Titration Pressures in Sleep Apnea Patients Using ThermoSmart® Versus Conventional Humidification: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Titration Pressures in Sleep Apnea Patients Using ThermoSmart® Versus Conventional Humidification (NCT00681083), a randomized na study. The primary outcome is Titration Pressures After Treatment Nights.

2. Clinical Question

The clinical question is about a measured pressure during CPAP titration, rather than a longer-term patient outcome. In the registry description, a sleep technician adjusts pressure during each titration to identify a therapeutic pressure intended to reduce the Apnea Hypopnea Index, a measure of obstructive sleep apnea severity. The trial compares the titration pressures recorded after nights using the two humidification arrangements.

The registry describes the trial as randomized, single-masked, and crossover. A crossover design means participants may receive more than one condition, so comparisons can potentially use information from the same person under both conditions. However, the record does not describe the sequence of conditions, the timing between nights, or the exact statistical handling of within-participant measurements. Those details matter when interpreting a comparison, and they are not reported in the registry record.

The posted primary outcome is a mean pressure in cmH20 at the end of the titration night. The result is therefore a comparison of the average values recorded under the two conditions. It does not by itself describe each participant’s response, the spread of individual differences between conditions, or a clinical consequence of any pressure difference.

3. Trial Design

The registry identifies this as a randomized, single-masked crossover study of CPAP titration in people with obstructive sleep apnea. The two device conditions were a heated breathing tube with ThermoSmart® and a non-heated breathing tube with conventional humidification. Its enrollment is listed as 26. The record lists the study status as completed and gives the study period as 2008-04 through 2008-07.

In a crossover design, participants receive more than one intervention condition, which can allow a comparison within participants rather than relying only on comparisons between separate groups. That general feature can be useful when participant characteristics influence the outcome. The registry does not report how participants were assigned to treatment order, whether the order was balanced, whether there was a washout interval, or how potential period or carryover effects were addressed. It is therefore not possible to reconstruct these design details from the record.

The primary endpoint is titled “Titration Pressures After Treatment Nights.” The timeframe is the end of the titration night, and the outcome is summarized as a mean with standard deviation. The registry describes technician adjustment of pressure during each night to identify an individual therapeutic pressure. The reported summaries list 20 observations for each condition; the record does not explain how those counts relate to the enrollment figure or whether they represent participants with complete measurements in both conditions.

One secondary outcome is listed: the relationship between breathing-tube condition and total sleep time. The record does not include a posted result for that outcome. The registry lists two outcome measures, but the displayed material does not provide a secondary-outcome estimate. The original sample-size assumptions, planned analysis details, and rules for handling incomplete or unusable titration records 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.

Night 1

Night 2 (Crossover of Night 1)

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 Titration Pressures After Treatment Nights, measured over End of titration night.

The primary endpoint is the titration pressure at the end of the titration night, measured in cmH20. The registry says that during each night a sleep technician manually adjusts CPAP pressure to determine the pressure considered best for reducing the participant’s Apnea Hypopnea Index. The pressure is summarized as a mean and standard deviation for each breathing-tube condition.

This endpoint is used to address the specific study question: whether the humidification arrangement is associated with a difference in the pressure identified during titration. Comparing mean pressures gives a concise description of the average values recorded under each condition. The accompanying standard deviations describe variation around each condition’s mean, though they do not show the distribution of paired changes for individual participants.

The endpoint is a titration measurement, not a direct measure of sleep quality, symptoms, long-term CPAP use, or a later health outcome. Those outcomes are not part of the posted primary result. Total sleep time appears as a secondary outcome in the registry, but its result is not reported in the registry record.

The crossover design makes the participant-level structure important: if the same people were measured under both conditions, the association between their two measurements can affect the uncertainty of the condition contrast. The registry reports condition summaries and a mean difference, but does not explain the analysis method or show the paired data. The result should therefore be read as the posted summary comparison, with that reporting limitation in mind.

7. Results Posted in the Registry

• Non Heated Breathing Tube: mean 10.90 versus 9.80 on control; difference 1.10 (95% CI -0.10 to 2.30), standardized effect d = 0.57; z-test p = 0.072.

8. Statistical Interpretation

9. Statistical Methods Explained

The statistical summaries can be understood by separating the measurement in each condition from the contrast between conditions. The condition summaries are means, which describe the average recorded titration pressure, and standard deviations, which describe how dispersed the recorded pressures are around those averages. The posted means are 9.8 cmH20 for the heated breathing tube and 10.9 cmH20 for the non-heated breathing tube. Their standard deviations are 1.89 and 1.98, respectively.

What does the mean difference represent?

The comparison reports a mean difference of 1.1 cmH20, with the non-heated condition listed as the comparison condition. In plain terms, the posted average for the non-heated condition is higher than the posted average for the heated condition. The difference is a summary of the two condition means; it does not mean that every participant had a higher pressure in the non-heated condition. Participant-level changes are not displayed.

In a crossover study, the same participant can contribute a measurement under each condition. A comparison that accounts for pairing uses the relationship between a participant’s measurements. That relationship can affect the standard error and confidence interval. The registry identifies a crossover design but does not report whether the comparison was calculated using paired measurements, a repeated-measures model, or another method. The reported comparison should therefore be described as the registry’s posted estimate, rather than as a reconstructed account of its analytic method.

What does the standard deviation tell us?

General explanation: a standard deviation describes variability among observed values around a mean. It is not the same as the uncertainty in the mean difference, and it does not directly show how much an individual’s pressure changed between conditions. In a crossover trial, the variability of paired changes can differ from the variability within either condition considered separately. The registry’s condition-level standard deviations do not provide that paired-change variability.

How should the confidence interval be read?

General explanation: a confidence interval gives a range of estimates compatible with the data and the method used to calculate it. The posted interval for the mean difference crosses zero and extends to 2.3 cmH20 at its upper end. Because zero lies within the interval, the data do not rule out no difference under the reported interval calculation. The interval also indicates that the estimate has uncertainty; its endpoints are not guarantees about the true effect, nor are they a range containing every participant’s response.

The lower endpoint is reported in the registry with more precision than is appropriate to reproduce. The key interpretive feature is that it lies below zero. The interval is based on a statistical calculation, and its validity depends on the analysis assumptions. The registry does not describe those assumptions or explain how the crossover structure was handled.

What does the p-value describe?

The reported p-value is 0.072. General explanation: a p-value measures how unusual data at least as discrepant as those observed would be under a specified null hypothesis and model. It does not give the probability that the null hypothesis is true, quantify the size or importance of the difference, or measure the chance that the result will reproduce. The trial’s original significance threshold and full analysis plan are not reported in the registry record. The 0.05 threshold appears in the registry’s sample-size planning assumptions, not as confirmed documentation of the trial’s original analysis rule.

Neither a p-value nor a confidence interval should be treated as a substitute for examining the design and data quality. Here, interpretation also depends on the crossover structure, the number of participants represented in the posted summaries, and the absence of detail about missing measurements. The registry does not report an adjusted analysis or a participant-level dataset in the posted results.

Why does over-dispersion matter in general?

General explanation: for count outcomes, over-dispersion occurs when variation exceeds what a simple count model assumes, and ignoring it can make uncertainty estimates too small. The primary endpoint is continuous pressure summarized by means and standard deviations, not a count outcome. Over-dispersion is therefore not the central issue for interpreting this primary comparison. The relevant uncertainty questions are the outcome’s variability and, especially for a crossover design, the relationship between measurements from the same participant.

The registry also provides a planning illustration based on the observed effect. Such calculations describe hypothetical sample sizes under specified assumptions; they do not tell us the statistical power actually achieved by the completed trial. The table’s assumptions are stated in the sample-size section, while the original design justification and original planned sample size are not reported in the registry record.

10. Confidence Intervals and Precision

The estimate is a mean difference of 1.1 cmH20, and its confidence interval extends from below zero to 2.3 cmH20. The interval therefore includes no difference and also includes positive differences. Its span signals uncertainty about the magnitude of the contrast. The point estimate alone gives a single best summary from the posted comparison, while the interval shows that the data are compatible with a broader set of values under the calculation used.

Precision is not the same as whether a result crosses a chosen significance threshold. A confidence interval that includes zero does not establish that the conditions are identical; it indicates that the posted estimate is not precise enough to exclude zero using that interval. Conversely, the point estimate does not prove that the true difference is 1.1 cmH20. The record does not provide an equivalence margin or a non-inferiority margin, so the result cannot be interpreted as demonstrating equivalence or non-inferiority.

The summaries list 20 observations in each condition, whereas enrollment is listed as 26. The record does not explain the difference between those figures or state whether the same 20 participants contributed to both condition summaries. Without that participant-flow information and a description of the crossover analysis, it is difficult to assess how the design affected the uncertainty estimate. In particular, the condition-level standard deviations do not reveal the variability of paired differences.

The confidence interval should thus be read alongside the reporting gaps, not in isolation. It gives a useful measure of uncertainty for the posted contrast, but the registry does not report enough analytic detail to independently evaluate its calculation. The interval concerns titration pressure only, not the unreported secondary result or longer-term outcomes.

11. 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 table and curve are planning illustrations based on the observed effect, not a report of the trial’s original sample-size justification. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The table considers planning for 100%, 75%, and 50% of the observed effect. These are hypothetical effect sizes used to illustrate how planning requirements change; they are not results from additional trial groups.

The entries are participants per arm, not total events. For each assumed effect, the 80% power column gives the number of participants per arm that the planning calculation estimates would be needed to have an 80% chance of detecting that effect under the stated assumptions. The 90% power column expresses the corresponding planning target for a 90% chance. These percentages describe the design calculation, not certainty that a future study will obtain a particular result.

The table shows the general relationship that smaller effects need more participants: planning for a smaller fraction of the observed effect requires larger per-arm sample sizes. The curve visualizes that relationship; it should be read as a planning aid, not as a description of the number enrolled in this study. The study itself is described as a crossover trial, while the planning illustration states equal allocation between two arms. The registry does not report whether these planning assumptions match the original design or how a crossover-specific sample-size calculation may have been made.

This is not observed power. It is a hypothetical calculation based on the observed effect and the assumptions stated for the illustration. The original sample-size justification, effect targeted at the design stage, and original power target are not reported in the registry record.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = 1.100; pooled standard deviation σ = 1.936.
2. n = 2 × (1.96 + 0.842)² × 1.936² / 1.100² = 48.6, rounded up to 49 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 <- 1.1                      # observed difference in means
sigma <- 1.93552318508459                     # 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(681083)
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 = 49 (80% power), 66 (90% power)
 75% of observed effect: n per arm = 87 (80% power), 116 (90% power)
 50% of observed effect: n per arm = 195 (80% power), 261 (90% power)
power.t.test: 49.6 
Simulated power at n = 49 per arm: 0.797 (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.

13. Multiplicity, Missing Data and Analysis Populations

The registry lists a primary outcome and one secondary outcome, the relationship between breathing-tube condition and total sleep time. It does not report a result for total sleep time. The record does not explain whether other outcomes were measured but not posted, how outcome selection was handled, or whether any adjustment for multiple comparisons was planned. A multiplicity plan is therefore not reported in the registry record.

Multiplicity matters in general because assessing several outcomes or contrasts can increase the chance that at least one result appears notable by chance. Whether that concern applies to the original analysis, and how it was addressed, cannot be determined from the posted record. The presence of one listed secondary outcome does not establish the complete set of analyses undertaken.

The registry identifies the design as crossover but does not report the analysis population, participant-flow details, or missing-data methods. Although the enrollment is listed as 26 and the summaries list 20 observations for each condition, the record does not explain exclusions, incomplete nights, or whether participants with data from only one condition contributed to any analysis. It also does not state whether all randomized participants were included in the primary analysis or whether a particular complete-case population was used.

For a crossover study, missing measurements in one condition can affect whether a participant can contribute to a paired comparison. The record does not describe imputation, sensitivity analyses, or other strategies for incomplete paired data. These omissions do not show that missing data occurred; they mean the registry does not report enough information to establish how missingness was assessed or managed.

The original analysis plan, including any prespecified analysis populations, multiplicity procedure, or missing-data approach, is not reported in the registry record. Consequently, the posted comparison can be described, but its correspondence to a prespecified analysis cannot be assessed from this record.

14. Safety Results

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

Deaths

Other (non-serious) adverse events

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

The serious adverse event summary lists 20 participants at risk in each breathing-tube condition and zero participants with a serious adverse event in either condition. Deaths are listed as zero for both conditions. The record also lists zero participants with other adverse events in each condition. These are the figures reported for the groups in the registry.

These counts are descriptive. A zero count in the posted summary means no events of the listed type were recorded in those group summaries; it does not establish that an event is impossible or that the conditions have identical safety profiles. The record does not give additional detail about event surveillance, duration of follow-up, or how adverse events were attributed in this crossover design. Those details are not reported in the registry record.

The at-risk counts in the safety section should not be assumed to explain the difference between the enrollment figure of 26 and the outcome-summary counts of 20 per condition. The registry does not describe participant flow or how the safety analysis population relates to the primary-outcome population. The safety numbers should be read as the posted event counts, not as a complete account of all possible harms or as a comparison with another population.

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

The result describes average titration pressures recorded under two breathing-tube conditions in a randomized crossover study. The posted mean was 9.8 cmH20 with the heated breathing tube and 10.9 cmH20 with the non-heated breathing tube. The reported difference was 1.1 cmH20 in the direction of a higher average in the non-heated condition. The confidence interval includes zero, so the estimate remains uncertain about whether a difference exists and about its magnitude.

This result does not establish that the conditions are equivalent. No equivalence or non-inferiority margin is reported, and an interval that includes zero is not by itself evidence of equivalence. Nor does the result establish that either approach is clinically better or worse. The endpoint is a pressure measured at the end of a titration night, and the posted summary does not describe clinical consequences or longer-term outcomes.

The registry lists total sleep time as a secondary outcome, but does not report its result. It also does not provide the paired participant-level values, explain the treatment order, or describe the statistical model. Those limitations are especially relevant to a crossover comparison, where the relationship between measurements from the same participant affects the analysis.

The reported safety summaries list no serious adverse events, other adverse events, or deaths in either condition. These counts should be understood as the registry’s posted summaries, not as proof that no risks exist. Taken together, the record supports a narrow description of the reported pressure comparison and event counts. It does not support conclusions about individual responses, longer-term effects, total sleep time, or the original analysis plan.

16. Why This Trial Matters Statistically

This trial raises a useful statistical issue: the analysis should reflect the design. In a crossover study, participants can contribute measurements under more than one condition. Within-person comparisons can account for stable differences between participants, but the analysis also needs to address the relationship between repeated measurements and any effects of treatment order or period. The registry identifies the crossover design but does not report how these features were handled.

The posted result also illustrates why an estimate and its uncertainty should be read together. The difference in means is 1.1 cmH20, while the confidence interval crosses zero and reaches 2.3 cmH20 at its upper end. The direction of the point estimate is clear, but the interval indicates that the data do not pin down the contrast precisely enough to exclude no difference. Treating the point estimate alone as definitive would overstate what the posted analysis establishes.

Participant accounting is another important consideration. Enrollment is listed as 26, while the outcome summaries list 20 observations for each condition. Without a flow description, it is not possible to determine how these figures relate or whether the same participants contributed to both condition summaries. Such information helps readers understand the analysis population and judge possible effects of incomplete data.

Finally, the sample-size illustration is explicitly a planning exercise based on the observed effect, not a record of the original design rationale. Distinguishing that calculation from the completed trial’s own design assumptions prevents planning numbers from being mistaken for evidence about the study’s achieved power. The record is therefore instructive both for reading an uncertain estimate and for recognizing the analysis details needed to evaluate a crossover trial fully.

17. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The registry provides limited information about how the crossover was conducted. It does not report the order in which participants received the two conditions, whether there was a washout interval, or how period and carryover effects were considered. These details could be relevant to interpreting titration pressures measured on different nights.

The relationship between enrollment and the outcome summaries is not explained. The trial lists 26 enrolled, but the primary summaries list 20 observations for each condition. The record does not state whether the same participants contributed measurements under both conditions, why the counts differ, or how incomplete data were handled. No participant-level paired results are posted.

The endpoint description says a sleep technician manually adjusted pressure during titration, but the record does not provide additional information about measurement procedures, standardization, or assessment reliability. Masking is listed as single, without specifying who was masked. The registry also does not report the analysis model or its assumptions, so the calculation of the mean difference and its uncertainty cannot be independently assessed from the record alone.

The total sleep time outcome is listed but has no posted result. The original sample-size justification, prespecified statistical plan, analysis populations, and methods for multiplicity and missing data are not reported in the registry record. The safety summaries contain zero recorded events in each listed category, but further surveillance and attribution details are not given. These limitations concern reporting available in the registry; they do not establish that the trial procedures or analyses were inadequate.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Titration Pressures in Sleep Apnea Patients Using ThermoSmart® Versus Conventional Humidification — NCT00681083.
• Registry record last updated 2019-06-12; status last verified 2019-05.
• Results first posted 2019-06-12.
• 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.

21. Record Summary

NCT00681083 is a completed randomized, single-masked crossover study sponsored by Fisher and Paykel Healthcare. It enrolled 26 participants with obstructive sleep apnea and compared CPAP titration using a heated breathing tube with ThermoSmart® against a non-heated breathing tube with conventional humidification. The registry lists the study period as 2008-04 to 2008-07.

The primary outcome was mean titration pressure at the end of the titration night, measured in cmH20. The posted means were 9.8 for the heated condition and 10.9 for the non-heated condition; the reported mean difference was 1.1. Its confidence interval includes zero, and the reported p-value is 0.072. The registry does not report the original statistical plan or enough detail to assess how the crossover structure was handled.

Total sleep time is listed as a secondary outcome without a posted result. The safety summary lists zero serious adverse events, other adverse events, and deaths in each condition. The relationship between enrollment and the outcome counts is not explained.