Condensed and Distributed Robotic Therapy in Spastic Stroke Post Botulinum Toxin Injection: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Condensed and Distributed Robotic Therapy in Spastic Stroke Post Botulinum Toxin Injection (NCT03321097), a randomized na study. The primary outcome is Fugl-Meyer Assessment (FMA).

2. Clinical Question

The central contrast is the timing of the training sessions, rather than a comparison of training with no training. Both groups are described as receiving robot-assisted training after botulinum toxin injection. The schedules differ in weekly frequency and overall duration, so the study asks whether the pattern of delivery is associated with different motor-learning or behavioral outcomes.

The registry describes assessments at 1 week before intervention, 5 weeks after injection during the intervention, 1 week after intervention, and 6 weeks after intervention. The outcome record identifies change from baseline at 1.5 months as the reported primary comparison. The registry record does not provide posted results for every listed assessment time, so the available comparison should not be treated as a complete account of the outcome trajectory over time.

3. Trial Design

This was a randomized, parallel-group trial marked completed in the registry record. The record lists an enrollment of 36 and identifies the two groups as the Condensed RT Group and Distributed RT Group. Each posted primary outcome group has 18 participants. Masking is listed as none, so the record does not describe a masked trial.

The trial concerns people with chronic spastic hemiplegic stroke. The brief summary says participants were randomly assigned to condensed or distributed robot-assisted training after botulinum toxin type A injection. The condensed schedule is described as 4 sessions per week for 6 weeks, while the distributed schedule is described as 2 sessions per week for 12 weeks.

There is an inconsistency in the descriptions of a training session. The brief summary says each session included 40 minutes of robot-assisted training followed by 40-minute functional training. The arm descriptions instead state 45 minutes of robot-assisted training followed by 30-minute functional training. The registry record does not clarify which session duration description applies to the delivered intervention.

The record lists the study start as 2017-10-01 and primary completion as 2019-05-07. The study status is completed. The registry record does not report the original sample-size justification, details of the randomization procedure, or an analysis population definition. Those omissions limit assessment of design choices and how the posted results relate to all participants who entered the trial.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as Fugl-Meyer Assessment (FMA), measured over assessed at 1 week before intervention, 5 weeks after injection (in the middle of intervention), 1 week after intervention (post-intervention), 6 weeks after intervention., change from baseline at 1.5 months reported.

The primary outcome is the upper-extremity subscale of the Fugl-Meyer Assessment (FMA). It is intended to assess neuromusculoskeletal and movement-related function, covering reflexes and movement of the shoulder, elbow, forearm, wrist, and hand, along with coordination and speed. The scale has 33 items, each scored on a 3-point ordinal scale: 0 means cannot perform, 1 means performs partially, and 2 means performs fully. The possible total score ranges from 0 to 66, with higher scores indicating better upper-extremity motor function.

The FMA is used in this study because the comparison concerns motor function following two schedules of robot-assisted training. A change score expresses how far a participant's score moved from the baseline assessment, rather than describing only the score at a single time. The registry record identifies the reported primary change as change from baseline at 1.5 months. It also lists planned assessments before intervention, during intervention, after intervention, and at follow-up.

The FMA is a bounded scale composed of item scores, while the posted summary reports a mean and standard deviation. A mean can offer a compact group-level description, but does not show the distribution of individual responses or how many participants changed by particular amounts. The registry record describes satisfactory psychometric properties for the measure, but does not give additional detail about the performance of the scale in this trial.

7. Results Posted in the Registry

• Distributed RT Group: mean 1.94 versus 3.45 on control; difference -1.51 (95% CI -3.73 to 0.71), standardized effect d = -0.44; z-test p = 0.182.

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.

Goal Attainment Scale (GAS)

• 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:
  • Distributed RT Group: mean 51.83 versus 47.11 on control; difference 4.72 (95% CI -0.13 to 9.57), standardized effect d = 0.64; z-test p = 0.057.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Distributed RT Group and the control. The interval gives the range of effects that remain compatible with the data.

The posted secondary result for Goal Attainment Scale (GAS) is numerically in the opposite direction from the primary FMA contrast: the distributed group has a higher posted mean change, while the primary FMA mean change is higher in the condensed group. The GAS estimate is uncertain, with a confidence interval that includes zero and an unadjusted p-value of 0.057. This mixed pattern does not establish that one schedule has a consistent advantage across outcomes.

The registry lists Canadian Occupational Performance Measure (COPM) and Goal Attainment Scale among secondary outcomes, and the trial summary also names the Modified Ashworth Scale, Wolf Motor Function Test, and Motor Activity Log. The outcome record posts GAS results, but does not give numerical COPM results or results for all the other measures in the registry record. The record therefore does not support a complete comparison of secondary outcome patterns across all listed measures.

Secondary endpoints can help describe whether group differences appear across different aspects of function and participation, but they do not replace the primary endpoint. When several outcomes or assessment times are examined, the chance of finding at least one apparently notable result by chance can increase. Unless analyses account for this multiplicity or identify a clear testing hierarchy in advance, an isolated secondary result deserves less weight than a prespecified primary comparison.

The registry record does not report a multiplicity adjustment or a prespecified hierarchy for the secondary analyses. The posted secondary finding should therefore be treated as exploratory rather than as confirmatory evidence. Its interpretation is further limited by the lack of reported results for some listed endpoints and the absence of detail about missing data and analysis methods. The overall secondary pattern is incomplete and does not resolve the uncertainty in the primary FMA comparison.

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

• Canadian Occupational Performance Measure (COPM)
• Goal Attainment Scale (GAS)

9. Statistical Interpretation

10. Statistical Methods Explained

What does the mean difference represent?

A mean difference subtracts one group's average outcome from the other's according to a stated comparison direction. In this record, the comparison is distributed relative to condensed. The estimate of -1.51 therefore describes the difference between the posted average changes, with the negative sign indicating a lower mean change in the distributed group. This is a group-level contrast; it does not describe the response of every participant.

The outcome is recorded on a bounded score scale. Means summarize the central level of the group results, while standard deviations describe the spread of participant values around the mean. A standard deviation is not a confidence interval and does not show the precision of the group mean. Here, the FMA means and standard deviations are posted separately for the two groups, and the comparison includes its own uncertainty interval.

What does the confidence interval add?

A confidence interval describes uncertainty around an estimated group difference under the analysis assumptions. It gives a range of values that are compatible with the observed data and the method used to construct the interval. A wider interval indicates less precision than a narrower one. The interval for the primary result crosses zero, so the posted data do not distinguish a difference from no difference at the conventional threshold based on the interval alone.

That does not mean the true difference is known to be zero. Nor does a confidence interval assign a probability to the true effect being in any one part of the range. Its interpretation depends on the statistical model and analysis procedure. The registry record does not report enough detail about the fitted model, covariate adjustment, or handling of repeated measurements to evaluate those choices fully.

How should the p-value be read?

The posted primary p-value is unadjusted. In general, a p-value measures how unusual results at least as discrepant as those observed would be if a specified null hypothesis and the analysis assumptions held. It is not the probability that the null hypothesis is true, and it is not a measure of the size or importance of an effect. A non-small p-value does not demonstrate equivalence. Equivalence requires a suitable design, a prespecified margin, and an analysis directed at that question; such details are not reported in the registry record.

The primary result includes both an estimated difference and its uncertainty. Those are more informative than treating the p-value as a pass-or-fail label. The observed estimate is modest relative to the uncertainty around it, and the available interval permits effects in either direction. The record does not report a clinically important difference threshold against which to interpret the estimate.

Why can over-dispersion matter?

General statistical context: over-dispersion occurs when observed variability is greater than a model expects. When it is not addressed, standard errors can be too small, making confidence intervals appear too narrow and p-values too small. Appropriate modeling depends on the outcome distribution and design. The FMA is a bounded score formed from ordinal item scores, so analysts may consider whether a normal approximation adequately represents the data, especially when group sizes are limited. This is a general consideration, not a claim that over-dispersion was detected in this trial. The registry record does not report a distributional diagnostic or a specific model that would permit such an assessment.

What does randomization contribute?

General statistical context: random assignment aims to make treatment groups comparable, on average, with respect to both measured and unmeasured baseline characteristics. It supports a causal interpretation of a contrast when allocation is implemented as planned and the analysis respects the randomized groups. Randomization does not guarantee balance in a particular trial, especially when group sizes are limited, and it does not remove uncertainty or the risk of missing outcome data. The registry record identifies randomized allocation but does not report the method used to generate or conceal assignments, nor does it provide baseline characteristics in the posted results.

The study is listed as unmasked. Lack of masking can matter for outcomes involving assessment or participant-reported performance, although the registry record does not specify who knew each participant's assignment or how assessors were handled. This is a possible source of measurement or performance bias to consider, not evidence that bias occurred.

What can be inferred from the reported summaries?

The posted summaries describe means, standard deviations, a mean difference, a confidence interval, and an unadjusted p-value. They do not reveal the analysis population, missing-data approach, whether the comparison adjusted for baseline values, or how multiple assessment times were handled. Nor do they show the participant-level distribution or the correlation between repeated measurements. Those details can affect both the estimate and its uncertainty. The registry record does not report them, so the summary statistics should be interpreted as a limited account of the analysis rather than a complete statistical report.

11. Confidence Intervals and Precision

The primary mean difference is -1.51 FMA points for distributed relative to condensed training. Its 95% confidence interval extends from -3.728 to 0.708. Because zero lies within the interval, the posted results are compatible with no group difference, but also with differences on either side of zero. The interval is the main guide to precision: it shows that the estimate remains uncertain and that the data do not pinpoint a single value.

The interval's lower and upper limits are not interchangeable with the observed group means or standard deviations. The means describe average change in each group, the standard deviations describe variation among participant scores, and the confidence interval describes uncertainty in the estimated between-group contrast. Each answers a different question. The p-value of 0.182 is consistent with the interval including zero, but it does not replace the interval or describe clinical importance.

Precision is limited by the size and variability of the observed groups. The primary outcome summaries report 18 participants in each group, with standard deviations of 4.22 and 2.29. The record does not give details on missing outcome data or the number included in the comparison beyond these posted summaries, so it is not possible to assess whether the analysis included everyone randomized or whether available cases differed from those without outcome data.

The interval should not be read as a guarantee that the true effect lies within its endpoints. It is a measure of uncertainty under the statistical procedure and assumptions used. Since the registry record does not describe the analysis model in detail, the interval's construction cannot be independently evaluated from the record alone. The registry also does not report a clinical importance threshold, preventing a direct assessment of whether the range represents small, meaningful, or large changes for patients.

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, not total events. They are illustrations based on the observed effect, rather than the trial's original sample-size plan. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario uses a stated fraction of the observed effect as the effect to detect.

The 80% power column gives the illustrative number of participants per arm for a design that would have an 80% chance of detecting the specified effect under the stated assumptions, if that effect were the true one. The 90% column uses a higher target probability of detecting that effect, and therefore generally requires more participants per arm. These are planning quantities, not observed outcomes.

For the primary FMA comparison, planning for 100% of the observed effect gives 80 participants per arm for 80% power and 107 participants per arm for 90% power. Planning for 75% of the observed effect gives 142 participants per arm for 80% power and 189 participants per arm for 90% power. Planning for 50% of the observed effect gives 318 participants per arm for 80% power and 425 participants per arm for 90% power. The decreasing effect scenarios require progressively larger planning samples because smaller effects are harder to distinguish from random variation.

These figures are not observed power, and they do not show what power the completed trial actually had. They are retrospective illustrations using the observed effect estimate, which itself is uncertain. The registry record does not report the original design assumptions or sample-size justification, so these illustrations should not be mistaken for the trial's planned enrollment target.

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 = -1.510; pooled standard deviation σ = 3.395.
2. n = 2 × (1.96 + 0.842)² × 3.395² / -1.510² = 79.4, rounded up to 80 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 <- -1.51                      # observed difference in means
sigma <- 3.39503313680441                     # 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(3321097)
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 = 80 (80% power), 107 (90% power)
 75% of observed effect: n per arm = 142 (80% power), 189 (90% power)
 50% of observed effect: n per arm = 318 (80% power), 425 (90% power)
power.t.test: 80.3 
Simulated power at n = 80 per arm: 0.801 (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 record lists several outcomes and multiple assessment times. The FMA is identified as the primary outcome, while GAS and COPM are identified as secondary outcomes; the summary also names additional measures of body function, activity, and participation. Testing multiple outcomes and time points creates a multiplicity issue: even when no underlying group differences exist, examining many comparisons increases the chance of at least one result appearing noteworthy by chance.

The record does not report a multiplicity adjustment, a testing hierarchy for secondary outcomes, or how comparisons across assessment times were handled. It also does not describe whether the reported primary change score was the only primary analysis or one of several analyses considered. Without that information, the unadjusted p-values should not be interpreted as controlling the overall false-positive risk across all outcomes and time points.

Missing-data handling is not reported in the registry record. The record does not state how many randomized participants contributed data at each assessment, why any measurements might be absent, whether imputation was used, or whether sensitivity analyses were performed. This matters because a complete-case comparison can be biased if the availability of outcome measurements is related to participant characteristics or outcomes. The posted group summaries alone do not establish whether missingness affected the estimate.

The analysis population is also not reported in the registry record. It is therefore unclear whether results were analyzed according to assigned group, only among participants who completed treatment, or under another definition. The record identifies randomized allocation, but does not describe an intention-to-treat analysis or an alternative population.

Details of baseline adjustment, repeated-measures modeling, and the method used to construct the confidence interval are not reported. These omissions do not invalidate the posted summaries, but they limit the ability to assess robustness and reproduce the analysis. No interim analysis plan or monitoring procedure is reported in the registry record, and none should be inferred.

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

The posted primary data estimate a difference in average FMA change between two schedules of robot-assisted training after botulinum toxin injection. The estimate is -1.51 points for distributed relative to condensed training, with a 95% confidence interval from -3.728 to 0.708. The interval includes zero, so the available results do not clearly distinguish a difference from no difference. They also leave uncertainty about the direction and size of any underlying difference.

This is not evidence that the schedules are equivalent. Equivalence is a distinct statistical question that requires a prespecified margin and a suitable design and analysis. The registry record does not report an equivalence margin. Nor does the result establish that either schedule is effective compared with no robot-assisted training, because both trial groups received a training schedule after injection and there is no untreated comparison group in the record.

The numerical result applies to the reported FMA change comparison at 1.5 months. The registry record lists measurements at other times, but does not provide a full set of outcome results for every listed assessment. The posted result therefore cannot establish whether groups differed at particular points during treatment or later follow-up, or whether a difference persisted.

The trial also does not isolate the effect of session frequency alone. The condensed and distributed programs differ in weekly frequency and intervention duration. In addition, the descriptions of session content conflict: one account states 40 minutes of robot-assisted training plus 40-minute functional training, while the arm descriptions state 45 minutes plus 30 minutes. The registry record does not resolve that difference.

These results describe a specific randomized comparison in people with chronic spastic hemiplegic stroke. They do not establish the same pattern in other populations, settings, or intervention programs. They do not provide an individual prediction, a safety conclusion, or medical advice. The appropriate statistical reading is a point estimate with substantial uncertainty and important reporting gaps.

16. Why This Trial Matters Statistically

This trial raises a practical statistical question about treatment scheduling: whether delivering robot-assisted training in a more condensed or more distributed pattern is associated with different outcomes after botulinum toxin injection. That question is distinct from whether the combined intervention is better than no intervention, and the two-arm comparison is structured around the schedule contrast.

The primary FMA result illustrates why effect estimates and uncertainty should be read together. The point estimate gives the observed direction and magnitude of the group contrast, while the confidence interval shows how imprecisely that contrast is estimated. A p-value alone would not communicate the range of effects compatible with the posted results, nor would it establish equivalence or clinical importance.

The record also demonstrates the value of clear reporting. A reader needs to know which intervention was delivered, what outcomes were analyzed, how missing measurements were handled, and whether several comparisons were considered. Here, session duration is described inconsistently, and details about analysis populations, multiplicity, and missing data are not reported in the registry record. These gaps make it harder to connect the numerical findings to the study procedures and to assess their robustness.

Finally, the planning illustrations show how sample-size requirements depend on the size of the effect a future study aims to detect. Smaller target effects require larger planning samples under the stated assumptions. Such illustrations can inform design discussions, but cannot substitute for the trial's unreported original design rationale or resolve uncertainty in the observed estimate.

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.

Several trial-specific limitations affect interpretation. The registry record gives conflicting descriptions of session content: the brief summary describes 40 minutes of robot-assisted training followed by 40-minute functional training, while the arm descriptions state 45 minutes followed by 30 minutes. It is not possible to determine from the record which description matches the sessions delivered.

The groups also differed in schedule frequency and program duration: the condensed schedule is described as 4 sessions per week for 6 weeks, and the distributed schedule as 2 sessions per week for 12 weeks. The comparison therefore cannot isolate frequency from the broader pattern of delivery and duration. Both groups are described as receiving training after botulinum toxin type A injection; the registry record does not include a group without that combination.

The record lists outcome assessments at several times, but does not provide results for all listed measures and time points. Numerical primary results are reported for change from baseline at 1.5 months, while the wider time course is not fully available in the posted results. Some listed secondary outcomes also lack posted numerical results.

Masking is listed as none. The record does not explain which people involved in treatment, assessment, or analysis knew group assignment. It also does not report baseline characteristics, allocation concealment details, analysis populations, missing-data methods, or a multiplicity strategy. These are reporting limitations; the record does not establish that any particular bias occurred.

Adverse-event entries list zero participants at risk and zero affected in both groups. With no participants recorded as at risk in those entries, these values do not support a safety conclusion. The registry record does not provide further adverse-event context or explain the zero at-risk entries.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Condensed and Distributed Robotic Therapy in Spastic Stroke Post Botulinum Toxin Injection — NCT03321097.
• Registry record last updated 2020-06-23; status last verified 2018-08.
• Results first posted 2020-06-23.
• 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 record describes a completed randomized, parallel-group trial of condensed versus distributed robot-assisted training after botulinum toxin type A injection in people with chronic spastic hemiplegic stroke. The study start is listed as 2017-10-01 and primary completion as 2019-05-07. Masking is listed as none.

The primary outcome is change in upper-extremity FMA score, with a reported comparison at 1.5 months. The mean difference for distributed relative to condensed training is -1.51, with a 95% confidence interval from -3.728 to 0.708 and an unadjusted p-value of 0.182. The interval includes zero and leaves meaningful uncertainty about the between-group difference.

GAS is the secondary outcome with numerical results posted in the record. Analysis details, missing-data handling, multiplicity procedures, and the original sample-size justification are not reported. Session-duration descriptions are inconsistent, and the posted adverse-event entries do not permit a safety interpretation.