Improving SCI Rehabilitation Interventions by Retraining the Brain: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Improving SCI Rehabilitation Interventions by Retraining the Brain (NCT03892746), a randomized phase 1, phase 2 study. The primary outcome is Change in Upper Extremity Motor Score (UEMS) With Manual Muscle Testing.

2. Clinical Question

3. Trial Design

The registry describes a randomized, parallel-group study with quadruple masking and lists its phase as phase 1 and phase 2. The two groups received either active tDCS plus task-oriented practice or sham tDCS plus task-oriented practice. The record does not describe the randomization sequence, allocation concealment, the identities of the masked parties, or how masking was maintained.

The stated enrollment is 47. For the primary outcome, the registry reports 16 participants in the active group and 20 in the sham group. Those outcome counts do not add up to the enrollment figure, and the registry record does not explain why. It also does not report how many participants were randomized, completed treatment, or contributed data at each assessment. These quantities should not be inferred from the enrollment count or the outcome group counts.

The study summary describes eligibility screening and informed consent, four testing visits measuring upper-limb motor function and neurophysiology, and 15 intervention visits. It says the intervention visits took place over several weeks, up to 8 weeks. The summary also describes repeat testing after the intervention visits and a follow-up visit 3 months after interventions. The primary outcome timeframe is baseline at 0 weeks and after intervention, up to 8 weeks.

The listed condition is cervical spinal cord injury. The registry status is completed. The record does not provide enough detail to determine the exact visit schedule for each participant, whether all participants received the same intervention duration, or the extent to which follow-up data were available.

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: Of the 47 enrolled SCI participants, six were excluded prior to group assignment. Reasons for exclusion include voluntarily withdrawal (5) and unable to proceed due to clinical care requirements (1). The remaining 41 participants were randomized and competed study procedures.

Overall Study

Reasons for not completing this period:

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 Upper Extremity Motor Score (UEMS) With Manual Muscle Testing, measured over Baseline (0 weeks), after intervention (up to 8 weeks).

The primary endpoint is change in Upper Extremity Motor Score (UEMS), measured with manual muscle testing. The registry describes testing five key muscles in each arm. Each muscle is graded from 0, indicating no contraction, to 5, indicating normal strength. The arm scores are summed, and the reported measure combines the scores for both arms. The maximum total score is 50 points.

UEMS is used in spinal cord injury to assess strength, or muscle power. Higher values indicate more muscle strength, while a higher change score indicates more improvement on this measure. The primary outcome compares the mean change from baseline to after intervention in the active tDCS plus practice group with the mean change in the sham tDCS plus practice group.

Manual muscle testing provides a structured measure of strength across specified muscles. It does not, by itself, describe every aspect of upper-limb function, activity, independence, or quality of life. Nor does the registry’s definition establish how a particular score change would be experienced by an individual. The results should therefore be read as a comparison on this specific strength measure and at the stated assessment time, rather than as a complete account of rehabilitation outcomes.

7. Results Posted in the Registry

• Active tDCS + Task Oriented Practice: mean 3.50 versus 2.55 on control; difference 0.95 (95% CI -0.91 to 2.81), standardized effect d = 0.33; z-test p = 0.316.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary measure is continuous: it can take values along a numerical scale, and the registry reports the mean change for each group. A mean summarizes the group’s average change, but it does not show how much participants’ individual changes varied or whether every participant changed in the same direction. The arm-level means are 3.5 points for active tDCS plus practice and 2.55 points for sham tDCS plus practice.

What does the mean difference represent?

The mean difference compares the average change in one group with the average change in the other. The reported contrast is active minus sham, estimated at 0.95 points. A positive estimate means the active group had the larger mean change in this sample. It is an estimate of the contrast, not a count of participants who improved and not a prediction for any one participant.

In general, a difference in group means is most informative when considered alongside uncertainty and the way the data were collected. The registry reports a standard error of 0.67 for each group mean. Standard error describes uncertainty in an estimated mean; it is not the standard deviation of participants’ outcomes. The record also reports a pooled standard deviation of 2.861 for the comparison, which describes variability on the outcome scale used for the standardized effect calculation.

How should the interval be understood?

A confidence interval represents a range of values reasonably compatible with the observed data under the assumptions of the statistical method. It conveys uncertainty around the estimated mean difference; it is not a range containing a specified proportion of individual participants’ outcomes. The registry’s interval runs from a negative lower limit to 2.807 points. Since it crosses zero, the results do not rule out no average difference. Its span also indicates that the data are compatible with materially different estimates, including values on either side of zero.

The confidence level and the method used to construct the interval are not reported in the registry record. Therefore, the interval can be described as posted, but its construction cannot be independently assessed from the registry information alone.

What does the p-value tell the reader?

The unadjusted p-value is 0.316. In general, a p-value measures how unusual data at least as discrepant as those observed would be under a specified null model and its assumptions. It is not the probability that the null hypothesis is true, and it does not measure the probability that the findings occurred by chance. A p-value does not describe the size or practical importance of an effect. Here, it should be read together with the estimated difference and interval, rather than on its own.

The record calls this p-value unadjusted. Whether the analysis accounted for other outcomes or comparisons is not reported in the registry record. A reader should not assume that an adjustment was or was not made beyond the label attached to the posted result.

What does the standardized effect add?

The comparison reports a standardized effect size of 0.332. A standardized effect expresses the contrast in standard-deviation units, allowing the magnitude to be described relative to the observed variability rather than only in UEMS points. It does not replace the original-scale estimate: the clinical measure remains a score with a maximum of 50 points. The registry does not report an interval for the standardized effect, so its uncertainty is not separately characterized in the posted result.

General interpretation of standardized effects depends on the measure, population, and research question. A particular standardized value does not automatically indicate a meaningful or unimportant difference. The registry record does not state a threshold for a clinically important UEMS change.

Why can over-dispersion matter?

In general, over-dispersion means that observed variability is greater than a statistical model expects. When a model assumes less variability than the data contain, standard errors can be too small and uncertainty can be understated. That concept is especially relevant to count outcomes or models with a specific variance assumption. The primary endpoint is a continuous score, and the registry does not report an over-dispersion assessment or a model-based variance analysis. It would therefore be inappropriate to claim that over-dispersion was present or addressed in this trial.

What can be inferred from the reported methods?

The registry identifies randomization, quadruple masking, and a parallel-group structure, but it does not report the detailed statistical analysis plan. The exact model, confidence-interval method, handling of baseline values, treatment of missing observations, and analysis population are not reported in the registry record. The posted comparison can be interpreted as the reported group mean contrast, but the available details do not establish whether it was adjusted for any covariates or how all design features entered the analysis.

The sample-size illustrations use a normal approximation and equal allocation for planning. Those are assumptions for the illustrations, not evidence about the method used for the trial’s original design or its outcome analysis. The original design assumptions and any justification for the planned enrollment are not reported in the registry record.

10. Confidence Intervals and Precision

The estimated difference in mean UEMS change is 0.95 points, with the active group having the higher observed mean change. The reported interval extends from a negative lower limit to 2.807 points. Because zero lies within that interval, the data are compatible with no mean difference. They are also compatible with a negative difference and with a positive difference up to the reported upper limit. The interval therefore does not pin down the direction or magnitude precisely.

In general, a confidence interval communicates both the estimate and its uncertainty. A narrow interval would indicate greater precision, while a wide interval would indicate more uncertainty, assuming the same interval method and scale. Here the interval covers values on either side of zero, so the observed positive estimate should not be read as a precise estimate of a positive underlying difference. The confidence level and construction method are not reported in the registry record, which limits a fuller evaluation of the interval.

The standard error of each group mean is 0.67. This quantifies uncertainty in the estimated mean, not the range of individual participants’ changes. The posted pooled standard deviation of 2.861 describes outcome variability in the comparison, while the standardized effect is 0.332. These quantities answer different questions and should not be substituted for one another.

The primary outcome results include 16 participants in the active group and 20 in the sham group, compared with registry enrollment of 47. The reason for the difference and the missing-data handling are not reported in the registry record. Without those details, the contribution of incomplete measurements to precision or potential bias cannot be evaluated from the posted information alone.

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 participants and not total events. The comparison is between two treatment groups, and the illustrations assume equal allocation. For an effect set at 100% of the observed effect, the display gives 143 participants per arm for 80% power and 191 participants per arm for 90% power. At 75% of the observed effect, the corresponding figures are 254 and 339 participants per arm. At 50% of the observed effect, they are 570 and 763 participants per arm.

In plain terms, the 80% power column gives the estimated number of participants per arm for a planned study to have an 80% chance of detecting the specified effect under the stated assumptions. The 90% power column describes the corresponding planning target for a 90% chance. These are design calculations, not observed properties of the completed trial. The figures are not observed power.

The planning 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 original trial’s own sample-size assumptions and justification are not reported in the registry record. The illustrations are therefore not evidence that the trial was planned using these assumptions.

Smaller effects require more participants to detect under the same assumptions. That pattern is reflected in the larger per-arm figures for planning around 75% or 50% of the observed effect rather than the full observed effect. The curve should be read as a planning illustration of how required sample size changes with the effect targeted; it is not a forecast of what a future study will achieve.

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 = 0.950; pooled standard deviation σ = 2.861.
2. n = 2 × (1.96 + 0.842)² × 2.861² / 0.950² = 142.4, rounded up to 143 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 <- 0.95                      # observed difference in means
sigma <- 2.86108782273662                     # 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(3892746)
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 = 143 (80% power), 191 (90% power)
 75% of observed effect: n per arm = 254 (80% power), 339 (90% power)
 50% of observed effect: n per arm = 570 (80% power), 763 (90% power)
power.t.test: 143.3 
Simulated power at n = 143 per arm: 0.797 (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 11 outcome measures, but it posts no secondary outcome results. It reports no analysis entries, while also providing the primary comparison statistics described for UEMS change. The record does not explain this difference in reporting, nor does it identify which analyses were planned in advance.

Multiplicity arises when several outcomes, time points, or comparisons are tested. In general, testing more hypotheses can increase the chance of finding at least one apparently notable result even when no true effects exist. Statistical plans may address this through prespecified primary outcomes, hierarchical testing, or adjustments to significance criteria. Whether any such approach was planned or used is not reported in the registry record. The posted p-value is labeled unadjusted, so it should not be interpreted as a multiplicity-adjusted result.

The primary outcome has results for 16 participants in the active group and 20 in the sham group; enrollment is listed as 47. The registry does not report the number randomized or explain why fewer participants appear in the primary outcome groups. It does not describe whether missing measurements occurred, why any data were unavailable, or what approach was used to handle missing data. It also does not say whether participants were analyzed according to their assigned groups or according to treatment received. The analysis population is not reported in the registry record.

These omissions matter because the observed-case comparison may differ from a comparison using all randomized participants if outcome availability is related to assigned group or to participants’ outcomes. This is a general concern, not evidence that such a bias occurred in this trial. Without information about missingness and analysis populations, the possibility and direction of any effect cannot be assessed from the registry record.

The registry also does not report interim analyses, stopping rules, protocol deviations, or a statistical analysis plan. Their presence or absence should not be assumed. The reported endpoint and comparison can be described, but the broader analytical decisions surrounding them remain unclear.

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 non-serious adverse event terms

The registry reports serious adverse events for 20 participants at risk in the active tDCS plus task-oriented practice group and 21 participants at risk in the sham tDCS plus task-oriented practice group. It records zero participants affected by serious adverse events in each group, and zero deaths in each group. No serious adverse event terms are listed.

These figures describe what the registry reports for the stated groups and risk counts. They do not establish that no adverse events of any kind occurred. The registry separately reports other adverse events affecting 16 participants at risk of 20 in the active group and 15 participants at risk of 21 in the sham group. Those are not serious adverse event counts and should not be conflated with the serious-event figures.

The record does not provide event descriptions for the serious-event category, exposure-adjusted rates, timing, severity details for other events, or the method used to collect safety information. The group counts alone do not establish that the interventions caused or did not cause an event. They are descriptive registry results and should be interpreted in light of the limited safety details reported.

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

The registry’s primary outcome results show mean UEMS changes of 3.5 points with active tDCS plus task-oriented practice and 2.55 points with sham tDCS plus task-oriented practice. The estimated mean difference is 0.95 points in the direction of a larger observed mean change in the active group. The interval spans values below and above zero, and the unadjusted p-value is 0.316. Together, these results describe a positive point estimate with substantial uncertainty.

The findings do not establish that active tDCS produces a greater average change than sham tDCS when both are combined with task-oriented practice. They also do not establish that the two approaches have identical effects. An interval that includes zero is not proof of no effect; it indicates that the posted data do not distinguish the estimate from no difference at the stated interval’s level of uncertainty. The confidence level itself is not reported in the registry record.

The comparison concerns the combined intervention packages. Because both groups received task-oriented practice and the registry record does not provide additional treatment details, the contrast is not a comparison of practice versus no practice. The primary result also addresses one strength measure at the post-intervention assessment. It does not by itself establish effects on all aspects of arm function, neurophysiology, daily activities, or longer-term outcomes.

The reported outcome groups contain fewer participants than the stated enrollment, and the registry does not explain the difference or describe missing-data handling. This limits conclusions about how representative the analyzed results are of everyone enrolled. No secondary outcome results are posted, so the registry record does not support conclusions about the other listed outcomes.

These statistics are evidence about the recorded sample and outcome, not medical guidance. They do not determine what treatment an individual should receive, and they do not establish a clinically important threshold for UEMS change. The registry record supports a cautious description of the observed group means and their uncertainty, while leaving important questions about analysis details and broader outcomes unanswered.

16. Why This Trial Matters Statistically

This trial illustrates why an estimated difference should be read with its uncertainty rather than as a standalone number. The active group’s mean change was higher than the sham group’s mean change, and the estimated contrast was 0.95 points. But the interval includes zero and the unadjusted p-value is 0.316. A positive point estimate alone would not show that the underlying groups differ reliably.

The record also highlights the distinction between enrollment and the number contributing primary outcome results. Enrollment is 47, while the recorded outcome groups include 16 participants in the active arm and 20 in the sham arm. Without a reported explanation, readers cannot determine why those figures differ or how the difference relates to missing data and analysis populations. Clear reporting of participant flow and outcome availability is essential for interpreting precision and assessing possible bias.

Planning illustrations are another important statistical distinction. The per-arm targets change substantially when the assumed effect is reduced from the full observed effect to smaller fractions. This demonstrates generally why studies designed around optimistic effect estimates may call for fewer participants than studies intended to detect more modest effects. The posted calculations are illustrations and do not reveal the original trial’s design assumptions.

Finally, the registry separates serious adverse events from other adverse events, and reports zero serious events in either group alongside other-event counts. Keeping these categories distinct avoids treating the absence of reported serious events as an absence of all adverse events. Together, the results demonstrate the value of reading effect estimates, precision, participant counts, planning assumptions, and safety reporting as related but separate parts of a trial record.

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 does not report a detailed statistical analysis plan, the original sample-size justification, the method used to construct the confidence interval, or the confidence level. It also does not describe the analysis model, adjustment for baseline values, or whether the posted group comparison was adjusted for other variables. These omissions make it difficult to assess all assumptions underlying the primary estimate.

The enrollment is listed as 47, but primary outcome group counts are 16 and 20. The record does not explain the difference, provide participant flow, or identify the analysis population. It does not report missing-data amounts, reasons for missingness, or how unavailable measurements were handled. These limitations prevent an assessment of how outcome availability may influence the reported contrast.

The registry lists 11 outcome measures and posts no secondary results. The relationship between the listed outcomes and the analyses performed is not reported. The record also does not describe interim analyses, stopping rules, protocol deviations, or any multiplicity strategy. No conclusion should be drawn about whether these procedures occurred.

The primary endpoint captures manual muscle testing of upper-limb strength. It does not represent every dimension of recovery or function, and the registry does not state a threshold for a clinically important change. The primary timeframe is after intervention, up to 8 weeks; although a follow-up visit 3 months after interventions is described in the study summary, follow-up outcome results are not included among the posted primary results.

Safety reporting is also limited: serious-event counts and counts for other adverse events are reported, but event details, timing, and collection methods are not. These are limitations of what the registry record reports, not evidence that particular analyses or assessments were not conducted.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Improving SCI Rehabilitation Interventions by Retraining the Brain — NCT03892746.
• Registry record last updated 2025-12-10; status last verified 2025-12.
• Results first posted 2025-12-02.
• 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, quadruple-masked, parallel-group phase 1 and phase 2 study in people with cervical spinal cord injury. It compares active tDCS plus task-oriented practice with sham tDCS plus task-oriented practice. Stated enrollment is 47.

The primary outcome is change in UEMS from baseline to after intervention, up to 8 weeks. Reported mean changes are 3.5 points for the active group and 2.55 points for the sham group. The estimated mean difference is 0.95 points, with an interval that includes zero and an unadjusted p-value of 0.316.

The registry reports 16 participants in the active primary outcome group and 20 in the sham group; it does not explain the difference from enrollment. It lists 11 outcome measures but posts no secondary outcome results. Serious adverse events affected zero participants in either group, and deaths were zero in both groups. Further details on analysis methods, missing data, and the original sample-size rationale are not reported in the registry record.