Novel Treatment of Comorbid Insomnia and Sleep Apnea in Older Veterans: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Novel Treatment of Comorbid Insomnia and Sleep Apnea in Older Veterans (NCT02027558), a randomized na study. The primary outcome is Sleep Quality.

2. Clinical Question

The study was designed to examine a combined behavioral approach: insomnia-focused treatment alongside PAP adherence support. The comparator also involved individual sessions and general sleep education, so the posted comparison concerns these two programs, not the combined treatment versus no contact or usual care. The registry describes the study purpose as assessing nighttime sleep and PAP adherence, while the primary outcome result discussed in this analysis is sleep quality. The registry record does not report a separate posted secondary outcome result. This distinction matters: the available primary result addresses the measured sleep-quality score at the stated follow-up, and should not be read as a result for every intended aspect of the intervention.

3. Trial Design

The registry describes a randomized, double-masked, parallel-group study. Participants were assigned to behavioral treatment or active control, with the groups followed as separate arms. Enrollment is recorded as 125. The status is completed; the record gives a study start date of 2014-01-01 and a primary completion date of 2017-09-30. The phase is not reported in the registry record.

Behavioral treatment consisted of manual-based cognitive behavioral treatment focused on sleep, sleep apnea and PAP adherence, delivered by allied health personnel in individual sessions. The active control was manual-based, non-directive general sleep education, also delivered by allied health personnel in individual sessions. This active comparator helps frame what the observed group contrast represents: it is the difference between two behavioral programs, rather than a comparison with no intervention.

The primary outcome was sleep quality measured with the Pittsburgh Sleep Quality Index total score three months after randomization. The record describes the outcome as a continuous score on a scale from 0 to 21, with higher scores indicating worse outcome. The posted arm summaries include 62 participants in behavioral treatment and 63 in active control. Those arm-specific values describe the outcome summaries; they should not be taken as information about all analysis populations or participant flow, which are not reported in the registry record.

The registry record names a Mixed Models Analysis for the sponsor's posted comparison. It does not report further details of the model specification, the masking procedures, the allocation sequence, adherence to assigned programs, or the population included in that analysis. The original design assumptions, including any planned sample-size justification, are not reported in the registry record. These omissions limit the ability to assess how the reported analysis followed the trial's intended statistical plan.

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 Sleep Quality, measured over Three months after randomization.

The primary endpoint is sleep quality measured with the total score on the Pittsburgh Sleep Quality Index, at three months after randomization. This is a continuous measure, meaning that it can take a range of numerical values rather than classifying each participant only as having or not having an event. The registry describes a scale ranging from 0 to 21 and states that higher scores indicate worse outcome.

A scored measure can capture differences in degree, which is useful when the research question concerns how sleep quality varies between groups. Comparing group means gives a summary of the central score in each arm. The difference between those means estimates the contrast in average score, while uncertainty intervals indicate how precisely that contrast is estimated. The score itself is not a diagnosis or a measure of PAP adherence. Although the study purpose also mentions nighttime sleep and PAP adherence, the primary outcome result is the sleep-quality score.

The choice of a three-month assessment sets the time point to which the reported comparison applies. It does not, by itself, establish how outcomes changed at other times or whether any difference persisted beyond that assessment. The registry record does not report a threshold for a clinically important difference, so the statistical estimates cannot establish whether a score contrast is clinically meaningful. Interpretation should therefore keep the scale direction, follow-up time and uncertainty in view.

7. Results Posted in the Registry

• Behavioral Treatment: mean 6.25 versus 9.87 on control; difference -3.62 (95% CI -5.13 to -2.11), standardized effect d = -0.84; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is a continuous score, and the registry reports group means and standard errors. The mean summarizes the central value within a group. A standard error describes the estimated uncertainty in a group mean; it is not the same as the spread of scores among individual participants. The standard errors are 0.56 for behavioral treatment and 0.53 for active control. The registry's reported primary comparison uses a Mixed Models Analysis and expresses the result as a net mean difference.

What does a mean difference represent?

A mean difference compares average scores between two groups. The recalculated contrast is expressed as behavioral treatment relative to active control: -3.62. Since higher Pittsburgh Sleep Quality Index scores indicate worse outcome, a negative contrast corresponds to a lower average score in the behavioral-treatment arm. This interpretation depends on both the group order and the scale direction. It does not mean that every participant's score was lower, and it does not describe the distribution of individual scores.

The recalculated result is an unadjusted comparison based on the posted summary statistics. It does not include covariate adjustment or the sponsor's mixed-model analysis. Recalculation can help readers understand the contrast implied by the arm summaries, but it is not a substitute for the analysis specified or conducted by the trial sponsor. The registry record does not report enough detail about the mixed model to determine which assumptions, covariates or repeated-measure structures were used.

What does the confidence interval add?

A confidence interval describes uncertainty around an estimate under the assumptions of the analysis. The recalculated 95% interval is -5.131 to -2.109. It provides a range of plausible values for the underlying mean contrast under that calculation, rather than a guarantee that the true value lies in the interval. Its width reflects uncertainty; the interval's position relative to zero gives information about the direction and statistical compatibility of the contrast. The sponsor-reported 95% interval is -4.58 to -1.83 for its net mean difference of -3.21.

How should the p-value be read?

The recalculated p-value is p < 0.001, and the sponsor-reported p-value is p <.001. In general, a p-value measures how unusual data at least as extreme as those observed would be if the null model and analysis assumptions held. It does not give the probability that the treatment has no effect, nor does it indicate the size or practical importance of the result. The p-value is best considered alongside the estimated contrast, confidence interval and study context.

Why can estimates differ across analyses?

The recalculation uses posted group summary values and is unadjusted. The sponsor's posted result is from a Mixed Models Analysis and reports a net mean difference. Different analytic approaches or model specifications can yield different estimates, but the registry record does not identify which details account for this difference. The discrepancy flag is false, so the registry does not identify a discrepancy requiring a special qualification. The sponsor's own reported analysis remains the trial's stated analysis; the recalculated figure is useful as a transparent summary-based comparison, not as a replacement.

What is the role of randomization?

In general, random assignment is intended to make comparison groups similar in expectation with respect to measured and unmeasured baseline characteristics. It can support a causal interpretation when assignment, follow-up, outcome measurement and analysis are appropriately carried out. Randomization alone does not guarantee that groups are balanced in a particular trial, ensure complete outcome data, or remove bias from deviations after assignment. The registry record does not report enough information about allocation procedures, missing data or analysis populations to evaluate those aspects fully. Double masking is recorded, but its implementation and success are not described.

What does over-dispersion mean in general?

Over-dispersion arises when the variation in data is greater than a statistical model expects. It is especially relevant to outcomes such as counts or binary events when the model's variance assumptions are too restrictive. A continuous mean outcome can also have modeling assumptions about its distribution and variance, but the registry record does not report an over-dispersion assessment or indicate that it was relevant to this endpoint. It would therefore be inappropriate to infer that an over-dispersion adjustment was used or needed.

The posted analysis and summaries answer a focused question about average sleep-quality scores at the stated follow-up. General statistical explanations clarify what the measures mean, but they do not fill gaps in the record about model details, missing data, outcome handling or prespecified analysis decisions. Those details are not reported in the registry record.

10. Confidence Intervals and Precision

The recalculated mean difference is -3.62, with a 95% confidence interval from -5.131 to -2.109. This interval communicates uncertainty around the unadjusted estimate based on the posted arm summaries. Its values are all below zero; given the contrast's direction and the scale's meaning, they correspond to a lower average score in behavioral treatment than in active control. The interval does not represent the range of scores among individual participants.

The sponsor-reported Mixed Models Analysis gives a net mean difference of -3.21 and a 95% confidence interval from -4.58 to -1.83. This interval also lies below zero. The two intervals arise from different analyses: the recalculation uses arm-level summary statistics, while the registry reports a mixed-model result. Their differing estimates should not be interpreted as proof of a specific model effect, because the registry record does not describe the model sufficiently to account for the difference.

In general, a confidence interval balances an estimate with its uncertainty under the model's assumptions. It helps readers assess both the direction and range of plausible values, while a single point estimate cannot convey that uncertainty on its own. A narrower interval generally indicates greater precision, but precision is not the same as validity or clinical importance. An interval may be precise around an estimate affected by bias, and statistical precision does not establish that a difference matters to patients.

The record does not report a clinically important difference threshold for the Pittsburgh Sleep Quality Index, nor does it provide enough detail about missingness or the analysis population to judge their impact on precision. The intervals therefore support interpretation of the reported statistical contrast, but do not settle whether its magnitude is meaningful in practice or how broadly it applies.

11. Planning a Similar Trial: Sample Size

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

The sample-size display gives planning illustrations based on fractions of the observed effect, not the original trial's design assumptions. The registry record does not report the trial's own sample-size justification or planning assumptions. These illustrations assume a two-sided significance level of 0.05, equal allocation between two arms and a normal approximation. The effect to detect is set to 100%, 75% or 50% of the observed effect. The figures are participants per arm, not total participants or total events.

For planning around 100% of the observed effect, the illustration gives 23 participants per arm for 80% power and 30 participants per arm for 90% power. At 75% of the observed effect, it gives 40 participants per arm for 80% power and 53 participants per arm for 90% power. At 50% of the observed effect, it gives 89 participants per arm for 80% power and 120 participants per arm for 90% power.

In plain terms, power is the probability that a planned study would detect an effect of the specified size at the chosen significance level, if the planning assumptions hold. The 80% and 90% columns describe different target probabilities for detecting that assumed effect. A higher target generally requires more participants under otherwise fixed assumptions. Likewise, smaller effects are harder to distinguish from random variation and need more participants; the displayed illustrations reflect that pattern.

These figures are planning illustrations, not observed power. They are calculated from the observed effect and do not reveal the actual power or original rationale of this completed trial. The sample-size curve should be read as a visual representation of how the planning requirement changes with assumed effect size under the stated assumptions, not as a record of the enrollment plan.

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 = -3.620; pooled standard deviation σ = 4.308.
2. n = 2 × (1.96 + 0.842)² × 4.308² / -3.620² = 22.2, rounded up to 23 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 <- -3.62                      # observed difference in means
sigma <- 4.30846265000685                     # 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(2027558)
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 = 23 (80% power), 30 (90% power)
 75% of observed effect: n per arm = 40 (80% power), 53 (90% power)
 50% of observed effect: n per arm = 89 (80% power), 120 (90% power)
power.t.test: 23.2 
Simulated power at n = 23 per arm: 0.799 (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 Mixed Models Analysis, with a net mean difference of -3.21, a 95% confidence interval from -4.58 to -1.83, and p <.001. This is the trial's own posted analysis and should be distinguished from the unadjusted recalculation based on the arm summaries.

The recalculated mean difference is -3.62, with a 95% confidence interval from -5.131 to -2.109 and p < 0.001. It uses the posted group means and summary information rather than the sponsor's mixed-model calculation. Both estimates have the same direction when behavioral treatment is compared with active control, but they are not identical. The registry record does not report enough model detail to explain the difference.

The discrepancy flag is false, so there is no stated discrepancy requiring the recalculation to be treated as a correction to the sponsor's result. The recalculated value is best read as a simple independent summary-based check; it does not supersede the sponsor-reported analysis. Neither estimate alone establishes clinical importance, and the reported analysis details are limited. Readers should interpret the sponsor estimate as the registry's stated trial analysis while using the recalculation to understand the contrast implied by the posted summaries.

14. Multiplicity, Missing Data and Analysis Populations

The registry record lists six outcome measures and six analyses, but it does not report secondary outcome results. No multiplicity adjustment or strategy for handling multiple outcomes or comparisons is reported in the registry record. When several hypotheses are tested, the chance of at least one apparently notable result can increase; methods for addressing that issue depend on the prespecified analysis plan. Since that plan is not reported, it is not possible to determine whether or how multiplicity was handled for the trial.

The record identifies sleep quality as the primary outcome and gives a three-month assessment time. It does not report the analysis population definition, such as whether the primary analysis followed assignment regardless of treatment attendance, or whether another population was used. It also does not provide participant flow or outcome completion information sufficient to assess who contributed to the posted result.

Missing-data procedures are not reported in the registry record. This includes the amount and pattern of missing outcome data, assumptions about missingness, and any imputation or sensitivity analyses. These details matter because a group comparison can be affected if outcome availability differs between arms or relates to participants' unobserved scores. A named Mixed Models Analysis does not, by itself, establish how missing data were handled or what assumptions were made.

The registry record also does not describe prespecification, interim analyses, adjustment for baseline characteristics, or detailed model terms. These omissions are not evidence that any particular procedure was or was not used; they mean that the posted record does not permit a full assessment. The reported primary estimate can be interpreted as presented, while conclusions about multiplicity, missingness and the analysis population remain limited by the unreported details.

15. Safety Results

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

Deaths

Other (non-serious) adverse events

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

Most frequent non-serious adverse event terms

The registry reports no serious adverse events in either arm: 0 among 62 participants at risk in behavioral treatment and 0 among 63 at risk in active control. The serious adverse-event terms list is empty. These are counts in the posted safety record, not evidence that no other safety outcomes occurred or were assessed.

For other adverse events, the record reports 1 among 62 at risk in behavioral treatment and 0 among 63 at risk in active control. It also reports 0 deaths in behavioral treatment and 1 in active control. The record does not give further detail about the other adverse event or the death, including timing, cause or relationship to the program. These counts alone cannot establish whether an event was caused by an intervention.

Safety counts should be read with their arm-specific denominators and the limited detail in the registry record. They are descriptive figures rather than a comparative safety analysis. The record does not report event definitions beyond the serious and other categories shown, ascertainment methods, exposure duration or statistical comparisons. The observed counts therefore should not be generalized beyond what is recorded or used to infer an explanation for individual events.

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

The posted primary outcome results describe average Pittsburgh Sleep Quality Index scores three months after randomization. The behavioral-treatment arm had a mean of 6.25, compared with 9.87 in active control. Since higher scores indicate worse outcome, the means describe a lower average score in behavioral treatment. The recalculated unadjusted difference is -3.62; the sponsor-reported mixed-model net difference is -3.21. Both reported confidence intervals lie below zero, and both analyses report p-values below 0.001 in their respective formats.

This statistical result does not establish how much the difference matters to participants. The registry record does not report a threshold for clinical importance, and a group average cannot show how individual scores varied or how many participants experienced a particular degree of change. Nor does the result establish that all parts of the combined program contributed equally. The intervention bundled insomnia-focused cognitive behavioral treatment with PAP adherence support, while the active control was general sleep education.

The finding is confined to the listed outcome, comparison and assessment time. The study purpose also mentions nighttime sleep and PAP adherence, but the primary result is sleep quality. No secondary outcome results are reported in the registry record. The estimate should not be treated as a result for PAP adherence, other sleep outcomes, longer-term follow-up or other populations.

The randomized design supports a group comparison, but the record does not provide enough information about allocation procedures, missing data, analysis population or model specification to judge all sources of potential bias. The active control also means the comparison is between two behavioral programs, not treatment against no program. The data support a description of the posted score contrast and its statistical precision, not a medical recommendation or a definitive claim about broader benefit.

17. Why This Trial Matters Statistically

This study raises a statistical question common in behavioral research: how to compare a multi-component program with a credible active control. Both arms involved individual sessions delivered by allied health personnel, but the content differed. The estimated contrast therefore concerns the overall programs as assigned, rather than isolating cognitive behavioral treatment, PAP adherence support or nonspecific attention separately.

The endpoint is a continuous patient-reported sleep-quality score with an explicit direction: higher values indicate worse outcome. That direction makes it possible to interpret the sign of the mean difference, but interpretation still requires context about score variability and clinical importance. The registry record does not give a threshold for meaningful change, so statistical evidence and clinical meaning cannot be treated as interchangeable.

The record also illustrates why it is useful to distinguish a sponsor-reported analysis from an unadjusted recalculation. The sponsor reports a mixed-model net difference, while an arm-summary calculation produces a different estimate. Their directions agree, but the record lacks model detail needed to explain the magnitude difference. Careful reporting of analytic populations, missing-data handling and model specifications would help readers understand how results were obtained and how robust they may be.

Finally, planning illustrations based on observed effects can help explain how assumed effect size and target power relate to participant requirements, but they do not reconstruct the original design or provide observed power. Keeping that distinction clear prevents retrospective planning figures from being mistaken for the trial's actual rationale. These statistical distinctions help frame what the study's posted results can and cannot answer.

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.

Several trial-specific details needed to evaluate the result are not reported in the registry record. The original sample-size justification and design assumptions are not reported, and the displayed planning illustrations use the observed effect rather than the trial's documented planning assumptions. The record does not describe allocation procedures beyond identifying the study as randomized, or explain how double masking was implemented.

The sponsor's analysis is identified as a Mixed Models Analysis, but the model specification, included covariates, assumptions and handling of repeated or incomplete measurements are not reported. The analysis population and participant flow are also not described in enough detail to determine how the arm-level summaries relate to participants included in the model. Missing-data amounts and methods are not reported.

The registry lists six outcome measures and six analyses, but no secondary outcome results are posted. A multiplicity plan is not reported, and the registry record does not provide a clinical-importance threshold for the Pittsburgh Sleep Quality Index. Consequently, the statistical result cannot by itself establish whether the size of the score contrast is meaningful in practice or how it relates to outcomes beyond sleep quality.

The intervention combines insomnia-focused cognitive behavioral treatment and PAP adherence support, so the overall comparison cannot identify the contribution of each component. The comparator is active general sleep education, which limits the interpretation to the difference between those programs rather than treatment versus no contact. The safety record gives sparse event counts without further descriptions of the other adverse event or death, their timing, or their relationship to study participation.

These limitations identify gaps in the registry record; they do not establish that omitted procedures were not conducted. They restrict what can be assessed from the posted information.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Novel Treatment of Comorbid Insomnia and Sleep Apnea in Older Veterans — NCT02027558.
• Registry record last updated 2019-06-03; status last verified 2019-02.
• Results first posted 2019-06-03.
• 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

NCT02027558, titled “Novel Treatment of Comorbid Insomnia and Sleep Apnea in Older Veterans,” is recorded as a completed randomized, double-masked, parallel-group study sponsored by the VA Office of Research and Development. Enrollment is listed as 125. The record gives a start date of 2014-01-01 and a primary completion date of 2017-09-30; the phase is not reported in the registry record.

The comparison was behavioral treatment focused on insomnia, sleep apnea and PAP adherence versus an active control of general sleep education. The primary outcome was Pittsburgh Sleep Quality Index total score three months after randomization, with higher scores indicating worse outcome. The registry posts a sponsor-reported Mixed Models Analysis and arm summaries. The record does not report secondary outcome results, detailed missing-data methods, the analysis population or full model specifications.