Rehabilitating Corticospinal Control of Walking: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Rehabilitating Corticospinal Control of Walking (NCT02132650), a randomized na study. The primary outcome is Change in Walk Speed From Pre-Intervention (0 Months) to Post-Intervention (3 Months).

2. Clinical Question

3. Trial Design

This was a randomized, parallel-group trial with single masking. The registry lists the phase as not applicable. The sponsor was the VA Office of Research and Development, and the trial is marked completed. The listed start date is 2014-06-02, and the listed primary completion date is 2019-05-31. The registry reports enrollment of 38.

The two behavioral interventions were accurate walking training and steady-state walking training. The registry describes the former as rehabilitation using accurate walking tasks and the latter as rehabilitation using typical steady-state walking. The brief summary presents the study as a test of whether accurate walking tasks are more effective than steady-state walking training, but the statistical comparison is the relevant evidence for the primary endpoint.

For the primary endpoint, the posted results give a group size of 19 for accurate walking training and 17 for steady-state walking training. These are the endpoint group sizes, not a replacement for the registry’s overall enrollment figure. The reason the posted endpoint group sizes do not account for the full enrollment figure is not reported in the registry record. The adverse-event record separately lists participants at risk for each safety category.

The trial compares the groups’ mean change in self-selected walking speed from pre-intervention to post-intervention. The listed assessment times are 0 months and 3 months. The registry does not report who was masked, how randomization was generated or concealed, the rehabilitation schedule, adherence, or the original sample-size justification. Those details should not be inferred from the randomized, single-masked, parallel-group labels.

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 Change in Walk Speed From Pre-Intervention (0 Months) to Post-Intervention (3 Months), measured over assessed pre-intervention (0 months) and post-intervention (3 months).

The primary endpoint is change in self-selected, preferred steady-state walking speed from pre-intervention at 0 months to post-intervention at 3 months. Walking speed is a continuous measure, reported in meters per second. The registry summarizes it with a mean and standard deviation. A change endpoint focuses on how the measured speed differs between the stated assessment times, while the group comparison asks whether the average change differs between training approaches.

Walking speed is used as a quantitative measure of walking function. A continuous endpoint retains information about the magnitude of measured speeds rather than reducing the outcome to a yes-or-no category. The registry’s brief summary explains that walking recovery is a common goal after stroke; that context helps explain the choice of walking speed as an outcome, but it does not establish that every measured difference is meaningful to participants.

The endpoint description identifies self-selected speed, rather than a maximum-speed test. The precise measurement procedure, equipment, number of walking trials, and rules for calculating each participant’s change are not reported in the registry record. A threshold for a clinically important difference is also not reported. The group means and their uncertainty therefore describe the posted statistical result, but do not alone indicate whether the size of the difference would be noticeable or important in practice.

7. Results Posted in the Registry

• Steady State Walking Training: mean 0.14 versus 0.13 on control; difference 0.01 (95% CI -0.07 to 0.09), standardized effect d = 0.08; z-test p = 0.804.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary measure is continuous: it records walking speed in meters per second, rather than assigning participants to outcome categories. The registry reports a group mean and standard deviation for each training arm. A mean describes the arithmetic average of measured changes; a standard deviation describes how spread out individual observations are around that average. The two quantities answer different questions. The mean is the group’s central estimate, while the standard deviation describes variation among participants.

What does the mean difference represent?

The comparison is expressed as a mean difference, with steady-state walking training compared against accurate walking training. The reported estimate is 0.01 meters per second. A difference in means gives the estimated separation between the two group averages on the endpoint’s original scale. It is not a percentage change, and it does not describe the change for every participant. Individual responses can vary even when group averages are close.

The reported means are 0.13 for accurate walking training and 0.14 for steady-state walking training. The direction of the comparison depends on which group is subtracted from which; the registry comparison identifies steady-state walking training as the arm being compared with the accurate-walking reference. Because the values are close, the estimate is near zero on the measured scale. No threshold for a clinically important difference is reported, so statistical scale alone cannot determine practical importance.

How should the confidence interval be read?

A confidence interval expresses the uncertainty around an estimated effect under the statistical method used. In general, a narrower interval indicates greater precision, while a wider interval indicates less precision. The reported interval for this mean difference includes negative and positive values. Thus, the results are compatible with a difference favoring either group, as well as values near no difference. A confidence interval is not a range containing a fixed proportion of individual participants, and it is not a probability statement about the true effect after observing the data.

Confidence intervals are useful because they show both the direction and the range of effect sizes reasonably compatible with the analysis. They should be considered alongside the estimate and the outcome scale. Here, the interval does not narrowly locate the difference. The estimate may be close to zero, but the uncertainty means that the data do not pin down the size or direction with high precision.

What does the p-value add?

The unadjusted p-value is 0.804. In general, a p-value measures how incompatible the observed data are with a specified null hypothesis, under the assumptions of the test. It is not the probability that the null hypothesis is true, and it is not the probability that the result happened by chance. It also does not quantify clinical importance. A large p-value can occur when the estimated effect is small, when data are variable, or when the study has limited precision; the registry record does not establish which factors account for this result.

The p-value and confidence interval address related questions, but the interval is particularly useful for understanding the range of effects consistent with the data. The p-value should not replace inspection of the estimate, interval, outcome definition, and design. The record labels the result unadjusted, and no adjusted comparison is reported.

Why do the group sizes and variability matter?

The endpoint group sizes are 19 and 17. Standard errors are reported as 0.025 and 0.032 for the two group means. A standard error describes uncertainty in an estimated mean, not the spread of individual measurements. In general, standard errors tend to be smaller with more observations and less variability, although the registry record does not provide enough information to attribute the observed precision to one specific factor.

The standard deviations, 0.11 and 0.13, describe within-group dispersion. When outcome variability is large relative to the difference between group means, it can be harder to estimate a group contrast precisely. This is a general statistical point, not evidence about why this particular result has its observed uncertainty. The registry comparison also reports a pooled standard deviation, but its numerical value is not needed to interpret the primary mean difference.

Why might dispersion affect planning?

In general, sample-size planning for a continuous outcome depends on the difference a study aims to detect, the amount of variability, the desired power, and the chosen significance level. More variability makes a given mean difference harder to distinguish from sampling noise. Detecting a smaller difference also generally requires more participants than detecting a larger one, if the other assumptions remain the same. This is why planning illustrations often show several assumed effect sizes rather than a single required group size.

The registry’s planning illustration is based on the observed effect and uses a normal approximation with equal allocation and a two-sided significance level of 0.05. It is not a report of the original trial design calculation. The original sample-size assumptions and justification are not reported in the registry record. The planning values should therefore be understood as hypothetical illustrations under stated assumptions, not as a retrospective judgment of the trial’s quality or a description of its actual design process.

What can randomization support?

Random allocation is intended to make the treatment groups comparable, on average, with respect to both measured and unmeasured characteristics at the start of a trial. In general, this supports a causal comparison when allocation is implemented appropriately and follow-up and analysis preserve the randomized comparison. The record identifies the study as randomized, but details of sequence generation, concealment, adherence, and handling of missing outcomes are not reported. The design label alone cannot resolve those details.

Single masking indicates that masking was used, but the identity of the masked parties is not reported. It is not appropriate to infer that participants, trainers, assessors, or analysts were masked based only on that label. The extent to which masking may have influenced outcome measurement cannot be assessed from the registry record.

10. Confidence Intervals and Precision

The estimated mean difference is 0.01 meters per second, with a confidence interval that extends from a negative value to a positive value. This span matters: the interval includes possible differences in either direction, so the estimate does not precisely settle which group had the higher underlying mean change. The interval also indicates that values near the estimate are not the only values compatible with the posted analysis.

Precision is different from whether an estimate is statistically significant. A confidence interval conveys uncertainty about the effect’s size and direction, while a p-value summarizes evidence against a specified null hypothesis under a statistical model. The reported p-value is 0.804. Neither statistic indicates whether a difference is important to participants. A threshold for meaningful change in walking speed is not reported in the registry record.

The group standard deviations are 0.11 and 0.13 meters per second, and the endpoint group sizes are 19 and 17. Those values provide context for the observed variation and the amount of endpoint data in each group. The registry does not report enough information to determine how missing observations, if any, affected the comparison. The enrolled figure and posted endpoint group sizes differ, and the reason is not reported in the registry record.

Overall, the confidence interval communicates limited precision about the between-group effect. The estimate is close to zero, but the interval’s span means that the data remain compatible with differing effects. It would be unwarranted to describe the result as proof of no difference or as evidence of equivalence. A prespecified equivalence margin and corresponding analysis are not reported.

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, not total event counts. The registry labels the calculation as an illustration based on the observed effect, rather than the trial’s original design. Its 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 the stated fraction of the observed effect.

The row using 100% of the observed effect gives 2,255 participants per arm for 80% power and 3,018 participants per arm for 90% power. The row using 75% of the observed effect gives 4,008 participants per arm for 80% power and 5,365 participants per arm for 90% power. The row using 50% of the observed effect gives 9,017 participants per arm for 80% power and 12,070 participants per arm for 90% power.

In plain terms, 80% power describes a planning target under which the specified analysis would have an 80% chance of detecting the assumed effect if that effect were the true one and the assumptions held. The 90% power column uses a higher target for that chance. Neither column is a statement about the probability that the trial result is correct. The curve visualizes the same planning relationship across assumed effect sizes; it should be read alongside the assumptions, not as a separate finding.

The smaller the effect to be detected, the more participants the illustration requires. These values are not observed power. The original trial’s own sample-size justification and assumptions are not reported in the registry record.

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 = 0.010; pooled standard deviation σ = 0.120.
2. n = 2 × (1.96 + 0.842)² × 0.120² / 0.010² = 2,254.0, rounded up to 2,255 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 <- 0.01                      # observed difference in means
sigma <- 0.119828308547737                     # 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(2132650)
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 = 2,255 (80% power), 3,018 (90% power)
 75% of observed effect: n per arm = 4,008 (80% power), 5,365 (90% power)
 50% of observed effect: n per arm = 9,017 (80% power), 12,070 (90% power)
power.t.test: 2255 
Simulated power at n = 2,255 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. Multiplicity, Missing Data and Analysis Populations

The registry lists two outcome measures and no posted secondary results. It reports one primary endpoint: change in self-selected walking speed from pre-intervention to post-intervention. The record lists no analyses. It does not report whether additional outcomes, time points, subgroup comparisons, or interim looks were prespecified or conducted.

Multiplicity arises when many hypotheses or comparisons are examined. In general, testing more outcomes or contrasts can increase the chance of obtaining at least one apparently unusual result even when no true effects exist. Statistical approaches can address that issue, but the appropriate approach depends on the planned family of tests and the inferential goal. The registry record does not report a multiplicity strategy. With no secondary results posted, the primary comparison should not be treated as a complete account of all outcomes that may have been measured.

Details of missing data are not reported in the registry record. The endpoint group sizes are 19 and 17, while enrollment is listed as 38. The record does not explain why these figures differ, whether endpoint observations were unavailable, or how any missing outcomes were handled. It does not report whether the analysis used all randomized participants, only participants with observed endpoint data, or another analysis population. Imputation methods and sensitivity analyses are also not reported.

These omissions limit assessment of how robust the estimate is to missing outcomes or choices about the analysis population. They do not show that data were missing or that a particular analytic approach was used; the relevant details are simply not reported in the registry record. The same caution applies to adherence and protocol deviations, which are not described. The randomized design is informative, but interpretation also depends on how the randomized groups were followed and analyzed.

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.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: unstable medical condition (5.6%), pain (5.0%).

The serious adverse-event record lists 20 participants at risk in the accurate walking training group, with 1 serious adverse event, and 18 participants at risk in the steady-state walking training group, also with 1 serious adverse event. The death count is 0 in each group. These figures describe the registry’s reported counts; they do not establish whether an event was caused by training.

The record also lists the serious adverse terms unstable medical condition at 5.6% and pain at 5.0%. The registry does not provide further detail in this record about how these terms relate to the group-level serious-event counts, their timing, duration, severity, or attribution. The terms should not be interpreted as evidence that a particular intervention caused them.

Safety counts need context. The at-risk denominators differ by group, and the registry does not report the event definitions, monitoring schedule, or an analysis comparing safety outcomes between groups. The figures therefore support a descriptive reading of the posted record, not a definitive comparative safety conclusion.

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

The primary result is a comparison of average change in preferred steady-state walking speed between accurate walking training and steady-state walking training. The posted means are 0.13 and 0.14 meters per second, respectively, and the estimated mean difference is 0.01 meters per second. The confidence interval includes negative and positive values, while the unadjusted p-value is 0.804. Taken together, the result is an imprecise estimate that does not clearly distinguish the groups on this endpoint.

This does not demonstrate that the approaches are equivalent. Equivalence requires a prespecified range of differences considered unimportant and an analysis designed to test whether the result falls within that range. Neither is reported in the registry record. The result also does not prove that neither approach changes walking speed; the comparison concerns the difference between groups, not whether either group changed from its own starting value in a way that is meaningful.

The record does not report a threshold for clinically important change, detailed eligibility criteria, the training protocols, or secondary outcomes. Therefore, the posted endpoint cannot answer whether any observed change would matter to participants, how the training was delivered in practice, or whether there were effects on outcomes other than walking speed. Generalizing beyond the participants represented in the trial also requires population information that is not reported in the registry record.

The trial’s brief summary explains the rationale for testing accurate walking tasks after stroke, but its stated expectation is not the result. Statistical interpretation should rest on the posted group data and uncertainty. Those data show a small estimated difference with uncertainty about both direction and magnitude. They do not establish superiority, equivalence, or the absence of clinically relevant effects.

These findings are best understood as evidence about the registered comparison and endpoint, with important gaps in the record about analysis details, missing data, and clinical thresholds. They are not a basis for individual treatment decisions.

16. Why This Trial Matters Statistically

This trial illustrates why an estimated effect should be read together with its uncertainty. The difference between the group means is 0.01 meters per second, but the confidence interval includes values on both sides of zero. Focusing only on the point estimate could make the comparison appear more conclusive than it is; focusing only on the p-value would also leave out the range of effect sizes compatible with the data.

It also shows the distinction between a nonsignificant comparison and proof of equivalence. The posted p-value is 0.804, but an equivalence conclusion would require a defined margin and an appropriate analysis. The registry record does not report either. Statistical conclusions depend on the question the analysis was designed to answer, not only on whether a p-value crosses a conventional threshold.

The planning illustration underscores how strongly sample-size needs depend on the effect chosen for detection. Its assumptions are explicit, and the figures rise as the target effect becomes smaller. Those planning values should not be mistaken for the original trial’s design rationale or for observed power. The original sample-size assumptions are not reported in the registry record.

Finally, the study concerns a rehabilitation question where endpoint interpretation depends on both measurement and context. The registered outcome captures preferred walking speed, but the record does not provide a threshold for meaningful change or the measurement details needed to assess all sources of variation. The statistical result is therefore most useful when its limits are made clear: it estimates a group contrast, conveys uncertainty, and does not settle every clinical or practical question raised by the study.

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 registry record leaves several trial-specific details unreported. Eligibility criteria and participant characteristics are not described in the endpoint record, limiting assessment of which stroke survivors the findings represent. Although the brief summary discusses Veteran stroke survivors, it does not provide the detailed population information needed to evaluate generalizability.

The intervention descriptions distinguish accurate walking tasks from typical steady-state walking, but do not specify the training dose, session frequency, duration, progression, adherence, or implementation. The record also does not identify which parties were masked under the single-masked designation. These omissions limit assessment of treatment delivery and the potential for differences in performance or outcome assessment.

The endpoint group sizes are 19 and 17, while registry enrollment is 38; the reason for this difference is not reported in the registry record. Missing-data handling, the analysis population, protocol deviations, and sensitivity analyses are not reported. As a result, the record does not allow a detailed assessment of how these issues may have affected the estimate.

The comparison is reported as unadjusted, and no analysis details beyond the posted summary are available in the registry record. A clinical-importance threshold, original sample-size assumptions, multiplicity strategy, and secondary results are also not reported. These limits do not invalidate the posted statistics, but they constrain how fully the design, precision, and practical meaning of the findings can be assessed.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Rehabilitating Corticospinal Control of Walking — NCT02132650.
• Registry record last updated 2022-05-05; status last verified 2022-04.
• Results first posted 2020-06-09.
• 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

The registry describes a completed, randomized, single-masked, parallel-group behavioral trial of accurate walking training versus steady-state walking training following stroke. The sponsor was the VA Office of Research and Development. Enrollment is listed as 38.

The primary endpoint is change in self-selected steady-state walking speed, measured in meters per second from pre-intervention at 0 months to post-intervention at 3 months. The posted means are 0.13 for accurate walking training and 0.14 for steady-state walking training. The estimated mean difference is 0.01 meters per second, with a confidence interval spanning negative and positive values and an unadjusted p-value of 0.804.

The registry lists two outcome measures and no posted secondary results. It reports 1 serious adverse event in each group and 0 deaths in each group. Important details about eligibility, missing data, analysis populations, intervention delivery, and the original sample-size rationale are not reported in the registry record.