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 Evaluation of the Philips Respironics BiPAP autoSV Devices in Subjects With Sleep Disorders (NCT01626989), a randomized na study. The primary outcome is Apnea-Hypopnea Index (AHI).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01626989 |
| Phase | NA |
| Condition | Sleep Disordered Breathing, Sleep Apnea, Central |
| Allocation | Randomized |
| Design model | Crossover |
| Masking | Single |
| Enrollment | 44 |
| Arms in the primary outcome | 3 |
| Lead sponsor | Philips Respironics |
| Results posted | Yes |
2. Clinical Question
Population
Participants with sleep-disordered breathing, including central sleep apnea, were enrolled. The registry summary describes the target group as participants with complex sleep apnea. Enrollment was 44; the primary analysis excluded 8 participants with missing or unscorable data.
Intervention
One intervention was the BiPAP Auto SV Advanced device. Participants received one night of treatment with each intervention, according to the primary-outcome timeframe.
Comparator
The other device was BiPAP Auto SV 4. The registry also posts baseline CPAP titration results, but the sponsor-reported comparison is between the two BiPAP devices.
Primary question
The primary outcome was apnea-hypopnea index (AHI), the number of apneas and hypopneas per hour of sleep. The stated clinical question was whether the newer device would treat participants no worse than its predecessor. The registry labels the reported analysis as non-inferiority or equivalence, but does not report a non-inferiority margin or an estimated treatment difference with a confidence interval.
The study was registered as a randomized, single-masked crossover trial. In a crossover design, participants receive more than one intervention, allowing comparisons to be made within the same participant. The primary timeframe lists baseline and two nights, one night for each intervention. This design is relevant to interpreting the posted results: the two device measurements are not necessarily independent groups, and an analysis that does not account for paired observations may not reflect the trial’s intended comparison.
The posted primary summaries include 19 participants for each device and for the CPAP titration results. The registry does not report the sequence assigned to each participant, the washout procedure, or which parties were masked. The research question concerns comparative AHI under the two devices, not whether either device is better than no treatment. The registered goal is a non-inferiority or equivalence question; a small p-value alone does not establish that conclusion without the relevant margin and analysis details.
3. Trial Design
This completed study enrolled 44 participants and compared Philips Respironics BiPAP autoSV devices. The record lists randomized allocation, single masking, and a crossover model. Its registered title is Evaluation of the Philips Respironics BiPAP autoSV Devices in Subjects With Sleep Disorders. The listed conditions are sleep-disordered breathing and central sleep apnea. The study phase is recorded as NA.
The two interventions are BiPAP auto SV Advanced and BiPAP auto SV 4. The primary outcome timeframe is baseline and two nights, with one night for each intervention. The primary registry results list 19 participants for each device and 19 for CPAP titration. The primary outcome description says that 8 participants had missing or unscorable data and were not included in the analysis. The record does not explain why the posted group counts are 19 or how missing or unscorable observations were handled beyond that statement.
CPAP titration appears as a posted outcome group, with a mean AHI of 38 events per hour. It is not one of the two named randomized device interventions in the intervention listing. The registry reports a sponsor analysis comparing the two BiPAP device groups using a nonparametric Wilcoxon Signed Rank test. It labels this analysis as non-inferiority or equivalence and gives p = .001. The registry does not post the test statistic, an effect estimate, a confidence interval, or a decision threshold for that analysis.
The record lists 14 outcome measures and 1 analysis. It posts 13 secondary outcomes. The registry does not report the original sample-size justification, the planned analysis details beyond the reported test, the masking arrangements, or the randomization sequence. Start and primary completion are recorded as 2010-06 and 2012-06, respectively; the overall status is completed.
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.
Screening Period
| Stage | Screening Population | BiPAP Auto SV Advanced First, Then BiPAP Auto SV 4 | BiPAP Auto SV 4 First, Then BiPAP Auto SV Advanced |
|---|---|---|---|
| STARTED | 44 | 0 | 0 |
| COMPLETED | 27 | 0 | 0 |
| NOT COMPLETED | 17 | 0 | 0 |
Reasons for not completing this period:
| Reason | Screening Population | BiPAP Auto SV Advanced First, Then BiPAP Auto SV 4 | BiPAP Auto SV 4 First, Then BiPAP Auto SV Advanced |
|---|---|---|---|
| Screen Failure | 15 | 0 | 0 |
| Withdrawal by Subject | 2 | 0 | 0 |
Fist Intervention (Night 1)
| Stage | Screening Population | BiPAP Auto SV Advanced First, Then BiPAP Auto SV 4 | BiPAP Auto SV 4 First, Then BiPAP Auto SV Advanced |
|---|---|---|---|
| STARTED | 0 | 15 | 12 |
| COMPLETED | 0 | 15 | 12 |
| NOT COMPLETED | 0 | 0 | 0 |
Second Intervention (Night 2)
| Stage | Screening Population | BiPAP Auto SV Advanced First, Then BiPAP Auto SV 4 | BiPAP Auto SV 4 First, Then BiPAP Auto SV Advanced |
|---|---|---|---|
| STARTED | 0 | 15 | 12 |
| COMPLETED | 0 | 15 | 12 |
| NOT COMPLETED | 0 | 0 | 0 |
Analysis population for the primary outcome, as defined in the registry: 8 participants had missing or unscorable data, therefore they are not included in the analysis.
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.
Population: All participants that signed consent.
| Characteristic | Unit | All Study Participants |
|---|---|---|
| Participants analysed | 44 | |
| Age, Categorical: <=18 years | Participants | 0 |
| Age, Categorical: Between 18 and 65 years | Participants | 27 |
| Age, Categorical: >=65 years | Participants | 17 |
| Age, Continuous | years | 61.71 (SD 13.4) |
| Sex: Female, Male: Female | Participants | 9 |
| Sex: Female, Male: Male | Participants | 35 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 0 |
| Race (NIH/OMB): Asian | Participants | 0 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 |
| Race (NIH/OMB): Black or African American | Participants | 4 |
| Race (NIH/OMB): White | Participants | 39 |
| Race (NIH/OMB): More than one race | Participants | 0 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 1 |
| Region of Enrollment: United States | participants | 44 |
| Body Mass Index (BMI) | kg/m^2 | 33.3 (SD 6.6) |
6. Primary Endpoint
The registry lists the primary outcome as Apnea-Hypopnea Index (AHI), measured over Baseline, and 2 nights (1 night for each intervention).
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Deviation |
| Unit | events per hour |
| Endpoint classification | Event-Rate Endpoint |
The primary endpoint is apnea-hypopnea index (AHI), measured in events per hour. It counts apneas and hypopneas during sleep and expresses their frequency relative to sleep time. The registry reports the mean and standard deviation for baseline CPAP titration and for each device night.
AHI is used to quantify the frequency of breathing events during sleep. For a comparison of two sleep devices, a measure that captures both apneas and hypopneas provides an overall event-rate outcome rather than focusing on only one event type. The registry’s stated clinical question is whether the newer device treats participants no worse than its predecessor, so the endpoint is intended to support a comparative assessment of device performance.
General statistical context: a mean describes the average value in a group, while a standard deviation describes variation among observed values. These summaries do not show the distribution of individual participant measurements or the within-participant differences that matter in a crossover study. The posted mean AHI was 38 events per hour at CPAP titration, 13 events per hour with BiPAP Auto SV Advanced, and 12 events per hour with BiPAP Auto SV 4. These are descriptive summaries; by themselves they do not establish the result of the sponsor’s paired comparison or a non-inferiority conclusion.
The primary outcome is measured over short, specified sleep-study periods: baseline and two treatment nights, one per intervention. The record does not report a minimal clinically important difference, an acceptable non-inferiority margin, or how those quantities were selected. Those details would be important for judging whether the observed device results meet the registered comparative objective.
7. Results Posted in the Registry
- BiPAP Auto SV Advanced: 13.00 versus 38.00 (events per hour) on control; rate ratio 0.34 (95% CI 0.30–0.40, approximate, Poisson model); p ≈ <0.001.
- BiPAP Auto SV 4: 12.00 versus 38.00 (events per hour) on control; rate ratio 0.32 (95% CI 0.27–0.37, approximate, Poisson model); p ≈ <0.001.
Rate ratio: BiPAP Auto SV Advanced
95% CI: 0.30 to 0.40
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 |
|---|---|---|---|---|
| Central Apnea Index(CAI) | Event-Rate Endpoint | Rate ratio | 0.08 (0.05 to 0.13) | 2 per arm |
| Obstructive Apnea Index (OAI) | Event-Rate Endpoint | Rate ratio | 0.07 (0.04 to 0.11) | 2 per arm |
| Mixed Apnea Index (MAI) | Event-Rate Endpoint | Rate ratio | 0.07 (0.03 to 0.18) | 5 per arm |
Central Apnea Index(CAI)
- Endpoint type: Event rate: events per unit of follow-up, compared as a rate ratio.
- Test: Poisson rate ratio, based on the estimated number of events and follow-up time.
- Result:
- BiPAP Auto SV Advanced: 1.00 versus 12.00 (events per hour) on control; rate ratio 0.08 (95% CI 0.05–0.13, approximate, Poisson model); p ≈ <0.001.
- BiPAP Auto SV 4: 1.00 versus 12.00 (events per hour) on control; rate ratio 0.08 (95% CI 0.05–0.13, approximate, Poisson model); p ≈ <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference (a ratio of 1), so the event rate is statistically lower for BiPAP Auto SV Advanced than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference (a ratio of 1), so the event rate is statistically lower for BiPAP Auto SV 4 than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Obstructive Apnea Index (OAI)
- Endpoint type: Event rate: events per unit of follow-up, compared as a rate ratio.
- Test: Poisson rate ratio, based on the estimated number of events and follow-up time.
- Result:
- BiPAP Auto SV Advanced: 1.00 versus 14.00 (events per hour) on control; rate ratio 0.07 (95% CI 0.04–0.11, approximate, Poisson model); p ≈ <0.001.
- BiPAP Auto SV 4: 2.00 versus 14.00 (events per hour) on control; rate ratio 0.14 (95% CI 0.10–0.20, approximate, Poisson model); p ≈ <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference (a ratio of 1), so the event rate is statistically lower for BiPAP Auto SV Advanced than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference (a ratio of 1), so the event rate is statistically lower for BiPAP Auto SV 4 than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Mixed Apnea Index (MAI)
- Endpoint type: Event rate: events per unit of follow-up, compared as a rate ratio.
- Test: Poisson rate ratio, based on the estimated number of events and follow-up time.
- Result:
- BiPAP Auto SV Advanced: 0.30 versus 4.00 (events per hour) on control; rate ratio 0.07 (95% CI 0.03–0.18, approximate, Poisson model); p ≈ <0.001.
- BiPAP Auto SV 4: 0.60 versus 4.00 (events per hour) on control; rate ratio 0.15 (95% CI 0.08–0.28, approximate, Poisson model); p ≈ <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference (a ratio of 1), so the event rate is statistically lower for BiPAP Auto SV Advanced than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference (a ratio of 1), so the event rate is statistically lower for BiPAP Auto SV 4 than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The posted secondary outcomes cover several aspects of sleep and breathing, including central, obstructive, and mixed apnea indices; sleep-stage percentages; sleep onset and REM onset latency; wake after sleep onset; and total sleep time. The registry lists 14 outcome measures overall and posts 13 secondary outcomes. Among the rate outcomes with posted summaries, the device means are generally lower than the CPAP titration means. This broad descriptive pattern is consistent with the primary AHI summaries, which also show lower means with both devices than with CPAP titration.
This pattern is context rather than an independent confirmation of the sponsor’s device-to-device non-inferiority or equivalence question. The secondary endpoints measure different features of sleep and breathing, and their comparisons against CPAP do not directly establish that the two devices are similar to each other. The record does not report sponsor analyses for the posted secondary outcomes. The recalculated comparisons are unadjusted and rely on the same exposure-model approach described for the primary endpoint.
Unadjusted results across multiple outcomes carry less weight because examining many outcomes can produce apparently strong results by chance. General context: multiplicity can be addressed through a prespecified hierarchy or statistical adjustment, but the registry does not report either for these secondary measures. The secondary results are therefore best viewed as descriptive and exploratory, rather than as a set of confirmatory tests. No interpretation of a particular secondary measure should be taken as an independent claim about the comparative performance of the two devices.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Non Rapid Eye Movement (NREM) and Rapid Eye Movement (REM) Percentage Based on Total Sleep Time (TST) Indices
- Central Apnea Index(CAI)
- Obstructive Apnea Index (OAI)
- Mixed Apnea Index (MAI)
- Sleep Onset Latency (SOL)
- REM Onset Latency (ROL)
- Wake After Sleep Onset (WASO)
- Total Sleep Time (TST)
9. Statistical Interpretation
The posted descriptive results show a mean AHI of 38 events per hour during CPAP titration, 13 events per hour with BiPAP Auto SV Advanced, and 12 events per hour with BiPAP Auto SV 4. Each device group has 19 participants in the posted primary results. These group summaries describe the observed values; they do not, on their own, account for the crossover structure or establish that the two devices are equivalent.
The registry’s sponsor-reported analysis directly compares the two device groups with a nonparametric Wilcoxon Signed Rank test and reports p = .001. The analysis is labeled non-inferiority or equivalence. The registry does not provide the paired difference, a confidence interval for that difference, the non-inferiority margin, or a statement of the decision rule. Without these details, the p-value cannot be interpreted as evidence that the devices met a specific non-inferiority criterion. A p-value indicates how compatible the observed data are with a specified null model; it does not convey the size of a difference or establish clinical equivalence.
Separately, the posted recalculation compares each device’s mean AHI with the CPAP titration mean using a Poisson rate model. It reports unadjusted p-values of <0.001 for both device-versus-CPAP comparisons. Those are not the sponsor’s crossover comparison. The recalculation uses a one-year exposure assumption because the timeframe could not be parsed, whereas the registered outcome timeframe is baseline and two nights, one night per device. Consequently, those comparisons should be read cautiously and should not be substituted for a paired device-to-device analysis.
The estimates and intervals from that recalculation are model-based, unadjusted comparisons with CPAP, not estimates from the sponsor-reported Wilcoxon test. The record does not report an adjusted analysis, so no adjustment should be assumed. Nor does the registry report a formal statistical comparison of either device against CPAP as the trial’s primary question.
The eight participants with missing or unscorable primary data are excluded from the posted analysis. The registry does not describe whether their missingness differed by device, whether they were excluded before or after treatment, or whether a sensitivity analysis was performed. The available results therefore apply to the observations included in the reported analysis and do not by themselves characterize the effect of missing data on the comparison.
10. Statistical Methods Explained
General statistical context: a crossover trial gives participants more than one intervention, so each participant can contribute observations under both treatments. This can reduce the influence of stable differences between people when the analysis compares each participant with themself. It also means that the analysis should preserve the pairing of observations. The registry identifies the design as crossover and reports a Wilcoxon Signed Rank test for the two device groups, a method used for paired data. The record does not report the sequence, period effects, or the full model or test details.
What does the sponsor-reported test assess?
The Wilcoxon Signed Rank test is a nonparametric method for paired measurements. In general, it ranks the magnitudes of within-participant differences and uses their signs to assess whether the paired differences are centered around zero. It does not require the paired differences to follow a normal distribution, though its interpretation depends on the study’s paired observations and the analysis assumptions. The registry reports p = .001 and labels the analysis as non-inferiority or equivalence. It does not post the paired differences, test statistic, confidence interval, non-inferiority margin, or a full description of the decision rule. Thus, the method name and p-value alone do not show how the non-inferiority or equivalence conclusion was reached.
What is the separate rate-model recalculation?
The recalculation treats AHI as an event rate and compares the posted group means using a Poisson model. General context: a Poisson model is commonly used for counts or event rates, often with an exposure term to account for the amount of time during which events could occur. The recalculated comparison is not the sponsor’s reported paired Wilcoxon analysis. The registry’s actual timeframe is baseline and two nights, with one night per device; the recalculation instead used an assumed one-year exposure because the timeframe was not parseable. That mismatch makes the resulting rate comparisons difficult to align with the clinical measurement period. The posted p-values for these recalculated device-versus-CPAP comparisons are unadjusted and are not results of the primary device-to-device crossover test.
General context: Poisson models assume a relationship between the event count and its mean that may be too restrictive when observations vary more than the model allows. This extra variation is called over-dispersion. If over-dispersion or dependence between repeated measurements is not handled, uncertainty can be understated. The registry does not report a check for over-dispersion or a correction for the crossover pairing in the recalculation. The reported rate-model results should therefore be treated as an illustrative, unadjusted calculation rather than as a replacement for the sponsor’s analysis.
What does a p-value say?
General context: a p-value measures how unusual data at least as extreme as those observed would be under a specified null hypothesis and model. It does not measure the probability that a treatment is effective, the probability that the null hypothesis is true, or the magnitude of a difference. A small p-value can indicate evidence against a particular null hypothesis, but a non-inferiority test also requires an explicit margin and a method for comparing the uncertainty interval with that margin. Those elements are not reported in the registry record for the sponsor analysis.
What do descriptive means and standard deviations add?
The AHI summaries are means with standard deviations. General context: the mean shows the average outcome, while the standard deviation describes the spread of measurements around the mean. Neither quantity supplies the distribution of paired differences. For crossover data, the variance of within-person differences can differ from the variation in each device group considered separately. Therefore, the group means and standard deviations cannot reconstruct the sponsor’s paired test or its uncertainty interval.
How should the secondary analyses be considered?
The record lists secondary sleep outcomes, including central, obstructive, and mixed apnea indices and measures of sleep timing and duration. The posted secondary summaries include mean and standard deviation for outcomes such as central apnea index, obstructive apnea index, and mixed apnea index. Recalculated rate comparisons are available for those outcomes, but the registry does not list reported sponsor analyses for them. The recalculated p-values are unadjusted. General context: when many outcomes are examined, the chance of obtaining at least one apparently notable result by chance increases unless the analysis accounts for multiple comparisons. The registry does not report a multiplicity adjustment or a hierarchy for interpreting secondary outcomes.
11. Confidence Intervals and Precision
Confidence intervals describe a range of values compatible with the observed data and the assumptions of the method used. General context: a narrower interval indicates greater statistical precision under that model, while a wider interval indicates more uncertainty. An interval does not capture every source of uncertainty, including missing data, model mismatch, or limitations in the study design.
The recalculated primary comparisons include intervals for rate ratios against CPAP titration. These intervals come from the Poisson rate-model recalculation, not from the sponsor’s Wilcoxon Signed Rank analysis of the two devices. They therefore do not quantify uncertainty in the paired device-to-device comparison that addresses the stated non-inferiority or equivalence question. The registry does not report a confidence interval for the sponsor analysis or for the paired difference.
The rate-model intervals depend on the assumptions used for the recalculation, including the one-year exposure assumption. That assumption does not match the registered timeframe of baseline and two nights, one night per intervention. The intervals should consequently be interpreted as conditional on a model and exposure specification that do not directly represent the stated measurement period. The registry also does not report a check for over-dispersion or an adjustment for within-participant dependence in that recalculation.
The sponsor-reported p-value does not supply the missing precision information. Without an interval for the paired device difference and without the margin used for non-inferiority or equivalence, readers cannot assess the range of plausible paired differences against the intended threshold. The posted group means and standard deviations provide useful descriptive context, but they are not a substitute for that interval.
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 | 1 | 1 |
| 75% of the observed effect | 2 | 2 |
| 50% of the observed effect | 2 | 3 |
The sample-size figures are planning illustrations based on the observed effect, not the trial’s original design calculations. For the non-time-to-event outcomes in this study, the displayed figures are participants per arm, not total events. The planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. The trial’s own sample-size justification and original design assumptions are not reported in the registry record.
The 80% power column gives the planned number of participants per arm under those assumptions for an 80% chance of detecting the specified effect if that effect is real. The 90% power column gives the corresponding number per arm for a 90% chance. These are design calculations, not guarantees about what a future study will find. They are also not descriptions of the enrolled or analyzed sample.
The rows that plan for 100%, 75%, and 50% of the observed effect illustrate how the assumed target difference changes the planning requirement. Smaller effects generally require more participants to detect, all else equal. The figures are driven by the observed effect in this small study and by the stated simplified planning assumptions; they should not be read as definitive design recommendations or as a reconstruction of the original trial plan. These calculations are not observed power.
Because the trial is crossover, a two-arm independent-groups planning illustration may not capture the design’s paired structure. The registry does not report the assumptions used in the original design or a planning calculation that accounts for within-participant correlation. The displayed planning counts are therefore best read as illustrations of how sample size changes under the stated assumptions, not as evidence about the adequacy of the actual enrollment.
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, λ0 and λ1 are event rates per patient-year, and T is follow-up per participant in years. This assumes Poisson counts and equal follow-up.
Worked calculation for this trial
- Control rate λ0 = 38.0000; treatment rate λ1 = 13.0000 events per patient-year; follow-up T = 1.00 years.
- n = (1.96 + 0.842)2 × (1/38.0000 + 1/13.0000) / (1.00 × [ln(0.342)]2) = 0.7, rounded up to 1 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
lambda0 <- 38 # control rate, events per patient-year
lambda1 <- 13 # treatment rate
tt <- 1 # follow-up per participant, years
n_per_arm <- function(power, frac = 1) {
l1 <- lambda0 * (lambda1 / lambda0)^frac # smaller effect = fraction of the observed log rate ratio
ceiling(round((z_a + qnorm(power))^2 * (1 / lambda0 + 1 / l1) / (tt * log(l1 / lambda0)^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 = ",")))
# Simulation 1: Poisson counts. Simulation 2: over-dispersed counts (variance = 1.5 x mean), analysed with the matching variance.
set.seed(1626989)
n <- n_per_arm(0.80)
reps <- 20000
m0 <- lambda0 * n * tt; m1 <- lambda1 * n * tt
x0 <- rpois(reps, m0); x1 <- rpois(reps, m1)
z <- log(x1 / x0) / sqrt(1 / x0 + 1 / x1)
cat(sprintf("Simulated power, Poisson counts, n = %s per arm: %.3f\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE)))
phi <- 1.5
y0 <- rnbinom(reps, mu = m0, size = m0 / (phi - 1)); y1 <- rnbinom(reps, mu = m1, size = m1 / (phi - 1))
z2 <- log(y1 / y0) / sqrt(phi * (1 / y0 + 1 / y1))
cat(sprintf("Simulated power, over-dispersed counts (phi = 1.5), same n: %.3f\n", mean(abs(z2) > z_a, na.rm = TRUE)))
Output from running the code
100% of observed effect: n per arm = 1 (80% power), 1 (90% power)
75% of observed effect: n per arm = 2 (80% power), 2 (90% power)
50% of observed effect: n per arm = 2 (80% power), 3 (90% power)
Simulated power, Poisson counts, n = 1 per arm: 0.944
Simulated power, over-dispersed counts (phi = 1.5), same n: 0.822
The first simulation draws Poisson counts and should land close to the target power. The second allows extra variability (variance 1.5 times the mean, a purely illustrative value), which lowers the power at the same sample size, so rate trials usually need more participants than the Poisson formula suggests.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| nonparametric Wilcoxon Signed Rank test | not reported | 0.001 |
The sponsor-reported analysis compares BiPAP Auto SV Advanced with BiPAP Auto SV 4 using a nonparametric Wilcoxon Signed Rank test. It is labeled as non-inferiority or equivalence and has p = .001. That is the analysis most directly aligned with the crossover design and the stated device-to-device question among the results posted in the registry.
The separate recalculation compares each device’s posted AHI mean with the CPAP titration mean using a Poisson rate model. It reports unadjusted p-values of <0.001. These recalculated comparisons are not the sponsor’s test, do not directly compare the two devices, and use an assumed one-year exposure despite the registered two-night treatment timeframe. They should not replace or override the sponsor’s analysis.
The sponsor’s own analysis takes precedence over the recalculation because it is the reported trial analysis. However, the registry does not post the sponsor’s effect estimate, confidence interval, non-inferiority margin, or decision rule. The p-value alone does not reveal whether a prespecified non-inferiority criterion was met. The record also does not provide enough detail to independently reproduce the sponsor’s analysis. The discrepancy flag is false, but that does not fill in the unreported analysis details.
15. Multiplicity, Missing Data and Analysis Populations
The record lists multiple outcomes: a primary AHI measure and secondary measures of sleep-stage percentages, several apnea indices, sleep timing, wake after sleep onset, and total sleep time. It reports one sponsor analysis, for the comparison between the two BiPAP devices. The record does not report a multiplicity adjustment, a prespecified hierarchy among outcomes, or a strategy for controlling the overall chance of false-positive findings across outcomes.
General context: when several hypotheses are tested, the chance of at least one small p-value under a collection of null hypotheses can increase. Prespecifying a primary endpoint and a testing hierarchy, or applying an appropriate adjustment, can help clarify how confirmatory claims should be evaluated. The registry identifies AHI as primary, but does not provide a fuller statistical analysis plan or state how secondary outcomes were intended to be interpreted. Secondary recalculations are unadjusted and should be treated with corresponding caution.
The primary results exclude 8 participants whose data were missing or unscorable. The registry does not report the reasons for those missing data, whether missingness affected one device or period more than another, or whether those participants differed from those analyzed. It does not report a sensitivity analysis, imputation method, or an analysis population definition beyond the exclusion statement. The posted results therefore represent the analyzed observations, and the possible influence of missing outcomes is not quantified.
The record does not report the original statistical analysis plan, interim analyses, or a sample-size justification. It also does not provide the sponsor’s non-inferiority margin or the confidence interval used to assess that objective. These omissions limit assessment of whether the analysis followed a prespecified plan and how the stated non-inferiority or equivalence label was operationalized. No details about interim analyses or stopping rules are reported in the registry record.
16. 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 |
|---|---|---|---|
| All Participants | 1 | 44 | 2.3% |
| BiPAP Auto SV Advanced | 0 | 27 | 0.0% |
| BiPAP Auto SV 4 | 0 | 27 | 0.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| All Participants | 0 of 44 |
| BiPAP Auto SV Advanced | 0 of 27 |
| BiPAP Auto SV 4 | 0 of 27 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| All Participants | 0 of 44 |
| BiPAP Auto SV Advanced | 0 of 27 |
| BiPAP Auto SV 4 | 0 of 27 |
Most frequent serious adverse event terms
| Event term | Organ system | All Participants | BiPAP Auto SV Advanced | BiPAP Auto SV 4 |
|---|---|---|---|---|
| Stents | Cardiac disorders | 1 of 44 | 0 of 27 | 0 of 27 |
Serious events with the highest arm-level rate: stents (2.3%).
The safety record lists 44 participants in the all-participants group, with 1 serious adverse event and 0 other adverse events. It lists 0 deaths. The serious adverse event term shown is Stents, with 2.3% reported. The registry does not describe the event in more detail or state whether it was related to either device.
The device-specific safety groups each list 27 participants at risk for serious and other adverse events. For BiPAP Auto SV Advanced and BiPAP Auto SV 4, the registry lists 0 serious adverse events, 0 other adverse events, and 0 deaths. Because this is a crossover trial, participants may contribute exposure to both devices; the device-specific groups should not be added to infer a unique total number of participants.
These are counts reported in the registry and should not be interpreted as proof that no other harms occurred. The record does not provide event descriptions, severity details beyond the serious-event classification, timing, attribution, or a fuller account of safety monitoring. The listed figures describe the posted safety information, not a comparative estimate of risk between devices.
17. What the Result Does, and Does Not, Mean
The registry reports lower mean AHI values with each BiPAP device than with CPAP titration in the posted primary summaries. It also reports a sponsor analysis comparing the two devices, labeled as non-inferiority or equivalence, with p = .001. These findings describe the posted summaries and analysis; they do not, by themselves, establish that either device is better, that the devices are clinically equivalent, or that a non-inferiority criterion was met.
For a non-inferiority conclusion, the size and uncertainty of the device-to-device difference must be considered against a prespecified margin. The registry does not report that margin or a confidence interval for the sponsor’s paired comparison. The p-value cannot stand in for those details. The recalculated Poisson comparisons address each device versus CPAP titration rather than the central two-device question, and their assumed one-year exposure differs from the registered treatment timeframe.
The trial enrolled 44 participants, while 8 participants had missing or unscorable primary data and were excluded from the analysis. The posted primary groups contain 19 participants each. The registry does not explain the missing data in enough detail to assess their potential effect on the comparison. The short treatment timeframe also means that these results concern measurements from the specified sleep-study nights; the record does not report longer-term outcomes.
The findings should be understood within the population and outcome recorded: participants with sleep disorders, AHI during baseline and two treatment nights, and the posted analyses. The record does not provide enough detail to generalize beyond that setting or to evaluate all aspects of device safety and performance. Statistical results are evidence to interpret alongside study design and analysis details, not a substitute for a complete account of the trial.
18. Why This Trial Matters Statistically
This trial is statistically interesting because it uses a randomized crossover design to compare two devices in the same participants. General context: a well-conducted crossover analysis can use within-participant comparisons, which may separate treatment differences from stable differences between participants. The registry reports a paired nonparametric test for the device comparison, making the choice of a paired method relevant to the design.
The record also illustrates why the precise estimand and analysis matter. The sponsor’s reported question concerns non-inferiority or equivalence between the devices, while the posted recalculation compares each device with CPAP titration. Those are different comparisons. The recalculation uses a rate model and an assumed one-year exposure, whereas the registered AHI timeframe consists of baseline and two nights. Results based on these distinct questions and assumptions should not be conflated.
The reported group means and sponsor p-value are not enough to judge the non-inferiority claim. An explicit margin and an uncertainty interval for the paired difference would make the decision process clearer. Missing or unscorable data, absent analysis details, and unreported multiplicity procedures further constrain interpretation. The many sleep outcomes can provide descriptive context, but unadjusted secondary findings should not be treated as multiple independent confirmations.
The central statistical lesson is that a small p-value is not the whole result. Readers need to know what was compared, how the design was represented in the analysis, what effect sizes and intervals were estimated, and what threshold defined an acceptable difference. The registry provides some of this information, but not the full set needed to independently evaluate the sponsor’s stated objective.
19. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
- Rate comparisons use a Poisson approximation unless the sponsor posted confidence limits; real event counts are often over-dispersed.
The main trial-specific limitation is incomplete reporting of the sponsor’s non-inferiority or equivalence analysis. The registry gives the Wilcoxon Signed Rank test and p = .001 but does not report the paired effect estimate, confidence interval, non-inferiority margin, or decision rule. The intended comparative claim therefore cannot be fully evaluated from the posted analysis details.
The registry identifies a crossover design, but does not report the treatment sequence, washout procedure, period effects, or how these were handled in the analysis. It does not identify who was masked. Such details matter to understanding whether observations from different treatment nights can be compared as intended.
The primary analysis excludes 8 participants with missing or unscorable data, and the analysis groups list 19 participants per condition. Reasons for missingness and sensitivity analyses are not reported. The posted recalculations use an assumed one-year exposure despite the short registered timeframe of baseline and two treatment nights. They are not a substitute for a paired comparison and do not report checks for over-dispersion or dependence.
Finally, the record does not report a full statistical analysis plan, sample-size justification, multiplicity approach, or interim-analysis details. Secondary outcomes are numerous, while their reported recalculations are unadjusted. Safety listings lack event attribution and fuller descriptions. These limitations concern what can be assessed from the registry record; they do not establish that the unreported procedures were or were not performed.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Evaluation of the Philips Respironics BiPAP autoSV Devices in Subjects With Sleep Disorders — NCT01626989.
- Registry record last updated 2019-04-25; status last verified 2019-04.
- Results first posted 2019-04-25.
- 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.
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23. Record Summary
NCT01626989 is a completed randomized, single-masked crossover study sponsored by Philips Respironics. It enrolled 44 participants and compared BiPAP Auto SV Advanced with BiPAP Auto SV 4 in people with sleep disorders. The primary endpoint was AHI, measured in events per hour over baseline and two intervention nights.
The posted primary means were 38 events per hour for CPAP titration, 13 for BiPAP Auto SV Advanced, and 12 for BiPAP Auto SV 4, with 19 participants listed in each group. Eight participants had missing or unscorable data and were excluded from the primary analysis. The sponsor reported a Wilcoxon Signed Rank test for the two-device comparison, labeled non-inferiority or equivalence, with p = .001.
The registry does not report the sponsor’s effect estimate, confidence interval, non-inferiority margin, or decision rule. Recalculated comparisons against CPAP are separate, unadjusted Poisson rate-model results and use an assumed exposure that differs from the registered timeframe. Secondary outcomes and safety counts are posted, but important analysis, missing-data, and safety details are not reported in the registry record.