Evaluation of Robotic Arm Rehabilitation in Stroke Patients: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Evaluation of Robotic Arm Rehabilitation in Stroke Patients (NCT00333983), a randomized na study. The primary outcome is Upper Extremity Portion of the Fugl-Meyer Motor Performance Assessment.

2. Clinical Question

3. Trial Design

The registry describes a randomized, parallel-group study with no masking. Enrollment was 62, and the study status is completed. The listed study dates are 2006-06 for start and 2010-04 for primary completion. The sponsor was the US Department of Veterans Affairs. The phase is listed as not applicable.

Three arms appear in the posted results: Planar Robot, Planar + Vertical, and Intensive Conventional Exercise. The analyzed arm counts were 20, 21, and 21, respectively. The study summary frames the clinical comparison as two training programs using robotic exercise devices versus supervised arm exercises in people with chronic, stable stroke-related deficits. The record does not report the allocation procedure beyond identifying the study as randomized, nor does it describe concealment or the details of the exercise protocols.

The primary outcome was the upper-extremity portion of the Fugl-Meyer assessment, measured from baseline to final training at 6 weeks. The registry reports one outcome measure and one analysis. Its analysis entry identifies a mixed-model analysis across the three groups, but does not provide the model specification, parameter estimate, or confidence interval. The reported group summaries and pairwise comparisons offer descriptive and recalculated views, but those do not disclose the details of the sponsor’s model.

Although the outcome population is described as intention-to-treat, the registry states that participants who were non-compliant or did not reach the midpoint evaluation were exceptions. The number and characteristics of any such participants are not reported. The original design assumptions, including the planned analysis population and the rationale for the enrollment target, are also 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: Participants were excluded prior to randomization if they did not meet inclusion/exclusion criteria. Some candidates declined after learning of the study length and schedule committment.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: The number of participants analyzed were based on an intention to treat methodology with the exception of individuals that were non-compliant with the protocol or did not progress to the midpoint (3 week) evaluation.

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 Upper Extremity Portion of the Fugl-Meyer Motor Performance Assessment, measured over Baseline to Final Training (6 weeks).

The primary endpoint was the upper-extremity portion of the Fugl-Meyer Motor Performance Assessment, expressed in units on a scale. The assessment is described as a stroke-specific, performance-based impairment index. The upper-extremity motor portion covers movement, coordination, and reflex action involving the shoulder, elbow, forearm, wrist, and hand. Each item is scored according to whether the movement can be performed fully, partially, or not at all. The stated total possible range is 0 to 66, with higher scores indicating a better outcome.

This measure was selected to assess motor impairment relevant to arm function after stroke. The registry describes the broader Fugl-Meyer assessment as covering motor functioning, balance, sensation, and joint functioning, while specifying that only the upper-extremity motor portion served as the primary outcome. It reports the outcome as a mean with standard deviation and identifies the timeframe as baseline to final training at 6 weeks.

The posted arm results are changes over that timeframe, not final scores alone. A mean change describes the average score movement within an arm; the standard deviation describes variation among participants around that arm’s mean. Neither summary alone establishes how individuals changed or whether the groups differed under the sponsor’s full model.

7. Results Posted in the Registry

• Planar + Vertical: mean 2.51 versus 3.27 on control; difference -0.76 (95% CI -2.78 to 1.26), standardized effect d = -0.23; z-test p = 0.461.
• Intensive Conventional Exercise: mean 1.82 versus 3.27 on control; difference -1.45 (95% CI -3.76 to 0.86), standardized effect d = -0.38; z-test p = 0.219.

8. Statistical Interpretation

9. Statistical Methods Explained

General: what does a mean change describe? A mean summarizes the average outcome within a group. Here, each arm’s posted value is the average change in the upper-extremity Fugl-Meyer score between baseline and final training. The standard deviation describes how dispersed individual changes are around that average. A standard deviation is not the uncertainty interval for the group mean, and it should not be read as a range containing every participant.

General: what does a between-group mean difference describe? A mean difference contrasts the average outcome in one arm with the average in a reference arm. The recalculated values use Planar Robot as the reference: Planar + Vertical has a mean difference of -0.76, and Intensive Conventional Exercise has a mean difference of -1.45. A negative sign indicates a lower mean change in the compared arm than in the reference arm, under this subtraction order. These are unadjusted recalculations from the posted summaries, not model estimates from the registry’s mixed-model analysis.

General: why use confidence intervals? A confidence interval expresses uncertainty around an estimated effect under the method used to calculate it. An interval that includes zero is compatible with no between-arm difference under that calculation, as well as with effects in either direction that fall within the interval. It does not prove that the groups are equivalent. The recalculated interval for Planar + Vertical runs from -2.78 to 1.26, so it includes zero. The interval for Intensive Conventional Exercise also extends from a negative value to a positive upper limit and includes zero. The record does not post confidence intervals for the sponsor’s mixed-model result.

General: what does a p-value contribute? A p-value summarizes how surprising data at least as inconsistent with a specified null hypothesis would be if that hypothesis and the analysis assumptions held. It does not measure the probability that the null hypothesis is true, the size of an effect, or clinical importance. The registry reports p = .025 for the three-group mixed-model analysis. The unadjusted recalculations report p = 0.461 and p = 0.219 for the two pairwise comparisons. Those values arise from different analyses and should not be treated as interchangeable.

General: what is a mixed model? Mixed models are a broad family of statistical methods that can represent relationships among repeated or otherwise related observations. Their usefulness depends on the data structure and the model specification. The registry names a mixed-model analysis but does not report its fixed effects, covariance structure, handling of missing observations, or other specification details. It is therefore not possible to determine from the record precisely how the model used the available measurements or how its p-value relates to particular pairwise contrasts.

General: why can over-dispersion matter? In count-data settings, over-dispersion means that the observed variability exceeds what a simple model assumes. It can make standard errors too small if ignored. This trial’s primary endpoint is a continuous score, not a count outcome, so over-dispersion is not the central issue in interpreting these results. More generally, valid uncertainty estimates depend on whether the analysis matches the outcome and data structure. The registry does not provide enough model detail to evaluate those assumptions for its mixed-model result.

What can be verified from the posted summaries? The arm counts, means, and standard deviations permit simple unadjusted comparisons, which are identified as recalculations. They do not recover an analysis that uses participant-level repeated measurements, covariate adjustment, or other model features. The recalculations also do not account for any multiplicity adjustment. No such adjustment is reported for the sponsor’s analysis, so whether or how it handled multiple comparisons is not known.

The discrepancy flag is important to interpretation: the recalculated pairwise results do not match the sponsor’s own reported analysis. The sponsor’s analysis takes precedence. That does not make the recalculations useless; they show what follows from the posted arm summaries under a simpler comparison. But they cannot be presented as a reproduction of the sponsor’s model or as a replacement for it. The missing model estimates and confidence intervals limit the ability to evaluate the magnitude and precision of the reported overall finding.

10. Confidence Intervals and Precision

Precision concerns how narrowly an estimate is determined by the data and analysis. The arm means are accompanied by standard deviations, which describe individual-level variability, while the recalculated pairwise comparisons include confidence intervals that express uncertainty around the mean differences. These are distinct forms of information: a standard deviation is not a confidence interval, and neither one alone describes every participant’s outcome.

For Planar + Vertical compared with Planar Robot, the recalculated mean difference is -0.76, with a confidence interval from -2.78 to 1.26. The interval spans negative and positive values and includes zero. For Intensive Conventional Exercise compared with Planar Robot, the recalculated mean difference is -1.45; its confidence interval starts at -3.761 and extends to a positive upper limit, also including zero. The exact upper endpoint is not restated because the posted value has more than three decimal places. Both recalculated intervals therefore leave uncertainty about the direction and size of the pairwise difference.

The intervals belong to unadjusted recalculations, not the sponsor’s mixed-model analysis. The registry reports p = .025 for that overall analysis but posts no model-based confidence interval or estimate. Consequently, the precision of the sponsor’s modeled effect cannot be assessed from the record. The discrepancy between the sponsor result and the recalculations further cautions against treating the simpler intervals as a complete account of the modeled finding.

Even a narrow confidence interval would address statistical uncertainty, not whether a difference matters clinically. The record does not state a threshold for a clinically important change. Nor does it report enough information to assess precision after accounting for missing data or the details of the repeated-measures model.

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 sample-size display is a planning illustration based on the observed effect, not the trial’s original design. The listed values are participants per arm, not totals across arms or total events. The 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 the stated fraction of the observed effect. The trial’s own original design assumptions are not reported in the registry record.

The 80% power column gives the illustrated number of participants per arm for an 80% chance of detecting the specified effect under those assumptions, if that effect and the calculation assumptions were true. The 90% power column applies the same idea at a higher target chance of detection. These are planning quantities; they are not observed power.

For Planar + Vertical compared with Planar Robot, the illustration lists 297 participants per arm for 80% power and 397 for 90% power when planning for 100% of the observed effect. Planning for 75% gives 527 and 705 participants per arm, respectively; planning for 50% gives 1,185 and 1,586. For Intensive Conventional Exercise compared with Planar Robot, the corresponding figures are 108 and 145 at 100%, 192 and 257 at 75%, and 431 and 577 at 50%.

The pattern reflects a general planning principle: smaller effects are harder to detect and require more participants under otherwise fixed assumptions. The fractions describe planning scenarios based on the observed effect; they do not establish what effect a future study will see. The curve should be read as a visual counterpart to these planning scenarios, not as a summary of the completed trial’s achieved power.

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 = -0.760; pooled standard deviation σ = 3.301.
2. n = 2 × (1.96 + 0.842)² × 3.301² / -0.760² = 296.1, rounded up to 297 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 <- -0.76                      # observed difference in means
sigma <- 3.30090547018192                     # 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(333983)
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 = 297 (80% power), 397 (90% power)
 75% of observed effect: n per arm = 527 (80% power), 705 (90% power)
 50% of observed effect: n per arm = 1,185 (80% power), 1,586 (90% power)
power.t.test: 297.1 
Simulated power at n = 297 per arm: 0.800 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

13. Analyses Reported by the Sponsor

The registry reports the sponsor’s analysis as a mixed-model analysis across Planar Robot, Planar + Vertical, and Intensive Conventional Exercise, with p = .025. It does not post the associated model estimate, confidence interval, or detailed model specification. The posted result therefore identifies an overall model-based finding but does not show its size or precise direction.

The pairwise comparisons are recalculated from arm-level summary statistics. They are unadjusted comparisons of each non-reference arm with Planar Robot. Their p-values are 0.461 for Planar + Vertical and 0.219 for Intensive Conventional Exercise. These do not match the sponsor’s reported p-value. Because a discrepancy is flagged, the sponsor’s own analysis takes precedence; the recalculations should not be treated as corrections to it or as a replication of the mixed model.

The distinction matters because a mixed model can use information and assumptions that are not recoverable from arm means and standard deviations alone. Without the model details and estimates, readers cannot determine which choices account for the difference. The recalculations remain useful as transparent, simple comparisons of the posted summaries, while the sponsor’s model is the relevant reported analysis. The record does not provide enough information to reconcile the two results further.

14. Multiplicity, Missing Data and Analysis Populations

The registry identifies one primary outcome and one reported analysis, with a mixed-model p-value across the three groups. It does not report whether the analysis plan specified additional hypotheses, how pairwise comparisons were handled, or whether any multiplicity adjustment was used. The recalculated pairwise contrasts are unadjusted. They should not be interpreted as adjusted tests or as proof that the sponsor used the same comparisons.

Multiplicity arises when several hypotheses are tested: the more opportunities there are to find a small p-value, the greater the chance of a false-positive result if each test is judged separately. Adjustment methods can address that issue, but the choice depends on the planned questions and analysis. Since the registry does not report a multiplicity procedure, its use cannot be assumed. The posted overall p-value does not, by itself, reveal how any follow-up comparisons were controlled.

The record describes the primary outcome population as intention-to-treat with exceptions for participants who were non-compliant or did not reach the midpoint evaluation at 3 weeks. Strictly including all randomized participants is not what that exception describes. The number excluded, reasons by arm, and consequences for the analysis are not reported in the registry record. It also does not explain how missing outcome measurements were handled in the mixed model or whether any imputation was used.

These omissions affect interpretation. Excluding participants after randomization can alter the comparability that randomization is intended to create, depending on who is excluded and why. Missing-data methods also rely on assumptions about why observations are unavailable. Without group-specific accounting and analysis details, readers cannot assess how these issues might affect the estimated group differences. The registry’s brief population description is informative, but it is not a complete account of participant flow or missing-data handling.

The registry does not report an interim-analysis plan, stopping rules, or a fuller statistical analysis plan. Those items should not be inferred from the single posted analysis entry. Their absence limits evaluation of prespecification and analysis flexibility, but does not establish that such procedures were or were not used.

15. Safety Results

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

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 1% reporting threshold.

Most frequent non-serious adverse event terms

The serious adverse event figures show zero affected participants among 20 at risk in Planar Robot, zero among 21 at risk in Planar + Vertical Robot, and zero among 21 at risk in Intensive Conventional Exercise. These are counts for the groups and denominators recorded in the safety results. The registry lists no serious adverse event terms.

The separate other-event counts are 2 of 20 in Planar Robot, 1 of 21 in Planar + Vertical Robot, and 1 of 21 in Intensive Conventional Exercise. These are reported as participants affected, not as a measure of event severity or a complete description of event types. The registry does not report deaths in the posted safety fields; a missing value should not be interpreted as a reported count of zero.

These figures are descriptive. They do not establish that the groups had identical safety experience, particularly with the small group sizes and without details about event definitions, timing, relatedness, or follow-up. The record does not provide enough information to infer the cause of an event or compare risks reliably. No medical conclusion should be drawn from the absence of recorded serious events alone.

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

The record describes a randomized comparison of three rehabilitation groups and posts arm-level changes in an upper-extremity motor assessment. The observed mean changes were 3.27 for Planar Robot, 2.51 for Planar + Vertical, and 1.82 for Intensive Conventional Exercise. Those descriptive values establish what was recorded at the arm level, but they do not alone show whether the groups differed beyond chance variation or whether any difference was important to participants.

The sponsor’s reported mixed-model analysis has p = .025 across the three groups, but the registry does not give a model estimate or confidence interval. The unadjusted recalculations compare each other arm with Planar Robot and have intervals that include zero. Because the recalculations differ from the sponsor’s analysis, the sponsor’s result takes precedence; the discrepancy also means the posted record does not allow a full assessment of the magnitude and precision of that result.

A p-value is not a measure of treatment benefit, clinical importance, or the probability that a finding is true. Likewise, a confidence interval describes statistical uncertainty under its calculation method, not certainty about an individual participant’s outcome. The record does not report a threshold for an important Fugl-Meyer change, detailed model results, or enough missing-data information to resolve these questions.

The results therefore support a limited statistical reading: there is a reported overall model-based result, while simple recalculated pairwise contrasts are uncertain and do not reproduce it. They do not by themselves establish which rehabilitation approach is preferable, explain the source of the discrepancy, or determine whether the findings apply to people beyond the study population. Such conclusions require evidence and context that are not reported in the registry record.

17. Why This Trial Matters Statistically

This trial is statistically instructive because the registry contains both an overall sponsor analysis and enough arm-level summary information to calculate simple pairwise contrasts. The overall analysis reports p = .025, while recalculated comparisons with Planar Robot report p = 0.461 and p = 0.219. Their difference demonstrates why an analysis reconstructed from summary statistics should not automatically be treated as a reproduction of a model-based result.

The endpoint also illustrates the distinction between an average change and the spread of individual changes. The arm means describe average score movement, while the standard deviations show substantial variation around those averages. A group mean can conceal diverse participant-level trajectories, and a group summary cannot reveal whether missing observations or protocol deviations influenced the result.

The record’s reporting gaps matter for reproducibility. It names a mixed model but does not provide the model estimates, confidence intervals, specification, or missing-data procedure. It describes an intention-to-treat approach with exceptions but does not state how many participants those exceptions affected. These omissions restrict independent evaluation of the analysis and its precision.

Finally, the planning illustrations show how assumptions about the effect to detect influence sample-size requirements. They are planning scenarios based on observed effects, not evidence that the completed study had a particular probability of detecting an effect. Keeping those planning calculations separate from observed findings is essential to avoid over-reading a completed trial’s data.

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 registry record does not provide full model results for the mixed-model analysis. In particular, it lacks a model-based effect estimate and confidence interval, as well as details about the model specification. This prevents direct assessment of the magnitude and precision of the sponsor’s reported overall result and makes the discrepancy with the unadjusted recalculations difficult to explain.

The participant analysis population is described as intention-to-treat with exceptions for non-compliance or failure to progress to the midpoint evaluation. Counts and reasons for those exceptions are not reported. The handling of other missing observations is also not reported, so the potential influence of exclusions and missing data cannot be assessed from the registry entry.

The outcome is a change score, but the registry does not provide participant-level observations or detail the timing and completeness of measurements beyond the stated baseline-to-final-training timeframe. The record also does not report a threshold for clinically important change. Statistical differences therefore cannot be translated into clinical importance using the registry information alone.

Although the study is identified as randomized and unmasked, details of sequence generation, allocation concealment, and the exercise protocols are not reported. The record does not report multiplicity handling or an interim-analysis plan. Safety reporting is limited to group counts for serious and other events, without event descriptions or information about relatedness. These limitations concern the information available in the registry record and do not establish what was or was not included in other study materials.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Evaluation of Robotic Arm Rehabilitation in Stroke Patients — NCT00333983.
• Registry record last updated 2014-03-20; status last verified 2014-02.
• Results first posted 2014-03-20.
• 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

NCT00333983, Evaluation of Robotic Arm Rehabilitation in Stroke Patients, is recorded as a completed, randomized, parallel-group study with no masking and enrollment of 62. It compared Planar Robot, Planar + Vertical, and Intensive Conventional Exercise in people with chronic, stable stroke-related deficits.

The primary outcome was change in the upper-extremity portion of the Fugl-Meyer Motor Performance Assessment from baseline to final training at 6 weeks. The registry reports a mixed-model analysis across the three groups with p = .025, but no model estimate or confidence interval. Unadjusted pairwise recalculations are available for comparisons with Planar Robot; because they differ from the sponsor’s result, the sponsor’s analysis takes precedence.

The record reports zero serious adverse events in each group and other-event counts of 2, 1, and 1, respectively. Details on model specification, missing-data handling, multiplicity, and the original design assumptions are not reported in the registry record.