Neuromuscular Electrical Stimulation and Mobility in Multiple Sclerosis: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Neuromuscular Electrical Stimulation and Mobility in Multiple Sclerosis (NCT02152085), a randomized na study. The primary outcome is Walking Endurance.

2. Clinical Question

The comparison concerns the difference between two stimulation approaches, not stimulation versus no treatment or usual care. That distinction matters when interpreting the findings: the posted primary result addresses whether the recorded average change differed between the narrow- and wide-pulse groups. It does not, by itself, estimate the effect of receiving stimulation compared with receiving no stimulation.

The registry lists 29 participants enrolled. The primary outcome summaries include 14 participants in the narrow-pulse group and 13 in the wide-pulse group. The record does not explain the difference between enrollment and the numbers contributing to those outcome summaries, nor does it report additional details about participant eligibility or the analysis population.

The primary outcome is a change measure, so its group summaries describe the recorded shift from before to after treatment rather than the walking distance at a single time point. The registry states that the six-minute walking distance was assessed after 18 sessions administered three times per week over a six-week period. The primary comparison is therefore specifically tied to that treatment period and measurement schedule.

3. Trial Design

This completed study is recorded as a randomized, double-masked, parallel-group trial. Its enrollment was 29, and the condition listed is multiple sclerosis. The study sponsor is the University of Colorado, Boulder. The registry records a start date of 2014-05 and a primary completion date of 2017-12-31.

Participants were allocated to one of two device interventions. The narrow-pulse arm used calf-muscle electrical stimulation with pulses lasting 0.4 ms, while the wide-pulse arm used pulses lasting 1 ms. Each intervention lasted six weeks. The registry describes 18 treatment sessions over that period, with three sessions per week. Because both groups received electrical stimulation, the trial compares pulse duration within this treatment approach.

Randomization and double masking are recorded, but details about how the allocation sequence was generated or concealed, who was masked, and how masking was maintained are not reported in the registry record. The record also does not report the trial's original sample-size justification or the assumptions used in its design. Those details cannot be inferred from the sample-size planning illustrations based on the observed results.

The primary outcome is walking endurance, defined as distance walked in 6 min, with the outcome timeframe specified as change from before to after the treatment sessions. Maximal Walking Speed is listed as a secondary outcome, also measured as change over the treatment period. The registry identifies three outcome measures, but the posted information includes one secondary outcome. Detailed protocols for the outcome assessments and further analysis-population definitions are not reported in the registry record.

The record marks the study as completed. Its listed phase is NA. The record does not describe a non-stimulation control group, a follow-up period beyond the treatment assessment, or additional design features such as interim analyses. Those features should not be assumed from the randomized, double-masked, parallel-group designation alone.

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.

Before assignment: Three potential participants did not meet eligibility requirements.

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 Walking Endurance, measured over Change from before to after 18 treatment sessions administered over a 6-week period (3 sessions/week)..

Walking endurance is measured as the distance walked in 6 min. The primary outcome is the mean change in that distance from before treatment to after 18 treatment sessions delivered over six weeks. The outcome is expressed in meters. The posted group summaries are 42.0 meters for the narrow-pulse group and 25.0 meters for the wide-pulse group, with standard deviations of 60.0 and 35.0, respectively. These values describe the recorded average change and the spread of individual changes within each group.

A six-minute walking distance measure captures the distance completed during a fixed-duration walking task. In general, a change score is used to describe how a measurement differs between two specified assessments. It can make the focus of the comparison explicit: in this trial, the endpoint concerns change over the treatment period rather than only the final measurement. The registry does not provide further details about the assessment procedure or how the walking test was administered.

The principal contrast is the difference in mean change between the two pulse-width groups. The posted estimate is -17.0 meters for wide pulse compared with narrow pulse. In this direction of comparison, a negative estimate means the recorded mean change was lower in the wide-pulse group. The interval around that estimate includes values on both sides of zero, so the data are compatible with a range of possible between-group differences. The endpoint is relevant to the study's stated question about walking, but this particular comparison does not establish how either group would have changed without stimulation.

7. Results Posted in the Registry

• Wide Pulse: mean 25.00 versus 42.00 on control; difference -17.00 (95% CI -53.74 to 19.74), standardized effect d = -0.34; z-test p = 0.364.

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.

Maximal Walking Speed

• 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:
  • Wide Pulse: mean 0.12 versus -1.92 on control; difference 2.04 (95% CI -0.25 to 4.33), standardized effect d = 0.65; z-test p = 0.081.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Wide Pulse and the control. The interval gives the range of effects that remain compatible with the data.

Maximal Walking Speed is the one secondary outcome with posted results. It is expressed in seconds and is recorded as change from before to after the same 18 sessions over six weeks. Its comparison estimate and uncertainty are distinct from the primary walking-endurance result; the secondary outcome does not replace or redefine the primary question.

Across the posted outcomes, the primary estimate favors a larger mean change in the narrow-pulse group, while the secondary estimate is positive for wide pulse relative to narrow pulse under its recorded comparison direction. This differing pattern cautions against treating one outcome as a stand-in for another. They measure different aspects of walking and have different units and variation. The registry record does not provide additional outcomes or a stated framework for combining them.

Secondary outcomes generally provide supporting or exploratory information. When several outcomes or comparisons are examined, the opportunity for chance findings increases unless the analysis accounts for multiplicity. The registry does not report a multiplicity correction, a prespecified hierarchy, or a detailed plan describing how secondary outcomes were to be interpreted. The posted secondary result is unadjusted, and should therefore carry less confirmatory weight than a prespecified primary outcome.

The registry identifies three outcome measures, while one secondary outcome is posted. It does not report analyses for additional secondary measures in the record. Their status, definitions, and results should not be inferred. Likewise, the absence of a reported analysis plan does not establish that no plan existed; it means that the plan is not reported in the registry record.

The overall secondary-outcome evidence is limited by the small outcome group counts and by the lack of reported multiplicity and analysis details. It can be considered alongside the primary result as context, but it does not resolve the primary estimate's uncertainty or establish a broad pattern across all possible walking outcomes.

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

• Maximal Walking Speed

9. Statistical Interpretation

10. Statistical Methods Explained

The primary outcome is continuous: it is a distance in meters, summarized as a mean and standard deviation. A mean describes the average change among participants included in the group summary. A standard deviation describes how spread out individual change values are around that group mean. It is not the same as the uncertainty in the estimated group mean or in the between-group contrast.

The posted comparison is a mean difference for wide pulse relative to narrow pulse. The estimate of -17.0 meters corresponds to the group means of 25.0 meters for wide pulse and 42.0 meters for narrow pulse. The sign depends on the order of comparison. A negative estimate indicates a lower mean change in the first-named comparison group, wide pulse, than in the reference group, narrow pulse. The estimate is measured in the same units as the outcome: meters.

The reported interval runs from -53.74 to 19.74 meters. In general, a confidence interval describes a range of estimates compatible with the observed data under a specified statistical procedure and its assumptions. Its width conveys precision: a wider interval leaves more uncertainty about the size and direction of the underlying difference. The confidence level and construction method for the posted interval are not reported in the registry record, so they should not be presumed.

The unadjusted p-value for the primary comparison is 0.364. In general, a p-value is calculated relative to a null hypothesis, commonly one of no difference, and the assumptions of the analysis. It summarizes how compatible the data are with that null model; it does not give the probability that the null model is true. The registry record does not report a detailed statistical analysis plan or identify a particular test for the sponsor's analysis. The posted result is therefore described as an unadjusted comparison without attributing an unreported method to the trial investigators.

The record also gives a pooled standard deviation of 49.6 meters and a standardized effect estimate of -0.343 for the primary contrast. In general, a pooled standard deviation combines within-group measures of spread for a two-group comparison, while a standardized effect expresses the mean difference relative to a measure of that spread. Standardized effects can help compare outcomes measured on different scales, but they do not replace the original-unit estimate. The record does not provide further detail about the exact formula used for the standardized estimate.

The statistical summaries include standard errors for the group means: 16.04 meters for narrow pulse and 9.707 meters for wide pulse. In general, a standard error describes the sampling variability of an estimate under an analysis model; it is not a description of the spread among individual participants. The standard deviations and standard errors answer different questions and should not be read interchangeably.

The comparison statistics are recalculated, simple unadjusted comparisons based on posted summary statistics. The registry does not report an analysis record for these comparisons. The discrepancy indicator is false, so the posted summaries do not flag a disagreement requiring the sponsor's own analysis to take precedence. This does not add details about how the original investigators analyzed their data; those details are not reported in the registry record.

Over-dispersion is a general concern when outcome variation is greater than assumed by a statistical model. If the model understates variability, standard errors can be too small and intervals can be too narrow. For a continuous endpoint such as walking distance, variation across participant change scores is represented by the standard deviations. The observed standard deviations describe spread, but the registry record does not report a model assessment or a test for over-dispersion. No conclusion about such a model issue can be drawn from the posted summaries alone.

Why distinguish a mean from a mean difference?

The group means describe average changes separately, while the mean difference directly contrasts those average changes. The primary estimate is the contrast of interest for the randomized comparison. Separate group values alone do not express the uncertainty in the contrast; the comparison interval and p-value address that inferential question under the method used.

What does an unadjusted result mean?

Unadjusted means that the reported p-value is not identified as having been corrected for multiple outcome or hypothesis testing. In general, testing several outcomes can increase the chance of obtaining an apparently notable result by chance. A multiplicity procedure, if prespecified and applied, can account for that testing context. Whether one was planned or used in the original trial is not reported in the registry record.

The design is randomized, double-masked, and parallel-group, but those design labels do not reveal every analytic choice. The registry does not report the original statistical plan, the handling of missing outcome data, whether analyses followed assigned groups, or any interim monitoring. Those omissions limit how specifically the posted estimates can be connected to the trial's intended analysis.

11. Confidence Intervals and Precision

The primary mean difference is -17.0 meters for wide pulse compared with narrow pulse. Its reported interval extends from -53.74 to 19.74 meters. Because this range includes zero, the posted data do not precisely settle whether the mean change was lower or higher in the wide-pulse group. The endpoints also indicate that a range of effect magnitudes remains compatible with the observed summaries under the procedure used to calculate the interval.

In general, a confidence interval communicates both an estimate and its uncertainty. A narrow interval indicates greater precision, while a wide interval indicates less precision. The interval for this comparison is wide relative to the point estimate and spans both negative and positive values. The registry record does not state the confidence level or the method used for the interval, so no further claim about its construction is warranted.

There are 14 participants in the narrow-pulse primary outcome summary and 13 in the wide-pulse summary. The corresponding standard deviations are 60.0 meters and 35.0 meters. Group size and outcome variability both contribute to uncertainty in a mean comparison. The posted standard errors for the group means are 16.04 and 9.707 meters, respectively. These quantify estimated sampling variability, not the range of individual participant responses.

The unadjusted p-value of 0.364 is another summary of the evidence under a null model, but it is not a measure of precision or effect size. The point estimate, interval, sample counts, and variation should be considered together. The registry does not report the original sample-size justification, missing-data methods, or analysis-population details; those omissions make it difficult to judge whether the observed precision was anticipated or how sensitive it may be to unreported analytic choices.

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 sample-size planning figures are illustrative calculations based on the observed effect, not the trial's original design assumptions. The registry's planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. The trial's own original sample-size justification and design assumptions are not reported in the registry record.

For these continuous outcomes, the planning figures are participants per arm, not total events. The 80% power column gives the estimated number of participants in each arm for a planning scenario designed to have an 80% chance of detecting the specified effect under the stated assumptions, if that effect and the assumptions are correct. The 90% power column describes the corresponding planning target for a 90% chance. These are design calculations, not guarantees about what a future study would observe.

The rows describe planning for 100%, 75%, and 50% of the observed effect. Smaller effects require more participants to detect under the same assumptions, so the counts increase as the assumed effect becomes smaller. The calculation uses the observed estimate as its starting point, which is uncertain; it should not be treated as a definitive estimate of the sample needed for a new trial. These figures are not observed power.

Power is a property of a planned design under assumptions about the effect, variability, allocation, and analysis. It is not a retrospective score for whether the completed study succeeded. The registry does not report the assumptions originally used by investigators to choose the enrollment target, and these planning illustrations should not be read as evidence that the original trial was designed around the displayed counts.

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 = -17.000; pooled standard deviation σ = 49.598.
2. n = 2 × (1.96 + 0.842)² × 49.598² / -17.000² = 133.6, rounded up to 134 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 <- -17                      # observed difference in means
sigma <- 49.598387070549                     # 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(2152085)
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 = 134 (80% power), 179 (90% power)
 75% of observed effect: n per arm = 238 (80% power), 319 (90% power)
 50% of observed effect: n per arm = 535 (80% power), 716 (90% power)
power.t.test: 134.6 
Simulated power at n = 134 per arm: 0.796 (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 a study tests more than one outcome, comparison, time point, or subgroup. In general, the more hypotheses examined, the greater the chance that at least one result may appear notable by chance alone. Prespecifying a primary outcome and analysis can help distinguish the main confirmatory question from supporting analyses, while an adjustment may be used to address multiple testing.

The registry identifies walking endurance as the primary outcome and lists Maximal Walking Speed as a secondary outcome. It also records three outcome measures, but only one secondary outcome is posted. No multiplicity adjustment, testing hierarchy, or plan for interpreting the full set of outcomes is reported in the registry record. The p-values discussed for the posted comparisons are unadjusted. They should not be treated as if they account for all possible tests conducted in the study.

The record does not report how missing outcome data were handled, whether imputation was used, or how participants with incomplete assessments were treated in the analysis. The numbers contributing to the primary and secondary summaries are recorded, but the reasons those counts may differ from enrollment or between safety and outcome summaries are not reported. It is therefore not possible to assess from the registry record whether missingness could have influenced the comparisons.

Analysis-population definitions are also not reported. The record does not specify whether outcomes were analyzed according to randomized assignment, treatment received, or another rule, nor does it describe exclusions after randomization. Random allocation is recorded as a design feature, but that alone does not establish which participants entered each analysis or how deviations from assigned treatment were handled.

The registry lists zero reported analyses. This does not show that no analyses were conducted; it means that analysis records are not reported in the registry record. The posted summary statistics allow an unadjusted comparison to be described, but they do not supply a complete account of the original statistical plan, missing-data procedures, analysis populations, or multiplicity control. These omissions limit reproducibility and the strength of conclusions that can be drawn from the posted results.

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.

The posted safety figures list 13 participants at risk in the narrow-pulse group and 14 in the wide-pulse group for serious adverse events. The recorded number affected is 0 in each group. For other adverse events, the figures list 13 participants at risk in the narrow-pulse group and 14 in the wide-pulse group, with 0 affected in each group. The deaths count is 0 for both groups.

These are registry counts for the participants listed as at risk; they do not provide event descriptions because no serious adverse-event terms are listed. The safety counts are not identical to the group counts in the primary outcome summaries, and the reason for the different counts is not reported in the registry record. No conclusion should be drawn about unreported event categories or about safety beyond the recorded period and participants.

In general, zero recorded events in a small study does not demonstrate that an event is impossible or that the intervention has no safety risks. These figures describe what was reported for this trial; they do not provide a precise estimate of the frequency of uncommon events.

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

The primary result estimates the difference in mean change in six-minute walking distance between two electrical-stimulation pulse widths over six weeks. The narrow-pulse group had a mean change of 42.0 meters, and the wide-pulse group had a mean change of 25.0 meters. The mean difference for wide pulse compared with narrow pulse was -17.0 meters, with a reported interval from -53.74 to 19.74 meters and an unadjusted p-value of 0.364.

These data do not determine the direction or size of the underlying difference precisely. The interval includes zero and values on either side of it. The result should be understood as an uncertain estimate from the posted comparison, not as proof that the two pulse widths are identical or that one produces a particular outcome. A non-small p-value is not evidence that no difference exists; it indicates that the posted result does not provide a precise distinction under the unadjusted analysis.

The comparison is between narrow- and wide-pulse stimulation. It does not compare stimulation with no stimulation, and it cannot establish what would have happened to participants without either intervention. The findings concern mean change over the specified treatment period, not all dimensions of mobility, longer-term outcomes, or effects in populations beyond the study participants.

The posted secondary outcome adds context but has less confirmatory weight because it is secondary and unadjusted, and no multiplicity plan is reported. The safety record lists zero affected participants for serious and other adverse events and zero deaths in the stated groups. Those counts are descriptive and do not rule out risks that a study of this size and reporting scope may not identify.

Important interpretive details—including missing-data methods, analysis populations, the original sample-size justification, and the complete statistical analysis plan—are not reported in the registry record. The result therefore supports a cautious description of the observed group summaries and their uncertainty, rather than a broad claim about treatment effects or clinical benefit.

17. Why This Trial Matters Statistically

This trial illustrates why a point estimate should not be interpreted without its uncertainty. The primary estimate is -17.0 meters, but its reported interval ranges from -53.74 to 19.74 meters. The estimate alone might invite a simple directional reading; the interval shows that the posted data leave substantial uncertainty about both direction and magnitude.

It also highlights the importance of distinguishing a head-to-head comparison from a comparison with no treatment. Both randomized groups received calf-muscle electrical stimulation, with pulse duration as the recorded difference. The result therefore addresses the contrast between those approaches, not the effect of stimulation itself. Clear identification of the comparator is essential to defining what a trial can answer.

The trial also shows how sample size, variability, and endpoint choice shape precision. The primary summaries include 14 and 13 participants, and their standard deviations are 60.0 and 35.0 meters. The planning illustrations indicate how required participants per arm vary with the assumed fraction of the observed effect, but those illustrations are not the original design rationale and are not observed power. Keeping those distinctions clear prevents retrospective calculations from being mistaken for the trial's protocol.

Finally, incomplete reporting of analysis populations, missing-data handling, multiplicity, and the original statistical plan constrains what can be concluded from posted summaries. Transparent reporting of these choices helps readers assess reproducibility and the role of secondary findings. Here, the statistical lesson is not a verdict about a treatment, but the need to read estimates alongside precision, design, and reporting context.

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 outcome sample counts are small: the primary summaries include 14 participants in the narrow-pulse group and 13 in the wide-pulse group. The reported group standard deviations indicate variation in change scores, while the primary interval is broad and crosses zero. Together, these features limit the precision of the estimated between-group difference.

The randomized comparison has no listed no-stimulation arm. As a result, the posted primary estimate addresses the difference between two pulse widths, rather than the effect of electrical stimulation compared with no stimulation. The follow-up described for the primary and secondary outcomes is the change from before to after the six-week intervention; longer-term outcomes are not reported in the registry record.

Several details needed to evaluate the analysis are not reported in the registry record. These include the original sample-size rationale, statistical analysis plan, analysis-population definitions, missing-data procedures, and multiplicity approach. The registry does not explain the reasons for differences between enrollment and outcome counts or between outcome and safety counts.

The record identifies three outcome measures but posts one secondary outcome, and it contains no reported analysis records. Consequently, the complete outcome and analysis landscape cannot be reconstructed from the posted record. The record also does not provide further details about how masking was maintained, the allocation process, or the measurement procedures. These limitations do not invalidate the posted summaries, but they restrict the scope and certainty of interpretation.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Neuromuscular Electrical Stimulation and Mobility in Multiple Sclerosis — NCT02152085.
• Registry record last updated 2021-05-07; status last verified 2021-05.
• Results first posted 2021-05-07.
• 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, double-masked, parallel-group study of neuromuscular electrical stimulation in people with multiple sclerosis. It records enrollment of 29 and compares six weeks of calf-muscle stimulation using narrow pulses lasting 0.4 ms with wide pulses lasting 1 ms.

The primary outcome is change in six-minute walking distance after 18 sessions. The posted mean difference for wide pulse compared with narrow pulse is -17.0 meters, with an interval from -53.74 to 19.74 meters and an unadjusted p-value of 0.364. One secondary outcome, Maximal Walking Speed, is posted. Safety figures list zero participants affected by serious or other adverse events and zero deaths in each recorded group.

The registry does not report the original sample-size justification, detailed analysis plan, missing-data methods, analysis populations, or multiplicity procedures. The posted comparison is therefore best read as an uncertain estimate of the difference between two pulse widths, with important analytic details not reported in the registry record.