Nutrition and Aerobic Exercise in Chronic Stroke: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Nutrition and Aerobic Exercise in Chronic Stroke (NCT02043574), a randomized na study. The primary outcome is The Change in Total Daily Energy Expenditure.

2. Clinical Question

3. Trial Design

The registry describes a randomized, parallel-group trial with no masking. The two reported groups received six months of treadmill training or six months of stretching. The study was sponsored by the VA Office of Research and Development and is listed as completed. The recorded enrollment was 51. The registry lists the phase as NA.

The primary outcome was change in total daily energy expenditure, measured at baseline and following six months of treadmill training or stretching. The measure is expressed as change in kcal/day. The registry describes wearing an accelerometer activity monitor on the belt for 5 to 7 days to determine caloric expenditure in daily activities. The registry also lists change in substrate oxidation and change in circulating nitrotyrosine as secondary outcomes.

The posted primary outcome results report 19 participants in the stretching group and 20 in the treadmill exercise group. These group counts describe the participants represented in the posted outcome results; the registry does not explain the relationship between those counts and total enrollment. The registry record does not report further details about random-sequence generation, allocation concealment, eligibility criteria, or the original sample-size justification. It also does not report an analysis population definition or a statistical analysis plan. The record contains no reported analysis entries.

The study summary frames the research around dietary patterns, sedentary behavior, fuel use, physical function, and oxidative stress in chronic stroke. However, the listed interventions for the comparison are treadmill exercise and stretching. A dietary-modification arm or a factorial comparison is not listed in the posted results. The registry record does not report whether dietary modification was delivered as part of either reported group.

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 The Change in Total Daily Energy Expenditure, measured over measured at baseline and following 6 months of treadmill training or stretching (control).

The primary endpoint is change in total daily energy expenditure, reported in kcal/day. The registry describes measurements at baseline and following six months of treadmill training or stretching. Participants wore an accelerometer activity monitor on a belt for 5 to 7 days to estimate caloric expenditure during daily activities.

This endpoint addresses the study's stated interest in energy utilization and everyday activity. It focuses on energy expenditure during daily activities rather than reporting a measure of exercise capacity alone. Comparing the groups' mean changes therefore describes how the recorded daily energy-expenditure measure changed over the study period in each group, and how those mean changes differed.

The endpoint is a continuous measure, and the posted group summaries use means and standard deviations. A mean describes the average change within a group; the standard deviation describes the spread of participant changes around that average. Neither quantity alone reveals the range of individual responses. The registry record does not report details such as the exact accelerometer-processing rules, the number of valid monitoring days required, or how measurements were handled when monitoring data were incomplete. The posted endpoint should consequently be interpreted as the recorded group-level change, not as a complete description of each participant's activity or energy use.

7. Results Posted in the Registry

• Treadmill Exercise: mean 32.86 versus -0.52 on control; difference 33.38 (95% CI 3.20 to 63.56), standardized effect d = 0.69; z-test p = 0.030.

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

The Change in Substrate Oxidation

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Treadmill Exercise: mean 0.08 versus 0.01 on control; difference 0.07 (95% CI 0.00 to 0.14), standardized effect d = 0.64; z-test p = 0.042.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically higher for Treadmill Exercise than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

The Change in Circulating Nitrotyrosine

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Treadmill Exercise: mean -36.50 versus -24.80 on control; difference -11.70 (95% CI -28.36 to 4.96), standardized effect d = -0.44; z-test p = 0.169.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Treadmill Exercise and the control. The interval gives the range of effects that remain compatible with the data.

The two secondary outcomes add information about measures related to the study's stated interest in energy use and oxidative stress. Across them, the posted estimates do not point in one uniform direction in terms of statistical certainty: one confidence interval lies on one side of zero, while the other spans zero. This mixed pattern means the secondary results do not offer a single, consistent statistical signal that simply duplicates the primary comparison.

These measures are related to the trial's broader scientific aims, but they are not substitutes for the primary endpoint. Change in substrate oxidation concerns fuel use, while circulating nitrotyrosine concerns a circulating marker. Total daily energy expenditure measures caloric expenditure in daily activities. A difference in one measure does not establish that another measure changed through the same process, and the registry record does not report a mechanistic analysis linking the outcomes.

Secondary findings generally carry less weight when many outcomes are assessed and no multiplicity adjustment or prespecified hierarchy is reported. Testing multiple outcomes creates more opportunities for apparently noteworthy results to arise by chance. The registry record lists two secondary outcomes but does not report how their interpretation was prioritized or whether any adjustment was planned. The secondary comparisons are explicitly unadjusted.

The secondary results are therefore best treated as additional descriptive evidence that can inform future questions, not as independent confirmation of the primary result. Their interpretation also depends on the precision of each estimate and on methods that are not described in the registry record, including missing-data handling and the analysis population. The record does not report analyses that combine the outcomes or assess whether changes in one measure explain changes in another.

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

• The Change in Substrate Oxidation
• The Change in Circulating Nitrotyrosine

9. Statistical Interpretation

10. Statistical Methods Explained

The posted outcomes are continuous measurements summarized using means and standard deviations. For a continuous outcome, a group mean is the arithmetic average of participant measurements. The standard deviation describes how dispersed those measurements are around the mean. Similar means can occur alongside different degrees of participant-to-participant variation; conversely, group means can differ while individual measurements overlap considerably.

The primary comparison is reported as a mean difference, with treadmill exercise compared against stretching. The estimate of 33.38 kcal/day expresses the difference between the groups' mean changes, in the direction defined by that comparison. It is not a change experienced by every participant, and it is not a relative percentage change. The same logic applies to the mean differences posted for the secondary outcomes, which use their own outcome units.

A confidence interval expresses uncertainty around an estimated difference under the statistical procedure used to form it. In general, a 95% confidence interval is a range produced by a method that, under its assumptions and repeated use, would cover the target parameter in 95% of such intervals. It is not a statement that there is a 95% probability that this particular fixed parameter lies inside the observed interval. A narrower interval indicates greater precision than a wider interval on the same scale. The registry record does not describe the precise procedure used to calculate these intervals.

A null difference for a mean-difference comparison is zero: zero represents equal group mean changes. When a confidence interval includes zero, the data and interval do not exclude that null value at the interval's stated confidence level. When the interval lies entirely on one side of zero, it indicates a range of differences on that side, subject to the method's assumptions. This is one way to read the primary and secondary estimates; it does not by itself determine clinical importance.

The posted p-values are identified as unadjusted. In general, a p-value measures how unusual data at least as incompatible with a specified null hypothesis would be under that hypothesis and the statistical model. It is not the probability that the null hypothesis is true, nor does it describe the size or practical importance of an effect. A p-value does not capture all uncertainty; the estimate and confidence interval give information about direction and plausible magnitude. The registry record does not report the full testing procedure used for these comparisons.

Over-dispersion is a general concern when the observed variability is greater than a model assumes. If variation is underestimated, standard errors can be too small and confidence intervals can be too narrow; if it is accounted for appropriately, uncertainty may be better represented. The posted summaries include standard deviations, but the registry record does not report a model-based assessment of over-dispersion or any adjustment for it. It is therefore not possible to say whether a particular over-dispersion method was applied.

Random allocation is intended, in general, to create groups that are comparable on average with respect to measured and unmeasured baseline characteristics. It does not guarantee that small groups will be identical at baseline, and it does not remove the need to understand how allocation was performed and how the data were analyzed. This registry record identifies the design as randomized but does not report the sequence-generation or allocation-concealment methods.

Standardized effect sizes express a difference relative to a measure of variability and can assist comparisons across measurement scales. The posted comparisons include standardized estimates, but their calculation procedure is not described in the registry record. The original sample-size justification and the trial's own design assumptions are also not reported in the registry record. Planning illustrations based on observed results are a separate use of assumptions and should not be mistaken for a prospective design calculation.

The registry lists no reported analysis entries. That does not establish that no analyses were conducted; it means the registry record does not report them in the analysis listing. The exact model, covariates, handling of baseline measurements, missing-data method, analysis population, and multiplicity strategy are not reported in the registry record. These omissions matter because analytic choices can affect the estimate and its uncertainty, particularly when outcomes are available for fewer participants than the recorded total enrollment.

11. Confidence Intervals and Precision

The primary mean difference is 33.38 kcal/day, with a 95% confidence interval from 3.203 to 63.56. The interval gives a range of uncertainty around the estimated difference, rather than a guarantee that the true difference equals the point estimate. Its lower and upper limits are both positive, while the distance between them indicates that the magnitude is not tightly pinned down by the posted results.

The group standard deviations, 40.89 kcal/day for stretching and 54.6 kcal/day for treadmill exercise, are sizeable in relation to the difference between the group means. They describe variation among participant changes and help explain why the estimate remains uncertain. The group sizes in these outcome results are 19 and 20. A confidence interval is affected by both the amount of variation and the amount of information available; it is not a measure of how much participants differed from one another.

The secondary confidence intervals also convey different levels of uncertainty. The substrate oxidation interval is entirely positive, whereas the circulating nitrotyrosine interval extends across zero. Those patterns describe the limits of the posted estimates, not proof of a mechanism or a definitive ranking of outcomes. Because the secondary results are unadjusted and the registry does not report a multiplicity strategy, the intervals should be considered alongside the exploratory status and the number of outcomes examined.

The registry record does not report the confidence-interval method or the details of the analysis set. Precision should therefore be read from the posted intervals without assuming a particular model beyond the reported comparisons. The results are more informative about the direction and plausible range of the group-level differences than about exact individual responses.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures are participants per arm, not total event counts. They are illustrations calculated from the observed effect, not the trial's original design justification. The listed assumptions are a two-sided significance level of 0.05, equal allocation between two arms, a normal approximation, and an effect to detect equal to the stated fraction of the observed effect. The original sample-size assumptions are not reported in the registry record.

For the primary outcome, planning for 100% of the observed effect gives 34 participants per arm for 80% power and 45 participants per arm for 90% power. Planning for 75% of the observed effect gives 59 participants per arm for 80% power and 79 participants per arm for 90% power. Planning for 50% of the observed effect gives 133 participants per arm for 80% power and 177 participants per arm for 90% power.

In plain terms, 80% power means that, under the stated planning assumptions and if the assumed effect were the true effect, the design would have an 80% chance of detecting an effect at the specified significance level. The 90% column describes the corresponding chance at the higher power target. Higher power generally requires more participants when other assumptions are held constant. Planning for a smaller effect requires more participants because a smaller group difference is harder to distinguish from random variation.

These figures are not observed power. They are planning illustrations based on the observed effect, and the observed effect may not be the effect a future study should expect. The illustrations do not reveal the trial's original sample-size rationale or whether its enrollment target was based on these assumptions.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = 33.380; pooled standard deviation σ = 48.418.
2. n = 2 × (1.96 + 0.842)² × 48.418² / 33.380² = 33.0, rounded up to 34 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 <- 33.38                      # observed difference in means
sigma <- 48.4176363333456                     # 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(2043574)
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 = 34 (80% power), 45 (90% power)
 75% of observed effect: n per arm = 59 (80% power), 79 (90% power)
 50% of observed effect: n per arm = 133 (80% power), 177 (90% power)
power.t.test: 34 
Simulated power at n = 34 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.

14. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when several outcomes or statistical tests are considered. Even when each test uses the same nominal threshold, examining multiple results increases the chance that at least one appears notable by chance. General approaches include prespecifying a primary outcome, defining a hierarchy for secondary outcomes, or adjusting for multiple comparisons. The registry identifies a primary outcome and two secondary outcomes, but a multiplicity adjustment or a hierarchy for interpreting the secondary tests is not reported in the registry record. The posted secondary p-values are unadjusted.

The registry record lists no reported analysis entries. It does not report which analyses were planned before the results were examined, whether the analysis was intention-to-treat or based on another population, or which model and covariates were used. These details are relevant to understanding whether the posted comparisons follow a prespecified analysis plan. They are not reported in the registry record, so it is not possible to assess departures from such a plan.

The outcome results include 19 participants in stretching and 20 in treadmill exercise, whereas recorded enrollment is 51. The registry record does not explain the difference between the enrollment figure and the numbers represented in the outcome results. It does not report the amount, reasons, or group distribution of missing outcome data, nor does it state how missing measurements were handled. No inference about attrition or missingness can be made from the group counts alone.

The record also does not report whether the analysis used all randomized participants, participants with complete measurements, or another defined population. It does not describe adherence to the assigned intervention, protocol deviations, imputation, or sensitivity analyses. These are unknowns in the registry record, not evidence that a particular procedure was or was not used in the trial. They limit the ability to evaluate how robust the estimates may be to missing measurements or analytic choices.

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 serious adverse event terms

Serious events with the highest arm-level rate: recurrent stroke (5.3%).

The posted serious adverse event figures report one affected participant among 19 at risk in the stretching control group and one among 20 at risk in the treadmill exercise group. The registry lists zero participants with other adverse events in each group and zero deaths in each group. Recurrent stroke is listed as the top serious adverse event term, with 5.3% reported.

These counts should be read as recorded safety summaries, not as a complete account of every possible event or as a comparison adjusted for differences in follow-up or participant characteristics. The registry record does not report detailed event narratives, timing, severity grading beyond the serious-event category, relatedness assessments, or the method for collecting adverse events. It does not identify which group is associated with the recurrent stroke term, so the term should not be assigned to a particular arm from the record alone.

Small group counts make the safety figures descriptive. They do not establish whether an event was caused by an intervention, and zero reported other events or deaths does not establish that no unrecorded events occurred. The figures describe what the registry lists for the reported groups.

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

The primary result describes a positive difference in mean change in total daily energy expenditure between the treadmill exercise and stretching groups. The estimate is accompanied by a confidence interval that is entirely above zero, while its width shows that the exact magnitude remains uncertain. The group means and standard deviations also show that individual changes varied, so the average difference should not be read as a prediction for each participant.

The results do not establish that the same difference would occur in other populations, settings, or intervention schedules. The registry record identifies people with chronic stroke as the population of interest, but it does not report detailed eligibility criteria or participant characteristics that would define how closely another group resembles these participants. The record also does not provide enough information to evaluate the implementation of randomization, outcome completeness, or the full analysis strategy.

The primary endpoint concerns daily caloric expenditure measured with an accelerometer, not every aspect of physical function, metabolism, diet, or recovery. The trial summary describes broader interests in fuel utilization, physical function, and oxidative stress, but the primary result alone cannot establish a change in those other domains or a mechanism for the observed difference. Secondary outcomes provide related but distinct measurements and have unadjusted comparisons.

The posted findings should not be interpreted as medical advice or as a general conclusion about an intervention. They report group-level changes and uncertainty for this trial's recorded outcomes. The record does not report enough methodological detail to resolve all questions about missing data, multiplicity, or the analysis population. Those limitations are relevant when judging how broadly and confidently to interpret the estimates.

17. Why This Trial Matters Statistically

This trial illustrates the distinction between an estimated effect and its precision. The primary comparison gives a mean difference and a confidence interval, allowing readers to consider both the direction of the estimate and the range of uncertainty. Reporting only a group mean or a p-value would leave out important information about the spread of participant changes and the precision of the comparison.

It also illustrates why outcome definitions matter. Total daily energy expenditure was assessed through accelerometer monitoring during daily activities, while the secondary outcomes address substrate oxidation and circulating nitrotyrosine. These are related to the study's broad scientific aims but represent different measurements. Statistical interpretation must follow what each endpoint actually measures rather than treating all outcomes as interchangeable evidence.

The registry also shows why a statistically notable estimate is not the whole analysis. The secondary comparisons are unadjusted, and the record does not report a multiplicity strategy, analysis population, missing-data method, or detailed statistical plan. Those elements affect how a reader evaluates the apparent strength and reproducibility of findings. Clear reporting of these choices would make the relationship between the planned questions and posted results easier to assess.

Finally, planning illustrations based on an observed effect should be kept distinct from the original design rationale. They demonstrate how assumed effect size and power targets influence participant requirements, but they do not tell readers what assumptions guided enrollment in this trial. That distinction is useful when considering future study planning without treating retrospective calculations as evidence that a study was adequately powered.

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 posted outcome group sizes are 19 and 20, while recorded enrollment is 51. The registry record does not explain this difference or report reasons that some enrolled participants are not represented in the posted outcome counts. The relationship between enrollment and the analyzed measurements therefore remains unclear.

The record does not provide detailed participant characteristics, eligibility criteria, recruitment setting, or information about how representative the enrolled population may be. It also does not describe random-sequence generation or allocation concealment. Randomization is identified, but the implementation details needed to assess potential selection concerns are not reported in the registry record.

The primary outcome relies on accelerometer monitoring over 5 to 7 days. The registry description does not report device-processing methods, criteria for valid wear time, or the handling of incomplete monitoring. It also does not explain whether the same measurement procedures were applied in both groups or how baseline and follow-up values were incorporated into the analysis beyond defining the change outcome.

The statistical analysis plan, model, analysis population, missing-data method, and multiplicity approach are not reported in the registry record. No reported analysis entries are listed. The secondary outcomes are unadjusted, and the record does not explain whether their results were prespecified or how they were prioritized. These reporting gaps limit assessment of robustness and the extent to which the posted comparisons reflect planned analyses.

Finally, the registry records stretching and treadmill exercise as the compared interventions, while the study summary also discusses dietary modification. How, or whether, dietary modification was incorporated into the reported groups is not reported in the registry record. The posted comparison should therefore be understood as the stated exercise-versus-stretching comparison, without assuming an unreported dietary intervention.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Nutrition and Aerobic Exercise in Chronic Stroke — NCT02043574.
• Registry record last updated 2020-01-31; status last verified 2020-01.
• Results first posted 2020-01-31.
• 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

The registry describes a completed, randomized, parallel-group trial of six months of treadmill training versus six months of stretching in people with chronic stroke. Masking is listed as none, and recorded enrollment is 51. The primary outcome is change in total daily energy expenditure, measured using a belt-worn accelerometer activity monitor at baseline and after six months. The posted primary outcome results include 19 participants in stretching and 20 in treadmill exercise.

The reported primary mean difference is 33.38 kcal/day, with a 95% confidence interval from 3.203 to 63.56 and an unadjusted p-value of 0.03. Two secondary outcomes are listed: change in substrate oxidation and change in circulating nitrotyrosine. The registry record does not report analysis entries, the original sample-size justification, a multiplicity strategy, an analysis population, or missing-data methods. Safety summaries list one serious adverse event in each group and zero deaths in each group.