAwake activation. Participants were assigned to one of two treatment sequences, each involving two weeks in one condition followed by two weeks in the other.
Primary question
Over a two-week period, how did the percentage of nights with at least four hours of Auto-CPAP use compare between the SensAwake-on and SensAwake-off conditions? The registry lists this as the primary measure of treatment compliance.
This is a question about device-recorded use, not a direct measure of sleep quality, symptom relief, or clinical outcomes. The primary measure counts nights meeting a specified use-duration threshold and expresses that as a percentage of nights. It therefore captures one aspect of adherence: whether treatment was used for at least four hours on a night. It does not describe how long the device was used on nights below that threshold, nor does the registry record report a patient-reported adherence measure.
The crossover setup means participants were scheduled to experience both device conditions in sequence. Such a design can make within-participant comparisons possible, but the registry results list condition-specific summaries rather than a reported crossover analysis. The analysis method, handling of treatment order, and any adjustment for period or carryover effects are not reported in the registry record. The posted comparison should therefore be read as the displayed comparison of the two condition summaries, not as evidence that a particular crossover model was used.
3. Trial Design
The registry describes a randomized, double-masked crossover study and records a completed status. It lists an enrollment of 35. The study start is recorded as 2015-03 and primary completion as 2016-03. The registry lists no applicable phase. Chang Gung Memorial Hospital is named as sponsor.
The two sequences differed in treatment order. One sequence began with CPAP without SensAwake activation for two weeks and then crossed over to CPAP with activation for an additional two weeks. The other began with activation for two weeks and then switched to the condition without activation for two weeks. Thus, the planned exposure involved consecutive two-week periods in both conditions. The registry does not report further details about randomization generation, allocation concealment, masking procedures, washout periods, adherence to assigned sequence, or protocol deviations.
The primary endpoint is described as objective data recorded in the Auto-CPAP machine: the percentage of nights with at least four hours of use during therapy, measured over two weeks. The posted primary results give means and standard deviations for 25 observations in each condition. These condition-specific counts should not be mistaken for the registry enrollment, and the record does not explain the relationship between the enrollment figure and the outcome counts.
The registry lists 12 outcome measures and names eight secondary measures, including device detections, pressures, leaks, residual apnea-hypopnea index, and use duration. It reports zero analyses in the analysis-count field. There are posted numerical summaries for three secondary outcomes in the record used for this description; detailed numerical results for the other listed secondary outcomes are not reported in the registry record. The statistical analysis plan, original sample-size justification, planned interim analyses, analysis populations, and 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.
First Intervention (2 Weeks)
| Stage | CPAP w/SensAwake First, Then CPAP w/o SensAwake | CPAP w/o SensAwake First, Then CPAP w/SensAwake |
|---|---|---|
| STARTED | 16 | 19 |
| COMPLETED | 14 | 15 |
| NOT COMPLETED | 2 | 4 |
Second Intervention (2 Weeks)
| Stage | CPAP w/SensAwake First, Then CPAP w/o SensAwake | CPAP w/o SensAwake First, Then CPAP w/SensAwake |
|---|---|---|
| STARTED | 14 | 15 |
| COMPLETED | 12 | 13 |
| NOT COMPLETED | 2 | 2 |
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.
| Characteristic | Unit | CPAP w/SensAwake First, Then CPAP w/o SensAwake | CPAP w/o SensAwake First, Then CPAP w/SensAwake | Total |
|---|---|---|---|---|
| Participants analysed | 12 | 13 | 25 | |
| Age, Continuous | years | 47.6 (SD 10.9) | 41.5 (SD 12.0) | 44.0 (SD 11.7) |
| Sex: Female, Male: Female | Participants | 0 | 3 | 3 |
| Sex: Female, Male: Male | Participants | 12 | 10 | 22 |
| Body Mass Index (BMI) | kg/m2 | 31.8 (SD 4.3) | 32.9 (SD 6.9) | 32.4 (SD 5.7) |
| Neck Circumference (NC) | cm | 42.3 (SD 2.1) | 41.0 (SD 2.2) | 41.6 (SD 2.2) |
| Apnea-hypopnea index (AHI) | events per hour | 55.3 (SD 30.8) | 54.0 (SD 35.3) | 54.6 (SD 32.5) |
| Sleep efficiency | % (percentage of minutes slept) | 82.0 (SD 8.9) | 73.0 (SD 21.3) | 77.1 (SD 17.1) |
| Total sleep time | minutes | 301.0 (SD 34.2) | 276.2 (SD 79.2) | 287.6 (SD 62.8) |
| Deep sleep - Stage 3 | % (percentage of minutes of stage 3) | 6.1 (SD 10.4) | 4.4 (SD 5.6) | 5.2 (SD 8.0) |
| Average used time of CPAP | minutes | 187.4 (SD 104.6) | 227.9 (SD 104.1) | 208.5 (SD 104.2) |
| Compliance of CPAP | % | 31.9 (SD 31.9) | 46.2 (SD 30.6) | 39.3 (SD 31.4) |
| Residual AHI under CPAP Tx | events per hour | 2.9 (SD 1.3) | 4.4 (SD 2.8) | 3.7 (SD 2.3) |
| Pittsburgh Sleep Quality Index (PSQI) | units on a scale | 7.4 (SD 2.3) | 10.1 (SD 3.8) | 8.8 (SD 3.4) |
| Epworth Sleepiness Scale (ESS) | units on a scale | 13.3 (SD 5.5) | 13.1 (SD 6.7) | 13.2 (SD 6.0) |
| Nasal Obstruction Symptom Evaluation (NOSE) | units on a scale | 13.5 (SD 6.8) | 15.6 (SD 8.4) | 14.6 (SD 7.6) |
6. Primary Endpoint
The registry lists the primary outcome as Compliance of Auto-CPAP Therapy, measured over 2 weeks.
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Deviation |
| Unit | percentage of nights |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is compliance of Auto-CPAP therapy, measured as the percentage of nights on which the device was used for at least four hours during a two-week period. The registry says the measure comes from objective data recorded by the Auto-CPAP machine. In the posted results, the condition means are 41.8 for SensAwake on and 39.7 for SensAwake off, with standard deviations of 35.0 and 32.6, respectively. The unit is percentage of nights.
This threshold-based endpoint is used to describe whether treatment is used for a minimum duration on a night. Because it is calculated from device records, it does not rely only on a participant’s recall of use. It provides a practical adherence summary across nights, but it compresses different patterns into one value: nights just below and far below four hours are both outside the threshold, while nights exceeding it count toward the same nightly classification.
As a general statistical point, a mean percentage describes the average level across the observations contributing to each condition summary. It does not show how individual participants changed between conditions. A crossover analysis may use each participant’s paired condition values, but the registry does not report participant-level changes or a paired analysis. The primary endpoint also does not itself establish changes in symptoms, sleep, or other clinical outcomes; those are separate questions.
7. Results Posted in the Registry
- SA OFF: mean 39.70 versus 41.80 on control; difference -2.10 (95% CI -20.85 to 16.65), standardized effect d = -0.06; z-test p = 0.826.
Mean difference: SA OFF
95% CI: -20.85 to 16.65
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Average SA Detections | Continuous Endpoint | Mean difference | -2.10 (-2.45 to -1.75) | 2 per arm |
| Average Pressures of Auto-CPAP Machine | Continuous Endpoint | Mean difference | 0.40 (-1.07 to 1.87) | 690 per arm |
| 90th Percentile Pressures of Auto-CPAP Machine | Continuous Endpoint | Mean difference | 0.60 (-1.04 to 2.24) | 380 per arm |
Average SA Detections
- 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:
- SA OFF: mean 0.00 versus 2.10 on control; difference -2.10 (95% CI -2.45 to -1.75), standardized effect d = -3.30; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for SA OFF than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Average Pressures of Auto-CPAP Machine
- 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:
- SA OFF: mean 7.30 versus 6.90 on control; difference 0.40 (95% CI -1.07 to 1.87), standardized effect d = 0.15; z-test p = 0.594.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between SA OFF and the control. The interval gives the range of effects that remain compatible with the data.
90th Percentile Pressures of Auto-CPAP Machine
- 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:
- SA OFF: mean 9.20 versus 8.60 on control; difference 0.60 (95% CI -1.04 to 2.24), standardized effect d = 0.20; z-test p = 0.472.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between SA OFF and the control. The interval gives the range of effects that remain compatible with the data.
The posted secondary outcomes span device detections, pressure measures, leak measures, residual apnea-hypopnea index, and device-use measures. Numerical summaries are available for average SA detections, average pressure, and 90th-percentile pressure. Detailed numerical results for the remaining listed secondary measures are not reported in the registry record. The available outcomes do not all point to the same kind of change: device detections differ between conditions, while the displayed pressure contrasts are comparatively small relative to their uncertainty.
These secondary measurements provide context about device operation and use, but they do not replace the primary adherence endpoint. The primary question concerns the percentage of nights reaching at least four hours of use. A change in a device detection measure or pressure summary is not, by itself, evidence of a change in the proportion of nights meeting that adherence threshold. Nor do these device metrics establish changes in symptoms or other clinical outcomes.
In general, secondary outcomes are often useful for exploring mechanisms, describing device behavior, or identifying patterns that warrant further study. Their evidential weight depends on whether they were prespecified, how many outcomes were examined, and whether the analysis plan accounted for multiple comparisons. The registry does not report a multiplicity adjustment or a prespecified hierarchy for secondary outcomes. The reported secondary p-values are unadjusted, so the chance of at least one apparently notable result can increase when many outcomes are examined.
The record lists 12 outcome measures and names eight secondary measures, but only a subset has detailed numerical results in the record used for this description. With no reported analyses, no multiplicity plan, and no crossover model output, the pattern should be regarded as descriptive and exploratory. It can help characterize what was measured, but it is not a set of independent confirmations of the primary comparison.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Average SA Detections
- Average Pressures of Auto-CPAP Machine
- 90th Percentile Pressures of Auto-CPAP Machine
- Average Leaks of Auto-CPAP Machine
- 90th Percentile Leaks of Auto-CPAP Machine
- Residual Apnea-Hypopnea Index (AHI)
- Time Used of Auto-CPAP Machine
- Percentage of Day Used of Auto-CPAP Machine
9. Statistical Interpretation
The posted primary summaries are close in magnitude: the mean percentage of nights with at least four hours of use was 41.8 with SensAwake on and 39.7 with SensAwake off. The displayed mean difference for SensAwake off relative to on is -2.1, with a 95% confidence interval from -20.85 to 16.65 and an unadjusted p-value of 0.826. The interval includes zero and spans values on either side of it. These results do not pinpoint a clear difference between the condition means.
The confidence interval is wide in relation to the estimated difference. It is compatible with a range of possible differences, including a lower mean in the off condition and a higher mean in the off condition. The point estimate alone should not be treated as a precise estimate of the condition contrast. The standard deviations, 35.0 and 32.6, are large relative to the means, indicating substantial spread in the recorded percentage values across observations. The registry does not provide participant-level data to describe that spread further.
The p-value is an unadjusted recalculation from the posted summary statistics, rather than a reported sponsor analysis. It is not evidence that the conditions are identical, and it does not measure the probability that the null hypothesis is true. In general, a p-value describes how unusual data at least as discrepant as those observed would be under a specified null model and its assumptions. The registry does not report a sponsor analysis for the primary comparison, nor does it report the statistical model used for a crossover design. The simple unadjusted recalculation does not account for paired observations, treatment sequence, period, or possible carryover.
That distinction matters because crossover data typically contain measurements from the same participant under both conditions. A paired comparison can use within-participant information and may differ from a comparison treating condition summaries as independent. The registry provides condition summaries but no paired differences, covariance, sequence-specific outcomes, or crossover model output. Consequently, the recalculated contrast is a descriptive, unadjusted comparison of the posted summary statistics; it cannot substitute for a trial-specific crossover analysis.
The posted secondary summaries show a different pattern across measures. Average SA detections were 2.1 times/hour with activation and 0.0 without it, with a posted unadjusted mean difference of -2.1 for off relative to on and p < 0.001. Average pressure and 90th-percentile pressure were slightly higher in the off condition, but their recalculated confidence intervals include zero and their unadjusted p-values are 0.594 and 0.472. These measures are not interchangeable with the primary adherence outcome. The registry does not provide a multiplicity plan or reported analyses for these outcomes, so secondary comparisons should be viewed as exploratory rather than as independent confirmation of the primary result.
In general, statistical uncertainty and clinical importance are distinct. A confidence interval describes uncertainty in an estimated contrast under the analysis assumptions; it does not by itself determine whether differences matter to participants. No threshold for a clinically important difference is reported in the registry record. The posted numbers therefore support a cautious reading: the condition means are similar in the displayed summaries, but the uncertainty is considerable and the analysis does not establish a precise crossover treatment effect.
10. Statistical Methods Explained
The primary measure is continuous: the outcome is a percentage, and the registry reports a mean and standard deviation for each condition. A mean summarizes the center of the observed values, while a standard deviation describes their dispersion around that mean. These summaries are useful for an overview, but they do not reveal the full distribution, possible floor or ceiling patterns, or the relationship between the two observations from each participant in a crossover study.
What does a mean difference represent?
The displayed comparison defines the contrast as SensAwake off relative to SensAwake on. For the primary outcome, the estimate is -2.1. In plain terms, the displayed off-condition mean is lower than the on-condition mean by the reported contrast. The estimate is calculated from the condition means, without adjustment. It is not a within-person change estimate unless the analysis explicitly uses paired observations; the registry does not report such an analysis.
For the secondary outcomes with numerical summaries, the same direction convention applies: a negative mean difference means the off-condition mean is lower than the on-condition mean, and a positive difference means it is higher. The posted average detections contrast is -2.1 times/hour. The mean differences for average pressure and 90th-percentile pressure are 0.4 and 0.6 cmH2O. These are descriptive contrasts; the record does not state that they came from a prespecified crossover model.
How should the confidence interval be read?
In general, a confidence interval gives a range of values reasonably compatible with the data and the assumptions of the calculation. It reflects sampling uncertainty in the estimated contrast, not the range containing most individual participants’ outcomes. For the primary comparison, the 95% interval runs from -20.85 to 16.65. Because it includes zero, the interval is compatible with no difference as well as with contrasts in either direction. The width signals that the estimate is not highly precise.
The recalculated intervals and p-values are simple, unadjusted calculations from the posted summary statistics. They are not reported sponsor analyses. For the primary outcome, the p-value is 0.826. For the three secondary outcomes with detailed results, the unadjusted p-values are p < 0.001 for average SA detections, 0.594 for average pressure, and 0.472 for 90th-percentile pressure. They should not be interpreted as accounting for multiple outcomes or for the crossover structure.
Why does the crossover structure matter?
General statistical explanation: when the same participant contributes an observation under each condition, the two measurements are usually related. A paired analysis accounts for that relationship. It may estimate a condition contrast more efficiently than an analysis that treats the observations as independent, but the appropriate method depends on the design and data. Period effects, sequence effects, and possible carryover can also matter in crossover trials. The registry record does not report an analysis addressing these features, so it is not possible to determine from the posted summaries how they were handled.
The registry’s two sequences place the on and off conditions in opposite orders, each for two weeks. This makes treatment order a design feature, not a detail that can be inferred away from the overall means. No sequence-specific summaries, period-specific summaries, or paired differences are reported. The sample counts shown for the conditions are 25 each, but the number of participants contributing complete paired observations is not reported in the registry record.
What does over-dispersion mean in general?
General explanation: when observations vary more than a simple model expects, standard errors can be too small if the model fails to represent that variability or dependence. Greater dispersion tends to make estimates less precise and intervals wider. Here the primary standard deviations are 35.0 and 32.6, while the means are 41.8 and 39.7. Those summaries indicate considerable variability in the measured percentage, but they do not identify its source. Participant differences, night-to-night fluctuation, and other explanations cannot be separated using the reported aggregate data.
The primary percentage has a bounded scale in principle, but the registry does not describe the distribution or transformation used. No model specification, adjustment covariates, robust standard-error method, or diagnostic checks are reported. It is therefore not possible to assess whether a particular model’s distributional assumptions were checked. The calculations displayed from summary statistics should be understood as a basic comparison, not as a complete statistical analysis plan.
What is and is not reported?
The registry lists zero analyses in its analysis count, and the secondary outcomes have no reported analyses. The posted comparisons and intervals in this statistical description are recalculated from the condition-level summaries. They do not establish which method the investigators used, whether any result was prespecified, or whether the analysis followed a protocol. The original statistical plan, sample-size justification, interim-analysis plan, missing-data methods, and analysis populations are not reported in the registry record. These omissions limit the ability to judge whether the posted summaries represent the intended primary analysis.
11. Confidence Intervals and Precision
The primary mean difference is -2.1 percentage points as reported, with a 95% confidence interval from -20.85 to 16.65. This interval is wide and includes zero. Its lower and upper limits also extend in opposite directions from the point estimate, so the data are compatible with a range of possible differences rather than a tightly determined contrast. The mean values, 41.8 with activation and 39.7 without activation, are only the centers of the condition summaries; they do not convey the uncertainty on their own.
In general, a confidence interval describes uncertainty in an estimated population contrast under the assumptions used to calculate it. It is not a range for individual participants’ outcomes, and it does not assign a probability to the true value after the data are observed. The recalculated primary interval is based on the posted summary statistics and an unadjusted comparison. It does not use reported paired crossover data, because those are not available in the registry record.
The two condition standard deviations, 35.0 and 32.6, show substantial variability in the primary measure. The registry does not provide the correlation between each participant’s on- and off-condition values, which is important for estimating uncertainty in a paired crossover contrast. Thus, the displayed interval may not represent the uncertainty from a full analysis of the crossover design. No sponsor-reported interval or primary analysis result is listed.
For the secondary outcomes, the interval for average SA detections is from -2.453 to -1.747, while the intervals for average pressure and 90th-percentile pressure are from -1.069 to 1.869 and from -1.036 to 2.236. These are also recalculated, unadjusted intervals. Their interpretation is subject to the same limitations about analysis structure, and the record does not report adjustment for examining multiple outcomes.
12. Planning a Similar Trial: Sample Size
This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 4,072 | 5,451 |
| 75% of the observed effect | 7,239 | 9,691 |
| 50% of the observed effect | 16,287 | 21,804 |
The sample-size figures are planning illustrations based on the observed effect, not the trial’s original design calculation. The listed assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each planning row uses the stated fraction of the observed effect as the effect to detect. For the continuous outcomes shown, values are participants per arm, not a total across arms or a count of events.
The 80% power column gives the number of participants per arm estimated to be needed for an 80% chance of detecting the assumed effect under those planning assumptions, if that effect and the model assumptions are correct. The 90% column gives the corresponding per-arm planning number for a 90% chance. These are prospective planning quantities, not a statement about the probability that the trial’s result is true or about the chance that an observed result occurred by chance.
The rows labeled 100%, 75%, and 50% of the observed effect show how the planning number changes when the target effect is set to a fraction of the observed contrast. Smaller effects are harder to distinguish from random variation, so planning for smaller effects requires more participants. The observed-effect value is uncertain, especially when estimated from a small study, so these illustrations should not be treated as reliable requirements for a future trial without an independently justified target effect and design.
These figures are not observed power. The trial’s own sample-size assumptions and justification are not reported in the registry record. The registry describes a crossover design, whereas the listed planning assumptions specify equal allocation between two arms and a normal approximation; the illustrations therefore do not reproduce a documented crossover sample-size method.
13. How the Sample Size Is Derived
Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z1−α/2 = 1.960) and the desired power (z1−β = 0.842 for 80% and 1.282 for 90%).
Formula
n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.
Worked calculation for this trial
- Observed difference Δ = -2.100; pooled standard deviation σ = 33.821.
- n = 2 × (1.96 + 0.842)2 × 33.8212 / -2.1002 = 4,071.7, rounded up to 4,072 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 <- -2.09999999999999 # observed difference in means
sigma <- 33.8212950668658 # 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(3294629)
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 = 4,072 (80% power), 5,451 (90% power)
75% of observed effect: n per arm = 7,239 (80% power), 9,691 (90% power)
50% of observed effect: n per arm = 16,287 (80% power), 21,804 (90% power)
power.t.test: 4072.7
Simulated power at n = 4,072 per arm: 0.803 (20000 replicates)
The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.
14. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when several outcomes, comparisons, time points, or analysis choices are examined. In general, each additional test creates another opportunity for a result to appear statistically notable by chance, even when no underlying effect is present. Statistical methods can address this, for example by adjusting the threshold or organizing outcomes into a prespecified hierarchy. The registry record does not report a multiplicity strategy, a hierarchy among outcomes, or which outcomes were designated as confirmatory beyond identifying the primary measure.
The record lists 12 outcome measures and eight named secondary outcomes. Detailed summaries are available for three secondary measures, while numerical results for the other listed secondary measures are not reported in the registry record. The unadjusted secondary p-values therefore should not be read as multiplicity-controlled evidence. The very small unadjusted p-value for average SA detections is a result for that individual comparison; the record does not indicate how it was handled in relation to the other outcomes.
Missing-data handling is also not reported in the registry record. The posted condition summaries include 25 observations for each primary condition, but the record does not say whether any measurements were missing, how missing periods were treated, or whether participants with incomplete crossover data were included. It also does not report an imputation method or sensitivity analysis. Equal displayed condition counts do not establish that the same participants contributed complete observations under both conditions.
The analysis population is not reported in the registry record. There is no statement about intention-to-treat, per-protocol, or another analysis set, and no explanation of exclusions or protocol deviations. Randomization and crossover can support a rigorous comparison, but interpretation depends on retaining participants appropriately and accounting for the assigned sequence and repeated measurements. The registry does not provide sufficient analysis detail to assess those decisions.
The registry’s analysis count is zero, and it does not report an original statistical analysis plan, interim-analysis plan, or primary sponsor analysis. In general, a prespecified plan helps distinguish planned analyses from choices made after outcomes are observed. Without those details, it is not possible to judge whether the posted summaries reflect the planned analysis or whether unreported analyses were conducted.
15. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| SA ON | 0 | 25 | 0.0% |
| SA OFF | 0 | 25 | 0.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| SA ON | 0 of 25 |
| SA OFF | 0 of 25 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 0% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| SA ON | 0 of 25 |
| SA OFF | 0 of 25 |
The registry reports zero serious adverse events and zero deaths in both the SensAwake-on and SensAwake-off groups. For each condition, 25 participants are listed as at risk for serious events and 25 as at risk for other adverse events; zero are listed as affected in each category. No serious adverse-event terms are listed.
These figures describe what is recorded for the trial and should be read in light of its size and duration. The registry describes two-week treatment periods in a crossover study, and the enrollment is 35. A record of zero events does not establish that an event is impossible or that the device conditions have identical safety profiles. It means no events are listed in these posted counts.
The registry does not report further details about adverse-event definitions, collection procedures, event timing, severity grading, or whether events were assessed as related to treatment. The number of participants at risk is shown separately for each condition; the record does not explain how repeated exposure within the crossover was handled for safety summaries. These limitations restrict the conclusions that can be drawn from the event counts.
16. What the Result Does, and Does Not, Mean
The posted primary summaries show mean percentages of nights with at least four hours of Auto-CPAP use of 41.8 with SensAwake activated and 39.7 without activation. The recalculated mean difference is -2.1 for off relative to on, with a 95% confidence interval from -20.85 to 16.65. This is an uncertain estimate: the interval includes zero and allows differences in either direction. The unadjusted p-value is 0.826, and no sponsor-reported primary analysis is listed.
These figures do not establish that the two conditions are equivalent. Equivalence requires a prespecified margin and an analysis designed to test whether the plausible difference falls within that margin; no such margin or equivalence analysis is reported in the registry record. Likewise, a non-significant unadjusted comparison does not prove that there is no effect. It indicates that this calculation did not distinguish the observed contrast from zero at conventional levels, while the wide interval leaves considerable uncertainty.
The displayed comparison also does not establish a causal crossover effect adjusted for participant pairing, treatment period, sequence, or carryover. Those features matter in a crossover design, but the necessary analysis details are not reported in the registry record. The reported condition means are useful descriptive summaries, not a substitute for a complete analysis of repeated measurements.
The endpoint measures device-recorded adherence according to a four-hour nightly threshold. It does not directly measure symptoms, sleep quality, health outcomes, or the reason for mask removal. Secondary device measures can add context, but they do not answer those clinical questions. The record does not report a threshold for a clinically important adherence difference, so statistical estimates cannot be translated into a judgment about clinical importance.
The study’s completed status and posted data are informative about the measurements recorded in this trial, but the result should be interpreted cautiously. The registry does not report the original sample-size justification, full analysis plan, missing-data procedures, or detailed crossover analysis. The numerical summaries describe the observed conditions; they do not by themselves settle whether the modification changes adherence or whether any difference would matter to participants.
17. Why This Trial Matters Statistically
This trial is statistically interesting because it uses a crossover design to compare device conditions in the same study population. In general, a crossover design can make each participant a reference for their own response, potentially reducing the influence of stable differences between participants. That benefit depends on measuring both conditions for the same people and analyzing the paired structure appropriately. The registry describes treatment sequences but does not report a paired analysis or the underlying participant-level data.
The primary endpoint is a device-recorded adherence measure rather than a subjective report. Objective recording can reduce reliance on recall, while the threshold definition makes the outcome easy to interpret as nights meeting a minimum duration. At the same time, a threshold-based measure can conceal variation in the amount of use within nights and between nights. The endpoint therefore answers a focused adherence question, not every question about treatment experience or clinical benefit.
The posted mean difference is small relative to the uncertainty represented by its confidence interval. That contrast between an apparently modest point estimate and a broad range is a useful lesson in why estimates need intervals, not just means or p-values. It also highlights the limits of interpreting aggregate summaries when the design involves repeated observations and the analysis details are absent.
The secondary outcomes illustrate another statistical lesson: a trial can record multiple device measures, but their interpretation depends on a clear plan for prioritization and multiplicity. Without that information, secondary patterns are best used to generate questions rather than to make strong confirmatory claims. Overall, the record supports careful description of what was measured and what remains uncertain.
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 limitation for interpreting the comparison is that the registry describes a crossover design but does not report a crossover-specific analysis. Condition means and standard deviations alone do not show the within-participant relationship needed for a paired estimate. No sequence-specific or period-specific results are reported, and possible carryover is not addressed in the posted analysis details.
The outcome counts also need context. Enrollment is listed as 35, while the posted primary summaries show 25 observations in each condition. The registry does not explain this difference, identify the number of complete pairs, or describe exclusions and missing measurements. The analysis population and handling of incomplete periods are not reported in the registry record.
The study description refers to moderate-to-severe obstructive sleep apnea and participants who remove the mask for unknown reasons during Auto-CPAP therapy. The registry does not provide detailed eligibility criteria, baseline characteristics, or information about how representative the enrolled participants were. Generalizability beyond the studied participants cannot be assessed from the available record.
The primary outcome is a threshold-based percentage of nights, which does not capture all dimensions of device use. The registry does not report a clinically important difference threshold. The sponsor’s original sample-size justification, statistical plan, masking details, allocation procedures, and interim-analysis plan are also not reported. The posted unadjusted calculations therefore provide a limited statistical view rather than a complete account of trial design and analysis.
Finally, the trial is recorded as completed, but the registry’s analysis count is zero and no sponsor analysis is listed. Detailed numerical results are not reported for all named secondary outcomes. These reporting gaps limit assessment of prespecification, multiplicity, and whether all planned outcomes are represented.
19. Related Tutorials
20. Related Statistical Calculators
21. Sources
- ClinicalTrials.gov: The Effectiveness of SensAwake™ for Continue Positive Airway Pressure Treatment of Obstructive Sleep Apnea Patients — NCT03294629.
- Registry record last updated 2018-06-12; status last verified 2017-06.
- Results first posted 2018-06-12.
- 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.
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22. Record Summary
NCT03294629 is a completed randomized, double-masked crossover study sponsored by Chang Gung Memorial Hospital. It compares Auto-CPAP with SensAwake activated against Auto-CPAP without activation in people with obstructive sleep apnea. The registry lists enrollment of 35 and two-week periods in each condition, with treatment order reversed between sequences.
The primary outcome is the percentage of nights with at least four hours of device use over two weeks. Posted means are 41.8 with activation and 39.7 without activation. The recalculated unadjusted mean difference for off relative to on is -2.1, with a 95% confidence interval from -20.85 to 16.65 and an unadjusted p-value of 0.826.
The registry does not report a sponsor analysis, crossover-specific model, original sample-size justification, analysis population, missing-data procedure, or multiplicity plan. The posted summaries are descriptive and leave substantial uncertainty about the condition contrast.