Does More Practice Improve Arm Movement After Stroke?: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Does More Practice Improve Arm Movement After Stroke? (NCT01146379), a randomized phase 2 study. The primary outcome is Change in Action Research Arm Test (ARAT) Score Per Week.

2. Clinical Question

3. Trial Design

This was a randomized, parallel-group, phase 2 trial with single masking. The registry record lists an enrollment of 85 and identifies Washington University School of Medicine as the sponsor. The study began in 2010-05, had primary completion in 2015-10, and is listed as completed. The identity of the people who were masked is not reported in the registry record.

Participants were assigned to one of four intervention groups: low movement dose, 3200 total reps; medium movement dose, 6400 total reps; high movement dose, 9600 total reps; or individual maximum high movement dose. The descriptions characterize the rehabilitation as intensive, task-specific upper extremity movement training, graded and progressed for each participant. The exact dose definition for the individual maximum group is not reported in the registry record.

The primary outcome was change in Action Research Arm Test score per week over 9 weeks. The posted group sizes were 20 for low movement dose, 21 for medium movement dose, 21 for high movement dose, and 20 for individual maximum high movement dose. The trial record lists one primary outcome measure and no posted secondary outcome measures. More detailed eligibility criteria, study locations, allocation procedures, and the original sample-size justification are 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.

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 Change in Action Research Arm Test (ARAT) Score Per Week, measured over 9 weeks.

The primary endpoint was the change in Action Research Arm Test score per week over 9 weeks. The Action Research Arm Test (ARAT) measures upper extremity functional capacity. A trained assessor scores performance on 19 items involving reaching, grasping, and manipulating objects. Scores range from 0 to 57, with higher scores representing better arm and hand functional capacity.

Rather than focusing only on a score at one assessment, the trial’s primary analysis evaluated the rate of score change over time, expressed in units per week. This makes the outcome relevant to the question of how arm function changed during the rehabilitation period and whether that rate differed across movement-dose groups. The registry record says scores were assessed weekly. It does not provide the actual weekly observations, the timing of every assessment, or further details about how the rate was estimated.

The endpoint is a measure of test performance, not a direct measure of every aspect of daily arm use or recovery. The registry record does not report additional functional outcomes with which to assess whether changes in the ARAT rate corresponded to changes in other activities.

7. Results Posted in the Registry

• Medium Movement Dose, 6400 Total Reps: mean -0.05 versus 0.40 on control; difference -0.45 (95% CI -0.96 to 0.06), standardized effect d = -0.54; z-test p = 0.081.
• High Movement Dose, 9600 Total Reps: mean 0.31 versus 0.40 on control; difference -0.09 (95% CI -0.61 to 0.43), standardized effect d = -0.10; z-test p = 0.735.
• Individual Maximum High Movement Dose: mean 0.66 versus 0.40 on control; difference 0.26 (95% CI -0.23 to 0.75), standardized effect d = 0.33; z-test p = 0.298.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry record names a mixed models analysis for the overall comparison among the four groups and two-sided t-tests for the three comparisons with the low movement dose group. The record does not describe the exact model specification, the treatment of repeated measurements, or whether any covariates were included. The concepts below are general explanations of these methods, not claims about unreported analysis choices.

What does a mixed model do?

In general, a mixed model can represent both systematic group patterns and the correlation among repeated measurements from the same participant. Repeated observations on one person are usually related rather than independent. A suitable model can account for that structure while estimating average patterns over time and differences between groups. The registry record identifies a mixed models analysis but does not say which time terms, covariance structure, or participant-level effects were used. It is therefore not possible to reconstruct the sponsor’s overall analysis from the registry record.

What does a two-sided t-test ask?

In general, a two-sided t-test assesses whether the data are compatible with a difference in either direction, rather than testing only whether one specified group is higher. The sponsor reports a separate two-sided t-test for each active-dose group versus low movement dose. The reported p-value measures how unusual the test statistic would be under the test’s null model; it is not the probability that the null hypothesis is true, nor a measure of clinical importance. The registry record does not report whether the pairwise tests were adjusted for making multiple comparisons.

How do means and standard errors differ?

The posted outcome is a mean rate of change, and its accompanying spread is reported as a standard error. A mean describes the average estimated rate in a group. A standard error describes uncertainty in estimating that mean; it is not the spread of individual participants’ outcomes. Standard errors help characterize precision, but the registry record does not give the underlying participant-level observations or enough detail to reproduce the mixed model.

The unadjusted recalculations compare each group mean with the low-dose mean using posted summary statistics. They are simple comparisons, not the sponsor’s mixed-model results. The recalculated mean differences are -0.45 units per week for medium movement dose, -0.09 for high movement dose, and 0.26 for individual maximum high movement dose. Their associated unadjusted p-values are 0.081, 0.735, and 0.298. Since the sponsor’s reported results differ, the sponsor’s own analysis takes precedence.

Why can analyses differ?

General statistical reasons for differences can include whether repeated measurements are modeled directly, how uncertainty is estimated, and whether the analysis uses the same assumptions as a summary-statistic comparison. These are possible methodological distinctions, not identified causes of the discrepancy in this trial. The registry record does not provide enough detail to determine why the sponsor’s overall and pairwise results differ from the unadjusted recalculations.

Over-dispersion is a general concern when observed variation is greater than a model assumes: standard errors can then be too small if the extra variation is ignored. The primary outcome is continuous, and the registry record does not report an over-dispersion assessment. More generally, model diagnostics help evaluate whether the assumptions behind a model are adequate, but diagnostic results are not reported in the registry record.

Finally, statistical significance and effect size answer different questions. A p-value summarizes compatibility with a specified null model under the method’s assumptions. A mean difference describes the estimated size and direction of a contrast, while an interval describes uncertainty around it. Neither a p-value nor a group mean alone establishes whether a difference is important in practice. The registry record does not report a threshold for an important ARAT rate difference.

10. Confidence Intervals and Precision

The recalculated comparisons include intervals for the mean difference between each group and the low movement dose group. All three intervals extend across zero. In general, an interval that includes zero is compatible with no mean difference as well as with differences in either direction, under the assumptions used to calculate it. The intervals are not narrow enough to identify a precise value for each contrast.

The medium-dose estimate is -0.45 units per week, the high-dose estimate is -0.09, and the individual maximum high-dose estimate is 0.26. The interval for each estimate crosses zero, so the direction and size of the underlying difference remain uncertain in these unadjusted comparisons. These intervals accompany recalculations from posted summary statistics, not the sponsor’s mixed-model analysis. The registry record does not give intervals for the sponsor-reported comparisons or identify a confidence level for the recalculated intervals.

The group standard errors are 0.15 for low movement dose, 0.21 for medium movement dose, 0.22 for high movement dose, and 0.2 for individual maximum high movement dose. A standard error reflects uncertainty in a group mean, while an interval for a difference reflects uncertainty in a contrast. Neither quantity describes the range of individual participant outcomes.

Precision should be considered alongside the estimated effects and the analysis discrepancy. The sponsor’s reported p-values and the recalculated comparisons are not interchangeable, and the registry record lacks enough detail to explain their differences. The posted results therefore leave uncertainty both about the size of the group contrasts and about how to reconcile the reported analyses.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures are participants per arm for 80% power and participants per arm for 90% power. These are not total event counts: the sample-size assumptions specify participant counts per arm for these non-time-to-event outcomes. For example, planning for 100% of the observed medium-versus-low effect gives 54 participants per arm for 80% power and 73 participants per arm for 90% power. The other comparisons and effect fractions have their own planning values.

The planning illustration assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It sets the effect to detect at the stated fraction of the observed effect. The 80% power column describes the planned participant count per arm associated with an 80% chance of detecting the assumed effect under those assumptions, if that effect and the other assumptions hold. The 90% power column uses a higher target chance of detection and therefore has a larger planned count in the listed comparisons.

Rows for 75% and 50% of the observed effect represent planning for progressively smaller effects. Smaller effects are harder to distinguish from random variation and need more participants under the same planning assumptions. These figures are planning illustrations based on observed effects, not observed power. The trial’s original design assumptions and sample-size justification are not reported in the registry record, so the illustration does not establish what enrollment the investigators originally planned or why.

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 = -0.450; pooled standard deviation σ = 0.833.
2. n = 2 × (1.96 + 0.842)² × 0.833² / -0.450² = 53.8, rounded up to 54 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 <- -0.45                      # observed difference in means
sigma <- 0.833158956114526                     # 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(1146379)
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 = 54 (80% power), 73 (90% power)
 75% of observed effect: n per arm = 96 (80% power), 129 (90% power)
 50% of observed effect: n per arm = 216 (80% power), 289 (90% power)
power.t.test: 54.8 
Simulated power at n = 54 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.

13. Analyses Reported by the Sponsor

The sponsor’s reported analysis consists of an overall mixed models analysis across the four groups, with p = .01, and pairwise two-sided t-tests comparing each of the other groups with low movement dose. The reported pairwise p-values are .036 for medium movement dose, 0.679 for high movement dose, and 0.209 for individual maximum high movement dose. The registry record does not provide sponsor-reported effect estimates or intervals for these tests.

The unadjusted recalculations use the posted group summary statistics and produce mean differences of -0.45, -0.09, and 0.26 units per week for medium, high, and individual maximum high movement dose, respectively. Their p-values are 0.081, 0.735, and 0.298. These results differ from the sponsor’s pairwise p-values, including the medium-dose comparison. The sponsor’s own analysis takes precedence when the posted sponsor results and the simple recalculations disagree. The recalculations are useful as transparent contrasts of the posted means, but they do not reproduce or supersede the sponsor’s mixed-model analysis. The registry record does not explain the discrepancy or provide enough model detail to determine its source.

14. Multiplicity, Missing Data and Analysis Populations

The registry record reports an overall mixed models analysis and three pairwise tests against the low movement dose group. Making multiple comparisons raises a general statistical concern: even when no group truly differs, the chance of at least one apparently unusual result can increase as more tests are considered. The record does not say whether the pairwise p-values were adjusted for multiplicity, whether an adjustment was planned, or how the overall and pairwise tests were intended to relate to a prespecified testing hierarchy. The reported p-values should therefore be read with that uncertainty in mind.

The record lists one primary outcome measure and no posted secondary outcome measures. It does not report whether other outcomes were collected but not posted. It also does not describe any interim analyses, stopping rules, or a prespecified statistical analysis plan. Those details are not reported in the registry record.

Missing outcome data can affect estimates when follow-up is incomplete, particularly if the likelihood of a missing measurement relates to the outcome. The registry record does not report missing-data counts, reasons for missing assessments, or the method used to handle missing outcome values. The mixed models analysis is named, but that label alone does not establish how missingness was handled.

The analysis population is also not described. The registry record does not say whether the sponsor analyzed participants according to randomized assignment, only those who completed treatment, or another population. It does not give a participant flow account or explain exclusions from the outcome analysis. These omissions limit assessment of whether the reported results reflect all randomized participants and how robust they are to missing data or analysis-population choices.

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 record reports zero serious adverse events in each of the four groups: low movement dose, medium movement dose, high movement dose, and individual maximum high movement dose. The number at risk is listed as 20, 21, 21, and 20 for those groups, respectively. It also reports zero other adverse events in each group, with the same group counts at risk. No serious adverse event terms are listed.

These figures describe adverse events recorded in the registry results. Zero reported events should not be interpreted as proof that no adverse events occurred outside the recorded reporting period or that the intervention has no risks. The record does not provide event definitions, collection procedures, follow-up duration for safety outcomes, or details about how adverse events were assessed. Death counts are not reported in the registry record.

The safety figures should be considered in the context of the trial’s reported participants and outcome follow-up, rather than as a complete assessment of safety. The registry record does not provide further detail to evaluate the sensitivity of event detection or the completeness of adverse-event reporting.

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

The posted results describe differences in mean rates of change on the ARAT during a 9-week rehabilitation period. The mean rate was 0.4 units per week in the low movement dose group, -0.05 in the medium movement dose group, 0.31 in the high movement dose group, and 0.66 in the individual maximum high movement dose group. These values describe the trial groups and this outcome; they do not by themselves establish that a particular movement dose caused a change.

The sponsor reported an overall mixed models p-value of .01 and pairwise p-values for the comparisons with low movement dose. The unadjusted recalculations differ, and their intervals for the mean differences include zero. Because of this discrepancy, the sponsor’s analysis takes precedence, while the recalculations remain simple comparisons of posted summary statistics. The registry record does not explain the discrepancy or provide enough detail to assess the sponsor model fully.

The results do not establish a consistent increase in mean rate across the three fixed movement-dose groups: the medium group’s mean is lower than the low group’s, and the high group’s mean is higher than the medium group’s but lower than the individual maximum group’s. The individual maximum group is a distinct intervention description, and its dose is not quantified in the registry record. These observed group means alone cannot demonstrate a dose-response pattern.

The endpoint measures performance on a standardized arm-function assessment, not every aspect of recovery or daily activity. The registry record does not report a threshold for a clinically important difference, outcomes beyond the primary measure, or longer-term results. The posted findings therefore do not establish the practical importance or durability of any observed difference, nor do they justify conclusions about people or rehabilitation settings beyond those represented in the trial record.

17. Why This Trial Matters Statistically

This trial raises an important statistical question about how to compare repeated functional measurements across several intervention groups. The primary outcome is a rate of change over time, so the choice of analysis must account for the pattern of repeated assessments and the uncertainty in that pattern. The registry record names a mixed models analysis, but does not report enough details to reproduce it. That makes the difference between the sponsor’s results and the simple unadjusted recalculations especially relevant.

The trial also illustrates why the size and precision of an estimate matter alongside a p-value. The sponsor reports an overall p-value and pairwise p-values, while the recalculated differences have intervals spanning zero. The registry record does not provide sponsor effect estimates or intervals to connect those p-values to the magnitude and precision of the estimated differences. A statistically unusual result is not, by itself, a measure of practical importance.

Several groups and pairwise comparisons also create a multiplicity question. Without a reported adjustment or testing plan, readers cannot tell how the sponsor intended to control the interpretation of the collection of tests. The missing analysis details are therefore not merely technical: they affect how confidently the comparisons can be interpreted together.

Finally, planning values based on observed effects demonstrate how strongly sample-size requirements depend on the assumed effect size. They are planning illustrations rather than evidence about the trial’s original design or its achieved power. In this way, the record is useful for understanding both the statistical challenges of a multi-group rehabilitation study and the limits of interpretation when model, missing-data, and planning details are absent.

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 limitations follow from what is and is not reported in the registry record. The sample is identified as people with stroke, but eligibility criteria and participant characteristics are not included in the available record. This limits assessment of which stroke populations the results represent. The registry lists an enrollment of 85, while the posted group sizes are 20, 21, 21, and 20; the record does not explain the relationship between enrollment and the analysis groups.

The intervention descriptions identify three fixed repetition totals and an individual maximum high-dose group, but the latter dose is not quantified. Details about treatment duration, session frequency, adherence, and the precise progression rules are not reported in the registry record. The record also says the trial was single-masked without identifying who was masked.

The outcome results focus on one primary measure. No secondary outcomes are posted, and longer-term follow-up results are not reported in the registry record. The outcome assessor is described as trained, but further assessment procedures are not given. The record does not report a threshold for an important ARAT difference.

Important analysis details are also absent: the mixed-model specification, multiplicity handling, missing-data methods, analysis population, and original sample-size justification are not reported in the registry record. These gaps prevent a full assessment of the sponsor’s analysis and the reasons it differs from the unadjusted recalculations. The available results should therefore be interpreted as registry-reported findings rather than a complete account of trial conduct and analysis.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Does More Practice Improve Arm Movement After Stroke? — NCT01146379.
• Registry record last updated 2017-02-24; status last verified 2017-01.
• Results first posted 2017-02-24.
• 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 record describes a completed randomized, parallel-group phase 2 trial sponsored by Washington University School of Medicine. It enrolled 85 and compared low, medium, high, and individual maximum high movement-dose rehabilitation groups among people with stroke. The primary outcome was the weekly rate of change in ARAT score over 9 weeks.

The sponsor reported an overall mixed models p-value of .01 and pairwise t-tests against low movement dose. Unadjusted comparisons recalculated from posted group summaries differ from the sponsor’s pairwise results, so the sponsor’s own analysis takes precedence. The registry record does not report the sponsor’s effect estimates or intervals, the original design assumptions, or key details about missing data and analysis populations.