Tailored Intervention to Promote Positive Airway Pressure Adherence: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Tailored Intervention to Promote Positive Airway Pressure Adherence (NCT01454830), a randomized phase 1 study. The primary outcome is Nightly CPAP Use.

2. Clinical Question

3. Trial Design

The registry describes NCT01454830 as a completed Phase I, randomized, triple-masked, parallel-group trial. It compared a tailored behavioral intervention with usual care in adults with newly diagnosed obstructive sleep apnea who were proceeding to CPAP treatment. The stated enrollment was 118. The study start is recorded as 2011-11 and primary completion as 2014-03. The sponsor was Milton S. Hershey Medical Center.

The intervention was individualized and addressed education, skills training, and cognitive perceptions. Usual care was described as the standard care delivered to newly diagnosed people proceeding to CPAP. The registry identifies both groups but does not report the detailed content, duration, delivery schedule, or fidelity procedures for either approach. Those details are not reported in the registry record.

The primary outcome was mean nightly CPAP use in hours per night at one week. The posted primary group summaries give 30 participants in each group, with means of 6.4 and 5.8 hours/night and standard deviations of 2.01 and 1.35, respectively. The registry also lists secondary measures concerning the proportion of sleep time on CPAP, protocol completion after allocation, withdrawal, and acceptability. Not all secondary outcomes have results posted in the record.

The registry identifies the allocation as randomized and the masking as triple, but it does not describe the randomization procedure, allocation concealment, or which roles were masked. The trial protocol, detailed analysis plan, and original sample-size justification are not reported in the registry record. The feasibility focus is important context: the record describes an early-phase study examining whether an individualized adherence intervention could be studied, rather than establishing a definitive estimate of longer-term benefit.

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

Reasons for not completing this period:

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 Nightly CPAP Use, measured over 1 week.

The primary endpoint is mean CPAP use per night, expressed in hours per night, over the one-week timeframe. It measures the average duration of device use, rather than the proportion of sleep time spent using CPAP or the proportion of participants who completed the protocol. The registry describes the endpoint as mean CPAP use, hours per night.

Average use is a continuous measure: each participant can contribute a duration, and the group summary represents the mean of those durations. Comparing group means gives an estimate of how much average nightly use differed between the tailored intervention and usual care. The measure is relevant to the study’s stated adherence aim because it directly records time using CPAP. It does not by itself describe why use varied, whether device use matched all sleep time, or whether the pattern continued beyond the stated assessment period.

The posted results report a mean of 6.4 hours/night for the tailored group and 5.8 hours/night for usual care, with standard deviations of 2.01 and 1.35. The standard deviations describe variation among the observations in each group; they are not measures of uncertainty in the group means. The endpoint is a short-term measure at one week. Longer-term use and other aspects of adherence are separate questions, and the registry does not report a longer-term primary endpoint.

7. Results Posted in the Registry

• Tailored: mean 6.40 versus 5.80 on control; difference 0.60 (95% CI -0.27 to 1.47), standardized effect d = 0.35; z-test p = 0.175.

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.

Proportion of Sleep Time on CPAP

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Tailored: mean 64.58 versus 65.73 on control; difference -1.15 (95% CI -9.11 to 6.81), standardized effect d = -0.08; z-test p = 0.777.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Tailored and the control. The interval gives the range of effects that remain compatible with the data.

Proportion of Participants Who Complete Protocol After Allocation

• Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Tailored: 88.5% (54/61) versus 86.0% (49/57) on control; risk difference 2.6 percentage points (95% CI -9.5 to 14.6), risk ratio 1.03 (0.90–1.18); unadjusted two-proportion z-test p = 0.677.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Tailored and the control. The interval gives the range of effects that remain compatible with the data.

The posted secondary results add context about CPAP use and participation, but they address different aspects of the study from the primary comparison of mean nightly use. The available results do not form a consistent pattern of clear separation between groups across the secondary measures. They should be read as supplementary descriptions rather than as a second, independent confirmation of the primary finding.

Some secondary outcomes have their own analyzed populations and measures, so their estimates do not necessarily describe the same observations or the same aspect of adherence as the primary endpoint. The registry lists outcomes for the proportion of sleep time on CPAP, protocol completion after allocation, withdrawal, and acceptability, but it does not post results for every listed secondary outcome. The missing outcome results limit how fully the overall pattern can be assessed.

Unadjusted secondary comparisons carry less weight when several outcomes are examined. In general, testing multiple outcomes creates more opportunities for a result to appear notable by chance. Without a reported multiplicity plan, it is not possible to tell whether or how the sponsor accounted for that issue. Secondary findings can help describe feasibility and generate questions for further study, but they should not be treated as definitive evidence simply because an estimate or p-value appears favorable.

The secondary results also do not resolve the uncertainty in the primary endpoint. A measure of sleep time on CPAP is not interchangeable with mean hours of nightly use, and completion or acceptability concerns participation rather than duration of use. Together, the registry’s posted outcomes suggest a broader assessment of intervention feasibility, but the incomplete reporting and distinct endpoint definitions call for cautious, outcome-specific interpretation.

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

• Proportion of Sleep Time on CPAP
• Proportion of Participants Who Complete Protocol After Allocation
• Proportion of Participants Who Withdrawal
• Acceptability of Study Intervention and Comparative Group

9. Statistical Interpretation

10. Statistical Methods Explained

The sponsor-reported primary analysis is a two-sided t-test comparing final mean values between the tailored and usual-care groups. A t-test evaluates whether the observed difference between group means is large relative to the variation and uncertainty in those means, under the test’s assumptions. A two-sided test allows evidence of a difference in either direction; it does not restrict the question to whether the tailored group has greater use.

What does the mean difference represent?

The mean difference is the tailored-group mean minus the usual-care mean. The posted means are 6.4 and 5.8 hours/night, and the sponsor reports a mean difference of 0.58. The unadjusted recalculation from the summary statistics is 0.6 hours/night. A positive estimate indicates a higher sample mean in the tailored group. It is an estimate of the contrast between group averages, not an individual-level prediction and not a measure of how many participants changed their behavior.

What does the standard deviation describe?

The standard deviation describes how spread out the observed values are around a group mean. It is different from the standard error, which describes the precision of an estimated mean or contrast. A group can show substantial variation among participants while still having an estimated mean; the standard deviation does not say how precisely that mean is known on its own. The primary group standard deviations are 2.01 and 1.35 hours/night.

How should the p-value be read?

The sponsor reports p = 0.20 for the two-sided t-test. The unadjusted recalculation gives p = 0.175. In general, a p-value measures how unusual a result at least as far from the null value would be if the null model and the test assumptions held. It is not the probability that the null hypothesis is true, and it does not measure the clinical importance of an estimate. A p-value above a conventional threshold is not proof that there is no difference; it indicates that the observed data do not provide strong evidence against the null under the specified test.

Why is an interval useful alongside the test?

A confidence interval displays a range of effect estimates compatible with the data and the method used to calculate it. The recalculated 95% interval runs from -0.266 to 1.466 hours/night. Because it crosses zero, the data are compatible with a negative difference as well as a positive one. The interval is more informative than a p-value alone because it shows both the uncertainty and the range of effect sizes that remain plausible under the calculation. It is not a guarantee that the true effect lies in that range, nor is it a probability distribution for the true effect.

What is an unadjusted recalculation?

The recalculated comparison uses the posted group summary statistics to form a simple, unadjusted estimate. It is not a replacement for the sponsor’s analysis, which is the analysis reported in the registry. The sponsor’s mean difference of 0.58 and p-value of 0.20 are close to the recalculated mean difference of 0.6 and p-value of 0.175. The registry does not describe any adjustment variables or additional model terms for the posted sponsor analysis.

What assumptions matter for a t-test?

In general, a t-test relies on an appropriate comparison of independent groups and on assumptions about the distribution of the outcome or the behavior of the mean estimate. The registry names the test but does not report diagnostic checks, transformations, adjustment methods, or a detailed analysis plan. The posted standard deviations show that observed variability differed between the groups, but they do not alone establish whether a particular assumption was met. The record does not report how missing endpoint values were handled or whether the analysis followed an intention-to-treat population.

All recalculated results are unadjusted. They do not account for the study’s other endpoints, possible participant characteristics, or any analysis choices not represented by the posted summary statistics. General statistical interpretation should therefore stay tied to the reported endpoint and the stated one-week timeframe.

11. Confidence Intervals and Precision

The primary recalculated 95% confidence interval for the mean difference extends from -0.266 to 1.466 hours/night. This interval includes zero. In plain terms, the data do not pin down whether the average difference is below or above zero, and they remain compatible with more than a negligible range of possible differences. The positive point estimate of 0.6 hours/night is therefore not precise enough to settle the direction or size of the underlying group contrast.

A confidence interval is a way to express sampling uncertainty around an estimate under a specified statistical method. It is not a range that contains every individual participant’s CPAP use, and it does not assign a probability to each possible true difference. The width of an interval reflects both the variation in the data and the amount of information available for the comparison. Larger variability or less information generally yields less precision; this is a general statistical principle, not a claim about unreported trial procedures.

The sponsor reports a mean difference of 0.58 and p = 0.20, but does not report a confidence interval for that analysis. The interval is from an unadjusted recalculation, not a sponsor-reported interval. The registry does not report a confidence interval for the sponsor’s test, so its precision cannot be assessed directly from that analysis record.

Precision also has a scope. The primary endpoint reflects mean nightly use at one week, and a narrow or wide interval for that endpoint would not resolve questions about longer-term adherence, protocol completion, or intervention acceptability. The available interval concerns the estimated short-term mean difference only.

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 a total across the trial. They are illustrations calculated from the observed effect, not a report of the trial’s original design assumptions. The listed planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect targeted in each planning scenario is the stated fraction of the observed effect.

The 80% power column gives the approximate participants per arm under those assumptions for a planned study to have an 80% chance of detecting the stated effect, if that effect is the true one and the assumptions hold. The 90% power column describes the corresponding planning target for a 90% chance. These are design calculations, not guarantees about a future result. The figures depend on the assumed effect and the planning method.

The rows for 100%, 75%, and 50% of the observed effect illustrate how the required sample size changes when the planned effect is smaller than the observed estimate. Smaller effects are harder to distinguish from sampling variation, so planning to detect them requires more participants per arm. The posted planning figures are therefore sensitive to the observed effect used as their starting point; they should not be treated as evidence that the original trial was designed around those assumptions.

The original trial’s sample-size justification and design assumptions are not reported in the registry record. These figures are not observed power: they do not describe the probability that the completed trial detected an effect. The planning curve should be interpreted in the same way as the table, as a visual representation of the stated planning scenarios rather than an additional analysis of trial outcomes.

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 = 0.600; pooled standard deviation σ = 1.712.
2. n = 2 × (1.96 + 0.842)² × 1.712² / 0.600² = 127.8, rounded up to 128 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 <- 0.600000000000001                      # observed difference in means
sigma <- 1.71210396880563                     # 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(1454830)
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 = 128 (80% power), 172 (90% power)
 75% of observed effect: n per arm = 228 (80% power), 305 (90% power)
 50% of observed effect: n per arm = 512 (80% power), 685 (90% power)
power.t.test: 128.8 
Simulated power at n = 128 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.

14. Analyses Reported by the Sponsor

The sponsor’s posted primary analysis reports a mean difference in final values of 0.58 hours/night and a two-sided t-test p-value of 0.20. The registry does not report a confidence interval for that analysis. The unadjusted recalculation from the posted group means and standard deviations gives a mean difference of 0.6 hours/night, a 95% confidence interval from -0.266 to 1.466, and p = 0.175.

The sponsor’s estimate and the recalculated estimate are close in direction and magnitude, and both p-values indicate that the posted comparison does not provide strong evidence of a difference. The recalculation is a simple comparison based on summary statistics; it is not an attempt to reconstruct analysis details that the registry does not report. Minor differences between the values do not, by themselves, establish why the analyses are not identical.

The registry does not flag a discrepancy between the sponsor analysis and the recalculation. The sponsor’s result remains the primary reported analysis, while the recalculated interval offers an additional view of uncertainty derived from the posted summaries. Readers should not treat the recalculation as a substitute for a fuller sponsor analysis or infer adjustment methods, analysis populations, or missing-data procedures that are not documented in the registry record.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists multiple secondary outcomes in addition to the primary endpoint. When several outcomes are tested, the chance of obtaining at least one apparently unusual result by chance can increase. This is the general multiplicity problem. Common approaches include identifying a primary outcome in advance, adjusting thresholds or intervals for multiple comparisons, or treating secondary analyses as exploratory. The registry record does not report a multiplicity adjustment or a detailed plan for interpreting the set of outcomes.

The record identifies the primary endpoint as mean nightly CPAP use and lists secondary measures concerning sleep time on CPAP, protocol completion, withdrawal, and acceptability. It reports results for some of these outcomes but not all. Without a complete results record and an analysis plan, readers cannot determine whether the posted secondary results were selected from a larger set of analyses, whether any outcomes were changed, or how missing outcomes were intended to be handled. Such possibilities should not be assumed; they are simply not reported in the registry record.

Missing data are relevant because the primary results are reported for 30 participants in each group, while the registry enrollment is 118. The record does not explain the relation between these numbers, identify which participants contributed to the primary endpoint, or describe whether observations were excluded or unavailable. It also does not report imputation, sensitivity analyses, or the reasons for missing endpoint data. The secondary results use different reported analysis counts, which further underscores the need not to assume a common analysis population.

The registry does not state whether the primary analysis followed intention-to-treat, per-protocol, or another population definition. It also does not report protocol deviations or a prespecified statistical analysis plan. These omissions limit assessment of whether the analysis preserved the randomized comparison and how robust the estimates are to missing data or analysis choices. They do not prove that the methods were inadequate; they mean the relevant details are unavailable in the registry record.

16. 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 registry reports zero serious adverse events and zero other adverse events for the tailored group, with 61 participants at risk for each category. For usual care, it reports zero serious adverse events and zero other adverse events, with 57 participants at risk for each category. These figures describe what was recorded for the groups and categories in the registry; they do not establish that no events of any kind occurred outside the reported categories or reporting period.

Deaths are not reported in the registry record. The record also does not provide serious adverse event terms, since no serious events are listed. The listed adverse event counts should not be confused with the primary endpoint analysis counts, which are different. The registry does not explain the relationship between those analysis populations and the participants at risk for adverse events.

In general, a zero count in a trial report is a description of observed and recorded events, not proof that an intervention has no safety risks. Interpretation depends on how events were defined, collected, and followed, details that are not reported in the registry record. The figures should therefore be read narrowly as the adverse event results posted for the trial.

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

The primary result estimates the difference in average CPAP use per night at one week between the tailored intervention and usual care. The posted group means are 6.4 and 5.8 hours/night. The sponsor reports a mean difference of 0.58, and the unadjusted recalculation gives 0.6 hours/night. The recalculated confidence interval crosses zero, so the result remains uncertain about both the direction and size of the group difference.

This finding does not show that the intervention works or does not work. It does not prove the groups are equivalent, and it does not show that any difference is clinically important. A non-significant test is not evidence that the true effect is exactly zero. Conversely, a positive point estimate does not establish that the intervention caused greater use. Randomization supports a comparative design, but interpretation also depends on outcome measurement, analysis populations, missing data, and other details not reported in the registry record.

The outcome is short-term and specific: mean nightly use over one week. It does not establish whether participants continued using CPAP over a longer period, whether the intervention was acceptable, or how much of participants’ sleep time was spent using the device. Those questions require their own reported outcomes and follow-up. The registry lists some related secondary measures, but not all have posted results.

The study was described as examining feasibility. The available record offers a preliminary comparison and a set of participation and adherence outcomes, but it does not provide the detailed intervention procedures, full analysis plan, or explanation of the primary analysis population. Those limitations constrain the conclusions that can be drawn from the posted estimates.

The most defensible reading is that the trial reports a modest positive sample mean difference in short-term use, alongside substantial statistical uncertainty. It provides a description of the observed comparison, not a definitive answer about longer-term adherence or the effectiveness of a tailored intervention.

18. Why This Trial Matters Statistically

This trial illustrates why a point estimate should be interpreted together with its uncertainty. The tailored group had a higher posted mean nightly use than usual care, but the recalculated confidence interval includes zero. That combination allows readers to distinguish the observed direction from the strength and precision of the evidence. A favorable direction alone is not enough to establish a reliable group difference.

The trial also highlights the importance of matching an outcome to the question. Mean nightly CPAP use, the proportion of sleep time on CPAP, protocol completion, withdrawal, and acceptability capture different dimensions of adherence and feasibility. Results for one dimension cannot automatically stand in for another. A short-term average is informative about the stated timeframe but does not answer whether use continues or whether participants find the intervention acceptable.

For biostatisticians and clinical researchers, the record is a reminder to distinguish the randomized enrollment from the analysis population reported for an endpoint. When those figures differ and the registry does not explain why, readers need to avoid assumptions about exclusions, missingness, or the flow of participants through analysis. Clear reporting of populations, missing data, and prespecified analysis choices is essential for judging the reliability of estimates.

Finally, planning calculations based on an observed effect are not a substitute for the trial’s original sample-size rationale. Their value is illustrative: they show how planning requirements respond to assumptions about the target effect. The original rationale is not reported in the registry record, so these calculations cannot establish whether the trial was designed to detect a particular difference. Together, these statistical distinctions help keep conclusions aligned with what the record actually documents.

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.

The primary outcome is measured over one week, which limits the result to short-term mean CPAP use. The registry does not report a longer-term primary assessment, so the posted result cannot characterize persistence. It also does not provide detailed information on how nightly use was recorded, how valid measurement periods were defined, or how the measure was summarized for participants with incomplete observations.

The analysis population is not explained. The registry reports enrollment of 118, while the primary group summaries each include 30 participants. It does not describe the flow from enrollment to those primary outcome summaries, identify reasons for missing observations, or state how missing data were handled. The secondary outcome analysis counts differ as well, and the record does not specify a shared analysis population.

The intervention is described in broad terms as individualized and addressing education, skills training, and cognitive perceptions. Detailed content, delivery, duration, and fidelity information are not reported in the registry record. The usual-care description is also broad. This limits assessment of what would need to be reproduced to evaluate the same intervention approach in another setting.

The registry identifies a two-sided t-test but does not report the full statistical analysis plan, adjustment variables, diagnostic checks, or the original sample-size justification. It also does not report how multiplicity across outcomes was addressed. These omissions prevent a complete appraisal of analysis choices and the reliability of secondary comparisons. They should not be taken as evidence that particular procedures were or were not used; the record does not report them.

Finally, results are not posted for all listed secondary outcomes, including withdrawal and acceptability. The absence of those results limits a full assessment of feasibility, which was the stated study purpose. The small primary analysis groups and imprecise estimate also mean that the observed group contrast should be treated as an uncertain estimate rather than a conclusive answer.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Tailored Intervention to Promote Positive Airway Pressure Adherence — NCT01454830.
• Registry record last updated 2016-11-23; status last verified 2016-09.
• Results first posted 2016-11-23.
• 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.

23. Record Summary

NCT01454830 is a completed Phase I randomized, triple-masked, parallel-group trial sponsored by Milton S. Hershey Medical Center. It examined a tailored behavioral intervention intended to promote CPAP adherence among adults with newly diagnosed obstructive sleep apnea who were proceeding to CPAP treatment. The registry states an enrollment of 118 and records the study start as 2011-11 and primary completion as 2014-03.

The primary endpoint was mean nightly CPAP use in hours per night at one week. The sponsor-reported mean difference was 0.58, with a two-sided t-test p-value of 0.20. An unadjusted recalculation from the posted summaries gives a mean difference of 0.6 and a 95% confidence interval from -0.266 to 1.466. The interval crosses zero, leaving uncertainty about the direction and size of the short-term group difference.

The registry also lists secondary adherence, completion, withdrawal, and acceptability outcomes, but results are not posted for every listed measure. The original sample-size rationale, detailed analysis plan, and explanation of analysis populations are not reported in the registry record.