Relaxation Treatment for Anxiety in Adults Aged 60 or Older: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Relaxation Treatment for Anxiety in Adults Aged 60 or Older (NCT02429778), a randomized na study. The primary outcome is Change in Anxiety Symptoms.

2. Clinical Question

The trial asks whether a self-directed relaxation program is associated with a different change in anxiety symptoms than a wait-list period among adults aged 60 or older with anxiety disorders. The registry describes BREATHE as a home-based program combining diaphragmatic breathing, progressive muscle relaxation, weekly DVD lessons, and telephone check-ins. Its comparator was a wait list, with the opportunity to participate in BREATHE after 8 weeks.

The posted group means were 17.95 for BREATHE and 26.2 for Wait List. The unadjusted contrast is expressed as Wait List minus BREATHE, so a positive estimate indicates a higher mean score in the wait-list group at the reported endpoint. That contrast describes the posted outcome summaries; it is not, by itself, a complete account of the trial’s model-based analysis.

3. Trial Design

The registry describes a randomized, parallel-group trial with no masking. The study status is completed, and the recorded enrollment is 40. The sponsor is Palo Alto Veterans Institute for Research. The registry lists the phase as NA. The recorded study start is 2015-05, and primary completion is recorded as 2017-06.

Participants were assigned to BREATHE or Wait List. BREATHE was a self-directed program delivered through weekly DVD lessons and telephone check-ins. Participants learned diaphragmatic breathing and progressive muscle relaxation. The arm description specifies a 4-week treatment program with home practice of the skills, followed by a request to continue practicing at home. The recorded description of the post-treatment practice duration is abbreviated. Wait List participants had an 8-week waiting period and could then receive BREATHE if interested.

The primary outcome was change in anxiety symptoms from baseline to 8 weeks, measured with the Geriatric Anxiety Scale. The record also names change in depressive symptoms and change in somatic symptoms as secondary outcomes. It lists 6 outcome measures overall, but detailed results for those secondary outcomes are not included in the posted results.

For the primary outcome, 20 participants are listed in each arm. The registry describes an intent-to-treat linear mixed effects model using maximum likelihood. The record does not report the full model specification, the allocation procedure beyond randomization, or whether any masking of outcome assessment was used. It also does not report the original sample-size justification, a detailed statistical analysis plan, or whether interim analyses were planned.

The primary results include group means and standard errors, along with an unadjusted comparison derived from the posted summary statistics. The model description and the summary-statistic comparison answer related but not identical questions: the former identifies the stated analysis approach, while the latter expresses a direct contrast between the posted group summaries.

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: A linear mixed effects model using maximum likelihood modeling was employed to analyze these data using intent-to-treat principles.

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 Change in Anxiety Symptoms, measured over Change from baseline to 8 weeks.

The primary endpoint is change in anxiety symptoms from baseline to 8 weeks, measured using the Geriatric Anxiety Scale (GAS). The GAS is a 30-item measure covering somatic, cognitive, and affective anxiety symptoms. Its first 25 items contribute to the total score; the final 5 items provide information about the content of worries or fears. Total scores range from 0 to 75, with higher scores indicating worse anxiety. Participants rate item severity on a four-point Likert-type scale.

A change score focuses on how the measured symptom level differs between the start of the study and the scheduled assessment. This is relevant to the trial’s question because the intervention was intended to address anxiety symptoms over a defined period. Comparing the groups’ endpoint summaries can describe whether the observed scores differed after that period, although a change outcome and an endpoint score are not interchangeable unless the analysis accounts for baseline in a suitable way.

The registry identifies change from baseline to 8 weeks as the primary timeframe and reports a mean for each arm. The posted results do not provide individual participant trajectories or a full model output. The scale is a measure of reported symptoms, not a direct measure of every aspect of anxiety or functioning. The record’s stated score direction is important for interpretation: higher scores indicate worse anxiety.

7. Results Posted in the Registry

• Wait List: mean 26.20 versus 17.95 on control; difference 8.25 (95% CI 2.03 to 14.47), standardized effect d = 0.82; z-test p = 0.009.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry describes random allocation to a parallel-group comparison. Randomization is intended to make assigned groups comparable on average at the start of a trial, including for factors that are not measured. It does not guarantee exact balance in any particular study, especially when the number of participants is limited. Because the trial was not masked, participants and study staff could know the assigned group. That can matter for a behavioral intervention and for outcomes based on participant symptom reports, although the registry record does not describe whether outcome assessors were masked.

What does the primary analysis description mean?

The stated primary analysis used a linear mixed effects model with maximum likelihood and intent-to-treat principles. A linear model represents the outcome using a combination of predictors and an error term. A mixed effects model can account for correlated measurements, such as repeated observations from the same participant, by including both fixed effects and random effects. Maximum likelihood is a method for estimating model parameters from the observed data. Intent-to-treat generally refers to analyzing participants according to their randomized assignment, rather than regrouping them according to what treatment they received.

Those terms describe a broad approach, not every analytic choice. The registry record does not report the model formula, the covariance structure, the specific fixed and random effects, the exact missing-data assumptions, or a full model output. It therefore is not possible to reconstruct the stated model from the available description alone. Maximum likelihood can use observed data under its assumptions, but the record does not give enough detail to assess whether those assumptions were appropriate or how much outcome information was missing.

How should the means and standard errors be understood?

The primary results give a mean score for each group and a standard error for each mean. The mean describes the group’s average score. The standard error reflects uncertainty in estimating that average; it is not the standard deviation of individual scores and should not be read as the range in which most participants’ scores fall. The displayed means are 17.95 for BREATHE and 26.2 for Wait List. Their reported standard errors are 2.34 and 2.14, respectively.

The registry also gives an unadjusted mean difference and confidence interval based on the posted summary statistics. The contrast is defined as Wait List minus BREATHE. An unadjusted comparison does not account for covariates or the model structure described for the primary analysis. It is useful as a direct summary of the posted means, but it should not be presented as though it were necessarily the coefficient from the mixed effects model. The record does not report a discrepancy between the summaries and the described analysis.

Why can a mixed model and a simple contrast differ?

In general, an unadjusted difference between group means and a model-based estimate can differ if the model accounts for baseline measurements, repeated observations, covariates, or different patterns of available data. The exact reason cannot be determined without the model specification and results. Thus the posted summary-statistic contrast should be interpreted on its own terms, while the record’s mixed-model description indicates the intended primary analytic framework.

What does the p-value say?

The unadjusted p-value is 0.009. In general, a p-value measures how often data at least as incompatible with a specified null model would arise if that model and its assumptions were correct. It is not a measure of the probability that the result occurred by chance, and it does not describe the size or practical importance of the difference. A p-value also does not correct for multiple testing unless a multiplicity procedure is applied. Whether such a procedure was planned or used is not reported in the registry record.

Why can over-dispersion matter?

In general, over-dispersion occurs when the observed variability is greater than a statistical model assumes. If a model understates variability, standard errors can be too small and uncertainty can appear narrower than it is. Over-dispersion is especially discussed for count outcomes, while this trial’s primary outcome is a continuous scale score. The registry record does not report an over-dispersion assessment, and the posted summary statistics do not establish that over-dispersion affected the analysis.

For a continuous outcome, it remains important to examine whether model assumptions fit the score distribution and the pattern of repeated measurements. The registry does not report diagnostic checks, residual assessments, or sensitivity analyses. Their absence from the registry record does not establish that they were not performed; it means the posted record does not document them.

Finally, the distinction between a prespecified analysis and a retrospective calculation matters. The registry gives the mixed-model description, while the displayed contrast is unadjusted. The original statistical analysis plan and the trial’s original sample-size assumptions are not reported in the registry record. The available information supports a careful description of the posted summaries, but not a full independent audit of the primary model.

10. Confidence Intervals and Precision

The unadjusted mean difference is 8.25 points, expressed as Wait List minus BREATHE. Its confidence interval extends from 2.035 to 14.47. In general, a confidence interval communicates the range of effect estimates compatible with the data and the method used, while reflecting sampling uncertainty. It is not a guarantee that the true effect lies within the interval, and its interpretation depends on the confidence level and analysis procedure. The registry record does not state the confidence level for this interval.

Every value in the reported interval is positive, matching the direction of the estimated contrast: the posted Wait List mean is higher than the BREATHE mean, and higher GAS scores indicate worse anxiety. The interval nevertheless covers a range of possible differences rather than identifying one exact value. Its width reflects uncertainty in the estimated contrast, and the sample size and outcome variability influence that uncertainty.

The group means are reported with standard errors of 2.34 for BREATHE and 2.14 for Wait List. These standard errors concern the precision of each estimated mean, not the variability of individual scores. The pooled standard deviation is 10.03 and describes a different quantity. Neither these summary measures nor the confidence interval reveals the full distribution of scores or the degree of overlap between individual participants.

The unadjusted p-value is 0.009, but statistical significance does not remove uncertainty or make the estimated magnitude exact. The interval and point estimate should be considered together, while keeping in mind that the contrast is an unadjusted summary-statistic comparison rather than a reported coefficient from the mixed effects model. The registry record does not provide the model-based interval or details needed to compare its precision with the unadjusted 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 estimates are participants per arm, not total events. They use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set at the stated fraction of the observed effect. The trial’s own original design assumptions and sample-size justification are not reported in the registry record.

For planning based on 100% of the observed effect, the estimate is 24 participants per arm for 80% power and 32 participants per arm for 90% power. At 75% of the observed effect, the estimates are 42 participants per arm for 80% power and 56 participants per arm for 90% power. At 50% of the observed effect, the estimates are 93 participants per arm for 80% power and 125 participants per arm for 90% power.

In plain terms, power is the chance that a study would detect an effect of the specified size under the planning assumptions if that effect were present. The 80% column gives the planned per-arm count associated with an 80% chance of detection under those assumptions; the 90% column gives the count for a higher chance of detection. Smaller effects need more participants to detect, which is why planning for a smaller fraction of the observed effect yields larger per-arm estimates. These figures are planning illustrations, not observed power.

Because the estimates are based on the observed effect, they should not be treated as proof that the observed effect is the appropriate target for another study. The registry record does not report the original rationale for choosing the enrolled sample size, the effect size assumed at trial planning, or whether the trial’s original design used the same assumptions.

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 = 8.250; pooled standard deviation σ = 10.028.
2. n = 2 × (1.96 + 0.842)² × 10.028² / 8.250² = 23.2, rounded up to 24 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 <- 8.25                      # observed difference in means
sigma <- 10.0275620167616                     # 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(2429778)
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 = 24 (80% power), 32 (90% power)
 75% of observed effect: n per arm = 42 (80% power), 56 (90% power)
 50% of observed effect: n per arm = 93 (80% power), 125 (90% power)
power.t.test: 24.2 
Simulated power at n = 24 per arm: 0.798 (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 6 outcome measures and names change in depressive symptoms and change in somatic symptoms as secondary outcomes. The primary outcome is change in anxiety symptoms. The posted results described for this analysis include the primary group means and an unadjusted comparison, but do not include estimates for the named secondary outcomes. Their results are therefore not reported in the registry record.

When a study examines multiple outcomes, time points, or contrasts, the chance of obtaining at least one apparently unusual result can increase. In general, multiplicity procedures can control error rates across a family of comparisons, but they may also affect the interpretation and precision of individual results. The unadjusted p-value of 0.009 is not described as adjusted for multiple testing. Whether any multiplicity strategy was prespecified, applied, or considered is not reported in the registry record.

The registry identifies an intent-to-treat approach and maximum-likelihood linear mixed effects modeling for the primary outcome. It does not provide the number of participants with observed primary outcomes at each time point, the amount or pattern of missing data, or the specific assumptions used to handle missing observations. The method description alone is insufficient to determine whether all randomized participants contributed outcome data or how missingness may have affected the estimate.

In general, maximum-likelihood methods can use available observations under assumptions about the relationship between missingness and observed or unobserved data. These assumptions cannot be checked from the reported group means and standard errors. The registry record does not describe imputation, a complete-case analysis, sensitivity analyses for missing data, or reasons for missing measurements. The absence of these details from the record should not be taken as evidence that any particular approach was or was not used.

The record does not report a complete analysis plan, a detailed participant flow for outcome availability, or a model-based primary estimate with its inferential statistics. These gaps limit evaluation of multiplicity, missing-data handling, and adherence to any prespecified analysis. They do not change the arithmetic description of the posted unadjusted contrast, but they constrain how fully it can be interpreted as the trial’s primary model-based result.

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 0% reporting threshold.

The registry reports serious adverse events for participants at risk in both groups. For BREATHE, 20 were listed as at risk and 0 as affected by a serious adverse event. For Wait List, 20 were listed as at risk and 0 as affected. The recorded number of deaths was 0 in each arm.

These figures describe the serious adverse event entries reported in the registry. They do not establish that no other symptoms, burdens, or non-serious events occurred. The registry also lists 0 affected by other adverse events in each group, but the available information does not give event descriptions or further details about how adverse events were collected, defined, or monitored. No serious adverse event terms are listed.

A zero count in a study group means no affected participants were recorded for that category in the registry; it does not show that the underlying risk is zero. The study was small, and the record does not report additional follow-up or safety-monitoring details. These safety figures should therefore be read as a summary of reported events rather than as a definitive estimate of safety in broader populations.

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

The posted primary outcome summaries show a lower mean GAS score in BREATHE than in Wait List at the 8-week assessment. Because higher GAS scores indicate worse anxiety, the direction of the group means favors a lower symptom score in BREATHE. The unadjusted mean difference, defined as Wait List minus BREATHE, is 8.25 points, with a confidence interval from 2.035 to 14.47 and an unadjusted p-value of 0.009.

This result does not establish that every participant’s symptoms changed in the same way. Group means conceal individual variation, and the standard errors are not measures of the spread of individual scores. The estimate also does not explain whether any group difference reflects the intervention itself, differences in expectations or contact, or other influences. No masking was used, and the outcome is based on participant symptom ratings.

The result is limited to the stated measure and assessment time. It does not establish longer-term outcomes, changes in functioning, or results for the secondary outcomes named in the registry. The secondary outcome estimates are not reported in the registry record. Nor does this primary comparison establish effects in people outside the recorded population of adults aged 60 or older with anxiety disorders.

The registry describes a mixed effects model using maximum likelihood and intent-to-treat principles, but the posted contrast is unadjusted. The full model output, missing-data details, multiplicity approach, and original sample-size rationale are not reported. These omissions mean the summary-statistic contrast should not be treated as a complete substitute for a detailed report of the primary analysis.

In general, randomized comparisons can help estimate differences between assigned groups, but interpretation also depends on trial conduct, outcome measurement, missing data, and analysis choices. The available record supports describing the observed direction and size of the posted contrast with its uncertainty. It does not justify a medical recommendation or a conclusion that the program will have the same results for other people or settings.

16. Why This Trial Matters Statistically

This trial illustrates several important statistical distinctions. First, an outcome’s direction matters: higher GAS scores indicate worse anxiety, so a lower mean score is the direction associated with fewer reported symptoms on this scale. Stating the contrast order is equally important. The reported mean difference is Wait List minus BREATHE, making its positive value consistent with the higher wait-list mean.

Second, a group mean and its standard error answer different questions. Means describe average scores, while standard errors describe uncertainty in estimating those averages. They do not convey the full spread of individual outcomes. The reported confidence interval adds information about uncertainty in the unadjusted contrast, but its confidence level and model basis are not stated in the registry record.

Third, the analysis description and the posted contrast should not be conflated. The registry describes a maximum-likelihood mixed effects model using intent-to-treat principles. The unadjusted comparison is a direct contrast of the posted summaries. Without the complete model specification and output, readers cannot verify whether or how the model-based result differs from that simple comparison.

Finally, a statistically small p-value is not a measure of clinical importance, and it does not resolve uncertainty about missing data, multiplicity, or generalizability. The outcome is a symptom scale at a defined assessment, while the registry also names other outcomes whose results are not reported. Recognizing these distinctions keeps the observed result informative without extending it beyond what the record documents.

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.

The record does not report the original sample-size justification, planned effect size, or the statistical assumptions used when the trial was designed. The planning estimates associated with the observed effect are illustrations and cannot establish whether the enrolled sample was adequate for the trial’s original aims.

The primary analysis is described as an intent-to-treat linear mixed effects model using maximum likelihood, but the model specification and model-based estimate are not reported. The available comparison is an unadjusted contrast from posted summary statistics. Missing outcome counts, reasons for missingness, the handling of missing observations, and sensitivity analyses are also not reported in the registry record.

The registry describes a randomized but unmasked study. Because participants knew whether they were receiving a behavioral program or waiting, expectations and attention could potentially influence self-reported symptoms. The record does not report whether outcome assessment involved any separate masking procedures. It also does not provide details about adherence, engagement with the DVD lessons, telephone check-ins, or home practice.

The primary measure is a self-reported anxiety scale assessed at 8 weeks. The record does not provide longer-term primary outcome results or detailed results for the named secondary outcomes. It therefore does not document whether the group pattern persisted or whether other symptom domains changed. Safety information is limited to the adverse-event entries reported in the registry; additional event-collection and monitoring details are not reported.

Finally, the enrollment and setting described in the record limit how broadly the result can be applied. The information available does not characterize participant demographics beyond the stated age and anxiety-disorder population, or describe the range of settings in which the program might be used. These limitations do not negate the posted comparison, but they bound what can be concluded from it.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Relaxation Treatment for Anxiety in Adults Aged 60 or Older — NCT02429778.
• Registry record last updated 2020-01-27; status last verified 2020-01.
• Results first posted 2020-01-27.
• 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

NCT02429778 is a completed randomized, unmasked, parallel-group study of self-directed relaxation for anxiety in adults aged 60 or older with anxiety disorders. The intervention, BREATHE, used DVD lessons, telephone check-ins, diaphragmatic breathing, and progressive muscle relaxation. The comparator was an 8-week wait list, after which participants could receive BREATHE if interested.

The primary outcome was change in Geriatric Anxiety Scale scores from baseline to 8 weeks. The posted means were 17.95 for BREATHE and 26.2 for Wait List. The unadjusted contrast, Wait List minus BREATHE, was 8.25, with a confidence interval from 2.035 to 14.47 and an unadjusted p-value of 0.009. Higher scale scores indicate worse anxiety.

The registry describes an intent-to-treat linear mixed effects analysis using maximum likelihood, but does not report its full specification or model-based output. Secondary outcome results, missing-data details, and the original sample-size rationale are not reported in the registry record.