Immediate Effects of rTMS on Excitability of the Quadriceps With Knee Osteoarthritis: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Immediate Effects of rTMS on Excitability of the Quadriceps With Knee Osteoarthritis (NCT02881775), a randomized na study. The primary outcome is Quadriceps Central Activation Ratio (CAR).

2. Clinical Question

3. Trial Design

The registry describes a randomized, double-masked crossover trial sponsored by the University of North Carolina, Chapel Hill. Its status is completed. The study began in 2016-09, and primary completion was 2018-06-26. Phase is listed as NA. Enrollment was 20.

In a crossover design, participants receive more than one study condition, allowing comparisons that can account for stable differences between participants. In this trial, the two conditions were rTMS with quadriceps exercise and sham rTMS with quadriceps exercise. The record describes participants receiving the conditions in either order: rTMS first and sham second, or sham first and rTMS second. The listed washout period between lab visits was 1 week. Randomization was reported, but the method used to generate the sequence and how allocation was concealed are not reported in the registry record.

The stated rTMS protocol was 10 Hz, with 5 sec on and 55 sec off, alongside quadriceps isometric exercise at 5% MVIC for 15 minutes. The arm descriptions indicate that the sham condition used the same stated stimulation timing and exercise. Details beyond those descriptions, including the exact sham procedure and whether participants, staff, or outcome assessors were masked, are not reported in the registry record. The record identifies masking as double but does not identify which parties were masked.

The primary endpoint was CAR within 1 hour post intervention. The registry also lists secondary outcomes covering pain ratings, pressure pain threshold, function, and measures of cortical excitability or inhibition. The record reports 8 outcome measures and 8 analyses, but does not explain their statistical model, the handling of the crossover sequence, or the intended analysis population. A sample-size justification and the statistical plan 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.

Baseline

First Intervention (1-hr Session)

Washout (1 Week)

Second Intervention (1-Hour Session)

Analysis population for the primary outcome, as defined in the registry: 4 subjects withdrew from the study after the baseline measures. This left 16 subjects for the intervention arm of the study. Four subjects declined to perform the test after the experience with the electrical stimulus in the baseline session.

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.

Population: Participants in the baseline population are the same as those in the intervention. All participants came for 3 laboratory sessions. The purpose of the first session was to collect baseline data on both the involved and uninvolved knee.

6. Primary Endpoint

The registry lists the primary outcome as Quadriceps Central Activation Ratio (CAR), measured over Within 1 hour post intervention.

Quadriceps Central Activation Ratio (CAR) is the primary endpoint. It is described as a percentage based on torque produced during the superimposed burst technique, using maximal voluntary isometric contraction (MVIC) and superimposed burst torque. The registry gives a scale from 0, described as worst activation, to 100%, described as best activation. The unit is % activation.

CAR is used to quantify how fully a participant activates the quadriceps during a voluntary effort. The study’s stated rationale is that quadriceps activity may be underactive in people with knee osteoarthritis and that this can make strengthening difficult. CAR therefore provides a measure related to the ability to activate the muscle, rather than a direct measure of pain relief or longer-term strength. The endpoint was assessed within 1 hour post intervention, matching the study’s focus on immediate effects.

The registry lists the endpoint summary parameter as a least-squares mean and its dispersion as a standard error. A least-squares mean is generally a model-based estimate of an average; the registry does not report the model details used to obtain it. A standard error describes the precision of an estimated mean, rather than the spread of individual participants’ measurements. The posted results do not provide a single summarized CAR comparison, its estimate, or a confidence interval, so the magnitude and precision of the contrast cannot be interpreted from the registry record.

7. Why No Re-analysis Is Shown

8. Statistical Interpretation

9. Statistical Methods Explained

The registry calls the study randomized, double-masked, and crossover. Those terms describe different aspects of design. Randomization assigns participants to study sequences by chance. Double masking indicates that masking involved two parties, but the registry does not say which parties. A crossover design means that participants receive both study conditions in different periods. Here, the listed sequences were rTMS and exercise followed by sham rTMS and exercise, or sham rTMS and exercise followed by rTMS and exercise.

What does crossover design change?

In general, crossover studies compare outcomes within the same participant across conditions. This can reduce the influence of stable differences between participants because each participant contributes measurements under both conditions. The comparison still depends on the order in which conditions occur. Period effects can arise when outcomes vary over time, and carryover can occur when an earlier condition influences later measurements. Randomized sequence assignment can help balance order, while a washout interval is intended to separate periods. The record lists a washout period of 1 week, but does not report tests for carryover, sequence effects, or period effects, or how these were incorporated in analysis.

What do least-squares means and standard errors describe?

The primary outcome is listed as a least-squares mean with standard error. In general, a least-squares mean is an estimated average derived from a statistical model. Depending on the model, it may account for specified design factors or covariates. The registry does not report which factors were included, the model form, or how the crossover observations were handled. A standard error describes the precision of an estimate: smaller standard errors generally indicate more precise estimates, while larger ones indicate more uncertainty. It is not the same as the variability of individual measurements. The posted results do not report numerical means or standard errors for a single primary comparison.

A confidence interval, when reported, gives a range of values compatible with the estimate and its uncertainty under the chosen statistical method. It can help readers assess the range of effects supported by the data, rather than relying only on a point estimate. No confidence interval for a single CAR comparison is reported in the registry record. A p-value, if reported, would address compatibility of the data with a specified null hypothesis under a statistical model; it would not by itself describe the size or practical importance of an effect. The registry record does not provide a p-value for a single summarized primary comparison.

Why can over-dispersion matter?

General statistical context: for count outcomes, over-dispersion means that observed variation exceeds what a chosen count model expects. A model that does not allow for that extra variation can produce uncertainty estimates that are too small. CAR is described as a continuous percentage outcome, and the registry lists a least-squares mean and standard error. It does not report that a count model or an over-dispersion adjustment was used, so over-dispersion is not an identified feature of the posted primary analysis.

The sample-size material is described as a planning illustration based on the observed effect, rather than the trial’s own design. Its stated assumptions are a two-sided significance level of 0.05, equal allocation between arms, and a normal approximation, with the effect to detect expressed as a fraction of the observed effect. For non-time-to-event outcomes, the illustration is described as participants per arm. Such illustrations concern hypothetical planning under stated assumptions; they are not observed power and do not establish how many participants were needed for this completed crossover trial. The actual numerical illustrations and the trial’s own sample-size justification are not reported in the registry record.

In general, statistical interpretation depends on a prespecified estimand or comparison, analysis model, handling of missing observations, and a description of uncertainty. The registry record does not report enough detail to establish these elements for a single primary CAR contrast. The reported design and endpoint definitions therefore should be distinguished from an inferential analysis that is not available in the posted results.

10. Multiplicity, Missing Data and Analysis Populations

The registry lists CAR as the primary outcome and gives 8 outcome measures and 8 analyses. It also names secondary outcomes: Numeric Pain Rating Scale (NPRS) Score, Pressure Pain Threshold (PPT) - Medial Knee, Timed Up & Go (TUG), Active Motor Threshold Motor Evoked Potential (AMT-MEP), Short Interval Cortical Inhibition (SICI), and Intra Cortical Facilitation (ICF). The posted information does not explain how these outcomes were prioritized across analyses or whether any adjustment for multiple testing was used.

Multiplicity matters when several outcomes, time points, or comparisons are examined. In general, the more questions assessed, the greater the chance that at least one result may appear notable by chance if each is evaluated separately. Methods such as prespecifying a primary comparison or adjusting inference can address this concern, but the registry record does not report a multiplicity strategy. It also notes that the primary outcome has several categories or time points and is not reduced to one comparison, so a single primary contrast cannot be identified from the posted results.

The record reports that 4 subjects withdrew after baseline measures, leaving 16 subjects for the intervention arm. It also says that 4 subjects declined to perform the test after the experience with the electrical stimulus in the baseline session. Whether those descriptions refer to overlapping participants is not reported in the registry record. The number contributing data to each outcome, the missing-data method, and whether any imputation or sensitivity analysis was used are also not reported.

The analysis population is not fully specified. The record does not state whether the primary analysis included all randomized participants, only participants completing both conditions, or another defined group. These omissions limit assessment of how missing observations and multiple analyses affect the interpretation of the posted results.

11. Safety Results

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

Deaths

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 adverse-event counts separately for rTMS and exercise and sham rTMS and exercise. In each condition, 20 participants were at risk for serious adverse events and 0 were reported as affected. The same counts are listed for other adverse events: 20 at risk and 0 affected in each condition. Deaths are listed as 0 in both conditions. No serious adverse-event terms are listed.

These are the counts recorded for the study conditions. A count of zero means that no events of that category were recorded among the participants listed as at risk; it does not establish that the risk is zero or that two conditions have equal safety. The registry record does not provide further details on event collection, duration of surveillance, or how the adverse-event counts relate to the participants contributing to the primary outcome. The figures should therefore be read as descriptive registry counts, not as a statistical comparison of safety.

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

The study addresses an immediate physiological question: whether quadriceps central activation, measured by CAR, differs after rTMS with exercise compared with sham rTMS with exercise in people with knee osteoarthritis. The registry describes a randomized, double-masked crossover design, intervention procedures, and an endpoint measured within 1 hour post intervention. It also records that the primary endpoint is expressed as a percentage of activation.

Those design and measurement details define what the investigators intended to study, but they do not by themselves establish an effect. The registry record does not provide a single summarized CAR contrast, a numerical estimate, a confidence interval, or a p-value for that comparison. As a result, the posted information does not show whether CAR was higher or lower after either condition, how large any contrast was, or how precisely it was estimated.

The endpoint is an activation measure, not a direct measure of longer-term change in strength, pain, mobility, or disease progression. Although the registry lists additional outcomes related to pain, pressure pain threshold, movement, and cortical measures, their results and analysis details are not reported in the record. The stated immediate time frame also does not answer questions about persistence of any response.

The safety counts report no serious or other adverse events and no deaths in either listed condition. Those observations describe the recorded events in this study; they do not prove that a condition has no risks or establish equivalence between conditions. The incomplete reporting of analysis populations, missing-data handling, and the primary comparison further limits the conclusions that can be drawn. The appropriate interpretation is therefore narrow: the registry records a study designed to compare immediate CAR under two conditions, but the posted primary-outcome information does not permit a quantitative conclusion about that comparison.

13. Why This Trial Matters Statistically

This trial is statistically interesting because its crossover design makes the choice of comparison and analysis especially important. Participants were assigned to receive both rTMS with exercise and sham rTMS with exercise, with the order varied and a washout period between visits. A within-participant design can help separate treatment-condition differences from stable participant differences, but order, period, and carryover effects still require consideration. The registry describes the design but does not report how those features were analyzed.

The primary endpoint also illustrates why a measurement definition is not a result. The record specifies CAR, its scale, the measurement window, and the summary parameter, yet it does not provide a single summarized contrast. Readers need an estimate and its uncertainty to understand both the direction and precision of a difference. Without those results, the endpoint’s definition and the completed status of the trial cannot answer the primary comparison.

The participant disposition is another key statistical issue. The record notes withdrawals after baseline and participants who declined the test following the electrical stimulus, but it does not clearly identify how these groups overlap or which participants contributed data by condition. In a crossover study, incomplete participation can affect the availability of paired measurements. The registry does not describe how such missing observations were handled.

Finally, the record lists multiple outcomes and analyses without a reported strategy for multiplicity. That matters for interpreting any collection of statistical tests, although a single primary result is not available in the posted information. The trial therefore highlights the value of reporting the planned comparison, analysis population, missing-data approach, treatment of crossover effects, and uncertainty estimates alongside the outcome definition.

14. 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 limitations specific to this trial follow from the registry entries. The primary outcome is described as having several categories or time points and is not reduced to a single comparison. No numerical CAR contrast, confidence interval, or p-value for a single comparison is reported in the registry record. This prevents assessment of the direction, magnitude, and precision of the primary result.

Participant flow is not fully resolved. The record says 4 subjects withdrew after baseline measures, leaving 16 subjects for the intervention arm, and separately says 4 subjects declined the test after the baseline electrical stimulus experience. Whether these statements describe overlapping participants is not reported. Nor does the record identify the number with complete measurements in both crossover conditions or the analysis population for each outcome.

The statistical methods are also incompletely described. The registry does not state the model used for the least-squares mean, how the crossover periods or treatment sequences were handled, or whether possible carryover effects were assessed. It does not report a missing-data strategy, a multiplicity approach, or the statistical analysis plan. Masking is identified as double, but the masked parties and the specific sham procedure are not described in detail.

The record lists a washout period of 1 week but does not explain how that interval was chosen or whether it was sufficient for the outcomes studied. The endpoint timing is limited to within 1 hour post intervention, so the stated endpoint does not characterize any longer-term response. The adverse-event counts are recorded, but event ascertainment details and follow-up duration are not reported. These limitations concern the information available in the registry record and do not establish whether additional information exists elsewhere.

15. Related Tutorials

16. Related Statistical Calculators

17. Sources

• ClinicalTrials.gov: Immediate Effects of rTMS on Excitability of the Quadriceps With Knee Osteoarthritis — NCT02881775.
• Registry record last updated 2019-06-11; status last verified 2019-03.
• Results first posted 2019-05-29.
• 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.

18. Record Summary

NCT02881775 is a completed randomized, double-masked crossover study sponsored by the University of North Carolina, Chapel Hill. It enrolled 20 people with knee osteoarthritis and compared rTMS with quadriceps exercise against sham rTMS with quadriceps exercise. The listed protocol used rTMS at 10 Hz, 5 sec on and 55 sec off, with quadriceps isometric exercise at 5% MVIC for 15 minutes; the conditions were separated by a washout period of 1 week.

The primary outcome was Quadriceps Central Activation Ratio (CAR), measured within 1 hour post intervention and reported as a least-squares mean with standard error. The record describes participant withdrawals and test refusals, but does not fully clarify the analysis population or missing-data handling. It does not report a single summarized primary comparison or its uncertainty. The adverse-event record lists zero serious adverse events, zero other adverse events, and zero deaths in each condition.