Physical Activity and Participation: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Physical Activity and Participation (NCT02268916), a randomized na study. The primary outcome is Physical Activity.

2. Clinical Question

3. Trial Design

The registry record describes a randomized, parallel-group trial with single masking. It lists the study as completed and reports enrollment of 104 participants. The start date was 2015-06-01, and the primary completion date was 2019-12-31. The study was sponsored by the VA Office of Research and Development. Its listed phase is NA.

The comparison was between occupational-therapy-led counseling based on home activity patterns and a wait-listed condition. Participants assigned to the wait-listed condition were to continue their usual activity during the study and receive the counseling at the end. The registry lists both counseling and usual education as behavioral interventions; the arm descriptions give the details of the counseling and wait-list arrangements.

The primary outcome analysis included only participants who completed the home monitoring activities. The reported outcome summaries contain 35 participants in the intervention arm and 42 in the wait-listed arm. The registry does not report why participants were excluded from this analysis or whether those without completed monitoring differed from those analyzed. The identity of the person or people masked, and how masking was maintained, are not reported in the registry record.

The record lists five outcome measures and seven analyses. It reports one mixed-model analysis for the primary comparison, described as a mean difference in final values. Detailed randomization procedures, allocation concealment, protocol deviations, and the original statistical analysis plan are not reported in the registry record. The record also does not describe the intended sample-size calculation or its assumptions. Those absences limit how fully the trial’s conduct and analysis choices can be assessed from the registry entry.

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: Only participants who completed the home monitoring activities were included in the outcomes analysis.

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: One participant was identified to not have diabetes diagnosis after consent, therefore, no baseline data collected on this participant and s/he was not included in further analysis.

6. Primary Endpoint

The registry lists the primary outcome as Physical Activity, measured over 6 months.

The primary endpoint is change in home physical activity from baseline to 6 months, expressed as a mean in KCal/week. The measure was based on CHAMPS, a validated survey that asks participants to report activities undertaken in a typical week, including examples such as walking, house work, and dancing. The endpoint therefore reflects reported activity rather than a direct count of all movement or an instrument-based activity measure.

Assessing change from baseline focuses the outcome on how reported weekly activity shifted over the study period. Comparing the groups’ changes is intended to distinguish the activity pattern observed in the counseling group from the pattern observed in the wait-listed group during the same period. The registry states that only participants who completed home monitoring activities were included in the outcomes analysis, so the reported endpoint summaries apply to that analysis population.

The registry record does not specify the precise calculation used to form each participant’s change score, such as how multiple survey responses were combined, or how incomplete survey items were handled. It also does not report a clinically meaningful threshold for interpreting a change in KCal/week. The endpoint describes an activity measure; by itself, it does not establish a change in social participation or any other outcome.

7. Results Posted in the Registry

• Wait-listed: mean -263.81 versus 401.88 on control; difference -665.69 (95% CI -2,526 to 1,194), standardized effect d = -0.16; z-test p = 0.483.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is continuous: it is summarized as a mean, with standard deviations describing the spread of participant-level observations. The recalculation uses the two arm means and their reported sample sizes to estimate an unadjusted difference in mean change. In plain terms, it subtracts the intervention mean from the wait-listed mean. A negative estimate therefore indicates a lower reported mean change in the wait-listed arm than in the intervention arm, under that direction of subtraction.

The standard deviation describes how dispersed individual values are around an arm’s mean. It is not the same as the uncertainty in the mean itself. The reported standard deviations are large relative to the arm means, which signals substantial variation in observed activity changes among analyzed participants. Such variability can make a group-average comparison imprecise even when the mean difference can be calculated. Variation in reported activity may reflect genuine differences in participant behavior as well as the measurement properties of a self-reported survey; the registry does not quantify the sources of that variation.

The recalculated standard error reflects uncertainty in the estimated difference in means, given the sample sizes and the observed variation. The arm-level standard errors are 660.8 for the intervention group and 681.2 for the wait-listed group. The recalculated difference has a 95% confidence interval from -2526.0 to 1194.0. A confidence interval gives a range of effect values compatible with the observed data under the calculation’s assumptions. It is not a range containing a known proportion of individual participants’ changes, nor does it assign a probability that the true effect lies in the particular calculated interval.

The unadjusted p-value is 0.483. A p-value describes how unusual data at least as incompatible with the zero-difference null would be under that null and the statistical model used for the calculation. It does not measure the probability that the null is true, the size or importance of the difference, or the probability that a future trial will reproduce the same result. Because this is an unadjusted recalculation, the p-value does not account for any covariates, repeated measurements, or other modeling choices that may be part of the sponsor’s analysis.

The registry’s reported analysis is a mixed-model analysis of mean difference in final values. Mixed models can account for structured measurements or grouping when the model specifies those structures. However, the registry record does not report the model formula, included covariates, correlation structure, estimation method, or handling of missing observations. Those details cannot be inferred from the label “Mixed Models Analysis.” The posted value is 0.39, with a 95% confidence interval from -0.18 to 0.97 and p = 0.18. Since the endpoint is described as a change from baseline but the reported model parameter is described as a difference in final values, the estimands are not presented in the same way. The scale of the model estimate is not reported in the registry record.

Over-dispersion is a general concern when observed variation is larger than a model’s assumptions allow. In such cases, standard errors may be understated if the analysis does not account for the extra variation. The posted summaries show substantial spread in the activity measure, but the registry record does not report an over-dispersion assessment or a specific variance model. It is therefore not possible to say whether this issue affected the sponsor’s model or the recalculation.

The randomized parallel design aims to compare groups assigned to different study conditions. Randomization can help balance baseline characteristics on average, but the registry does not give enough detail to assess the randomization sequence, concealment, or balance on specific characteristics. Single masking is recorded, but the masked party is not identified. The registry record does not report protocol deviations, a pre-specified analysis plan, interim analyses, or a multiplicity adjustment. These omissions do not establish that such procedures were absent; they mean that they cannot be evaluated from this record.

All of these analyses are comparisons of group summaries or model estimates, not individual treatment effects. The recalculation is specifically an unadjusted comparison based on the posted summary statistics. It should be distinguished from the sponsor’s mixed-model analysis and from any unreported analyses. The registry record does not state whether the reported model result was adjusted for baseline values or other prognostic variables. It also does not provide enough information to reconstruct that model independently.

10. Confidence Intervals and Precision

Precision is reflected in the width of a confidence interval: narrower intervals indicate less uncertainty about the estimated group difference, while wider intervals leave more plausible values compatible with the data. The recalculated difference in mean change is -665.7 KCal/week, and its 95% confidence interval extends from -2526.0 to 1194.0. Because that interval includes zero and includes values on both sides of zero, it does not pin down the direction of the difference. Its range also leaves considerable uncertainty about the magnitude.

The interval should be interpreted for the specific unadjusted comparison of change-score summaries and the analyzed participants. It does not represent uncertainty about every possible outcome, population, or analysis method. The reported standard deviations, 3910.0 in the intervention arm and 4415.0 in the wait-listed arm, indicate substantial spread in observed changes. In general, more variability reduces the precision of a mean comparison when the number of analyzed participants is limited.

The sponsor-reported mixed-model estimate has a 95% confidence interval from -0.18 to 0.97. It is a separate analysis of final values, and its units or scale are not stated in the registry record. Its interval also includes zero. Because the model estimate and recalculated change-score estimate are not described on the same scale or as the same estimand, their interval widths should not be compared as if they measured precision for an identical quantity.

Confidence intervals do not remove uncertainty about the analysis population, missing data, measurement, or model specification. The registry record does not report enough information to assess how those issues affect precision. The intervals quantify uncertainty under their respective calculations, not every source of uncertainty relevant to interpretation.

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 illustrations based on the observed effect, not the original trial design. The registry record does not report the trial’s own sample-size justification or original design assumptions. For this illustration, the stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to a stated fraction of the observed effect. The figures are participants per arm, not total participants or total events.

The 80% power column describes the number of participants per arm in a hypothetical study that would have an 80% chance of detecting the specified effect under the stated assumptions, if that effect were the true one. The 90% power column gives the corresponding planning target for a 90% chance. These are planning concepts, not guarantees that a study of that size will produce a statistically significant result.

For the full observed effect, the illustration lists 623 participants per arm for 80% power and 834 participants per arm for 90% power. For planning for 75% of the observed effect, the corresponding figures are 1,108 and 1,483 participants per arm. For planning for 50% of the observed effect, they are 2,492 and 3,336 participants per arm. Smaller effects are harder to distinguish from random variation, so detecting them at the same power generally requires more participants. In this illustration, the required numbers rise as the effect used for planning becomes smaller.

This is not observed power. It is a forward-looking planning illustration derived from the observed effect, and it should not be read as evidence that the completed trial had a particular probability of success. The record does not establish that these assumptions were used to design the trial.

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 = -665.690; pooled standard deviation σ = 4193.315.
2. n = 2 × (1.96 + 0.842)² × 4193.315² / -665.690² = 622.9, rounded up to 623 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 <- -665.69                      # observed difference in means
sigma <- 4193.31467206791                     # 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(2268916)
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 = 623 (80% power), 834 (90% power)
 75% of observed effect: n per arm = 1,108 (80% power), 1,483 (90% power)
 50% of observed effect: n per arm = 2,492 (80% power), 3,336 (90% power)
power.t.test: 623.8 
Simulated power at n = 623 per arm: 0.800 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

13. Analyses Reported by the Sponsor

The registry reports a sponsor analysis using a mixed model, with the parameter described as a mean difference in final values. The reported estimate is 0.39, with a 95% confidence interval from -0.18 to 0.97 and p = 0.18. The registry does not report the scale or units for this estimate, nor does it give sufficient model details to reproduce the analysis.

The unadjusted recalculation instead uses the posted arm summaries for change from baseline to 6 months. It estimates a wait-listed-minus-intervention mean difference of -665.7 KCal/week, with a 95% confidence interval from -2526.0 to 1194.0 and an unadjusted p-value of 0.483. Because the sponsor analysis is described as comparing final values while the recalculation compares changes, they address different stated quantities. The registry also does not provide the model details needed to determine precisely how the two analyses relate.

Both reported intervals include zero, but that shared feature does not make the analyses interchangeable. The sponsor’s result should be read as the registry’s reported mixed-model result; the recalculation is a transparent, unadjusted analysis of the posted summaries, not a replacement for the sponsor’s model. The record does not flag a discrepancy between the analyses.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists five outcome measures and seven analyses. It does not report whether the primary outcome and analysis were designated in a protocol or statistical analysis plan before the results were examined. Nor does it report a multiplicity strategy, such as how the chance of false-positive findings across multiple outcomes or analyses was addressed. The existence of several listed outcomes and analyses makes it important to know whether the primary comparison was pre-specified and whether other comparisons were exploratory, but the record does not establish those details.

The registry says that only participants who completed home monitoring activities were included in the outcomes analysis. It does not report how many randomized participants did not complete monitoring, why they were not included, or whether missing observations were imputed. The approach to incomplete survey responses, missing baseline measurements, and other missing data is not reported in the registry record. It is also not stated whether participants were analyzed according to their randomized assignment or whether the outcome analysis used another population definition.

These details matter because excluding participants with unavailable outcomes can affect the interpretation of a group comparison if outcome availability is related to activity levels, group assignment, or other participant characteristics. This is a general statistical concern, not evidence that such bias occurred in this trial. The registry record does not report sensitivity analyses to evaluate the effects of missing outcomes.

The model’s covariate adjustment and assumptions are not reported, and the identity of the party masked is not reported. The record also does not report interim analyses or any adjustment associated with them. These unreported elements prevent a complete assessment of the inferential plan. Their absence from the registry entry should not be treated as proof that no such procedures were used.

15. Safety Results

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

Deaths

Other (non-serious) adverse events

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

Most frequent non-serious adverse event terms

The registry reports serious adverse event counts of 0 in the intervention group and 0 in each of the two wait-listed categories: wait-listed without occupational-therapy-led counseling and wait-listed with occupational-therapy-led counseling. The number at risk is listed as 52 for each category. No serious adverse event terms are listed.

These counts describe the registry’s reported serious adverse events for the named groups; they do not by themselves establish that no serious events occurred outside the reported monitoring or reporting period. The registry record does not describe the serious-event definition, collection procedures, follow-up period, or how the two wait-listed categories relate to the primary randomized comparison. The primary outcome arm summaries use an intervention and a wait-listed group, whereas the safety record distinguishes wait-listed participants with and without counseling.

The record also lists other adverse event counts of 2 for the intervention group, 0 for the wait-listed group without counseling, and 1 for the wait-listed group with counseling. Deaths are reported as 0 in all three categories. These figures are event counts in the registry record and should be interpreted in the context of the stated group definitions; they are not evidence on their own about comparative safety.

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

The primary outcome results quantify mean change in a self-reported measure of home physical activity from baseline to 6 months among participants included in the outcomes analysis. The unadjusted recalculation gives a mean difference of -665.7 KCal/week for wait-listed minus intervention, with a 95% confidence interval from -2526.0 to 1194.0. The interval includes zero and spans values in either direction, so the estimate is not precise enough to determine the direction or size of the group difference from this comparison alone.

The sponsor-reported mixed-model result is a different analysis, described as a comparison of final values. Its estimate is 0.39, with a 95% confidence interval from -0.18 to 0.97 and p = 0.18. The registry does not report the scale of this estimate or enough model detail to connect it directly to the change-score recalculation. Both results should be understood with their stated analytic descriptions rather than treated as duplicate estimates.

The study’s brief purpose mentions improving both physical activity and social participation among veterans with diabetes, but the primary result concerns physical activity. A result for social participation is not reported in the registry record. The outcome is based on participant reports of a typical week and should not be interpreted as a direct measurement of every activity undertaken.

The results do not establish that counseling does or does not change physical activity, and they do not establish equivalence between the groups. The uncertainty interval allows for a range of differences, including values on either side of no difference. The result also cannot be generalized automatically beyond the participants included in the analysis. Information about the analyzed population is limited to the requirement that participants completed home monitoring activities.

These findings are statistical descriptions of the posted results, not medical advice. They do not address whether a particular person should undertake counseling, nor do they establish effects on health outcomes that were not reported as the primary endpoint. Interpretation should account for the uncertainty in the estimates and the unreported analysis details.

17. Why This Trial Matters Statistically

This trial illustrates why the definition of an endpoint matters. The primary measure is change in reported weekly home activity, whereas the registry’s sponsor analysis is described as a difference in final values. Statistical estimates cannot be compared as if they answer the same question unless their estimands, scales, and modeling choices are understood. The registry record gives only limited detail about the mixed model, so the unadjusted recalculation and sponsor result need to remain distinct.

The result also demonstrates how substantial variability can limit precision. The arm means differ in the posted summaries, but the recalculated confidence interval is broad and spans zero. Looking only at the point estimate would give an incomplete account of the evidence; the interval communicates how uncertain the estimated difference is. A non-significant p-value is not proof of no effect or equivalence.

Analysis population and outcome completion are also central. The outcomes analysis included only participants who completed home monitoring, yet the record does not explain missing outcome data or the reasons participants were excluded. That information is needed to assess how well the analyzed group represents those randomized.

Finally, the planning illustration shows that sample-size targets depend on the effect a future study aims to detect. Smaller target effects require larger participant counts under the stated assumptions. These calculations are not evidence about the design of this completed trial; its original sample-size justification is not reported in the registry record. Together, these considerations show why an estimate, its precision, the analysis population, and the analysis plan all matter when interpreting a trial result.

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 primary outcome relies on a survey of typical weekly activity. Although the registry describes CHAMPS as validated, the record does not report survey administration details, validation characteristics in this study population, or how responses were converted into the reported change measure. Self-reported activity can be affected by recall and reporting, but the registry does not quantify such measurement error for this trial.

Only participants who completed home monitoring activities were included in the outcome analysis. The reasons for non-completion, the number of participants with unavailable outcomes, and the handling of incomplete responses are not reported in the registry record. Consequently, the extent to which the analyzed participants represent all randomized participants cannot be assessed from the entry.

The reported arm summaries are accompanied by substantial standard deviations, and the recalculated confidence interval is broad. This limits precision about the mean difference. The sponsor’s reported mixed-model analysis is not fully reproducible from the available description: the model specification, covariates, scale, and missing-data approach are not reported. Its estimate is described as a difference in final values, while the primary endpoint description concerns change from baseline.

The registry identifies single masking but does not say who was masked or how masking was implemented. It does not report allocation concealment, detailed baseline characteristics, protocol deviations, or a pre-specified analysis plan. The study purpose mentions social participation, but a posted result for that outcome is not included among the primary outcome results described. These limitations concern what can be evaluated from the registry record; they do not establish that unreported procedures were absent.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Physical Activity and Participation — NCT02268916.
• Registry record last updated 2022-09-19; status last verified 2022-09.
• Results first posted 2022-09-19.
• 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

NCT02268916, titled “Physical Activity and Participation,” is a completed randomized, parallel-group study of occupational-therapy-led counseling based on home activity patterns compared with a wait-listed condition among veterans with type 2 diabetes mellitus. The registry reports enrollment of 104 participants and single masking.

The primary endpoint was mean change in home physical activity from baseline to 6 months, measured in KCal/week using the CHAMPS survey. Only participants completing home monitoring activities were included in the outcomes analysis. The unadjusted recalculation estimates a wait-listed-minus-intervention mean difference of -665.7 KCal/week, with a 95% confidence interval from -2526.0 to 1194.0 and an unadjusted p-value of 0.483. The registry also reports a mixed-model final-values analysis with an estimate of 0.39, a 95% confidence interval from -0.18 to 0.97, and p = 0.18.

The registry record does not report the original sample-size justification, detailed model specification, missing-data approach, or multiplicity plan.