Telemedicine Interventions for Obstructive Sleep Apnea (OSA): Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Telemedicine Interventions for Obstructive Sleep Apnea (OSA) (NCT01108081), a randomized phase 3 study. The primary outcome is Change Over 6 Months in Epworth Sleepiness Scale Score.

2. Clinical Question

3. Trial Design

The registry identifies this as a randomized, single-masked, phase 3 trial with a factorial model. Enrollment was 169, and the trial status is completed. The recorded start was 2010-10 and primary completion was 2015-11. The sponsor was the VA Office of Research and Development.

Four behavioral arms are described: physical activity, diet, health education, and combined physical activity and diet. The brief summary says the project was investigating whether physical activity and dietary weight loss would independently reduce sleep apnea symptoms and improve quality of life. Although the registry labels the model factorial, the posted comparisons are arm-to-arm contrasts with physical activity as the reference. The record does not report a factorial analysis of main effects or an interaction estimate.

The primary outcome was collected at baseline and 6 months. The registry also lists change over 6 months in quality of life as a secondary outcome. The record reports two outcome measures and no reported analyses. The number of participants contributing to the posted primary endpoint differs by arm, and the primary-outcome description notes missing questionnaire scores for two participants. The handling of missing values and the analysis population are not reported in the registry record.

Random assignment can support comparisons between assigned groups, but the design label alone does not disclose how randomization was implemented, whether allocation was concealed, or how masking was maintained. Those details are not reported in the registry record. The original design’s sample-size assumptions, planned primary analysis, and any interim analyses are also not reported.

4. Participant Flow and Accounting

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

Overall Study

Analysis population for the primary outcome, as defined in the registry: Two participants did not complete the questionnaire and therefore had missing Epworth Sleepiness Scale scores. One participant in Diet arm and one participant in Health education arm.

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 Change Over 6 Months in Epworth Sleepiness Scale Score, measured over baseline and 6 months.

The primary endpoint is change in Epworth Sleepiness Scale score from baseline to 6 months. The scale measures self-reported sleepiness; the registry states that total scores range from 0-24 and that higher scores indicate more sleepiness. Change scores describe how the measured score differed between the two assessment times, while the arm means describe average change among the participants included in each arm’s posted result.

Using a continuous scale preserves information about the degree and direction of change, rather than reducing the result to a yes-or-no category. Comparing average change between randomized arms can help assess whether the observed outcome pattern differs across intervention assignments. The standard error reported with each arm mean describes uncertainty around that estimated average, not the range of individual participant scores.

A negative change means the follow-up score was lower on average than the baseline score; a positive change means it was higher on average. Because higher scale scores indicate more sleepiness, a lower score corresponds to less reported sleepiness on the measure. That interpretation concerns the scale direction and does not establish the clinical importance of a change. The registry record does not report a threshold for a meaningful change, a responder definition, or additional information about the scale’s use in this trial.

7. Results Posted in the Registry

• Diet: mean -1.05 versus -0.23 on control; difference -0.82 (95% CI -2.36 to 0.72), standardized effect d = -0.22; z-test p = 0.298.
• Health Education: mean 0.43 versus -0.23 on control; difference 0.66 (95% CI -1.21 to 2.53), standardized effect d = 0.15; z-test p = 0.489.
• Combined Physical Activity/Diet: mean -2.62 versus -0.23 on control; difference -2.39 (95% CI -4.17 to -0.61), standardized effect d = -0.57; z-test p = 0.008.

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.

Change Over 6 Months in Quality of Life

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
• Result:
  • Diet: mean 0.15 versus 0.24 on control; difference -0.09 (95% CI -1.07 to 0.89), standardized effect d = -0.04; z-test p = 0.857.
  • Health Education: mean -0.33 versus 0.24 on control; difference -0.57 (95% CI -1.59 to 0.45), standardized effect d = -0.23; z-test p = 0.274.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Diet and the control. The interval gives the range of effects that remain compatible with the data.
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Health Education and the control. The interval gives the range of effects that remain compatible with the data.

Quality of life was recorded as a secondary outcome over the same baseline-to-6-month period. The arm averages do not all move in the same direction: the posted change is positive in the physical activity, diet, and combined-intervention arms, and negative in the health education arm. The record does not state the scale’s direction or identify a threshold for meaningful change, so the signs alone do not establish whether a change represents improvement.

The available unadjusted comparisons with physical activity do not provide a clear separation from zero. These results do not independently confirm the primary endpoint pattern, nor do they establish that the primary and secondary outcomes measure the same aspect of participants’ experience. The record does not provide a combined-intervention comparison for this secondary outcome among the listed contrasts, or a reported analysis for the measure.

Secondary outcomes are often useful for describing broader outcome patterns, but they generally carry less confirmatory weight when the analysis plan and multiplicity approach are not reported. Testing multiple outcomes and contrasts increases the opportunity for a seemingly notable result to arise by chance. Because the record does not report a prespecified hierarchy or adjustment, the secondary results are best read as descriptive evidence with uncertainty, rather than as definitive support for a separate claim.

The contrast between sleepiness and quality-of-life patterns also cautions against treating one measure as a proxy for another. A change on the Epworth Sleepiness Scale does not automatically imply a corresponding change in quality of life. The registry record does not report an analysis of the relationship between these outcomes, and the secondary result should be interpreted on its own stated scale and with its own uncertainty.

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

• Change Over 6 Months in Quality of Life

9. Statistical Interpretation

10. Statistical Methods Explained

What does a mean change represent?

A mean is the arithmetic average of the observed change scores among participants included in an arm’s result. Here, the outcome is the difference between baseline and 6-month Epworth Sleepiness Scale scores. A negative arm mean reflects a lower average score at follow-up, while a positive arm mean reflects a higher average score. The average does not show how changes were distributed among individuals, and it can coexist with participants having different directions or sizes of change.

The displayed standard errors quantify uncertainty in the arm means. They are not standard deviations and should not be interpreted as the typical distance of individual scores from the mean. Standard errors are affected by both the variability in observations and the amount of information contributing to the estimate. The registry record does not report individual-level data, so the shape of each arm’s outcome distribution cannot be assessed from these summaries.

How should the arm comparisons be read?

Each mean difference compares an intervention arm with physical activity. A negative estimate means the comparison arm had a lower average change than physical activity; a positive estimate means it had a higher average change. The estimate for combined physical activity and diet was -2.39, with an unadjusted p-value of 0.008. The diet and health education estimates were -0.82 and 0.66, respectively, with unadjusted p-values of 0.298 and 0.489.

A confidence interval describes a range of values compatible with the observed data under the statistical model and its assumptions. An interval that includes zero is compatible with no average difference as well as with differences in either direction. An interval that excludes zero is evidence against a zero difference under that model, but does not measure the probability that a hypothesis is true. The registry record does not report a full analysis specification for these comparisons.

The p-value assesses how unusual data at least as inconsistent with a zero difference would be if the zero-difference model and its assumptions held. It is not the probability that there is no difference, nor is it a measure of clinical importance. The posted p-values are unadjusted. When several contrasts and outcomes are examined, individual p-values do not account for the chance of a misleading result across the full set of tests.

Why does over-dispersion matter?

For continuous outcomes, the standard deviation describes variability among individual observations. If participants vary considerably, the arm mean may be less precise than it would be with less variability and the same amount of information. In planning, over-dispersion means actual variability is greater than assumed; that reduces precision and can make a study less able to detect a specified difference. This is a general statistical explanation, not a finding about this trial. The registry record does not report an over-dispersion adjustment or a model addressing it.

The posted comparisons include pooled standard deviations and standardized effect estimates. A pooled standard deviation combines the variability estimates from the two compared arms into a common scale for a two-arm contrast. A standardized effect expresses the mean difference relative to that variability, which can help compare effects measured on different scales. These summaries are not substitutes for the original scale: the Epworth scale units remain important for interpreting the result. The record does not report an adjusted model or a prespecified standardized-effect analysis.

What does the factorial label establish?

A factorial design can be used to study intervention components and, where planned, whether their effects depend on being combined. The registry describes physical activity and diet as intended to be studied independently and identifies the model as factorial. However, the displayed estimates compare each listed arm with physical activity. They do not, on their own, provide a main-effect estimate for each component or an interaction estimate for the combined intervention. The statistical analysis plan and any factorial-model results are not reported in the registry record.

Randomization is intended to make assigned groups comparable on average, but the registry description does not give details on sequence generation, concealment, deviations from assignment, or the analysis population. These details matter when assessing whether the posted comparison can be interpreted as an unbiased estimate of assignment effects. They are not reported in the registry record.

11. Confidence Intervals and Precision

The uncertainty around a comparison is conveyed by its confidence interval, not by the point estimate alone. For diet versus physical activity, the interval includes zero, as does the interval for health education versus physical activity. Both results remain compatible with no mean difference under the comparison model, as well as with differences in either direction. Their point estimates should therefore not be treated as precise descriptions of the underlying contrast.

The interval for combined physical activity and diet versus physical activity excludes zero. This indicates that the posted data distinguish that contrast from zero under the unadjusted analysis, but the interval still spans a range of possible effect sizes. Its precision does not answer whether the magnitude is meaningful to participants. The registry record does not report a threshold for meaningful change on the Epworth scale.

All three primary comparisons have uncertainty, and the standard errors attached to the arm means provide additional context for the variability in the estimated averages. The confidence intervals also rely on statistical assumptions; they do not account for unreported analysis choices, missing-data handling, or multiplicity. In particular, the reported intervals are not evidence that all relevant sources of uncertainty have been incorporated.

For the secondary quality-of-life outcome, the available comparison intervals include zero. This limits how confidently the posted comparisons distinguish the arms on that outcome. The record does not report a prespecified precision target or a clinically meaningful threshold for quality-of-life change. The original trial’s intended precision and sample-size justification are not reported in the registry record.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures are participants per arm, not total events. They are illustrations based on the observed effect, not the trial’s original sample-size design. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. For each row, the effect to detect is the stated fraction of the observed effect.

The 80% power column gives the estimated participants per arm for a planning scenario designed to have an 80% chance of detecting that specified effect under the stated assumptions, if the assumptions hold. The 90% power column gives the corresponding planning estimate for a 90% chance. These are prospective planning calculations; they do not describe the probability that the completed trial detected an effect. This is not observed power.

Rows for 100% of the observed effect use the full observed contrast as the assumed target; rows for 75% and 50% use smaller targets. Smaller effects are harder to distinguish from background variation and therefore require more participants per arm under the same assumptions. The planning estimates vary substantially between comparisons because the observed contrasts differ in size relative to their variability. In particular, planning from a small observed contrast yields large estimates, and planning from a larger contrast yields smaller estimates.

These estimates should not be treated as a reconstruction of the trial’s actual design rationale. The original sample-size assumptions and justification are not reported in the registry record. The calculations also do not incorporate details that are not included in the stated assumptions, such as missing-data handling, a multiplicity adjustment, or a factorial analysis. The planning figures are conditional illustrations, not guarantees of precision or successful detection.

13. How the Sample Size Is Derived

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

Formula

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

Worked calculation for this trial

1. Observed difference Δ = -0.820; pooled standard deviation σ = 3.710.
2. n = 2 × (1.96 + 0.842)² × 3.710² / -0.820² = 321.3, rounded up to 322 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 <- -0.82                      # observed difference in means
sigma <- 3.70981680689771                     # 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(1108081)
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 = 322 (80% power), 431 (90% power)
 75% of observed effect: n per arm = 572 (80% power), 765 (90% power)
 50% of observed effect: n per arm = 1,286 (80% power), 1,721 (90% power)
power.t.test: 322.3 
Simulated power at n = 322 per arm: 0.802 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists a primary endpoint and a secondary quality-of-life endpoint, alongside several arm comparisons. The posted p-values are unadjusted, and the registry record does not report a multiplicity plan. When several comparisons or outcomes are assessed, the chance of at least one apparently notable result can increase. A correction or prespecified testing hierarchy can address this issue, but neither is reported in the registry record. The unadjusted p-value for the combined-intervention comparison should therefore be interpreted as a result for that individual contrast, not as a multiplicity-adjusted finding.

The primary-outcome description states that two participants did not complete the questionnaire and had missing Epworth Sleepiness Scale scores: one participant in the diet arm and one participant in the health education arm. The record does not report how missing scores were handled, whether any imputation was used, or whether the analysis included all randomized participants or only participants with available measurements. The population used for analysis is not reported in the registry record.

The posted outcome counts differ across arms, but the record does not explain all differences between enrollment and the analyzed outcome counts. It is not possible to determine from the registry summary whether missingness was related to participants’ outcomes or whether exclusions occurred for other reasons. This limits assessment of potential bias from incomplete data.

The trial is identified as factorial, but the record does not report a factorial analysis, component main effects, or an interaction test. It also does not report the original statistical analysis plan, interim analyses, or a sample-size justification. These omissions prevent evaluation of how closely the displayed contrasts align with the planned confirmatory analysis.

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 5% reporting threshold.

The adverse-event record lists zero serious adverse events and zero other adverse events in each arm. The numbers listed as at risk are 46 for physical activity, 42 for diet, 38 for health education, and 43 for combined physical activity and diet. These are the groups used for the adverse-event figures, and they should not be assumed to match the outcome analysis counts.

The death fields are null, which means deaths are not reported in the registry record; null should not be read as zero. No serious adverse-event terms are listed. The posted event counts describe what was entered in the registry and do not, by themselves, establish that no events occurred outside the recorded reporting framework or that the interventions are free of risk. The registry record does not provide further details on event definitions, collection procedures, or follow-up for safety.

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

The posted primary results describe average changes in sleepiness scores across four behavioral arms. Relative to physical activity, the combined physical activity and diet arm had a lower average change, and its unadjusted confidence interval excluded zero. The diet and health education comparisons had intervals that included zero. These are comparisons of group averages, with uncertainty, rather than guarantees about individual responses.

The result does not establish that a particular intervention will produce a specified change for a given person, nor does it show that every participant’s score moved in the same direction. The registry record does not report a threshold for clinically meaningful change, participant-level outcome distributions, or additional analysis that would establish the importance of the observed difference. Statistical evidence against a zero contrast is not equivalent to evidence of a clinically important effect.

The factorial designation and the project’s stated interest in independent effects do not mean that component effects or interaction effects have been demonstrated by the posted arm comparisons. The available primary contrasts use physical activity as the reference. The record does not report the factorial analyses needed to determine whether the interventions acted independently or whether their combined effect differed from what would be expected from their separate effects.

The quality-of-life outcome offers additional context, but the record does not identify the scale direction or a meaningful-change threshold. Its unadjusted comparisons also have uncertainty. Missing questionnaire scores, unreported analysis populations, unadjusted testing, and absent details about the analysis plan further constrain interpretation. The findings describe the posted registry results; they do not provide medical advice or establish a treatment recommendation.

17. Why This Trial Matters Statistically

This trial illustrates why a reported mean difference should be considered alongside its confidence interval, standard error, and analysis context. A point estimate gives a direction and magnitude on the measured scale, while the interval indicates how uncertain that estimate is. The primary comparisons do not all have the same degree of statistical separation from zero, and none should be interpreted without its uncertainty.

The factorial label also highlights the distinction between an arm comparison and a component-level question. A four-arm arrangement can be used to examine intervention components, but the posted comparisons against physical activity do not themselves answer whether physical activity and diet have independent effects or interact. Those questions require analyses that are not reported in the registry record.

The trial also shows why unadjusted results need context when several outcomes and contrasts are available. A nominal p-value describes an individual comparison, while multiplicity concerns the set of analyses. The registry does not report an adjustment or testing hierarchy, so a single p-value cannot convey the overall evidence across all outcomes and comparisons.

Finally, posted planning estimates based on observed effects are not the same as a trial’s original design assumptions or evidence of achieved power. They can illustrate how target effect size affects planning, but they do not explain the completed trial’s precision or validate its design. The registry record does not report its original sample-size rationale or full statistical plan.

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 registry summary leaves important details unavailable for interpreting the primary contrast. It does not report the full statistical analysis plan, how randomization was generated or concealed, how masking was maintained, or which analysis population was used. It also does not report how missing questionnaire values were handled. These omissions limit assessment of potential bias and alignment between the posted comparisons and the intended analysis.

The primary outcome description identifies missing scores for two participants, one in the diet arm and one in the health education arm. The record does not explain whether other participants lacked outcome data or why the outcome counts differ across arms. Without those details, the potential effect of missing data cannot be evaluated from the registry record.

The trial is labeled factorial, but component-level and interaction results are not reported. The available contrasts compare each listed arm with physical activity, which does not fully address the stated interest in independent effects. The registry also does not report multiplicity handling, a threshold for meaningful change, or additional information about the quality-of-life scale’s direction.

Adverse-event entries show no events in the listed categories, but death data are not reported and safety collection details are absent. The original sample-size rationale, interim analyses, and design assumptions are not reported in the registry record. These limitations do not erase the posted estimates; they define what can and cannot be concluded from the available registry results.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Telemedicine Interventions for Obstructive Sleep Apnea (OSA) — NCT01108081.
• Registry record last updated 2017-02-10; status last verified 2016-12.
• Results first posted 2017-02-10.
• 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

NCT01108081 is a completed randomized, single-masked, phase 3 trial with a factorial model and enrollment of 169. It compared physical activity, diet, health education, and combined physical activity and diet. The primary endpoint was change in Epworth Sleepiness Scale score from baseline to 6 months; quality-of-life change was listed as a secondary outcome.

The estimated primary mean difference versus physical activity was -2.39 for combined physical activity and diet, with an unadjusted p-value of 0.008 and a confidence interval excluding zero. The diet and health education comparison intervals included zero. The registry record does not report multiplicity adjustment, missing-data methods, the analysis population, or factorial component and interaction results. Adverse-event entries list zero serious and zero other adverse events in each arm; deaths are not reported.