Peer Support for Exercise in Older Veterans With Psychotic Disorders: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Peer Support for Exercise in Older Veterans With Psychotic Disorders (NCT02958007), a randomized na study. The primary outcome is Attendance.

2. Clinical Question

This is a comparison of two behavioral interventions, not a comparison with no intervention. Both arm descriptions include promotion of supervised fitness training and general physical activity; the distinguishing features described in the record are peer coaching in one arm and individual support from non-peer staff in the other. The posted outcome addresses attendance, rather than directly measuring exercise intensity, general physical activity, physical fitness, or functional independence. Those broader topics appear in the study summary, but the primary result is session attendance.

3. Trial Design

The registry classifies the study as randomized, single-masked, and parallel. The record does not identify who was masked, so the masking label alone does not establish whether participants, staff, outcome assessors, or another group were unaware of assignment. The phase is listed as NA. The study status is completed, with a listed enrollment of 22.

The two behavioral arms were Peer Education on Exercise for Recovery and Enhanced Supervised Fitness Training. Each intervention is described as lasting 24 weeks. The peer arm used group-based coaching delivered by a VA Peer Specialist; the comparator used individual support from non-peer staff. Both descriptions refer to promoting participation in supervised fitness training and general physical activity. The primary outcome, however, is specified at 12 weeks, so it is an assessment before the stated end of the 24-week interventions.

The primary measure is a continuous outcome: the mean number of supervised fitness sessions attended. The registry reports 11 participants in each arm for this outcome. The peer-coaching arm had a posted mean of 11.8 sessions and a standard deviation of 10.6; the enhanced-training arm had a mean of 9.5 and a standard deviation of 7.1. These are descriptive summaries for the outcome, not a complete account of participant flow or missing observations.

The listed study start is 2018-06-01, and primary completion is listed as 2021-11-30. The registry record does not report the trial's original sample-size justification, detailed allocation procedures, or a fuller protocol description. It also does not report an analysis-population definition or explain how participants with incomplete attendance data were handled. Those omissions limit what can be concluded about the design and analysis beyond the recorded classifications and results.

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

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 Attendance, measured over 12 weeks.

The primary endpoint is attendance, defined in the registry as the mean number of supervised fitness training sessions attended. It is measured in sessions, with the primary timeframe listed as 12 weeks. The posted means describe average attendance in each randomized arm, while the standard deviations describe the spread of individual attendance values around each arm's mean.

Attendance is a direct measure of participation in the supervised training activity that both interventions sought to encourage. It can therefore address whether participants attended sessions, but it does not by itself show how much physical activity they completed outside supervised sessions or whether their physical fitness, function, or health changed. The study summary mentions exercise, physical activity, and physical fitness or function as interests of the pilot, but the primary result is attendance.

The mean is useful for comparing overall attendance between arms, but it can conceal substantial variation among participants. That matters in this result because the reported standard deviations are large relative to the arm means. An average difference should consequently be read alongside the confidence interval and the observed spread, rather than as a description of every participant's attendance. The registry record does not provide a distribution of individual values or additional detail on how attendance was captured.

7. Results Posted in the Registry

• Enhanced Supervised Fitness Training: mean 9.50 versus 11.80 on control; difference -2.30 (95% CI -9.84 to 5.24), standardized effect d = -0.25; z-test p = 0.550.

8. Statistical Interpretation

9. Statistical Methods Explained

Attendance is a continuous outcome, reported as a mean and standard deviation for each arm. A mean gives the arithmetic average of the recorded session counts. A standard deviation describes how dispersed those counts are around the mean; it is not a confidence interval for the mean and does not describe the range of all observed values. Large spread can make a comparison less precise, particularly when the group sizes are modest.

What does the mean difference represent?

The unadjusted recalculation compares the enhanced-training arm with the peer-coaching arm by subtracting the peer-arm mean from the comparator mean. The estimate is -2.3 sessions, based on means of 9.5 and 11.8. The negative sign follows from that comparison direction: the observed comparator mean was lower. It is an unadjusted summary contrast, not an estimate adjusted for baseline characteristics or other covariates. The registry record does not report an adjusted analysis for this endpoint.

A mean difference compresses the arm summaries into a single contrast. It is useful for expressing the direction and size of the observed average difference in the outcome's original units, sessions. It does not imply that every participant in one arm attended fewer sessions than every participant in the other. Nor does it convey the full shape of the attendance distributions. The standard deviations are important context because they indicate broad variation around each mean.

What does the t-test assess?

The registry reports a 2-sided t-test for the comparison. In general, a 2-sided test assesses departures in either direction from a null hypothesis of no mean difference. It uses the observed contrast relative to its estimated sampling uncertainty to produce a p-value. A 2-sided test does not assume that only a lower or only a higher attendance value would be relevant. The registry record does not report further details about the test implementation, such as any adjustment for covariates or a specific variance assumption.

The recalculated p-value is 0.55, while the registry's own reported test gives 0.544. A p-value is not a measure of effect size and is not the probability that the null hypothesis is true. It is interpreted under the assumptions of the test and the null model. It should be considered together with the estimated mean difference, its confidence interval, the spread of attendance, and the small amount of outcome data in each arm.

Why does variability matter?

Variation among participants affects how clearly a trial can distinguish an average difference from random fluctuation. When observations vary widely, the same average contrast is generally estimated less precisely than it would be with less variation, all else being equal. In this comparison, the standard deviations are 10.6 and 7.1 sessions. Those values describe meaningful dispersion around the means, but they do not reveal why participants differed or whether the distributions were symmetric, skewed, or affected by unusually high or low attendance.

The trial's outcome groups each contain 11 participants. Estimates based on small groups can be sensitive to individual observations, and uncertainty may remain substantial even when an observed mean difference appears notable. This is a general statistical consideration, not evidence that any specific observation drove this result; individual-level attendance values are not reported in the registry record.

What is and is not established by the analysis?

The reported statistics concern the mean attendance comparison at 12 weeks. The registry record lists one analysis and three outcome measures overall, but does not report secondary outcome results in the posted results. It does not describe a statistical analysis plan, a missing-data method, an intention-to-treat definition, or sensitivity analyses. Consequently, it is not possible to determine from the record whether the reported attendance comparison accounts for missing outcome information or whether analysis choices were prespecified.

The sample-size planning figures use the observed effect and stated planning assumptions. They are illustrations of how group size could relate to the ability to detect effects of selected sizes in a future design, not a description of the original trial's design rationale. The original design assumptions are not reported in the registry record. General statistical methods explain how uncertainty and power relate, but they cannot fill in those missing design details.

Finally, a pilot comparison can provide estimates that help characterize attendance and its variability, while still leaving the effect uncertain. The size and precision of the estimate matter more than a binary reading of a p-value. Here, the interval extends across both directions of effect, and the record offers no stated threshold for a meaningful difference. The appropriate interpretation is therefore descriptive and cautious: the observed means differed, but the posted data do not precisely establish the direction or magnitude of the underlying average difference.

10. Confidence Intervals and Precision

The confidence interval for the recalculated mean difference extends from -9.839 to 5.239 sessions. It is centered around the estimated difference of -2.3 sessions but allows a broad range of plausible values under the calculation's assumptions. Values below zero correspond to lower mean attendance in the comparator under the stated subtraction direction; values above zero correspond to higher mean attendance in the comparator. Because the interval spans both directions, the data do not pin down which arm had the higher underlying average.

A confidence interval communicates uncertainty about an estimated effect, rather than the spread of individual participants' attendance. The standard deviations of 10.6 and 7.1 sessions describe individual-level dispersion within arms, whereas the interval describes uncertainty in the arm-to-arm mean difference. These two kinds of variability are related but answer different questions.

The registry record does not report the confidence level attached to the recalculated interval, so no confidence percentage should be inferred from the record. The interval also depends on the method and assumptions used for the unadjusted recalculation. It should not be mistaken for a range containing every participant's attendance or as a guarantee about a future study's result.

The width of the interval reflects the limited precision of this comparison. With 11 participants per arm and substantial observed variability, a range of mean differences remains compatible with the data. The interval is more informative than the point estimate alone because it makes that uncertainty explicit. It does not establish that all values in the interval are equally likely, and the posted record does not supply enough detail to interpret the interval as an adjusted or protocol-specified 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 are participants per arm for 80% power and participants per arm for 90% power. They are not total event counts: the outcome is continuous, and the planning assumption specifies equal allocation between the two arms. The figures are based on the observed effect, with illustrations for detecting 100% of that effect, 75% of the observed effect, and 50% of the observed effect. For each effect size, the 90% power column gives a larger planned group size than the 80% power column.

In general, power is the chance that a study will detect an effect of the specified size under the planning assumptions if that effect is present. The 80% and 90% columns therefore describe different design targets, not results from the completed trial. Smaller effects are harder to distinguish from random variation, so the planning figures rise as the targeted fraction of the observed effect becomes smaller. The listed assumptions are a 2-sided significance level of 0.05, equal allocation, and a normal approximation; the effect to detect is the stated fraction of the observed effect.

The sample-size calculations are planning illustrations computed from the observed effect, not the trial's own design rationale. The original design assumptions are not reported in the registry record. These values are not observed power. They should be read as conditional projections under the listed assumptions, not as a measure of what the completed trial achieved or as evidence that a particular future study would have a guaranteed result. A planning curve likewise relates assumed effect size and planned group size; it does not add new observed evidence about attendance.

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 = -2.300; pooled standard deviation σ = 9.021.
2. n = 2 × (1.96 + 0.842)² × 9.021² / -2.300² = 241.5, rounded up to 242 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 <- -2.3                      # observed difference in means
sigma <- 9.02136353330249                     # 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(2958007)
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 = 242 (80% power), 324 (90% power)
 75% of observed effect: n per arm = 430 (80% power), 575 (90% power)
 50% of observed effect: n per arm = 967 (80% power), 1,294 (90% power)
power.t.test: 242.5 
Simulated power at n = 242 per arm: 0.802 (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's own analysis is a 2-sided t-test and reports p = 0.544 for the comparison. The posted unadjusted recalculation gives a mean difference of -2.3 sessions, a confidence interval from -9.839 to 5.239, and p = 0.55. The recalculated contrast is derived from the posted arm means and is not an adjusted estimate. The registry record marks no discrepancy between the trial's reported analysis and the recalculation.

The sponsor's analysis is the trial's own reported inferential result and should take precedence as the account of the analysis conducted for the study. The recalculation provides a simple, unadjusted comparison from the posted summary statistics, useful for interpreting the direction and approximate scale of the difference. Its close p-value does not establish that all analytic details were identical; the registry record does not report enough detail to verify the full calculation or analysis plan.

Neither p-value should be interpreted in isolation. The arm means, substantial standard deviations, confidence interval, and small group sizes all matter when judging precision. The sponsor-reported test does not provide a posted mean-difference estimate or confidence interval, so the numerical effect estimate and interval discussed in the interpretation are from the unadjusted recalculation.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists three outcome measures and one analysis, while the posted primary result concerns attendance. The registry record does not report results for secondary outcomes in the posted analysis information. It also does not report whether the primary outcome was designated before analysis in a protocol or statistical analysis plan, or whether any adjustment was planned for testing multiple outcomes. Multiplicity procedures and prespecification therefore cannot be assessed from this record.

When researchers examine multiple outcomes or comparisons, the chance of obtaining an apparently unusual result by chance can change. In general, multiplicity methods may be used to control that issue, but no such method should be presumed. The reported p-value should be interpreted as the result of the listed comparison, not as an account of a family of tests whose structure and handling are undocumented.

Missing-data handling is also not reported in the registry record. The outcome summaries list 11 participants in each arm, but the record does not explain whether these are all randomized participants, all participants with available attendance records, or another analysis population. It does not state whether participants with incomplete observations were excluded, imputed, or handled by another method. The posted group counts alone cannot establish the completeness of follow-up or the treatment of missing sessions.

The analysis-population definition is not reported in the registry record. There is no stated intention-to-treat, per-protocol, or other population description for the attendance analysis. The record also does not describe adherence-based exclusions, protocol deviations, or sensitivity analyses. These omissions make it difficult to evaluate whether the analysis retained participants according to random assignment or how robust the finding might be to alternative assumptions.

These are reporting limitations, not evidence that a particular method was or was not used. Without the protocol, analysis plan, and fuller participant accounting, readers cannot determine whether decisions about outcomes, missing data, or analysis populations were made in advance or how they might affect the estimate. The result should therefore be interpreted as the comparison reported in the registry, with these analysis details unresolved.

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 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: acute hypoxic respiratory failure- unrelated to study (9.1%).

The registry reports serious adverse events in the peer-coaching arm for 0 of 11 participants and in the enhanced-training arm for 1 of 11 participants. It reports other adverse events for 4 of 11 participants in each arm. Deaths are reported as 0 in both arms. These are counts in the registry's safety record and should be read separately from the primary attendance outcome.

The record lists Acute hypoxic respiratory failure- unrelated to study as a serious adverse event term and gives 9.1%. The term itself is explicitly labeled unrelated to study in the registry. The record does not provide a fuller narrative or additional details about timing, severity assessment, or the basis for that relationship assessment, so none should be inferred.

These figures describe events recorded in this trial; they are not, by themselves, a comparative safety analysis. The small groups and the limited information in the registry make the counts imprecise as a basis for comparing event risks. The difference in serious-event counts does not establish a causal effect, and equal counts of other adverse events do not establish equivalence. The record does not report additional safety analyses or detailed event listings beyond the stated information.

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

The posted attendance summaries show a mean of 11.8 supervised fitness sessions in the peer-coaching arm and 9.5 in the enhanced-training arm at 12 weeks. The unadjusted recalculated mean difference is -2.3 sessions when expressed as comparator minus peer arm. Its confidence interval, from -9.839 to 5.239, is broad and includes values in both directions. The registry's own 2-sided test reports p = 0.544, while the unadjusted recalculation gives p = 0.55.

Taken together, these statistics describe a difference in observed average attendance but leave substantial uncertainty about the underlying difference. The result does not establish that either intervention produced higher attendance, nor does it establish that the interventions had the same attendance. The record does not state a minimum difference that would be considered practically important, so the importance of the estimate cannot be judged against a prespecified benchmark.

The scope of the finding is narrow. Attendance at supervised sessions is not interchangeable with overall physical activity, fitness, physical function, or health. The study summary identifies these broader areas as interests, but the primary result is an attendance measure. No conclusion about those outcomes follows from the attendance comparison alone.

The study was a randomized pilot with 11 participants per arm in the primary outcome summary. The estimates can be informative about the observed means and variability, but their precision is limited. The registry record does not report detailed missing-data methods, analysis populations, or a prespecified threshold for meaningful change. Those gaps further limit interpretation of the posted result.

The findings are neither proof of benefit nor proof of no difference. They are a small, imprecise comparison of attendance between two active behavioral interventions. Any broader claim about acceptability, feasibility, effectiveness, or clinical outcomes would require evidence beyond this primary result.

17. Why This Trial Matters Statistically

This trial matters statistically because it illustrates how a modest pilot comparison can produce an interpretable estimate while leaving considerable uncertainty. The arm means offer a straightforward description of attendance, but the standard deviations show substantial variation, and the confidence interval spans effects in both directions. Reading the point estimate without that context would overstate what the data can resolve.

It also highlights the distinction between a p-value and an effect estimate. The registry's test gives p = 0.544, and the unadjusted recalculation gives p = 0.55, but neither value conveys the session-scale magnitude or the broad range of uncertainty. The estimate and interval are necessary for understanding what differences remain compatible with the observed data.

Planning illustrations can help researchers see how assumptions about the effect to detect, allocation, and power affect a future study's required group size. They are not evidence that the original study was designed around those assumptions, and they are not a retrospective measure of trial success. The registry record does not report the original sample-size rationale, so the planning figures should be kept separate from the completed trial's design history.

Finally, the endpoint directs attention to an important statistical distinction: an outcome can measure a behavioral step, such as attendance, without answering every question about activity, fitness, function, or feasibility. Clear interpretation depends on staying close to what was measured and acknowledging the unanswered analysis and reporting questions.

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.

The comparison is based on a small number of participants in each arm, with 11 reported for the primary outcome per arm. The attendance standard deviations are substantial, and the confidence interval is broad. As a result, the estimated mean difference is imprecise and should not be treated as a stable estimate of the contrast in a larger population.

The primary outcome captures supervised-session attendance at 12 weeks. It does not directly measure activity outside the sessions, physical fitness, or function. The intervention descriptions last 24 weeks, but the primary attendance timeframe is 12 weeks; the registry record does not explain whether another attendance assessment was planned or how the timing was selected.

The registry record does not report participant characteristics in detail, eligibility criteria beyond the target population description, or the full recruitment and retention process. It also does not report who was masked, the allocation procedure, a statistical analysis plan, or the original sample-size rationale. Missing-data methods and analysis-population definitions are not reported, limiting assessment of possible bias and analytic robustness.

The posted result is one comparison and does not include reported secondary-outcome results in the analysis information. The record does not explain multiplicity handling or provide a stated threshold for a practically meaningful attendance difference. Those gaps make it difficult to place the estimate against broader study objectives or to evaluate whether all relevant planned outcomes are available.

As a pilot study, the findings are best treated as preliminary descriptive evidence. They do not settle the broader questions about acceptability, feasibility, exercise, or physical fitness and function raised in the study summary. These limitations qualify interpretation of the posted result without implying that a different result would necessarily follow from a larger or differently analyzed study.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Peer Support for Exercise in Older Veterans With Psychotic Disorders — NCT02958007.
• Registry record last updated 2023-09-25; status last verified 2022-11.
• Results first posted 2023-09-25.
• 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

NCT02958007 is a completed randomized, single-masked, parallel study titled Peer Support for Exercise in Older Veterans With Psychotic Disorders. The listed enrollment is 22. The two behavioral arms were Peer Education on Exercise for Recovery and Enhanced Supervised Fitness Training, each described as a 24-week intervention. The registry lists 2018-06-01 as the study start and 2021-11-30 as primary completion.

The primary outcome was mean attendance at supervised fitness training sessions at 12 weeks. The peer-coaching arm had a mean of 11.8 sessions and a standard deviation of 10.6; the enhanced-training arm had a mean of 9.5 and a standard deviation of 7.1, with 11 participants reported per arm. The registry's 2-sided t-test reports p = 0.544. An unadjusted recalculation gives a mean difference of -2.3 sessions, with a confidence interval from -9.839 to 5.239 and p = 0.55.

The estimate is uncertain and addresses attendance rather than broader physical activity, fitness, or function. The record does not report the original sample-size rationale, missing-data method, or analysis-population definition.