Effects of Continuous Positive Airway Pressure (CPAP) on Glucose Metabolism: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Effects of Continuous Positive Airway Pressure (CPAP) on Glucose Metabolism (NCT01503164), a randomized na study. The primary outcome is Insulin Sensitivity (SI).

2. Clinical Question

3. Trial Design

The registry describes a randomized, parallel-group trial with no masking. Participants were assigned to positive pressure therapy (PAP) or lifestyle counseling. The enrollment was 111: 55 randomized to PAP and 56 randomized to lifestyle counseling. The primary-outcome description records 2 dropouts in the PAP group and 1 in the lifestyle group. The arm counts in the posted baseline results are 53 for PAP and 55 for lifestyle counseling. These counts are reported for the baseline summaries; the record does not specify a separate analysis population or explain how missing measurements were handled.

The study is listed as completed. Its recorded start was 2011-09, and its primary completion was 2013-12. The phase is listed as NA. Johns Hopkins University is the sponsor. The registry identifies a device intervention, positive pressure therapy, and a behavioral intervention, lifestyle counseling. It describes PAP as a mask worn over the nose during sleep and connected to a PAP machine, but gives no corresponding description of the counseling program.

The primary outcome is insulin sensitivity, measured with an insulin-modified frequently sampled intravenous glucose tolerance test and derived using the minimal model (MINMOD). The outcome description says measurement was planned before and 2-months after study intervention. However, the posted results identify the primary outcome timeframe as Baseline. The results therefore do not report the change from baseline or the post-intervention difference between groups. Registry information about allocation concealment, the trial’s original sample-size assumptions, masking procedures beyond NONE, and the statistical analysis plan is 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: 55 randomized to PAP (2 dropout); 56 randomized to lifestyle (1 dropout)

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

Population: 55 randomized to PAP (2 dropout); 56 randomized to lifestyle (1 dropout)

6. Primary Endpoint

The registry lists the primary outcome as Insulin Sensitivity (SI), measured over Baseline.

The primary endpoint is insulin sensitivity, labeled SI and expressed in [mU/L]^-1 x [min]^-1. The registry describes an insulin-modified frequently sampled intravenous glucose tolerance test (IVGTT). The procedure includes a weight-adjusted intravenous glucose bolus, scheduled blood sampling over 3-hours, and administration of regular insulin at the 20-minute mark. Serum glucose and insulin measurements are then analyzed with the minimal model, MINMOD, to derive SI.

Insulin sensitivity is used as a measure of how responsive the body is to insulin. The registry explains the direction of the measure: a low SI signifies low insulin sensitivity, while a high SI represents high insulin sensitivity. That makes SI relevant to the study’s question about glucose metabolism and insulin resistance. This is a description of the endpoint’s intended meaning, not a claim about what PAP did in the trial.

Although the endpoint description refers to measurements before and 2-months after intervention, the posted primary outcome is labeled Baseline. It reports the group means and standard deviations at baseline, not follow-up values or within-person changes. Consequently, these results can describe the groups’ recorded starting levels, but they cannot establish whether either group changed after intervention or whether changes differed between groups.

7. Results Posted in the Registry

• Lifestyle Counseling: mean 2.22 versus 1.95 on control; difference 0.27 (95% CI -0.23 to 0.77), standardized effect d = 0.20; z-test p = 0.293.

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.

Glucose Effectiveness (SG)

• 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:
  • Lifestyle Counseling: mean 0.02 versus 0.01 on control; difference 0.00 (95% CI -0.00 to 0.00), standardized effect d = 0.06; z-test p = 0.751.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Lifestyle Counseling and the control. The interval gives the range of effects that remain compatible with the data.

Disposition Index (DI)

• 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:
  • Lifestyle Counseling: mean 1,093 versus 931.40 on control; difference 161.70 (95% CI -214.64 to 538.04), standardized effect d = 0.16; z-test p = 0.400.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Lifestyle Counseling and the control. The interval gives the range of effects that remain compatible with the data.

Acute Insulin Response to Glucose (AIRG)

• 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:
  • Lifestyle Counseling: mean 632.38 versus 537.48 on control; difference 94.90 (95% CI -125.06 to 314.86), standardized effect d = 0.16; z-test p = 0.398.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Lifestyle Counseling and the control. The interval gives the range of effects that remain compatible with the data.

The registry names Glucose Effectiveness (SG), Disposition Index (DI), Acute Insulin Response to Glucose (AIRG), and Endothelial Function among secondary outcomes. Numerical secondary results are posted for SG, DI, and AIRG, with group summaries and recalculated unadjusted comparisons. The record’s reported secondary analyses list is empty. Numerical findings for endothelial function are not included among the posted secondary outcome entries.

Across the posted secondary comparisons, the estimated differences are small relative to the reported variability, and each reported confidence interval spans zero. The unadjusted p-values are 0.751 for SG, 0.4 for DI, and 0.398 for AIRG. This broad pattern is consistent with uncertainty about baseline differences across the posted measures. As with the primary outcome, these secondary results are labeled Baseline. They do not show post-intervention changes or treatment effects, so they do not establish whether PAP altered any of these measures.

These outcomes concern related aspects of glucose metabolism and insulin response, but they are distinct measurements. A pattern across them can provide context about the range of measures recorded; it cannot substitute for the primary treatment comparison. Nor should multiple unadjusted results be treated as independent confirmation. When many outcomes are examined, the chance of seeing an apparently notable result by chance can increase. A multiplicity plan would clarify which results are confirmatory and how inference across outcomes is handled. Such a plan is not reported in the registry record.

The secondary findings therefore carry less inferential weight than a prespecified, appropriately analyzed primary follow-up comparison. The registry does not report post-intervention secondary analyses, an adjustment strategy for multiple testing, or a detailed analysis plan. The posted baseline summaries are best read as descriptive context for the enrolled groups, not as evidence of intervention effects.

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

• Glucose Effectiveness (SG)
• Glucose Effectiveness (SG)
• Disposition Index (DI)
• Disposition Index (DI)
• Acute Insulin Response to Glucose (AIRG)
• Acute Insulin Response to Glucose (AIRG)
• Endothelial Function
• Endothelial Function

9. Statistical Interpretation

10. Statistical Methods Explained

What does a mean summarize?

For a continuous outcome such as insulin sensitivity, the mean is the arithmetic average of the observed values in a group. It provides a compact description of the group’s central level, but it does not show whether values cluster closely around that level or vary widely. The posted primary means are 1.95 for PAP and 2.22 for lifestyle counseling. The standard deviations, 1.21 and 1.45 respectively, describe the amount of variation among measurements around each group mean.

A standard deviation is not the same as a standard error or a confidence interval. It describes the spread of individual observations. A standard error describes the precision of an estimated statistic, such as a mean, and depends in part on the amount of information available. Confidence intervals use uncertainty in the estimate to give a range of values compatible with the data and the method used.

What is a mean difference?

A mean difference expresses the contrast between two group means on the outcome’s original scale. In the posted comparison, the contrast is lifestyle counseling relative to PAP: 2.22 compared with 1.95, yielding a recalculated difference of 0.27. The confidence interval is -0.233 to 0.773. A positive difference indicates a higher group mean for lifestyle counseling in this baseline comparison; a negative difference would indicate a higher mean for PAP. Since the outcome timeframe is Baseline, this contrast is not a comparison of treatment-related changes.

The comparison is unadjusted: it is calculated from group-level summary statistics rather than an adjusted model using participant-level data or covariates. An unadjusted contrast can be useful as a transparent description of the posted summaries. It does not account for other factors that might be relevant to a treatment-effect analysis. Whether the trial investigators used an adjusted analysis is not reported in the registry record.

How should the p-value be read?

The recalculated unadjusted p-value for the primary baseline contrast is 0.293. A p-value describes how compatible the observed data are with a specified null hypothesis under the assumptions of the statistical test. It is not the probability that the null hypothesis is true, nor does it measure the size or clinical importance of a difference. The registry record does not report an investigator analysis for this baseline contrast; the displayed p-value is a recalculation from the posted summary statistics.

A p-value should be considered alongside the estimated difference and its confidence interval. The p-value alone does not convey the range of plausible differences or the precision of the estimate. It also does not transform a baseline comparison into evidence about change after treatment.

What does the confidence interval add?

A confidence interval gives a range of estimates that are compatible with the observed data under the statistical procedure used. In repeated applications of a method under its assumptions, intervals constructed this way would cover the true parameter at the stated confidence level at the method’s nominal rate. It is not correct to interpret one computed interval as assigning a probability to the fixed true value. For this comparison, the interval spans values below and above zero, so the posted summary statistics leave uncertainty about the direction of the baseline mean difference.

The registry lists standard deviations, group sizes, and means for the primary outcome. The mean difference, interval, p-value, and planning illustrations are recalculations from the posted summaries, not a reported investigator treatment analysis. The discrepancy flag is false. No sponsor-reported analysis is listed among the reported analyses.

Why distinguish baseline from follow-up?

Randomization is intended to create groups that can be compared fairly for treatment outcomes, but random assignment does not mean the baseline values must be identical. A baseline comparison describes the groups before the intervention; a treatment-effect analysis evaluates outcomes after assignment, changes over time, or another prespecified contrast that uses follow-up information. The registry describes planned measurements before and 2-months after intervention, but the posted primary results are labeled Baseline. Without the corresponding follow-up result or change analysis, the primary treatment question remains unanswered by these posted results.

11. Confidence Intervals and Precision

The recalculated primary mean difference is 0.27 for lifestyle counseling relative to PAP, with a 95% confidence interval from -0.233 to 0.773. This interval describes uncertainty around the baseline difference estimated from the posted group summaries. Its inclusion of zero means that the summaries are compatible with no baseline mean difference under the calculation method. Values on either side of zero are also within the interval, so the direction and size of the baseline contrast are not precisely determined.

The interval’s width matters as much as whether it includes zero. A confidence interval is not a guarantee that the true value lies within its endpoints, nor does it provide a probability that the true value is at a particular point. It communicates how much uncertainty remains under the statistical assumptions used. The p-value, 0.293, is consistent with the interval’s uncertainty but does not replace it or describe the size of the difference.

Precision of a baseline contrast should not be confused with precision of a treatment effect. The interval does not quantify the effect of PAP after intervention, because the posted primary results are baseline summaries rather than follow-up outcomes or changes. The registry’s endpoint description mentions a measurement before and 2-months after intervention, but follow-up primary results are not reported in the registry record.

There is also appreciable variation in individual values, as reflected in the group standard deviations of 1.21 for PAP and 1.45 for lifestyle counseling. A mean difference and its interval condense the data and do not show all individual observations or the shape of their distribution. These precision statements apply to the recalculated, unadjusted baseline comparison 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 illustrations express required enrollment as participants per arm, not a total across both arms. They are calculated from the observed primary mean difference and show hypothetical sample sizes for detecting the stated fraction of that observed effect. For the full observed effect, the illustration gives 386 participants per arm for 80% power and 516 participants per arm for 90% power. For planning for 75% of the observed effect, it gives 685 participants per arm for 80% power and 917 participants per arm for 90% power. For planning for 50% of the observed effect, it gives 1,542 participants per arm for 80% power and 2,064 participants per arm for 90% power.

The assumptions for these illustrations are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect. Smaller target effects require more participants because a smaller separation between group means is harder to distinguish from random variation. The 80% and 90% power columns describe the probability of detecting the specified effect under the planning assumptions if that effect is present; the higher power target requires a larger planned sample.

These calculations are planning illustrations, not observed power. They are based on the observed baseline difference, while the registry’s posted primary results do not report a post-intervention treatment effect. The trial’s own original sample-size justification and design assumptions are not reported in the registry record. Thus, the figures should not be read as the enrollment target used by investigators or as evidence about what the completed trial could detect.

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 = 0.270; pooled standard deviation σ = 1.338.
2. n = 2 × (1.96 + 0.842)² × 1.338² / 0.270² = 385.3, rounded up to 386 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 <- 0.27                      # observed difference in means
sigma <- 1.33765565132041                     # 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(1503164)
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 = 386 (80% power), 516 (90% power)
 75% of observed effect: n per arm = 685 (80% power), 917 (90% power)
 50% of observed effect: n per arm = 1,542 (80% power), 2,064 (90% power)
power.t.test: 386.3 
Simulated power at n = 386 per arm: 0.805 (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 outcome and several secondary outcomes, including glucose effectiveness, disposition index, acute insulin response to glucose, and endothelial function. It also records 12 outcome measures and 10 posted secondary results. The available record does not describe how the investigators controlled the chance of false-positive findings across multiple outcomes or comparisons. A prespecified multiplicity strategy, such as prioritizing a limited set of confirmatory tests or adjusting inference across a family of tests, is not reported in the registry record.

Multiplicity matters because interpreting many separate statistical tests at the same nominal threshold can make at least one apparently unusual result more likely even when there is no underlying effect. This is a general statistical concern, not a claim that a particular error occurred in this trial. The reported secondary comparisons are unadjusted recalculations, and their p-values should be interpreted with that context. There are no investigator-reported secondary analyses listed in the registry record.

The record identifies dropout counts in the primary outcome description and baseline result counts by arm, but it does not explain how missing data were handled. It does not report whether participants with unavailable measurements were excluded, whether any imputation method was used, or whether sensitivity analyses were performed. The reported arm counts should not be assumed to establish the analysis population or the handling of missing measurements.

Likewise, the registry record does not state whether the primary analysis followed an intention-to-treat principle, whether a per-protocol analysis was planned, or how adherence to PAP or participation in counseling was incorporated. It does not report an analysis plan, model specification, adjustment for baseline values, or interim analyses. These absences limit assessment of how the study’s intended treatment question was analyzed. The posted results themselves are baseline summaries and recalculations, rather than a reported follow-up analysis.

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.

The registry reports zero serious adverse events among 55 participants at risk in the PAP group and zero among 56 participants at risk in the lifestyle counseling group. It also records zero other adverse events among 55 at risk in the PAP group and zero among 56 at risk in the lifestyle group. Deaths are recorded as zero in each group. No serious adverse event terms are listed.

These counts describe what the registry record reports for the stated groups and at-risk numbers. They should not be interpreted as proof that no adverse events occurred outside the categories or reporting procedures captured in the record. The registry does not provide additional detail about adverse-event definitions, collection methods, severity categories beyond the posted groupings, or the time period over which events were assessed. The figures are safety reporting counts, not a comparison of treatment effects on health outcomes.

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

The posted results mean that the registry contains baseline summaries for insulin sensitivity and several secondary glucose-related measures in the PAP and lifestyle counseling groups. For the primary outcome, the baseline group means were 1.95 and 2.22, with an unadjusted recalculated mean difference of 0.27 for lifestyle counseling relative to PAP. The confidence interval includes zero and extends in both directions. These statistics describe the groups’ recorded starting values and the uncertainty around their baseline contrast.

They do not show whether PAP improved insulin sensitivity, whether lifestyle counseling changed it, or whether the interventions differed in their effects. The outcome description refers to pre-intervention and 2-months post-intervention measurement, but the posted primary results are identified as Baseline. Follow-up values, changes from baseline, and an investigator-reported treatment-effect analysis are not reported in the registry record. The same distinction applies to the posted secondary summaries.

A non-significant p-value should not be interpreted as proof of equality or as evidence that an important effect is impossible. The interval describes a range of baseline differences compatible with the recalculated analysis, and uncertainty remains. More fundamentally, even a very precise baseline comparison would not answer the intervention question without follow-up evidence.

The randomized design and completed status provide context for the intended comparison, but the posted figures alone do not establish the results of that comparison. They also do not establish the effectiveness, safety, or clinical value of PAP or lifestyle counseling. The adverse-event figures report zero events in the categories recorded, but the registry gives limited detail about event ascertainment. The appropriate interpretation is confined to what is posted: baseline group summaries, unadjusted recalculations, and recorded adverse-event counts, with treatment effects not reported.

17. Why This Trial Matters Statistically

This trial is statistically informative as an example of why the timing and meaning of a result matter as much as its numerical form. The registry describes a randomized comparison and a primary outcome designed to assess insulin sensitivity before and after intervention. Yet the posted primary result is labeled Baseline. A mean difference, confidence interval, and p-value can look like a treatment comparison while in fact describing only the groups’ starting values. Keeping that distinction explicit prevents baseline summaries from being mistaken for evidence about intervention effects.

The record also illustrates how uncertainty should be read. The recalculated baseline difference is accompanied by an interval that includes zero and allows values on either side. That interval is more informative than a yes-or-no reading of the p-value, but it still concerns only the baseline contrast. Precision cannot remedy a mismatch between the statistic posted and the causal question of interest.

Finally, the sample-size illustrations show how planning depends on the effect one wishes to detect and on stated statistical assumptions. They are not the trial’s original design justification and not observed power. Their interpretation is especially limited when the observed estimate comes from baseline data rather than a reported treatment effect. Together, these points make the registry record useful for teaching careful distinctions among randomization, baseline balance, treatment-effect estimation, uncertainty, and prospective sample-size planning.

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.

A key limitation is that the posted primary outcome is labeled Baseline, despite the endpoint description referring to measurement before and 2-months after intervention. No post-intervention primary values, changes, or treatment-effect analysis are reported in the registry record. This prevents the posted results from addressing the trial’s central question about whether PAP changes insulin sensitivity or glucose metabolism.

The registry provides limited detail about who was eligible, the counseling content, PAP adherence, and the handling of the reported dropouts. It lists baseline result counts of 53 for PAP and 55 for lifestyle counseling, but does not explain the analysis population or missing-data methods. It also does not report whether an intention-to-treat analysis, adjusted model, sensitivity analysis, or interim analysis was used or planned.

For the secondary outcomes, numerical results are available for three measures, while endothelial function is also named among the outcomes but has no numerical findings among the posted secondary entries. The record does not describe a multiplicity strategy, and no investigator-reported analyses are listed. The recalculated comparisons are unadjusted and should not be taken as substitutes for a prespecified analysis of follow-up outcomes.

The sample-size figures are planning illustrations based on the observed difference and stated assumptions, rather than the original trial’s design justification. The registry’s adverse-event reporting gives group counts but little detail about how events were defined or collected. These limitations concern what can be concluded from the registry record; they do not determine what may have been analyzed or reported elsewhere.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Effects of Continuous Positive Airway Pressure (CPAP) on Glucose Metabolism — NCT01503164.
• Registry record last updated 2017-10-19; status last verified 2017-10.
• Results first posted 2017-10-19.
• 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

NCT01503164 is a completed randomized, parallel-group study sponsored by Johns Hopkins University. It enrolled 111 participants and compared positive pressure therapy with lifestyle counseling. The primary endpoint was insulin sensitivity, measured using an insulin-modified IVGTT and derived with MINMOD.

The primary and secondary results posted in the registry are labeled Baseline. The recalculated primary baseline mean difference is 0.27 for lifestyle counseling relative to PAP, with a 95% confidence interval from -0.233 to 0.773 and p = 0.293. The registry record does not report post-intervention estimates or analyses of treatment effects. It records zero serious and other adverse events, and zero deaths, in both groups.