Breathing Interventions for Relaxation: Dosing Through Extended Exhale: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Breathing Interventions for Relaxation: Dosing Through Extended Exhale (NCT02870868), a randomized na study. The primary outcome is Magnitude of Change in High Frequency Heart Rate Variability.

2. Clinical Question

3. Trial Design

This was a randomized, single-masked, parallel-group study sponsored by Vanderbilt University Medical Center. The registry lists the study as completed and records enrollment of 99. The study began on 2016-10-14, and primary completion is recorded as 2018-12-19. The phase is listed as not applicable.

The two behavioral interventions were both described as slow breathing. The distinction of interest was the breathing pattern: one approach used an exhalation longer than inhalation, while the other used equal durations for exhalation and inhalation. The descriptions also refer to gradual changes in breath length based on an initial assessment. For the equal-duration group, the description specifies that both phases increased over 4 weeks. The record does not provide a complete account of all procedures: the arm descriptions stop during their account of what happened before practice.

Random assignment supports a comparison of the groups as assigned, but the registry record does not report details of sequence generation, allocation concealment, or who was masked. The masking field says single; it does not identify the masked role. The number enrolled is not the same as the number contributing to the posted primary outcome summaries: the record reports 41 for the exhalation-longer group and 35 for the equal-duration group. It does not explain the difference between enrollment and those outcome counts or report the analysis population definition.

The registry lists six outcome measures, but no secondary outcomes are posted. The primary outcome has a posted group comparison. Further details of the original statistical plan, including its planned sample-size assumptions, 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:

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 Magnitude of Change in High Frequency Heart Rate Variability, measured over Baseline.

The primary outcome is titled magnitude of change in high-frequency heart rate variability, measured in milliseconds squared. The registry describes high-frequency heart rate variability as a proxy for parasympathetic tone. In general, a proxy measure is used to represent an underlying process that is not measured directly by the outcome itself. The record’s description gives average reference values of around 600 ms² in normal healthy adults, around 100 ms² in hypertensive adults, and around 20 ms² in patients with autonomic failure. Those reference values are part of the endpoint description; they are not results from the two randomized groups.

The endpoint is reported as a continuous measure with a mean and standard deviation. In general, a mean describes the center of a group’s observed values, while a standard deviation describes how dispersed those values are around the mean. The posted summaries give a mean of 399.0 ms² with a standard deviation of 355.0 for the group assigned to exhalation longer than inhalation, and a mean of 421.0 ms² with a standard deviation of 350.0 for the equal-duration group.

There is an important qualification in the record: although the outcome title refers to change, its timeframe is recorded as Baseline. The posted summaries do not include a change-from-baseline value or a later measurement in the outcome details. The registry record therefore does not clarify whether the displayed means represent baseline values or how a change was defined and analyzed. The comparison should be read as the reported mean difference, not assumed to be a change contrast.

7. Results Posted in the Registry

• Slow Breathing With Exhale Equal to Inhale: mean 421.00 versus 399.00 on control; difference 22.00 (95% CI -136.91 to 180.91), standardized effect d = 0.06; z-test p = 0.786.

8. Statistical Interpretation

9. Statistical Methods Explained

What does the mean difference represent?

The comparison is reported as a mean difference. In general, a mean difference subtracts one group’s average from the other group’s average, using a stated group as the reference. In this record, the comparison is expressed as the equal-duration group relative to the longer-exhalation group. The reported estimate is 22.0 ms², with group means of 421.0 and 399.0 ms², respectively. The posted comparison also reports the group standard deviations and a pooled standard deviation of 352.7 ms².

A mean difference retains the measurement unit, which makes its scale interpretable in the same units as the endpoint. It summarizes a difference in group averages; it does not describe every participant’s response, the distribution of individual differences, or the range of outcomes within either group. The standard deviations, 350.0 and 355.0, indicate substantial spread in the observed values around their respective group means. In general, variation within groups matters because it affects how precisely a difference between averages can be estimated.

What do the uncertainty interval and p-value add?

The interval for the mean difference extends from -136.9 to 180.9 ms². In general, a confidence interval conveys uncertainty around an estimate by identifying a range of values compatible with the data and the statistical procedure used. The record does not state the confidence level or give further details of the procedure used to construct this interval. Its endpoints should therefore be read as the posted uncertainty limits, without adding an unreported confidence level.

The unadjusted p-value is 0.786. In general, a p-value describes how unusual the observed data, or data more extreme, would be under a specified null model. It is not the probability that the null hypothesis is true, and it does not quantify the size or importance of a difference. Here, the registry calls the value unadjusted. It does not report an adjustment for testing multiple outcomes or comparisons, nor does it provide enough information to determine whether the result was part of a broader testing strategy.

Why does the endpoint wording matter?

The outcome title refers to magnitude of change, while the recorded timeframe is Baseline. The posted comparison is a mean difference between group summaries; the record does not provide change scores, later measurements, or a definition of change for this outcome. In general, a baseline contrast and a change-from-baseline contrast answer different statistical questions. A baseline contrast compares groups at the starting measurement; a change contrast compares how values differ over time, often by comparing within-person changes between groups. The available record does not resolve which interpretation was intended for the primary result. Consequently, the estimate should not be relabeled as a treatment-related change.

What can be said about variability and precision?

The standard deviation describes variation among observations within a group, whereas the standard error describes uncertainty in an estimated statistic. These quantities have different meanings and are not interchangeable. The comparison reports standard errors of 55.44 and 59.16 for the group means. In general, standard errors are influenced by both variability and the amount of information available. The registry reports the outcome counts as 41 and 35, but does not provide a missing-data account or analysis-population definition to explain how those counts arose.

Over-dispersion is a general concern when observed variability is greater than a statistical model assumes. If a model understates variability, standard errors may be too small and intervals may be too narrow. The posted summaries give group standard deviations and a pooled standard deviation, but the registry does not describe a model-based variance assumption or identify over-dispersion as an issue. It would therefore be inappropriate to claim that over-dispersion affected this analysis. The broader point is that the assumed variability model can matter for precision, especially when statistical methods rely on such assumptions.

What can randomization and masking tell the reader?

Randomization is intended to make assigned groups comparable on average with respect to measured and unmeasured characteristics. In general, this supports an interpretable between-group comparison, subject to issues such as missing outcomes, departures from assigned treatment, and the analysis population. The registry identifies the design as randomized and parallel, but does not report sequence generation, allocation concealment, adherence, or the analysis population. Those details cannot be inferred from the design label alone.

The record identifies the study as single-masked but does not specify who was masked or how masking was maintained. The intervention involved breathing exercises, but that fact does not establish which participants, assessors, or analysts knew group assignment. The registry record also does not report the original statistical analysis plan, the intended handling of missing data, or whether an intention-to-treat analysis was conducted. These omissions leave important aspects of the analysis process unclear.

The displayed recalculation is an unadjusted comparison based on the posted summary statistics; it should be distinguished from a fully described trial analysis. The discrepancy flag is false, so the record does not identify a disagreement between the posted comparison and a recalculation. Even so, a summary-statistic comparison cannot fill gaps in the registered analysis plan or clarify the baseline-versus-change ambiguity. The posted result is best read as the registry’s reported group contrast with its accompanying uncertainty, rather than as a complete account of all trial analyses.

10. Confidence Intervals and Precision

The mean difference is 22.0 ms², with an interval from -136.9 to 180.9 ms². The interval includes negative and positive values, so the posted data do not tightly establish the direction of the group contrast. In general, a confidence interval is useful because it shows uncertainty around an estimate rather than presenting a single value as if it were exact. The registry record does not state the confidence level or further details of the interval method.

The endpoint standard deviations are 355.0 and 350.0 ms², and the pooled standard deviation reported for the comparison is 352.7 ms². These values indicate considerable variation in the outcome relative to the estimated mean difference. The reported standard errors for the two means are 55.44 and 59.16. In general, a large amount of within-group variation can make a difference between group averages harder to estimate precisely.

The interval’s breadth means that the point estimate should not be treated as a precise estimate of the underlying contrast. Its lower and upper limits permit materially different interpretations of direction and size. The record does not give a threshold for what would count as a meaningful difference in high-frequency heart rate variability, so statistical uncertainty cannot be translated into a judgment about practical importance.

Interpretation is further limited by the endpoint description: the title refers to change, but the timeframe is Baseline, and no change values are posted. Thus, the uncertainty interval quantifies the reported mean-difference comparison, not a clearly defined change-from-baseline effect. The absent analysis-population and missing-data details also leave uncertainty about which observations contributed to the estimate.

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 planning figures refer to participants per arm, not total events. This is a continuous-outcome comparison, and the planning illustration states that it uses equal allocation between the two arms. It assumes a two-sided significance level of 0.05 and a normal approximation. Each scenario uses a stated fraction of the observed effect: 100%, 75%, or 50%. These are planning illustrations based on the observed effect, not the trial’s original design assumptions; the original assumptions are not reported in the registry record.

For planning at 100% of the observed effect, the figures are 4,035 participants per arm for 80% power and 5,402 participants per arm for 90% power. At 75% of the observed effect, the corresponding figures are 7,174 and 9,603 participants per arm. At 50% of the observed effect, they are 16,140 and 21,607 participants per arm.

In plain language, the 80% power column represents the planned number of participants per arm under the stated assumptions for a design with an 80% chance of detecting the specified effect if that effect is real and the assumptions hold. The 90% power column makes the analogous planning target more demanding. Smaller effects need more participants to detect because they are harder to distinguish from random variation. These calculations are not observed power; they are prospective planning illustrations derived from the observed contrast and stated assumptions.

The observed mean difference is 22.0 ms², and the interval around it is broad. Because the planning scenarios are built from that observed effect and its stated fractions, they should not be treated as confirmation that the original trial was designed to detect those effects. The registry record does not report its own target effect, planned power, or sample-size justification.

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 = 22.000; pooled standard deviation σ = 352.712.
2. n = 2 × (1.96 + 0.842)² × 352.712² / 22.000² = 4,034.9, rounded up to 4,035 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 <- 22                      # observed difference in means
sigma <- 352.711504498231                     # 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(2870868)
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 = 4,035 (80% power), 5,402 (90% power)
 75% of observed effect: n per arm = 7,174 (80% power), 9,603 (90% power)
 50% of observed effect: n per arm = 16,140 (80% power), 21,607 (90% power)
power.t.test: 4035.8 
Simulated power at n = 4,035 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.

13. Multiplicity, Missing Data and Analysis Populations

The registry lists six outcome measures, but no secondary outcome results are posted. The primary comparison is reported, while the registry indicates zero analysis entries. The record does not explain how the listed outcomes relate to the reported primary result or whether additional analyses were performed but not entered. Statistical analysis plan details, including a prespecified testing sequence or multiplicity control, are not reported in the registry record.

Multiplicity arises in general when several outcomes, time points, subgroups, or comparisons are tested. If many tests are considered without an appropriate strategy, the chance of at least one apparently unusual result can increase. That general concern does not establish that this study used multiple tests or that the reported result is misleading. The available information is insufficient to assess which comparisons were planned, how they were prioritized, or whether any adjustment was intended. The reported p-value is explicitly unadjusted.

The record reports 41 observations for the longer-exhalation group and 35 for the equal-duration group in the primary outcome comparison, while overall enrollment is listed as 99. It does not state why these numbers differ, whether all randomized participants were included in the analysis, or how missing outcome values were handled. The analysis population is not reported in the registry record. It is not possible to determine from these summaries whether the comparison followed assignment, included only participants with complete outcome data, or used another population definition.

Missing data can matter in general when the chance of an outcome being unavailable is related to group assignment or to the outcome itself. The record does not describe the extent, reasons, or statistical handling of missingness. It also does not report sensitivity analyses that would show whether conclusions depend on assumptions about missing values. These are information gaps; they do not demonstrate that missing data occurred in a particular way or altered the result.

The registry record does not report an interim-analysis plan, stopping rules, or further details of the statistical plan. Their absence from the record should not be taken as proof that such procedures were or were not used. Without those details and without secondary outcome results, readers cannot fully evaluate multiplicity, missing-data handling, or the alignment between planned and posted analyses.

14. 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 non-serious adverse event terms

The adverse-event record reports the number at risk and the counts recorded for serious adverse events, other adverse events, and deaths. For slow breathing with exhalation longer than inhalation, 49 were at risk; the recorded serious adverse event count was 0, the other adverse event count was 0, and deaths were 0. For slow breathing with exhalation equal to inhalation, 50 were at risk; the corresponding recorded counts were 0, 0, and 0.

These are registry-reported counts, not proof that no event of any kind occurred outside the collection or reporting represented in the record. The record does not provide event definitions, surveillance procedures, follow-up duration for safety, or details about how adverse events were solicited and classified. It also does not provide serious-event terms; none are listed. The counts should be read as the adverse-event results entered in the registry, with the limits of that reporting context.

The at-risk figures in the safety record differ from the group counts in the primary outcome comparison. The registry does not explain the difference, so these sets of counts should not be assumed to describe identical analysis populations. No calculation of comparative risk or rate is needed to read the reported counts, and the zero counts do not by themselves establish the absence of risk.

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

The central posted result is a mean difference of 22.0 ms² in high-frequency heart rate variability, comparing slow breathing with exhalation equal to inhalation against slow breathing with exhalation longer than inhalation. The associated interval ranges from -136.9 to 180.9 ms², and the unadjusted p-value is 0.786. The estimate is therefore uncertain, with the interval covering both directions of difference. The record’s outcome counts are 41 and 35 for the two groups.

The result does not establish that either breathing approach caused a change in the endpoint. The primary outcome title refers to magnitude of change, but the recorded timeframe is Baseline, and the posted results do not include a change-from-baseline estimate or later measurement. The comparison is therefore best understood as the mean contrast recorded in the registry, not as a demonstrated difference in change over time.

Nor does the result prove that the two approaches are equivalent. In general, a result that does not establish a clear difference is not the same as evidence that any difference is sufficiently small to be unimportant. Equivalence requires a defined margin and an analysis designed to evaluate whether the interval lies within that margin. The registry record does not report an equivalence margin or such an analysis.

The outcome is described as a proxy for parasympathetic tone. A proxy measure may inform understanding of a biological process, but a result on that measure should not automatically be interpreted as a direct measure of all aspects of that process or of a clinical outcome. The registry record does not report clinical outcomes or a threshold for a meaningful change in high-frequency heart rate variability.

The findings are specific to the randomized comparison and the information posted for this study. The record does not provide enough detail to assess the analysis population, missing data, masking roles, or the complete statistical plan. Those limits, together with the baseline timeframe and broad interval, constrain what can be concluded from the posted summary. The statistics describe the observed comparison and its uncertainty; they do not provide medical advice or establish a treatment effect.

16. Why This Trial Matters Statistically

This trial illustrates why an endpoint’s label, timeframe, and statistical contrast need to be read together. A title referring to magnitude of change suggests a longitudinal question, while the registered timeframe is Baseline and the posted comparison is a mean difference between groups. Without change values or follow-up details, the statistical result cannot simply be interpreted as a difference in change. This distinction is important whenever a registry outcome’s wording and its reported measurement timing do not align clearly.

The comparison also shows why an estimate should be considered alongside its uncertainty. The mean difference is 22.0 ms², but the interval from -136.9 to 180.9 ms² spans both negative and positive values. The point estimate alone would give an incomplete account; the interval indicates that the data do not pin down the direction and size of the contrast precisely. The unadjusted p-value, 0.786, adds a test-based summary but does not replace the estimate and interval.

Planning illustrations based on an observed effect can help readers understand how a target effect size relates to sample-size requirements. They are not a substitute for the original design assumptions. The registry does not report the study’s sample-size justification, and calculations derived from the observed contrast are planning exercises rather than evidence about the design process or the probability that the study detected an effect.

Finally, the record demonstrates the value of transparent reporting about analysis populations, missing outcomes, multiplicity, and endpoint timing. Those details determine how a result should be interpreted, yet they are not reported. Recognizing such gaps is part of statistical appraisal, not a claim that the study was conducted incorrectly.

17. 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 the mismatch between the primary outcome title, which refers to magnitude of change, and its recorded timeframe, Baseline. The posted comparison does not include change scores or later measurements. This prevents a clear interpretation of the result as change over time and leaves the intended primary estimand uncertain.

The registry reports overall enrollment of 99, but the primary outcome summaries use counts of 41 and 35. Safety at-risk figures are 49 and 50. The record does not explain these differences or define the populations used for the outcome and safety summaries. It does not describe missing data, exclusions, adherence, or the analysis population, so the relationship between enrollment and each reported result cannot be assessed from the record.

The trial is identified as randomized, single-masked, and parallel, but the record does not say who was masked or describe sequence generation and allocation concealment. The intervention descriptions also end during their account of pre-practice procedures, leaving those details incomplete. The record does not report the original statistical analysis plan, sample-size justification, or intended approach to multiple outcomes. These omissions limit assessment of the design and analysis without establishing that any particular procedure was absent.

The primary comparison has a broad interval, from -136.9 to 180.9 ms², and the registry provides no threshold for a meaningful difference in the endpoint. There are no posted secondary outcome results, and no further clinical outcome context is available in this record. The adverse-event counts are recorded as zero, but event definitions and safety follow-up details are not reported. Together, these limitations restrict interpretation to the posted summaries and their stated context.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Breathing Interventions for Relaxation: Dosing Through Extended Exhale — NCT02870868.
• Registry record last updated 2024-05-29; status last verified 2024-05.
• Results first posted 2024-05-29.
• 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.

21. Record Summary

NCT02870868 is a completed, randomized, single-masked, parallel-group behavioral study sponsored by Vanderbilt University Medical Center. It compared slow breathing with exhalation longer than inhalation against slow breathing with equal inhalation and exhalation. The registry lists enrollment of 99 and identifies healthy adults and stress as study conditions.

The primary outcome is titled magnitude of change in high-frequency heart rate variability, with a Baseline timeframe. The posted mean difference for equal-duration versus longer-exhalation breathing is 22.0 ms², with an interval from -136.9 to 180.9 ms² and an unadjusted p-value of 0.786. The group summaries report counts of 41 and 35. No secondary outcome results are posted.

The registry records zero serious adverse events, zero other adverse events, and zero deaths in both safety groups. It does not report the original sample-size assumptions, analysis population, missing-data handling, or full statistical plan. The baseline timeframe and change-oriented outcome title also leave the intended interpretation of the primary endpoint unclear.