Primed vs. Unprimed rTMS in Chronic Stroke: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Primed vs. Unprimed rTMS in Chronic Stroke (NCT01757821), a randomized na study. The primary outcome is Change in Cortical Excitability: Paired-Pulse.

2. Clinical Question

3. Trial Design

This was a randomized, triple-masked, crossover trial. In a crossover design, participants receive more than one intervention, so comparisons may be informed by measurements from the same participants under different conditions. The registry describes three interventions, received in randomized order. It does not report the details of the masking procedures, who was masked, or how the sequence was generated.

The interventions were real 6-Hz priming followed by low-frequency rTMS, sham 6-Hz priming followed by low-frequency rTMS, and real 1-Hz rTMS alone. The brief summary describes 10 minutes of priming followed by 10 minutes of low-frequency stimulation for the primed approaches, and 20 minutes of low-frequency stimulation alone for the third approach. It also describes weekly visits and pretests, but the visit schedule is cut off in the registry summary. The complete schedule, including any interval between intervention periods, is not reported in the registry record.

The registry lists 11 participants enrolled, while the brief summary describes a planned study in twelve adults. The primary outcome groups each contain 10 participants. The record does not explain the difference between these counts or report the flow of participants through the intervention periods and outcome assessments. The start date is 2013-04, primary completion is 2014-07, and status is completed.

The registry describes a crossover model, but the posted comparisons are presented as mean differences between each active intervention and sham priming. The posted results do not describe a crossover-specific statistical model or explain whether period, sequence, or within-participant correlation was included in the analysis. The original design assumptions 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.

Before assignment: All subjects received all 3 interventions

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 Change in Cortical Excitability: Paired-Pulse, measured over Change from Baseline to 20 minutes.

The primary endpoint is change in cortical excitability, measured using paired-pulse transcranial magnetic stimulation in the primary motor cortex on the stroke hemisphere. The timeframe is change from baseline to 20 minutes. The outcome is continuous, and the registry reports its mean and standard deviation in milivolt.

Paired-pulse stimulation uses a pair of magnetic stimuli to assess aspects of motor-cortex response. In general, cortical excitability is a physiological measure of how responsive neural circuits are to stimulation. It is used as a mechanistic or physiological outcome: the question is whether the interventions are followed by differences in the measured response. The endpoint is not itself a direct measure of everyday function, disability, or rehabilitation progress. Those outcomes are not among the posted primary results.

A change score relates the measured value after an intervention to the baseline value. The registry names the change timeframe but does not give further detail about how the change was calculated, including whether it was calculated for each participant before group summaries were formed. It also does not describe the paired-pulse protocol beyond identifying the assessment method and target region.

The registry reports average changes and their standard deviations for the three intervention groups. The standard deviation describes the spread of participant values around the group mean; it is not the uncertainty of the mean itself. The posted outcome data therefore describe both the average direction of change and the observed variability, but do not by themselves establish how the physiological measure relates to clinical function.

7. Results Posted in the Registry

• Real 6-Hz Priming: mean -18.00 versus 18.00 on control; difference -36.00 (95% CI -46.32 to -25.68), standardized effect d = -3.06; z-test p = <0.001.
• Real 1-Hz rTMS Only: mean 12.00 versus 18.00 on control; difference -6.00 (95% CI -12.38 to 0.38), standardized effect d = -0.82; z-test p = 0.065.

8. Statistical Interpretation

9. Statistical Methods Explained

What does the mean difference represent?

A mean difference expresses the difference between two group averages in the outcome's original units. Here, each reported contrast compares an rTMS approach with sham 6-Hz priming, and the outcome is change in cortical excitability from baseline to 20 minutes. The reported mean difference is -36.0 milivolt for real 6-Hz priming and -6.0 milivolt for real 1-Hz rTMS alone. A negative value means the intervention-group mean was lower than the sham-priming mean in the posted comparison. The direction of a mean difference depends on which group is subtracted from which, so the stated comparator matters.

What does the standard deviation describe?

The standard deviation describes variability among participant outcome values around their group mean. It is not a confidence interval and it does not indicate the precision of the mean difference by itself. The posted standard deviations are 14.0 milivolt for real 6-Hz priming, 9.0 milivolt for sham 6-Hz priming, and 5.0 milivolt for real 1-Hz rTMS alone. General statistical interpretation: greater variation makes group means less precise when the number of observations is held constant. The uncertainty in a comparison also depends on the study design and on the relationship between repeated measurements for the same participant.

How should the confidence intervals be read?

A confidence interval gives a range of values compatible with the data under the assumptions of the interval procedure. It is not a guarantee that the true effect lies in that particular interval, and it is not a range containing most individual participant outcomes. For real 6-Hz priming, the reported interval is -46.32 to -25.68 milivolt. For real 1-Hz rTMS alone, the interval extends from -12.38 milivolt to above zero. The first interval is entirely below zero; the second includes zero. General statistical interpretation: an interval that includes zero leaves zero difference among the values reasonably compatible with the data under the specified procedure, while an interval that excludes zero indicates greater evidence against a zero difference. The exact coverage and validity depend on the analysis assumptions.

What does an unadjusted p-value indicate?

A p-value measures how incompatible the observed data, or more extreme data, are with a specified null model, assuming that model and the analysis assumptions are correct. It is not the probability that the null hypothesis is true, nor is it a measure of clinical importance. The registry reports p < 0.001 for real 6-Hz priming versus sham priming and 0.065 for real 1-Hz rTMS alone versus sham priming. Both are labeled unadjusted. The registry does not state the exact test or model used to obtain these values.

Why does the crossover design matter?

General statistical explanation: in a crossover study, the same participant may contribute measurements under more than one intervention. Analyses can account for within-participant correlation, and they may need to consider whether intervention order or period affects outcomes. The registry identifies the design as crossover and says intervention order was randomized, but it does not report a crossover-specific model, treatment-period analysis, washout interval, or handling of possible carryover. The posted arm-level summaries and comparisons do not provide enough detail to determine how these design features were handled. The trial's original statistical analysis plan is not reported in the registry record.

What is the distinction between posted and recalculated results?

The displayed comparison estimates are reported as mean differences, with confidence intervals and unadjusted p-values. No sponsor analysis details are posted, and the registry reports no discrepancy between a sponsor result and a recalculated result. The statistical method used for the comparison is not reported in the registry record. General statistical explanation: a simple unadjusted recalculation based on summary statistics may not reproduce an analysis that accounts for crossover structure, covariates, or other design features. The registry record does not provide enough analysis detail to characterize such adjustments.

These methods describe the numerical results, not a clinical treatment recommendation. The endpoint is a short-term physiological response, and the record does not include an analysis connecting that response to functional outcomes.

10. Confidence Intervals and Precision

The mean difference for real 6-Hz priming versus sham priming is -36.0 milivolt, with a confidence interval from -46.32 to -25.68. The interval lies below zero and is relatively separated from zero in the units of the endpoint. It nonetheless spans a range of possible mean differences, rather than identifying one exact value. The group standard deviations are 14.0 milivolt for real priming and 9.0 milivolt for sham priming, with 10 participants in each posted group.

The mean difference for real 1-Hz rTMS alone versus sham priming is -6.0 milivolt. Its confidence interval runs from -12.38 milivolt to a positive upper limit, so it includes zero. That range is compatible with a negative difference as well as with no difference and a positive difference under the interval procedure. The p-value for this comparison is 0.065. The result is therefore less precise with respect to the direction and size of the contrast than a single point estimate alone might suggest.

General statistical explanation: confidence intervals reflect both the amount of information in the data and the variability of the measured outcome, together with the analysis assumptions. A small group can yield an imprecise estimate, especially when outcomes vary. In a crossover study, precision can also depend on within-participant correlations, but the registry does not report those correlations or the analysis method used for the posted contrasts.

There are 10 participants in each primary outcome group, while total enrollment is 11. The record does not explain this difference or give participant-level missingness information. No confidence intervals for the group means themselves are posted, and no interval is posted for the adverse-event figures. The reported uncertainty therefore pertains to the posted mean-difference comparisons, not to every possible interpretation of the trial results.

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

The 80% power column gives the number of participants per arm estimated to be needed for an 80% chance of detecting the specified effect under those assumptions, if that effect is the true one. The 90% power column gives the corresponding number for a 90% chance. These are planning probabilities under a statistical model, not guarantees about a future study. The figures are presented separately for each observed comparison and each effect fraction, so the relevant comparison and planning scenario should be considered together.

For the real 6-Hz priming comparison, the listed figures range from 2 participants per arm for 80% power and 3 for 90% power when planning for 100% of the observed effect, to 7 and 9 when planning for 50% of the observed effect. For the real 1-Hz rTMS-alone comparison, the corresponding range is 24 and 31 for 100% of the observed effect, and 93 and 124 for 50% of the observed effect. Planning for 75% of the observed effect falls between those scenarios in each comparison.

Smaller effects require more participants to detect at the same power under the stated assumptions. These figures are not observed power: they are sample-size planning illustrations, not a retrospective measure of how likely the completed trial was to detect its result. The original trial sample-size justification and its design assumptions are not reported in the registry record. The planning model also describes equal allocation between two arms, while the clinical study is identified as a crossover trial with three interventions, so these illustrations should not be mistaken for a reconstruction of the trial's own design calculation.

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 = -36.000; pooled standard deviation σ = 11.769.
2. n = 2 × (1.96 + 0.842)² × 11.769² / -36.000² = 1.7, rounded up to 2 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 <- -36                      # observed difference in means
sigma <- 11.7686022959398                     # 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(1757821)
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 = 2 (80% power), 3 (90% power)
 75% of observed effect: n per arm = 3 (80% power), 4 (90% power)
 50% of observed effect: n per arm = 7 (80% power), 9 (90% power)
power.t.test: 3 
Simulated power at n = 2 per arm: 0.399 (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. Multiplicity, Missing Data and Analysis Populations

The registry posts one primary outcome and two comparisons against sham 6-Hz priming. It reports unadjusted p-values and does not report whether the original analysis controlled for multiple comparisons. When several comparisons are examined, the chance of at least one apparently unusual result can increase if each is evaluated separately. General statistical explanation: multiplicity procedures can address that issue, but the appropriate approach depends on which outcomes and comparisons were prespecified. The trial's multiplicity plan is not reported in the registry record.

No secondary outcome results are posted. The registry reports zero posted analyses, so details such as covariate adjustment, model specification, and the treatment of repeated measurements are not available. The primary outcome description gives the measure and timeframe, but does not report a full statistical analysis plan. Interim analyses are not reported in the registry record.

Although the design is described as crossover, the record does not state how the analysis handled within-participant correlation, intervention sequence, period effects, or possible carryover. It also does not report a washout period. These details matter because observations from the same participant are not necessarily independent. The registry's arm-level summaries alone do not establish whether such dependence was incorporated into the inferential analysis.

The record reports enrollment of 11 and 10 participants in each primary outcome group, but does not explain the difference or provide participant flow by intervention period. It does not report a missing-data method, reasons for missing measurements, or whether all randomized participants were included in the primary analysis. The analysis population—such as an intention-to-treat population or a per-protocol population—is not reported in the registry record. The timing and completeness of outcome measurements for participants who did not contribute to a group summary are also not reported.

Without these details, the posted summaries can be described, but important aspects of the analysis and its susceptibility to missing data or design-related bias cannot be assessed from the registry record alone.

14. 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.

Most frequent serious adverse event terms

Serious events with the highest arm-level rate: tumor (9.1%).

The registry lists 11 participants at risk for serious adverse events in each intervention group. It records 1 serious adverse event for real 6-Hz priming, 1 for sham 6-Hz priming, and 1 for real 1-Hz rTMS alone. The same record lists 0 other adverse events in each group.

The serious-event term identified among the top serious-event terms is Tumor, reported as 9.1%. The record does not specify in this summary which intervention group or groups this term is associated with, so it should not be assigned to a particular intervention. The serious-event counts do not establish that an event was caused by an intervention. The registry's group figures describe reported events during the recorded study, not comparative estimates of risk.

Death counts are not reported in the registry record. A missing death count should not be interpreted as a count of zero. The record does not provide event narratives, timing, severity details beyond the serious-event classification, or a comparative statistical analysis of adverse events. With these small group counts, the figures are descriptive and do not provide a precise estimate of uncommon harms.

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

The posted primary results show a difference in average short-term cortical excitability change between real 6-Hz priming and sham 6-Hz priming: the reported mean difference is -36.0 milivolt, with a confidence interval from -46.32 to -25.68 and an unadjusted p-value of <0.001. For real 1-Hz rTMS alone versus sham priming, the reported mean difference is -6.0 milivolt, with a confidence interval that includes zero and an unadjusted p-value of 0.065. These are findings about the measured physiological endpoint at 20 minutes.

The results do not establish whether a difference in cortical excitability translates into better movement, daily function, or rehabilitation progress. Those clinical outcomes are not reported as primary results in this record. Nor do the results establish how long a physiological change lasts beyond the stated 20-minute timeframe. A short-term measurement cannot, by itself, answer questions about sustained effects.

The second comparison's interval includes zero, but this does not demonstrate equivalence between real 1-Hz rTMS alone and sham priming. Demonstrating equivalence or noninferiority requires a prespecified margin and an analysis designed for that purpose; such a margin and analysis are not reported in the registry record. Similarly, the first comparison's interval excludes zero, but that statistical evidence should not be recast as proof of a clinically important effect. Clinical importance depends on the interpretation of the measure and its relationship to outcomes that matter to participants, which the registry does not establish.

The study is small, the groups each include 10 participants in the posted outcome results, and the record does not explain the participant counts or provide detailed crossover analysis methods. The posted results should therefore be read as estimates with the stated uncertainty, not as definitive evidence about a broader population or the relative clinical value of the interventions. They do not support medical advice or a conclusion that any approach does or does not work.

16. Why This Trial Matters Statistically

This trial raises a statistical question about whether priming changes the measured response to low-frequency rTMS in the stroke hemisphere. Its randomized crossover design is relevant because participants receive all three interventions in randomized order, allowing comparison of several conditions within a study structured around repeated intervention exposure. General statistical explanation: when analyzed appropriately, within-participant comparisons can make efficient use of measurements from the same person. That advantage depends on the analysis accounting for the repeated observations and relevant period or sequence effects.

The posted primary comparison for real 6-Hz priming has a mean difference of -36.0 milivolt and a confidence interval that lies below zero. The real 1-Hz-only contrast is smaller in its reported mean difference and has an interval that includes zero. The contrast between these results illustrates why estimates, confidence intervals, and study design all matter: a point estimate alone does not convey the range of uncertainty, and separate unadjusted comparisons do not automatically answer a question about the overall pattern across all interventions.

The endpoint is a physiological measure rather than a functional outcome. Statistically, that distinction matters because an association or difference in a mechanistic measure does not automatically establish a corresponding difference in clinical outcomes. The posted record therefore contributes information about short-term cortical excitability, while leaving questions about functional relevance and durability unresolved.

The record also illustrates the limits of registry summaries for evaluating a crossover analysis. The design is identified, but key analysis details—including handling of within-participant correlation and period effects—are not reported. The participant counts differ between total enrollment and the outcome groups, without an explanation in the record. These omissions constrain how fully the numerical results can be independently assessed.

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.

The posted outcome groups each contain 10 participants, while total enrollment is 11. The record does not explain the difference, provide participant flow, or indicate whether any intervention-period measurements were missing. This limits assessment of how complete the outcome data were and whether participants contributed observations under all three interventions.

The registry identifies a randomized, triple-masked crossover design, but does not report the masking roles, intervention sequence-generation method, or a crossover-specific analysis model. It also does not report a washout interval or how possible carryover and period effects were addressed. These omissions are particularly relevant when each participant receives more than one intervention. The results should not be assumed to have accounted for these features unless the registry record states so.

The primary outcome is a physiological measurement at 20 minutes. The posted results do not include a functional or rehabilitation endpoint, and there are no posted secondary outcome results. The registry does not establish whether the measured excitability change predicts a clinical outcome or how long any change persists.

The two posted p-values are unadjusted, and a multiplicity plan is not reported. The statistical test, full model, and analysis population are also not reported. In addition, the record does not provide detailed adverse-event narratives or report a death count. Finally, the planning illustrations use a two-arm normal-approximation framework, while the trial is described as a three-intervention crossover study; the original sample-size justification is not reported. These limitations make the numerical results informative as posted estimates, but incomplete as a full account of the trial's design and analysis.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Primed vs. Unprimed rTMS in Chronic Stroke — NCT01757821.
• Registry record last updated 2017-12-02; status last verified 2017-10.
• Results first posted 2017-12-02.
• 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 describes a completed randomized, triple-masked crossover study of three rTMS interventions in adults with chronic stroke. The primary outcome is change in paired-pulse cortical excitability in the primary motor cortex on the stroke hemisphere, from baseline to 20 minutes.

For real 6-Hz priming versus sham priming, the posted mean difference is -36.0 milivolt, with a confidence interval from -46.32 to -25.68 and an unadjusted p-value of <0.001. For real 1-Hz rTMS alone versus sham priming, the mean difference is -6.0 milivolt, with a confidence interval that includes zero and an unadjusted p-value of 0.065. Each outcome group contains 10 participants.

The record lists 1 serious adverse event in each intervention group and 0 other adverse events in each group; death counts are not reported in the registry record. Detailed crossover analysis methods, missing-data handling, multiplicity procedures, and the original sample-size justification are not reported.