Robotic and Conventional Hand Therapy After Stroke: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Robotic and Conventional Hand Therapy After Stroke (NCT03020576), a randomized na study. The primary outcome is Impairment Based Arm Measures - Change in Upper Extremity Portion of the Fugl Meyer.

2. Clinical Question

3. Trial Design

The registry classifies this as a randomized, single-masked, parallel-group pilot study. Participants were assigned to robotic therapy or conventional therapy. The brief summary describes assignment as having a 50:50 chance of entering either group. Further details of the randomization procedure are not reported in the registry record.

The record lists enrollment of 31. The brief summary states that 28 subjects from two sites participated, and the primary outcome summaries report 14 participants in each group. These figures describe different parts of the record; the reason for the difference between the registry enrollment and the number in the summary is not reported in the registry record.

The study is marked completed. Its recorded start was 2011-04, and primary completion was 2012-03. The study is identified as a pilot; phase is listed as NA. Columbia University is listed as sponsor. Participants in the robotic group received Amadeo-based therapy for the wrist and hand. The conventional group received therapy for the affected upper limb, with the arm description indicating that treatment was dose matched to the robotic group.

Primary outcome assessment covered baseline and the 8-week completion point, described as an average of 8 weeks through study completion. The registry record does not report the trial's original sample-size justification, planned primary analysis, masking details, or whether any interim analyses were planned. Those details should not be inferred from the sample-size illustrations or the posted summaries.

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

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 Impairment Based Arm Measures - Change in Upper Extremity Portion of the Fugl Meyer, measured over Through study completion, an average of 8 weeks (at baseline and at the 8-week completion point).

The primary endpoint is change in the upper-extremity portion of the Fugl-Meyer measure, reported in units on a scale. The registry describes this as a quantitative measure of arm and hand impairment, ranging from 0 (minimum) to 66 (maximum) points. A higher score represents more skilled movements of the arm and hand.

Change is assessed from baseline to the study's 8-week completion point, with the timeframe described as an average of 8 weeks. Comparing changes between groups focuses the clinical question on whether average change differed between participants assigned to robotic training and those assigned to conventional therapy. The measure was used to assess impairment in arm and hand movement, which is directly relevant to the study's focus on hand rehabilitation after stroke.

The registry record reports group means and standard deviations for change, along with a mean difference and confidence interval. It does not report a separate clinically important difference or a threshold defining a meaningful change on this measure. Statistical uncertainty in the mean difference therefore should not be confused with a judgment about whether a particular score change is important to an individual participant.

7. Results Posted in the Registry

• Robotic Group: mean 2.10 versus 5.90 on control; difference -3.80 (95% CI -14.95 to 7.35), standardized effect d = -0.25; z-test p = 0.504.

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.

Change in Range of Motion Measures

• 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:
  • Robotic Group: mean 3.33 versus 3.53 on control; difference -0.20 (95% CI -0.68 to 0.28), standardized effect d = -0.31; z-test p = 0.415.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Robotic Group and the control. The interval gives the range of effects that remain compatible with the data.

Change in Hand and Pinch Strength

• 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:
  • Robotic Group: mean 0.84 versus 1.63 on control; difference -0.79 (95% CI -5.73 to 4.15), standardized effect d = -0.12; z-test p = 0.754.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Robotic Group and the control. The interval gives the range of effects that remain compatible with the data.

Change in Motor Activity Log Amount

• 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:
  • Robotic Group: mean 2.53 versus 9.35 on control; difference -6.82 (95% CI -33.80 to 20.16), standardized effect d = -0.19; z-test p = 0.620.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Robotic Group and the control. The interval gives the range of effects that remain compatible with the data.

The registry lists seven secondary outcome topics, including range of motion, hand and pinch strength, Motor Activity Log measures, mobility and activities of daily living, hand dexterity, and spasticity. Numerical group summaries are posted for range of motion, hand and pinch strength, and Motor Activity Log amount. The other listed topics do not have numerical results in the summaries.

The directions of the posted secondary mean differences align with the primary estimate: the robotic group's reported average changes were lower than the conventional group's for each of these reported comparisons. The intervals for the three secondary comparisons extend across zero. Viewed alongside the primary result, this pattern does not provide a clear separation between groups across the reported measures. It also does not establish that the therapies are equivalent or that the same pattern would occur in a larger study.

These secondary measures address different aspects of upper-limb function and activity, so they add context rather than serving as interchangeable versions of the primary endpoint. Their results are not a substitute for the primary comparison. The registry does not report a hierarchy specifying which secondary outcome would be confirmatory or how secondary findings were to be interpreted.

Unadjusted secondary results warrant less weight because evaluating several outcomes creates more opportunities for chance findings. In general, multiplicity procedures can control the overall chance of false-positive conclusions across a family of tests, but the record does not report a correction or a prespecified strategy for multiplicity. The posted secondary comparisons should therefore be treated as exploratory signals with substantial uncertainty, rather than independent confirmation of the primary result.

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

• Change in Range of Motion Measures
• Change in Hand and Pinch Strength
• Change in Motor Activity Log Amount
• Change in Mobility and Activities of Daily Living
• Change in Hand Dexterity
• Change in Spasticity Measures
• Change in Motor Activity Log How Well

9. Statistical Interpretation

10. Statistical Methods Explained

The primary result is a comparison of mean change between two randomized groups. The registry reports each group's mean and standard deviation, then gives an unadjusted mean difference for the robotic group relative to the conventional group. These summaries make the direction and scale of the estimated between-group contrast explicit.

What does a mean difference represent?

In general, a mean is the arithmetic average of the observed values in a group. A mean difference subtracts one group's mean from the other's, following a stated order. Here, the reported difference is robotic minus conventional, so a negative value indicates a lower mean change in the robotic group. The primary mean difference is -3.8 points. Its units are points on the Fugl-Meyer change scale, not a percentage or a ratio.

In general, the standard deviation describes how dispersed participant-level observations are around a group's mean. It is not the uncertainty interval for the mean difference and it does not show the full shape of the observations. The registry reports standard deviations of 13.7 in the conventional group and 16.3 in the robotic group. The means and standard deviations alone do not show whether the observations were symmetric, whether there were outliers, or how change was distributed across individuals.

How should the confidence interval be read?

In general, a confidence interval describes statistical uncertainty around an estimate under the assumptions of the method used to construct it. It is not a range containing a fixed proportion of individual participant outcomes. The primary interval is -14.95 to 7.354 points. Because it extends across zero, the posted summary does not distinguish the estimate from no between-group difference at conventional levels by this interval. The record does not identify the exact interval method in the information available for these results.

What does the p-value add?

In general, a p-value measures how incompatible the observed data are with a specified null hypothesis, under the statistical model and assumptions used. It does not measure the size or clinical importance of a difference, and it is not the probability that the null hypothesis is true. The primary unadjusted p-value is 0.504. The registry does not report a complete statistical analysis plan or identify whether this p-value came from the trial's prespecified analysis. It is therefore best read alongside the estimated difference and confidence interval, not as a stand-alone conclusion.

What is meant by unadjusted?

In general, an unadjusted comparison is not corrected for other variables or for the evaluation of multiple outcomes. The comparison posted for the primary endpoint is presented as an unadjusted mean difference. The record does not report a model that adjusts for baseline score, site, or other participant characteristics. It also does not report whether a baseline-adjusted analysis was conducted separately. No such adjustment should be assumed.

Random allocation provides the design basis for comparing assigned groups, but it does not by itself specify the analysis method. The registry identifies a parallel randomized design and reports two group summaries. It does not report whether the primary analysis followed intention-to-treat principles, whether participants were analyzed according to treatment received, or how departures from assigned treatment were handled. Those distinctions can matter when interpreting a trial comparison, and remain unreported in the registry record.

In general, a confidence interval and a p-value depend on assumptions about sampling variability and the analysis procedure. The registry does not state the exact inferential test, degrees of freedom, or distributional checks for the primary comparison. It is possible to describe the posted contrast and uncertainty without claiming that a particular unreported model was used. No formal conclusion about the adequacy of those assumptions can be drawn from group summaries alone.

11. Confidence Intervals and Precision

The primary mean difference is -3.8 points, with a 95% confidence interval from -14.95 to 7.354 points. The interval is wide relative to the point estimate and spans both negative and positive values. That range indicates limited precision: the posted data do not pin down the size or direction of the average difference closely.

In general, a confidence interval reflects uncertainty in an estimate under the method's assumptions. It does not describe the range of likely changes for individual participants. The reported standard deviations, 13.7 in the conventional group and 16.3 in the robotic group, describe variation in participant changes within each group; they are different quantities from the confidence interval around the between-group mean difference.

The interval includes zero, so the primary summary is compatible with no average difference as well as with differences in either direction. It also includes values that could represent nontrivial differences on the scale, but the registry record does not report a threshold for clinical importance. Precision and clinical importance are separate questions: an interval can be interpreted statistically without deciding whether any value within it would matter to participants.

Each group summary includes 14 participants. With this limited number of observations, the estimate remains uncertain, and the results should not be treated as a precise estimate of the average contrast for a broader population. The interval should be read as the uncertainty around this trial's comparison, rather than as evidence that the true difference must lie at the point estimate.

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 event counts. They are illustrations based on the observed effect, not a record of the sample-size calculation used to design the trial. The trial's own original sample-size assumptions and justification are not reported in the registry record.

The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect equal to the stated fraction of the observed effect. The 80% power column gives the illustrative number of participants per arm for a design with an 80% chance of detecting the assumed effect under those assumptions, if that effect and the model assumptions were correct. The 90% power column gives the corresponding planning number for a 90% chance.

For the primary outcome, planning for 100% of the observed effect gives 247 participants per arm for 80% power and 330 participants per arm for 90% power. Planning for 75% of the observed effect gives 439 and 587 participants per arm, respectively. Planning for 50% of the observed effect gives 986 and 1,320 participants per arm, respectively. The planning figures increase as the assumed effect becomes smaller, because smaller between-group differences are generally harder to distinguish from random variation.

The displayed curve should be read as a visual representation of these planning relationships, not as evidence about how much power the completed study had. These figures are not observed power. They are conditional planning illustrations, and they should not be interpreted as the trial's intended or achieved sample size.

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 = -3.800; pooled standard deviation σ = 15.056.
2. n = 2 × (1.96 + 0.842)² × 15.056² / -3.800² = 246.4, rounded up to 247 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 <- -3.8                      # observed difference in means
sigma <- 15.0562279472649                     # 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(3020576)
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 = 247 (80% power), 330 (90% power)
 75% of observed effect: n per arm = 439 (80% power), 587 (90% power)
 50% of observed effect: n per arm = 986 (80% power), 1,320 (90% power)
power.t.test: 247.4 
Simulated power at n = 247 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 a primary endpoint and multiple secondary outcome topics. The results record includes an empty reported-analyses list for the posted secondary outcomes, and the record does not describe a prespecified strategy for controlling multiplicity across outcomes. It does not report whether a particular outcome hierarchy, family of tests, or adjustment procedure was planned. Without those details, the secondary comparisons should not be read as a set of confirmatory tests.

In general, when multiple outcomes or comparisons are examined, the chance of at least one apparently unusual result can increase even when no real differences exist. Adjustments or a clear testing hierarchy can help interpret that situation. Their absence from the registry record does not establish that no such approach was used; it means that the approach is not reported in the registry record. The listed unadjusted secondary results should be considered exploratory.

The record also does not report how missing outcome data were handled, whether any values were imputed, or whether participants with incomplete follow-up were excluded from particular analyses. Each primary group summary lists 14 participants, but the record does not give a participant flow account sufficient to establish whether all randomized participants contributed to every outcome. The trial's analysis population and handling of protocol deviations are not reported in the registry record.

The record lists enrollment of 31, while its brief summary says 28 subjects participated and the primary outcome summaries include 14 participants in each group. The reason these figures differ is not reported. This discrepancy in participant counts cannot be resolved from the posted information and should not be treated as proof of attrition or of any particular exclusion.

Baseline adjustment, site adjustment, the prespecified primary analysis, and any interim analyses are also not reported in the registry record. These omissions limit assessment of whether the posted summaries match the intended analysis plan. They do not justify assuming that any specific method was or was 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 0% reporting threshold.

The registry lists 14 participants at risk for serious adverse events in each group and reports zero participants affected by serious adverse events in both groups. It also lists 14 participants at risk for other adverse events in each group and reports zero participants affected in both groups. No serious adverse event terms are listed.

The record does not report a death count for either group. Deaths are therefore not reported in the registry record; a blank or unavailable count should not be interpreted as zero. The adverse-event figures are counts of participants affected, as represented in the record, and do not provide event descriptions, timing, severity gradations, or details of how events were collected.

These entries describe what was recorded for this small study. Zero affected participants in the posted categories does not establish that no adverse events could occur, nor does it provide a precise estimate of safety in a larger population. The registry record also does not provide enough detail to compare the completeness of event ascertainment between groups.

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

The posted results estimate the average change in upper-extremity Fugl-Meyer score for each randomized group and the unadjusted difference between those averages. The estimate is -3.8 points for robotic therapy relative to conventional therapy. Its confidence interval, from -14.95 to 7.354, includes zero and allows for differences in either direction. The data therefore leave considerable uncertainty about the size and direction of the average comparative change.

This finding does not show that the groups are equivalent. Establishing equivalence would require a prespecified equivalence margin and an analysis designed for that question; neither is reported in the registry record. Nor does the result establish that either intervention does or does not work. The trial compares two active therapy approaches, and the reported contrast is between their group-average changes, not between treatment and no treatment.

The result also does not say how any one participant changed. Group means can conceal a wide range of individual outcomes, and the posted standard deviations indicate variation within groups. The registry does not report a clinically important threshold for the scale, so statistical uncertainty cannot be translated into a judgment about the importance of a particular score difference.

The randomized pilot design gives a structured comparison, but its small outcome groups limit precision. Findings from this sample should not automatically be generalized to all people after stroke, to different stages or types of stroke, or to different treatment programs. Further details about participant selection, treatment delivery, missing data, and long-term outcomes are not reported in the registry record.

The appropriate reading is descriptive and cautious: the posted summaries show a negative point estimate for the robotic-versus-conventional comparison, substantial uncertainty around that estimate, and no basis for a definitive claim about comparative benefit, equivalence, or broader effectiveness.

17. Why This Trial Matters Statistically

This trial is statistically informative as a small randomized pilot comparison of a hand-focused robotic device with conventional upper-limb therapy. Its primary outcome is expressed on a defined impairment scale, and the registry reports group means, standard deviations, a between-group estimate, and a confidence interval. Together, these statistics make it possible to distinguish the estimated direction of the contrast from the uncertainty around it.

The primary estimate illustrates why the point estimate alone is not enough. A negative mean difference describes the direction of the sample average, while the interval extending across zero shows that the data do not closely determine the comparative effect. The p-value likewise cannot replace the estimate and interval. Considering all three helps prevent a small pilot result from being reduced to a simple positive-or-negative label.

The planning illustrations are also useful for understanding the relationship between assumed effect size and sample size. They show that designs aiming to detect smaller effects require more participants under the stated assumptions. These illustrations are not the study's original design calculation and should not be mistaken for evidence that a particular sample size was justified or that the completed trial had a given level of power.

Finally, the record demonstrates the importance of complete reporting. The participant counts differ between registry enrollment and the brief summary, and information about missing data, analysis populations, multiplicity, and the original statistical plan is not reported in the registry record. These gaps limit how fully readers can assess the analysis, even though the posted summary statistics support a transparent description of the central comparison.

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 main limitation for interpreting this particular trial is the small number of participants in the primary outcome summaries: 14 in each group. The study is identified as a pilot, and its confidence interval is broad. The estimate is consequently not precise enough to support a narrow conclusion about the average difference between groups.

The participant counts are not fully reconciled in the registry record. Registry enrollment is 31, the brief summary says 28 subjects participated, and the primary outcome summaries list 14 participants per group. The record does not explain the difference. It would be inappropriate to infer why the counts differ or how that difference affected the analysis.

The record identifies a two-site study and chronic ischemic stroke in the official title, but it does not provide detailed eligibility criteria or enough participant characteristics to assess how representative the sample may be. It describes an average study duration of 8 weeks, but longer-term outcomes are not reported in the registry record. Numerical summaries are available for the primary endpoint and three secondary measures, while seven secondary outcome topics are listed overall.

Important analysis details are also missing from the registry record. These include the original sample-size justification, the primary analysis plan, handling of missing data, analysis populations, any baseline or site adjustment, and a multiplicity strategy. The registry lists single masking but does not identify who was masked. These gaps restrict assessment of the analysis and reporting, but do not establish that a particular method was absent from the conduct of the trial.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Robotic and Conventional Hand Therapy After Stroke — NCT03020576.
• Registry record last updated 2018-01-25; status last verified 2018-01.
• Results first posted 2018-01-25.
• 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

NCT03020576 is a completed randomized, single-masked, parallel-group pilot study titled Robotic and Conventional Hand Therapy After Stroke. It compared Amadeo robotic hand training with conventional therapy in people described as having chronic ischemic stroke. Columbia University is listed as sponsor. The recorded study start was 2011-04, and primary completion was 2012-03.

The primary endpoint was change in the upper-extremity portion of the Fugl-Meyer measure through study completion, an average of 8 weeks. The robotic-minus-conventional mean difference was -3.8 points, with a 95% confidence interval from -14.95 to 7.354 and an unadjusted p-value of 0.504. The interval indicates substantial uncertainty about the comparative average change. Further details on the original sample-size rationale, analysis plan, missing-data methods, and analysis populations are not reported in the registry record.