Optimizing Rehabilitation for Phantom Limb Pain Using Mirror Therapy and Transcranial Direct Current Stimulation (tDCS): Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Optimizing Rehabilitation for Phantom Limb Pain Using Mirror Therapy and Transcranial Direct Current Stimulation (tDCS) (NCT02487966), a randomized na study. The primary outcome is Changes in the Visual Analog Scale for Phantom Limb Pain.

2. Clinical Question

3. Trial Design

The registry describes a randomized, triple-masked, factorial controlled trial at two sites. Participants were assigned to one of four combinations: active tDCS with active Mirror Therapy; active tDCS with sham Mirror Therapy; sham tDCS with active Mirror Therapy; or sham tDCS with sham Mirror Therapy. The sham tDCS and sham Mirror Therapy group received 20 minutes of sham tDCS and 15 minutes of sham Mirror Therapy. The active and sham Mirror Therapy descriptions distinguish use of an active mirror from use of a covered mirror. The listed device was Soterix tDCS.

A factorial design varies more than one intervention component within the same trial. In principle, it can estimate the effect associated with each component and assess whether the components act differently in combination. Those questions usually require analyses that account for the factorial structure. The posted results instead give group means and pairwise mean differences using active tDCS with sham Mirror Therapy as the reference. The registry record does not report a factorial model, main-effect estimates, or an interaction estimate, so the posted pairwise contrasts should not be treated as those analyses.

The registry lists enrollment of 132 and status active, not recruiting. It lists the study phase as NA. The primary endpoint timeframe is 4 weeks, and the secondary outcomes are changes in VAS stump pain and VAS phantom limb sensation over 4 weeks. The listed study start is 2015-07 and primary completion is 2020-03-27. The registry record does not report the original sample-size justification, the detailed allocation procedure, or the masking procedures for each role. The trial's own statistical analysis plan is not reported in the registry record.

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: Please note that from 132 subjects enrolled, 112 started (were randomized) as 20 subjects screened out after signing the consent form (time commitment=8; loss of interest=5; no more phantom limb pain=3; personal reasons=4).

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 Changes in the Visual Analog Scale for Phantom Limb Pain, measured over 4 weeks.

The primary endpoint is change in VAS phantom limb pain from baseline to 4 weeks, calculated as the value at 4 weeks minus the baseline value. It is a continuous outcome, reported as a mean and standard deviation for each treatment group. The registry describes the VAS as a 10-point scale, with 0 meaning no pain and 10 meaning pain as bad as one can imagine. Under the stated change-score convention, a negative value represents a reduction in pain, and a more negative change indicates a larger reduction in the score.

A change score expresses how the measure shifted over the specified follow-up interval rather than reporting only a follow-up value. Comparing group mean changes can describe whether the average movement differed among randomized groups. The measure is used as the primary endpoint because it records pain severity on a scale that can be summarized quantitatively and compared across the assigned treatment combinations. The registry record does not report further justification for selecting this endpoint, details on the scale's administration, or a threshold for interpreting a change as clinically important. The posted summaries therefore describe average scale changes, not the proportion of participants who experienced a particular level of benefit.

7. Results Posted in the Registry

• Active tDCS and Active Mirror Therapy: mean -2.84 versus -3.35 on control; difference 0.51 (95% CI -1.10 to 2.12), standardized effect d = 0.16; z-test p = 0.535.
• Sham tDCS and Active Mirror Therapy: mean -1.78 versus -3.35 on control; difference 1.57 (95% CI -0.06 to 3.20), standardized effect d = 0.51; z-test p = 0.058.
• Sham tDCS and Sham Mirrory Therapy: mean -2.58 versus -3.35 on control; difference 0.77 (95% CI -0.82 to 2.36), standardized effect d = 0.25; z-test p = 0.344.

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.

Changes in the Visual Analog Scale for Stump Pain

• 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:
  • Active tDCS and Active Mirror Therapy: mean -1.31 versus -1.90 on control; difference 0.59 (95% CI -1.25 to 2.43), standardized effect d = 0.17; z-test p = 0.529.
  • Sham tDCS and Active Mirror Therapy: mean -0.91 versus -1.90 on control; difference 0.99 (95% CI -0.85 to 2.83), standardized effect d = 0.28; z-test p = 0.291.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Active tDCS and Active Mirror Therapy and the control. The interval gives the range of effects that remain compatible with the data.
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Sham tDCS and Active Mirror Therapy and the control. The interval gives the range of effects that remain compatible with the data.

Changes in the Visual Analog Scale for Phantom Limb Sensation

• 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:
  • Active tDCS and Active Mirror Therapy: mean -1.86 versus -2.55 on control; difference 0.69 (95% CI -0.66 to 2.04), standardized effect d = 0.27; z-test p = 0.316.
  • Sham tDCS and Active Mirror Therapy: mean -1.35 versus -2.55 on control; difference 1.20 (95% CI -0.18 to 2.58), standardized effect d = 0.45; z-test p = 0.089.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Active tDCS and Active Mirror Therapy and the control. The interval gives the range of effects that remain compatible with the data.
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Sham tDCS and Active Mirror Therapy and the control. The interval gives the range of effects that remain compatible with the data.

The two secondary outcomes are changes in VAS stump pain and VAS phantom limb sensation over 4 weeks. The posted group means for these outcomes are generally negative, indicating average reductions under the registry's change-score convention. The available pairwise comparisons likewise show uncertainty: their confidence intervals include zero, and their unadjusted p-values do not provide a clear separation from the reference group. The posted summaries therefore present a broadly similar pattern of imprecise contrasts rather than a consistent, clearly resolved difference across the secondary measures.

These outcomes provide related but distinct information. Stump pain is not the same measure as phantom limb pain, and phantom limb sensation is a separate reported experience. Their results may add context to the primary endpoint, but they do not replace it or establish the same treatment effect. The registry record does not report a combined outcome or an analysis tying changes across these measures together.

Unadjusted secondary findings carry less inferential weight because multiple outcomes and contrasts create more opportunities for apparently notable results by chance. The registry record does not report a multiplicity adjustment, a hierarchy for testing outcomes, or confirmatory status for the secondary analyses. Their estimates can be read as exploratory descriptions with uncertainty, not as independent confirmation of a primary finding. No secondary result should be elevated solely because its numerical estimate or p-value appears more favorable than another; the design and analysis plan needed to support such a conclusion are not reported.

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

• Changes in the Visual Analog Scale for Stump Pain
• Changes in the Visual Analog Scale for Phantom Limb Sensation

9. Statistical Interpretation

10. Statistical Methods Explained

What does a mean change describe?

A mean is the arithmetic average of the recorded values within a group. For this outcome, each participant's reported value represents the VAS score at 4 weeks minus the baseline score. A negative group mean therefore indicates that the average score fell over that interval. The standard deviation describes how dispersed the individual change scores are around their group mean. It is not the uncertainty in the mean itself: uncertainty in an estimated mean depends both on variability and on the amount of information available.

Means and standard deviations are useful summaries for a continuous outcome, but they can conceal variation among participants. A group average does not tell how many people had a decrease, how many had an increase, or whether a small number of values strongly influenced the mean. The registry record does not report individual participant data or additional distributional summaries that would answer those questions.

What is a mean difference in these comparisons?

Each posted contrast compares a group's mean change with the mean change in active tDCS and sham Mirror Therapy. The difference is expressed in the original scale units. Since the reference mean is -3.35, a positive contrast indicates that the compared group's mean is closer to zero, or less negative, than the reference mean. The sign describes direction under this subtraction convention; it does not establish importance or causation beyond the randomized comparison.

The reported standard errors quantify the estimated sampling uncertainty in the group means used for the contrasts. A confidence interval combines an estimate with its uncertainty to show a range of values compatible with the data under the calculation's assumptions. A wider interval reflects less precision. The posted interval calculations are unadjusted pairwise calculations based on group summaries, not a reported model accounting for the factorial structure or other covariates. The registry record does not report whether the sponsor used a different prespecified analysis.

Why does the factorial structure matter?

The four groups represent combinations of two components, tDCS and Mirror Therapy, each with an active and sham version. A factorial analysis can use all groups to estimate an average contrast for each component while considering the other component, and can examine whether the effect of one component depends on the level of the other. A set of pairwise contrasts against one reference group answers a narrower question: how each of three combinations compares with that selected combination. These are not interchangeable summaries. The registry record does not report estimates for the separate component effects or their interaction, so conclusions about those factorial questions cannot be drawn from the posted pairwise results alone.

How should the p-values be read?

The unadjusted p-value is calculated for a particular contrast under a null hypothesis of no mean difference, given the assumptions of that calculation. It is not the probability that the null hypothesis is true, nor does it measure the size or importance of a difference. An unadjusted value also does not account for the fact that several contrasts and outcomes are examined. The registry record does not report a multiplicity procedure, so the p-values should be treated as nominal results rather than as an adjusted family of tests.

For the posted comparisons, each confidence interval includes zero, and none of the unadjusted p-values is below 0.05. These observations do not prove that the groups are equivalent. Demonstrating equivalence requires a prespecified margin and an analysis designed for that purpose; such a margin and analysis are not reported in the registry record. The estimates and intervals are more informative about the range and direction of uncertainty than a threshold-only reading of p-values.

What is and is not reported about the analysis?

The posted primary and secondary contrast estimates are recalculated, unadjusted comparisons derived from the group means, standard deviations, and group sizes. No sponsor-reported analysis is listed in the registry record. It does not report an analysis population definition, covariate adjustment, missing-data method, protocol deviations, or a prespecified statistical analysis plan. These omissions limit assessment of whether the posted summaries reflect the intended primary analysis and how incomplete outcome data were handled.

The sample-size illustrations use a normal approximation and an equal-allocation assumption between the two arms being compared, with a two-sided significance level of 0.05. They scale the observed effect to illustrate planning under different effect sizes. These calculations are planning illustrations, not a reconstruction of the trial's original design. The original design assumptions and sample-size justification are not reported in the registry record. The illustrations should not be mistaken for a formal assessment of the trial's ability to detect its planned factorial effects.

11. Confidence Intervals and Precision

The confidence intervals convey the precision of the three primary pairwise estimates. For active tDCS with active Mirror Therapy compared with active tDCS and sham Mirror Therapy, the estimated mean difference is 0.51, with a 95% confidence interval from -1.1 to 2.12. For sham tDCS with active Mirror Therapy, the estimate is 1.57 and the interval runs from -0.056 to 3.196. For sham tDCS with sham Mirror Therapy, the estimate is 0.77 and the interval runs from -0.824 to 2.364.

Each interval crosses zero, the value corresponding to no mean difference. The intervals therefore include both no difference and values on either side of it. Their span shows that the posted estimates do not pin down the size or direction of the comparison with high precision. In particular, a nonsignificant result is not the same as proof of no difference: an interval can include zero while also allowing nonzero differences.

In general, a 95% confidence interval is a range produced by a method that, over repeated studies under its assumptions, would cover the true parameter in 95% of such intervals. It is not a statement that there is a 95% probability that the fixed true effect lies in this particular interval. These intervals come from unadjusted recalculations based on posted summaries. The registry record does not report whether they match the sponsor's intended model-based intervals, nor does it report a clinically important difference threshold. As a result, statistical uncertainty can be described, but the clinical importance of values within these ranges cannot be classified from the registry record alone.

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 for 80% power and participants per arm for 90% power. They are not total event counts. The calculations use 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 design assumptions and sample-size justification are not reported in the registry record.

The 80% column describes the number of participants per arm estimated to give an 80% chance of detecting the selected effect under the calculation's assumptions if that effect is real. The 90% column gives the corresponding planning target for a 90% chance. These are design targets, not guarantees: actual performance depends on whether the assumptions, including the effect size and variability, are appropriate. Smaller effects require more participants than larger effects, so the illustrations increase the planned group size when the target is reduced to 75% or 50% of the observed effect.

The values are based on effects observed in this trial and are therefore sensitive to the uncertainty of those estimates. An observed effect may differ from the effect a future study is intended to detect, and it should not automatically be treated as the best planning target. These figures are planning illustrations, not observed power; observed power is not a useful substitute for interpreting the estimates and confidence intervals after a study has been completed. The registry record does not report whether these illustrations reflect the trial's original planning process.

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 = 0.510; pooled standard deviation σ = 3.096.
2. n = 2 × (1.96 + 0.842)² × 3.096² / 0.510² = 578.4, rounded up to 579 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 <- 0.51                      # observed difference in means
sigma <- 3.09576015044624                     # 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(2487966)
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 = 579 (80% power), 775 (90% power)
 75% of observed effect: n per arm = 1,029 (80% power), 1,377 (90% power)
 50% of observed effect: n per arm = 2,314 (80% power), 3,098 (90% power)
power.t.test: 579.4 
Simulated power at n = 579 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

The registry lists one primary outcome and two secondary outcomes, and the posted summaries include several pairwise comparisons. Repeated testing across outcomes and contrasts raises a multiplicity issue: without an adjustment or prespecified testing sequence, nominal p-values do not control the chance of at least one false-positive finding across the full set of questions. The registry record does not report a multiplicity strategy, a hierarchy of hypotheses, or which comparisons were intended as confirmatory. The unadjusted p-values should therefore not be interpreted as multiplicity-controlled evidence.

The factorial design also creates analytic questions beyond the pairwise contrasts that are posted. The registry record does not report an analysis of the tDCS main effect, the Mirror Therapy main effect, or the interaction between components. It does not report whether the analysis incorporated site or other covariates. The pairwise recalculations cannot substitute for those unreported analyses.

Missing outcome data can affect both estimated group means and comparisons if availability differs across groups or relates to participants' outcomes. The registry record does not report the extent or pattern of missing data, the approach used to handle missing values, or sensitivity analyses. It also does not specify the analysis population, such as whether results were based on all randomized participants or a subset with observed measurements. The posted group sizes alone do not establish how missingness was handled or whether group summaries use the same population definition as the randomized allocation.

These omissions do not show that the analyses were inadequately conducted; they mean that the registry record does not provide enough detail to assess those features. Interpretation should remain centered on the posted descriptive summaries and unadjusted contrasts, with the analysis and missing-data uncertainties kept in view.

15. Safety Results

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

Deaths

Other (non-serious) adverse events

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

Most frequent non-serious adverse event terms

The registry reports serious adverse event counts of 0 in each of the four treatment groups, with the listed at-risk group sizes of 29, 28, 28, and 27, respectively. Deaths are also listed as 0 in each group. No serious adverse event terms are listed. These figures describe the registry's posted counts for the groups; they do not demonstrate that serious events are impossible or that risk is absent.

Other adverse events are listed for the groups as 7, 6, 6, and 6. The registry record does not provide event terms or further detail in the registry record for those counts, so their nature, severity, timing, and relation to study treatment cannot be characterized. Counts alone also do not show whether one participant experienced more than one event.

Safety findings should be interpreted in the context of the reporting period, definitions, and collection methods, which are not reported in the registry record. The posted serious-event counts are not evidence of comparative safety between combinations, particularly without a reported safety analysis and fuller event descriptions.

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

The posted results describe average 4-week changes in phantom limb pain across four randomized combinations of active and sham tDCS and Mirror Therapy. All four group means are negative under the stated change-score convention. The pairwise estimates compare each combination with active tDCS and sham Mirror Therapy. Their confidence intervals all include zero, and their unadjusted p-values do not indicate a clear difference under a conventional threshold. The intervals also permit effects in either direction, so the estimates do not establish equivalence or rule out meaningful differences.

These results do not show that any intervention works or does not work. They describe the observed group summaries and the uncertainty in simple pairwise recalculations from those summaries. The record does not provide the sponsor's formal analysis, a clinically important difference threshold, or an analysis that estimates the separate factorial component effects and their interaction. Without those details, a reader should not translate the estimates into a claim that one treatment combination is superior or that the combinations are interchangeable.

The endpoint is a self-reported pain scale change over the specified follow-up. Group averages do not reveal how many participants improved, worsened, or had little change. Nor do the reported values by themselves establish whether a given change matters to participants. The secondary outcomes and posted safety counts provide additional descriptions, but their reporting and analysis details are also limited.

The trial record is best read as documenting a randomized, triple-masked factorial study and posting outcome summaries for its treatment groups. The numerical contrasts offer an account of how group averages relate, while the missing analysis-plan, missing-data, and multiplicity information restricts stronger conclusions. Statistical uncertainty is central to the interpretation: the point estimates are not the only relevant quantities, and the confidence intervals show that the differences remain imprecisely determined.

17. Why This Trial Matters Statistically

This trial is statistically notable because it uses a factorial design to study two treatment components, while the posted comparisons are pairwise contrasts against one combination. That distinction matters. Factorial designs can address component effects and possible interaction, but those questions require suitable analyses and clear reporting. Readers should not infer that the posted pairwise contrasts answer the full set of factorial questions.

The study also illustrates why point estimates and uncertainty belong together. The group averages and mean differences describe the observed pattern, but the confidence intervals include zero and allow a range of possible differences. Reading only the numerical ranking of the group means or only the p-values would miss this uncertainty. The lack of a reported clinically important threshold also means statistical estimates cannot, by themselves, identify which differences would matter in practice.

Finally, the record distinguishes between planning calculations and the trial's original design. The planning illustrations are based on observed effects and stated assumptions, while the original sample-size justification is not reported. Keeping those separate prevents retrospective planning numbers from being mistaken for evidence that the trial was designed around a particular effect or had a particular achieved ability to detect one. Clearer reporting of the analysis plan, missing data, multiplicity approach, and factorial estimates would make the results easier to evaluate and reproduce.

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.

Several trial-specific reporting gaps constrain interpretation. Although the registry describes a two-site randomized, triple-masked factorial study, it does not report how randomization was implemented, who was masked, or how masking was maintained. It also does not report the analysis population or whether the posted group summaries include all randomized participants. These details matter when assessing the credibility and generalizability of outcome comparisons.

The registry record does not report a formal statistical analysis plan, sponsor-reported inferential analyses, covariate adjustments, or a model for the factorial structure. The posted pairwise calculations are unadjusted, and no main-effect or interaction estimates are listed. The record also does not describe missing outcome data, methods for handling them, or sensitivity analyses. These omissions prevent assessment of whether the reported contrasts align with a prespecified primary analysis.

The primary endpoint is a VAS change score, but the registry record does not provide an interpretation threshold for clinically important change or information about the distribution of individual responses. The posted summaries cannot show responder proportions or whether a few observations influenced the group means. The registry also does not report a multiplicity procedure for the primary comparisons and secondary outcomes, which limits confirmatory interpretation of nominal p-values.

Safety reporting is similarly limited: serious adverse event counts and other event counts are listed, but descriptions of other events and further details of collection and follow-up are not reported in the registry record. These limitations identify what the record does not resolve; they do not establish that the trial lacked procedures or that unreported analyses were not conducted.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Optimizing Rehabilitation for Phantom Limb Pain Using Mirror Therapy and Transcranial Direct Current Stimulation (tDCS) — NCT02487966.
• Registry record last updated 2025-09-25; status last verified 2025-09.
• Results first posted 2021-06-21.
• 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 randomized, triple-masked, factorial study of active and sham tDCS and Mirror Therapy for phantom limb pain. The primary outcome is change in VAS phantom limb pain from baseline to 4 weeks, with lower, more negative change indicating a greater reduction in the scale score. The record lists enrollment of 132 and status active, not recruiting.

Posted group means are negative in all four arms. Each of the three unadjusted pairwise mean-difference confidence intervals includes zero. The record also posts secondary summaries for stump pain and phantom limb sensation, along with adverse-event counts. Formal reported analyses, a factorial component analysis, multiplicity procedures, missing-data methods, and the original sample-size justification are not reported in the registry record. The results therefore describe group summaries and uncertain pairwise contrasts, rather than resolving all treatment questions raised by the factorial design.