Improving Obstructive Sleep Apnea Management Via Wireless Telemonitoring: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Improving Obstructive Sleep Apnea Management Via Wireless Telemonitoring (NCT00682838), a randomized phase 2, phase 3 study. The primary outcome is Nightly CPAP Adherence.

2. Clinical Question

3. Trial Design

The registry describes a randomized, single-masked, parallel-group study, with an enrollment of 280. The listed phase is PHASE2 and PHASE3. The sponsor was the VA Office of Research and Development. The study status is completed; the listed start is 2009-07 and the primary completion is 2012-05.

Four groups appear in the posted primary outcome results: self-management, telemonitored care, self-management plus telemonitored care, and usual care. The self-management intervention was educational and focused on sleep apnea and CPAP from a self-management perspective. Telemonitored care involved a CPAP therapist monitoring care at a distance and acting on the data according to a set protocol. The combined group received both approaches. Usual care is identified as the control group, but its content is not described in further detail.

The registry labels the allocation randomized and the model parallel. It identifies the study as single-masked but does not say which participants, clinicians, assessors, or other parties were masked. The method used to generate the allocation sequence, conceal assignments, or maintain masking is not reported in the registry record. The original design assumptions, including any sample-size justification, are also not reported in the registry record.

The primary outcome was nightly CPAP adherence, expressed as a mean in hours per night and measured over 3 mos. The posted outcome results include 65 participants in self-management, 67 in telemonitored care, 75 in the combined group, and 73 in usual care. These outcome-group counts describe the posted results; the registry record does not explain how participants with missing outcome data, if any, were handled.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

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: The target population for this study is all Veterans with OSA. It was expected that most participants would be middle-aged and older men and women, from a variety of ethnic backgrounds and with a full range of medical co-morbidities.

6. Primary Endpoint

The registry lists the primary outcome as Nightly CPAP Adherence, measured over 3 mos.

The primary endpoint is nightly CPAP adherence, recorded as hours per night and summarized as a mean over 3 mos. It is a continuous measure: each participant’s adherence can take a range of values, and the group result is described by a mean and standard deviation rather than a count of participants meeting a threshold. The posted group means were 3.7 hours per night in each active-intervention group and 3.2 hours per night in usual care. The corresponding standard deviations were 1.8, 2.3, 2.2, and 2.3, respectively.

Adherence is relevant to the trial’s stated focus because the study summary describes low adherence to CPAP as a concern and proposes self-management and wireless monitoring as strategies for supporting treatment use. Measuring hours of use captures the amount of CPAP use during the specified period. It does not, by itself, describe why use differed, whether adherence was consistent across nights, or whether the observed use led to changes in symptoms or other clinical outcomes. Those matters are not addressed by this single posted primary endpoint.

The registry describes the measure as nightly adherence over the three-month period and gives the timeframe as 3 mos. It does not report details about the measurement device, the exact calculation of adherence across nights, the treatment of days without recorded data, or a clinically important threshold. Therefore, the result can be read as a comparison of group-average hours per night, with the reported variation around those means, rather than as a proportion reaching a particular adherence target.

7. Results Posted in the Registry

• Self-management: mean 3.70 versus 3.20 on control; difference 0.50 (95% CI -0.19 to 1.19), standardized effect d = 0.24; z-test p = 0.153.
• Telemonitored Care: mean 3.70 versus 3.20 on control; difference 0.50 (95% CI -0.26 to 1.26), standardized effect d = 0.22; z-test p = 0.199.
• SM+TC: mean 3.70 versus 3.20 on control; difference 0.50 (95% CI -0.23 to 1.23), standardized effect d = 0.22; z-test p = 0.177.

8. Statistical Interpretation

9. Statistical Methods Explained

What does a mean difference describe?

Nightly CPAP adherence is a continuous outcome, and the registry reports the mean and standard deviation for each group. A mean difference compares the average hours per night in one group with the average in another. The posted results show a mean of 3.7 hours per night for each active group and 3.2 hours per night for usual care. The recalculated mean differences against usual care are each 0.5 hours per night. This is an unadjusted comparison based on the posted group summaries, rather than a model that adjusts for other participant characteristics.

A group mean describes the center of the observed values, not every participant’s experience. Two groups can have different means while their individual values overlap substantially. The standard deviation describes the spread of observations around a group mean. The registry reports standard deviations of 1.8 for self-management, 2.3 for telemonitored care, 2.2 for the combined group, and 2.3 for usual care. These measures of spread help place the mean differences in context: an average contrast should not be read as a uniform difference for each participant.

What does a confidence interval add?

A confidence interval expresses uncertainty around an estimated difference. In general, it gives a range of values compatible with the data and the method used to construct the interval. A narrower interval indicates greater precision, while a wider interval indicates less precision. Each recalculated interval for the comparisons with usual care crosses zero. Zero represents no difference in group means. Because the intervals include values on both sides of zero, the posted data do not pin down the direction and size of the underlying difference with high precision.

The registry record does not identify the confidence level for the intervals associated with the recalculated comparisons. They are therefore described as the posted intervals without assigning them a confidence level not documented in the record. Confidence intervals should also not be read as a range containing every individual participant’s outcome; they address uncertainty in the estimated group contrast, not the spread of individual adherence values.

How should the p-values be read?

The recalculated comparisons have unadjusted p-values of 0.153, 0.199, and 0.177. In general, a p-value describes how compatible the observed data are with a specified null hypothesis under the assumptions of a statistical test. It is not the probability that the null hypothesis is true, nor a measure of the probability that an intervention is beneficial. The listed recalculations are unadjusted, so their p-values do not account for testing several active groups against the same usual-care group.

The registry’s own reported analysis is listed as a one-sided t-test and has a p-value of 0.50. All four outcome groups are listed for that analysis, but the registry does not report the test statistic, a parameter estimate, a confidence interval, or a fuller description of the comparison. The reported test should therefore be kept distinct from the unadjusted pairwise recalculations. The record does not say whether the one-sided direction was specified in advance or how the test relates to the three active-versus-usual-care contrasts.

Why can variability affect the comparison?

When an outcome varies widely among participants, a difference between group means can be difficult to estimate precisely. In general, over-dispersion means that the observed variability is greater than a model assumes; that can make standard errors too small if the model fails to account for the extra variation. The registry does not characterize this outcome as over-dispersed or describe a model that assumes a particular variance structure. For these continuous results, the posted standard deviations provide a direct indication of within-group variation, while the recalculated intervals reflect uncertainty around the mean differences under the stated simple comparison.

These recalculations are not a substitute for a full analysis plan. The registry record does not report whether the sponsor adjusted for baseline adherence, stratification factors, or other covariates; whether distributional assumptions were checked; or whether any robust or alternative methods were used. Those details should not be inferred from the means and standard deviations alone.

What can be concluded from the methods reported?

The available information supports a descriptive comparison of the posted group summaries and a cautious reading of the simple unadjusted contrasts. It does not establish how the original investigators handled repeated nightly measurements, missing records, participants who discontinued, or deviations from assigned care. Although the outcome is described as adherence measured over a three-month period, the registry does not report whether the participant-level value was averaged from all recorded nights or derived another way.

In general, randomization is intended to support fair comparisons by assigning participants to groups without choosing an intervention based on their characteristics. However, the registry’s randomized designation does not by itself show how allocation was implemented or how complete the analyzed data were. The record states that the study was single-masked but does not identify who was masked. These reporting gaps are important when judging the possibility of bias and the reproducibility of the analysis.

10. Confidence Intervals and Precision

The recalculated mean difference is 0.5 hours per night for each active group compared with usual care. The estimates are accompanied by intervals that include zero: for self-management, the limits are -0.185 and 1.185; for telemonitored care, -0.263 and 1.263; and for the combined group, -0.225 and 1.225. These limits show that the observed data are compatible with both a difference in favor of the active group and a difference in the opposite direction. The intervals are not narrow enough to identify a single, precise value for the underlying contrast.

The intervals also show why the point estimate alone is incomplete. A mean difference of 0.5 is the center of the recalculated comparison, but uncertainty around it matters when considering what the data can distinguish. The unadjusted p-values—0.153, 0.199, and 0.177—are consistent with the same cautious interpretation: the comparisons do not provide strong evidence against a null difference under the tests used for these recalculations. They do not demonstrate that the groups have identical average adherence.

The registry record does not state the confidence level for these recalculated intervals. The posted standard deviations, which range from 1.8 to 2.3 hours per night, describe participant-level variation and are separate from the uncertainty in the mean differences. The intervals and standard deviations answer different questions: one concerns precision of a group contrast, the other the spread of observations within each group. Taken together, the posted summaries indicate uncertainty around modest observed contrasts and considerable variation in adherence among participants.

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 planning figures are participants per arm, not total events. They are illustrations based on the observed effect, not the trial’s original design assumptions. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario asks how many participants per arm would be needed to detect a stated fraction of the observed effect.

The 80% power column means the planned comparison would have an 80% chance of detecting the specified effect under the planning assumptions, if that effect were the true one. The 90% power column describes a higher chance of detecting that same specified effect under those assumptions. These are design targets for a future comparison, not statements about the probability that the trial’s result is correct. This is not observed power.

Planning for 100% of the observed effect uses the full estimated contrast as the target. Planning for 75% or 50% of the observed effect uses smaller target differences. Smaller effects need more participants to distinguish them from random variation at the same significance and power settings. The effect-size scenarios are planning illustrations; they do not establish that a future study would reproduce the observed contrast.

The figures are comparison-specific because the posted variability differs among the active groups. The registry’s original sample-size justification, assumed effect, power target, allocation details for the original design, and adjustment assumptions are not reported in the registry record. The planning values should therefore not be interpreted as a reconstruction of why the completed study enrolled its participants.

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 = 0.500; pooled standard deviation σ = 2.080.
2. n = 2 × (1.96 + 0.842)² × 2.080² / 0.500² = 271.6, rounded up to 272 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 <- 0.5                      # observed difference in means
sigma <- 2.07973414590593                     # 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(682838)
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 = 272 (80% power), 364 (90% power)
 75% of observed effect: n per arm = 483 (80% power), 647 (90% power)
 50% of observed effect: n per arm = 1,087 (80% power), 1,455 (90% power)
power.t.test: 272.6 
Simulated power at n = 272 per arm: 0.801 (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. Analyses Reported by the Sponsor

The registry reports the sponsor’s analysis as a one-sided t-test involving the four listed outcome groups, with a p-value of 0.50. It does not provide an estimate, confidence interval, test statistic, or further description of the test’s precise structure. The record therefore does not support treating that result as a fully described pairwise comparison between each active group and usual care.

The three comparisons against usual care are simple unadjusted recalculations from the posted means, standard deviations, and group sizes. Each gives a mean difference of 0.5 hours per night, with an interval that crosses zero. Their p-values are 0.153 for self-management, 0.199 for telemonitored care, and 0.177 for the combined group. Because these calculations address individual contrasts while the sponsor’s reported result lists all four groups, the results need not be identical or answer exactly the same question.

The registry does not report enough detail to reconcile the test structures or establish whether the sponsor’s analysis used additional adjustments. The reported sponsor analysis should be read as the result recorded for the sponsor’s test; the recalculations offer a transparent, unadjusted view of the posted group summaries, not a replacement for the analysis described by the registry.

14. Multiplicity, Missing Data and Analysis Populations

Three active-intervention groups are each compared with usual care in the recalculated results. When several comparisons are examined, the chance of at least one apparently unusual result can increase. In general, multiplicity procedures can address that issue by adjusting the interpretation or the statistical thresholds. The recalculated p-values are explicitly unadjusted, and the registry record does not report a multiplicity adjustment, a prespecified hierarchy of comparisons, or which comparison was intended to be primary among the active groups.

The registry lists one primary outcome and no posted secondary outcomes. That does not establish that no other analyses were conducted; it means that no secondary outcome results are posted in the registry record. The record does not report whether additional outcomes or subgroup analyses were planned, whether analyses were prespecified, or whether any selective reporting assessment was performed.

Missing-data handling is not described. The outcome-group counts are reported, but the record does not state whether every randomized participant contributed an outcome, how incomplete nightly records were handled, whether missing values were imputed, or whether participants were excluded from the analysis. The analysis population is also not identified as intention-to-treat, per-protocol, or another defined set. Without those details, it is not possible to determine how closely the posted group summaries represent all randomized participants or to assess the impact of missing data.

The registry states that the trial was randomized and single-masked, but it does not identify the masked parties or describe the implementation of randomization. It does not report baseline adjustment, sensitivity analyses, or a detailed statistical analysis plan. These omissions constrain assessment of bias and analytic choices. They do not prove that the investigators failed to use such methods; they mean that the methods are not reported in the registry record.

15. Safety Results

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

Other (non-serious) adverse events

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

The posted adverse-event results list 65 participants at risk in the self-management group, 67 in telemonitored care, 75 in the combined group, and 73 in usual care. The count affected by serious adverse events is 0 in each group. The count affected by other adverse events is also 0 in each group. These are the counts recorded in the registry, interpreted in relation to the reported numbers at risk.

These figures describe what was recorded in the adverse-event fields; they do not provide information about event definitions, ascertainment procedures, severity grading, or the time period used for safety collection. The registry record does not report deaths for these groups. A zero count in the posted results should not be read as proof that no events occurred outside the registry’s reporting and collection procedures, nor does it establish comparative safety. The groups and reported counts are descriptive and do not provide a detailed safety analysis.

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

The posted primary outcome results show mean nightly CPAP adherence of 3.7 hours in each active-intervention group and 3.2 hours in usual care over 3 mos. The recalculated mean differences against usual care are all 0.5 hours per night. This describes the observed group averages; it does not establish that each participant in an active group used CPAP more, or that an individual participant would have the same change.

The uncertainty around the estimates is substantial in relation to the observed contrasts. Each recalculated interval includes zero, and the unadjusted p-values are 0.153, 0.199, and 0.177. These results do not give a precise estimate of the underlying differences. At the same time, they do not demonstrate equivalence or rule out a potentially meaningful difference, because the intervals cover values on both sides of zero. The registry does not report a threshold for a clinically important change in adherence, so the clinical importance of a particular mean difference cannot be determined from the record alone.

The endpoint is a measure of CPAP use, not a direct measure of symptoms, quality of life, long-term health, costs, or productivity. Although the study summary describes those broader concerns, no results for those outcomes are posted. The primary endpoint also concerns a specified period; it does not show whether any group differences persisted after 3 mos.

The sponsor’s recorded one-sided test has a p-value of 0.50, but its exact comparison is not described beyond listing the four groups. It should not be conflated with the pairwise recalculations. Overall, the posted data describe higher average adherence in the active groups than in usual care, with uncertainty that prevents a firm conclusion about the size or direction of the underlying contrasts. The registry record does not provide enough methodological detail to assess missing data, adjustment choices, or the original design assumptions.

17. Why This Trial Matters Statistically

This trial is statistically informative because it compares several behavioral approaches with usual care using a continuous measure of treatment adherence. The four-group structure makes it possible to see the observed means for self-management, telemonitored care, their combination, and usual care. That structure also raises an interpretive issue: separate comparisons against a shared control are not the same question as a single test involving all four groups.

The posted summaries illustrate the difference between an observed contrast and a precise estimate. Each active group has a mean of 3.7 hours per night, compared with 3.2 hours in usual care, but the recalculated intervals cross zero. The standard deviations show substantial variability in participants’ adherence. A statistical reading therefore needs to consider both the direction of the point estimates and the uncertainty around them, rather than treating a difference in sample means as a definitive result.

The record also gives a useful example of how registry reporting limits interpretation. It identifies randomization, masking, the primary endpoint, and the sponsor’s test, but does not describe the analysis population, missing-data handling, multiplicity strategy, or original sample-size rationale. These are not minor details when interpreting a multi-group trial: they affect how the estimates and tests should be understood and how readily another analyst could reproduce the analysis.

Finally, planning calculations based on an observed effect can show how design targets respond to smaller assumed differences. They are useful for understanding planning trade-offs, but they do not reveal the original investigators’ assumptions or turn the completed trial’s result into a measure of certainty. The distinction between planning power and evidence from observed data is central to responsible interpretation.

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 main outcome has limited detail about how adherence was measured and aggregated. The registry describes nightly hours over 3 mos, but does not report the monitoring device, the number of nights contributing to each participant’s value, or how incomplete recordings were handled. The group summaries therefore cannot show whether measurement completeness differed among groups.

The registry record does not describe the content of usual care beyond identifying it as the control group. This makes the comparator less reproducible from the record. It also gives no detailed eligibility criteria or baseline characteristics, so the similarity of groups at the start of the trial cannot be assessed from the posted outcome information.

Important analysis details are absent: the analysis population, handling of missing data, covariate adjustment, multiplicity strategy, and the full statistical analysis plan are not reported in the registry record. The sponsor’s one-sided t-test is reported with a p-value, but without an estimate, confidence interval, test statistic, or fuller explanation of the comparison. The single-masked designation does not identify who was masked.

The posted primary result concerns adherence at 3 mos and does not provide secondary outcome results. The record therefore does not establish whether the approaches were associated with changes in symptoms, quality of life, or other outcomes mentioned in the study summary. Finally, the recalculated comparisons are unadjusted and should be understood as descriptive contrasts based on the posted group summaries, not as a complete account of the sponsor’s statistical analysis.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Improving Obstructive Sleep Apnea Management Via Wireless Telemonitoring — NCT00682838.
• Registry record last updated 2016-09-01; status last verified 2016-07.
• Results first posted 2016-09-01.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

This completed randomized, single-masked, parallel-group study evaluated self-management, telemonitored care, their combination, and usual care for sleep apnea syndromes. The registry lists an enrollment of 280 and identifies nightly CPAP adherence over 3 mos as the primary outcome.

Mean adherence was 3.7 hours per night in each active group and 3.2 hours per night in usual care. Simple unadjusted recalculations give a mean difference of 0.5 hours per night for each active group versus usual care, with intervals crossing zero. The registry also reports a one-sided t-test with a p-value of 0.50 for an analysis listing all four groups, but further test details are not reported. The record does not describe missing-data handling, the analysis population, multiplicity procedures, or the original sample-size rationale.