Understanding the Sleep Apnea/Insomnia Interaction: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Understanding the Sleep Apnea/Insomnia Interaction (NCT01824472), a randomized na study. The primary outcome is Insomnia Severity Index Score.

2. Clinical Question

The trial’s title is “Understanding the Sleep Apnea/Insomnia Interaction.” Its stated purpose is to examine whether some insomnia symptoms are caused by obstructive sleep apnea and are therefore likely to respond to CPAP, and whether additional CBT for insomnia is beneficial. These are the study’s motivating questions, not conclusions that can be established from the primary result alone.

The registry lists one primary outcome measure and one analysis. The primary measure is a continuous score, with more negative change scores representing larger improvement. The reported analysis compares the three groups using a Kruskal-Wallis method. This provides a group-level statistical test; it does not, by itself, establish which particular pair of groups differs or answer every component of the study’s broader purpose.

3. Trial Design

The registry describes a randomized, single-masked, parallel-group trial sponsored by the University of Pennsylvania. Enrollment is listed as 45. The study status is completed, with a start date of 2013-03 and primary completion in 2017-03. The registry does not report further details about the masking procedure, randomization sequence, or allocation concealment.

Three intervention groups are described. CPAP+CC received continuous positive airway pressure therapy for sleep apnea and contact control as a placebo or sham for CBT. Sham CPAP+CC received sham CPAP, described as ineffective CPAP or placebo/sham for sleep apnea, together with contact control. CPAP+CBT received CPAP therapy and cognitive-behavioral therapy for insomnia. No fourth arm is described in the posted outcome information.

The primary outcome is reported for study participants who completed protocol. The arm-level outcome counts are 16 for CPAP+CC, 6 for Sham CPAP+CC, and 11 for CPAP+CBT. These are the reported numbers contributing to the primary outcome, not a description of all participants enrolled or randomized. The registry record does not explain the difference between enrollment and the reported outcome counts, or give reasons participants may not have contributed an outcome.

The outcome timeframe is between baseline and Day 42. The record reports a mean and standard deviation for each group’s change score and a single overall comparison across the three groups. It does not report group-specific confidence intervals or a separate inferential comparison for each pair of arms. Details of the protocol’s planned sample-size justification, interim analyses, and statistical analysis plan 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.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Study participants who completed protocol

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 Insomnia Severity Index Score, measured over Between Baseline and Day 42..

The primary endpoint is the Insomnia Severity Index (ISI) score, a continuous measure with a minimum of 0 and a maximum of 28. Higher scores indicate a worse outcome. The registry defines the endpoint as change between baseline and Day 42, calculated by subtracting the baseline score from the follow-up score. Under that convention, a more negative change means a larger improvement in the score.

The ISI total score is described as the addition of the question totals, with no specific subscale modification required. A continuous measure can retain differences in score across participants rather than reducing each result to a simple improved/not-improved category. That can be useful when the research question concerns the amount of symptom change. This is a general explanation of continuous outcomes, not a claim about how the trial selected or validated its measure.

The registry reports mean change and standard deviation by group. In the posted results, the mean changes are -8.2 for CPAP+CC, -7.33 for Sham CPAP+CC, and -6.27 for CPAP+CBT. The corresponding standard deviations are 6.49, 7.28, and 5.9. These summaries describe the completed-protocol participants whose data were included in the outcome record. They do not describe individual participants’ changes, and the group means alone do not indicate how precisely the differences between groups are estimated.

The analysis is a comparison across all three groups. The endpoint concerns score change, but the record does not provide a confidence interval for each group mean or for a pairwise contrast. The registry also does not report secondary outcome measures in this record.

7. Why No Re-analysis Is Shown

8. Statistical Interpretation

9. Statistical Methods Explained

The registry identifies the primary outcome as a continuous measure and reports a mean and standard deviation for each group. A mean is a summary of the group’s average observed change; a standard deviation describes the spread of participant-level scores around that average. These summaries answer different questions: the mean describes the group’s central value, while the standard deviation describes variability among the recorded outcomes. Neither alone quantifies uncertainty in a difference between groups.

The outcome is defined as follow-up score minus baseline score. This direction matters when interpreting signs. For this endpoint, the registry says that more negative change indicates a larger improvement. The group means are therefore read using that convention, rather than assuming that a positive change must be beneficial or that every measure uses the same sign direction.

The sponsor-reported method is Kruskal-Wallis, and the registry describes the parameter as a mean difference compared across three groups. In general, Kruskal-Wallis is a rank-based method for comparing observations across independent groups. It uses the ordering of observations rather than relying on a comparison of raw group means in the same way as a standard analysis of variance. Its interpretation concerns differences in the distributions or ranks; under additional assumptions, it may be discussed in terms of location differences. It is not automatically a direct test of the listed means, and the registry’s brief description does not specify further assumptions or details of the implementation.

The result is reported as 0.43, with p = 0.8. The registry does not define the scale or construction of the reported 0.43 statistic beyond its description as a mean difference compared across three groups. It also does not report a confidence interval, degrees of freedom, or a detailed test statistic. The p-value summarizes the test result under its null model, while the statistic is the reported numerical result. Neither provides a direct estimate of the uncertainty around a particular pairwise contrast.

In general, a confidence interval gives a range of values compatible with the observed data and specified statistical procedure. It helps distinguish an estimate that is precise from one that is uncertain. The absence of reported intervals means that readers cannot use the registry result to identify a plausible range for the overall or pairwise effect. A non-significant or large p-value does not itself show that any possible difference is small. Establishing that differences are sufficiently small would require an appropriate margin and analysis, neither of which is reported in the registry record.

The reported sample sizes differ by group, and the outcome population is defined as participants who completed protocol. In general, unequal group sizes can affect the precision of comparisons, especially when one group has fewer observations. The registry does not state how missing outcome data were handled, whether all randomized participants were included in any analysis, or whether the primary analysis followed a specific intention-to-treat or per-protocol strategy. The outcome population wording should therefore be retained when interpreting the results.

Sample-size calculations are planning tools, not observed results. In general, they estimate the number of participants needed under chosen assumptions about the effect to detect, variability, significance level, allocation, and statistical method. The planning assumptions associated with this record describe a two-sided significance level of 0.05, equal allocation between two arms, a normal approximation, and effects defined as fractions of the observed effect. Such calculations should be read as illustrations based on assumptions, not as the trial’s observed power. The registry does not report that these were the trial’s own design assumptions or provide a sample-size justification in the record.

Over-dispersion is a general concern when the variability in data exceeds what a model assumes. If a method underestimates variability, uncertainty can be understated and tests may be too optimistic; if a method accommodates the data’s actual variability, uncertainty is better represented. The posted primary endpoint is continuous and the reported method is rank-based, so the registry does not provide a count-model dispersion parameter or identify over-dispersion as a feature of its analysis. This general concept should not be mistaken for a reported issue in this trial.

Multiplicity refers to the increased chance of at least one false-positive finding when multiple hypotheses are tested. The registry lists one primary outcome measure and one analysis, and no secondary outcome measures are posted in this record. That does not establish that the full study involved no other analyses or outcomes; a comprehensive analysis plan and multiplicity strategy are not reported in the registry record. The single posted overall test should be distinguished from unreported subgroup, pairwise, or exploratory analyses, if any.

Finally, the primary endpoint is a score-based measure, while the study includes three treatment combinations. The overall test does not isolate each component of the treatment combinations. For example, it does not by itself provide a specific estimate of the effect of CBT added to CPAP, because that would require a defined contrast and its uncertainty. Likewise, it does not separately quantify CPAP’s effect against sham CPAP within each behavioral condition. Such component-specific estimates are not reported in this record.

10. Confidence Intervals for Each Arm

No two-arm comparison is shown for this trial, but each arm's mean can be given with a t-based 95% confidence interval computed from the posted mean, spread and number of participants.

R code and output

arm <- c("CPAP+CC", "Sham CPAP+CC", "CPAP+CBT")
n   <- c(16, 6, 11)
m   <- c(-8.2, -7.33, -6.27)
sp  <- c(6.49, 7.28, 5.9)
sd  <- sp      # posted standard deviations
for (i in seq_along(n)) {
  se <- sd[i] / sqrt(n[i]); h <- qt(0.975, n[i] - 1) * se
  cat(sprintf("CARM|%s|%d|%.3f|%.3f|%.3f|%.3f\n", arm[i], n[i], m[i], sd[i], m[i] - h, m[i] + h))
}

CARM  CPAP+CC  16  -8.200  6.490  -11.658  -4.742
CARM  Sham CPAP+CC  6  -7.330  7.280  -14.970  0.310
CARM  CPAP+CBT  11  -6.270  5.900  -10.234  -2.306

11. Analyses Reported by the Sponsor

The registry reports the sponsor’s analysis as a Kruskal-Wallis comparison across three groups, with a reported value of 0.43 and p = 0.8. No confidence interval is reported for this result. The registry does not provide a separate unadjusted re-calculation for a two-arm comparison of this continuous endpoint; the record notes that values are missing or not estimable for such a comparison.

There is therefore no recalculated pairwise estimate to set beside the sponsor-reported result. The sponsor’s overall test remains the posted inferential analysis, and no discrepancy between a sponsor analysis and a re-calculation is identified in the record. The listed means and standard deviations are descriptive summaries, not an alternative inferential test.

The overall test asks whether the three groups differ under the reported method; it does not specify which group pairs account for any observed variation. With no pairwise estimate or confidence interval, the magnitude and precision of a particular contrast cannot be assessed from this result. The reported p-value should not be interpreted as proof that the groups are equivalent or as a measure of the probability that a treatment effect exists.

12. Multiplicity, Missing Data and Analysis Populations

The registry record lists one primary outcome measure and one analysis, and reports no secondary outcome measures in this results entry. The primary analysis compares three groups on change in ISI score. The record does not report a multiplicity adjustment or a broader statistical analysis plan. It is therefore possible to describe the multiplicity information posted in the record, but not to conclude that the full study had no additional analyses or outcome measures.

The outcome population is described as study participants who completed protocol. The posted outcome counts are 16 for CPAP+CC, 6 for Sham CPAP+CC, and 11 for CPAP+CBT, whereas total enrollment is listed as 45. The registry does not explain the relationship between enrollment and these outcome counts, report reasons for missing outcomes, or state how missing data were handled. It does not say whether any imputation, sensitivity analysis, or other missing-data approach was used.

The analysis population is not identified as intention-to-treat, modified intention-to-treat, or per-protocol. The wording about protocol completers is the available description, and it should not be expanded into an assumption about the treatment of participants who did not complete the protocol. The record also does not report how participants were assigned across the arms before the endpoint population was defined.

These omissions matter because missing outcomes can affect both the composition of the analyzed groups and the uncertainty of the estimated results. This is a general statistical consideration, not evidence that missingness biased the findings in a particular direction. Without details on missingness and analysis populations, readers cannot determine from the registry record whether the reported endpoint analysis includes all randomized participants or how robust it is to alternative assumptions about unobserved outcomes.

The overall three-group test is the only posted primary analysis. Pairwise results, subgroup analyses, and additional outcome analyses are not reported in this record. Their absence from the registry entry should not be taken as evidence that they were or were not performed elsewhere.

13. 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 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: kidney problems (7.7%), gastroenteritis (7.7%).

The registry reports serious adverse event counts by group, along with the number at risk. CPAP+CC had 0 serious adverse events among 17 participants at risk; Sham CPAP+CC had 2 among 13; and CPAP+CBT had 0 among 15. Deaths are listed as 0 for each group. These are counts in the posted safety record, not estimates of a comparative treatment effect.

The registry identifies Kidney problems and Gastroenteritis as top serious adverse event terms, each with a listed percentage of 7.7%. The record does not attribute those terms to a particular arm in the information, so they should not be assigned to a group based on the group-level serious-event counts. The listed terms and percentages do not by themselves describe severity, timing, causality, or whether events were considered related to an intervention.

Other adverse events are reported separately: 4 participants in CPAP+CC, 1 in Sham CPAP+CC, and 1 in CPAP+CBT were affected among their respective at-risk groups of 17, 13, and 15. Serious and other adverse events are distinct categories in the registry record and should not be combined. These counts are descriptive. Differences in denominators and the limited information about event definitions and follow-up prevent a detailed comparative safety interpretation.

The safety information should be read alongside the posted denominators and the study’s outcome population, not as proof of benefit or harm. The registry record does not provide further detail on event ascertainment or attribution.

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

The primary result describes change in ISI score among participants who completed protocol and were included in the posted outcome summaries. All three group means are negative under the registry’s follow-up-minus-baseline convention. The overall Kruskal-Wallis result is reported as 0.43 with p = 0.8. Taken together, these data describe the observed scores and the posted group-level test; they do not demonstrate that the treatment combinations are identical.

The result does not establish a precise effect for any one pair of groups. No pairwise contrast or confidence interval is reported, and the overall test does not identify which groups, if any, differ. The descriptive means can be compared as summaries, but a reader should not treat a visual or numerical difference between means as proof of a statistically reliable contrast.

The study’s motivating questions include whether insomnia symptoms may be associated with obstructive sleep apnea and whether CBT may add benefit. The posted primary analysis does not isolate all those component questions. In particular, a specific estimate of CBT added to CPAP, with uncertainty, is not reported. Nor does the overall result independently quantify CPAP against sham CPAP within each behavioral condition.

The record also does not establish the outcome for people who did not complete protocol, because missing-data handling and reasons for the different endpoint counts are not reported. Nor does this primary result provide a complete account of secondary or exploratory outcomes, since none are posted in the record. The safety counts are a separate descriptive set of data and should not be used to infer the primary outcome’s effectiveness or the cause of any event.

In general, a trial result is most informative when its estimate, uncertainty, analysis population, and planned comparisons are all clear. Here, the group means and overall test are available, but confidence intervals and important analysis details are not reported in the registry record. The appropriate interpretation is therefore bounded: the record reports an overall test that does not indicate a group difference, while leaving the size and precision of specific contrasts unresolved.

15. Why This Trial Matters Statistically

This trial illustrates why a three-group result needs to be interpreted in light of both its design and its analysis. The groups combine sleep-apnea treatment and insomnia-related behavioral conditions in different ways. An overall comparison can address whether the observed outcome distributions differ across the set of groups, but it does not automatically identify the contribution of each treatment component. A clearly defined contrast is needed to answer a component-specific question.

It also illustrates the distinction between descriptive and inferential statistics. Group means show the average change recorded in each arm, and standard deviations show the spread of participant outcomes. The Kruskal-Wallis result is the reported inferential test. Neither the means alone nor a p-value alone provides a complete account of effect size and precision. Confidence intervals for relevant contrasts would help communicate uncertainty, but none are reported in the registry record.

The outcome counts are not the same across groups, and the record defines the primary population as participants who completed protocol. These details make transparency about missing data and analysis populations important. The registry record does not give the reasons for the available counts or explain how missing outcomes were handled. That limits what can be concluded about the robustness of the posted comparison.

Finally, the safety record shows why event counts should be read with denominators and event categories in view. Serious and other adverse events are reported separately, and the listed serious event terms are not linked to a particular group in the posted details. Keeping these descriptive safety data distinct from the primary outcome analysis prevents a reader from making unsupported cross-interpretations.

These are general lessons in reading clinical trial results. In this record, they support a cautious reading of the overall test without turning it into a claim about equivalence, a component-specific treatment effect, or unreported outcomes.

16. 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.

Several trial-specific limitations arise from the information available in the registry record. The outcome summaries include participants who completed protocol, but the record does not explain why the endpoint counts are 16, 6, and 11 across the groups or how these counts relate to the enrollment of 45. Reasons for missing outcomes and the approach to missing data are not reported. Consequently, the influence of incomplete outcome data cannot be evaluated from the posted result.

The statistical result is an overall three-group Kruskal-Wallis comparison. No pairwise treatment contrasts, confidence intervals, or detailed test specifications are reported. The reported value of 0.43 is described as a mean difference compared across three groups, but the record does not explain its construction further. Readers therefore have limited information for assessing the magnitude and precision of particular differences.

The endpoint is defined clearly in terms of score direction and timing, but the registry does not report additional measurement or analysis details, such as whether any adjustments were made. The analysis population is not labeled as intention-to-treat or per-protocol, beyond the description of participants who completed protocol. The masking procedure and other implementation details are also not reported in the registry record.

The study description raises questions about insomnia symptoms related to sleep apnea and the possible role of CBT. However, the posted primary result is an overall test across treatment combinations, not a set of component-specific estimates. Secondary outcome measures are not reported in this entry, and the statistical plan, sample-size justification, and interim analyses are not reported in the registry record.

These limitations describe what cannot be assessed from the posted record; they do not establish that the study’s conduct or analysis was inadequate. They mean that interpretation should remain tied to the specific outcome summaries and overall test that are reported.

17. Related Tutorials

18. Related Statistical Calculators

19. Sources

• ClinicalTrials.gov: Understanding the Sleep Apnea/Insomnia Interaction — NCT01824472.
• Registry record last updated 2020-08-05; status last verified 2020-07.
• Results first posted 2020-08-05.
• 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.

20. Record Summary

NCT01824472, “Understanding the Sleep Apnea/Insomnia Interaction,” is listed as a completed, randomized, single-masked, parallel-group trial sponsored by the University of Pennsylvania. Enrollment is 45. The record lists a start date of 2013-03 and a primary completion date of 2017-03.

The primary outcome is change in Insomnia Severity Index score between baseline and Day 42, among study participants who completed protocol. Three groups are reported: CPAP+CC, Sham CPAP+CC, and CPAP+CBT. The registry reports mean change and standard deviation for each group, with a Kruskal-Wallis comparison across all three groups. The reported value is 0.43 and p = 0.8.

No confidence interval or pairwise comparison is reported for the primary result. Missing-data handling, detailed analysis-population definitions, and the protocol’s statistical plan are not reported in the registry record. Serious adverse events, other adverse events, and deaths are listed separately by group; the safety counts are descriptive and do not establish a comparative treatment effect.