Optimized tDCS for Fibromyalgia: Targeting the Endogenous Pain Control System: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Optimized tDCS for Fibromyalgia: Targeting the Endogenous Pain Control System (NCT03371225), a randomized na study. The primary outcome is Conditioning Pain Modulation (CPM).

2. Clinical Question

The trial addresses whether combining active tDCS with active exercise is associated with a different conditioned pain modulation (CPM) result than combinations using sham tDCS, sham exercise, or both. CPM was assessed at 6 weeks. The registry describes the study as a mechanistic trial of interventions delivered over 4 weeks, intended to evaluate endogenous pain regulation and central sensitization.

The primary endpoint is not a direct report of pain relief in daily life. It is a laboratory measure based on pain ratings before and during a conditioning stimulus. Positive CPM values are defined as better endogenous pain inhibition, while negative values are defined as worse inhibition. The registry also identifies temporal slow pain summation as an intended measure of central sensitization, but the posted primary outcome is CPM.

3. Trial Design

The registry describes a randomized, triple-masked, factorial trial sponsored by Spaulding Rehabilitation Hospital. Its factorial structure combines tDCS assignment, active or sham, with exercise assignment, active or control. The four reported arms are active tDCS with active exercise, sham tDCS with active exercise, active tDCS with sham exercise, and sham tDCS with sham exercise. The overall registry enrollment is 116.

For the active tDCS and active exercise arm, the description specifies 20 min of active tDCS and 30 min of active exercise at 60-70% max HR. In the sham tDCS and active exercise arm, exercise is active and tDCS is sham. In the active tDCS and sham exercise arm, the tDCS is active and sham exercise is described as being within 10% baseline HR. The remaining arm uses sham tDCS and sham exercise. The trial summary describes 16 tDCS sessions combined with exercise and says the interventions were evaluated over 4 weeks.

The primary outcome is CPM, measured at 6 weeks. The record lists the study phase as NA and the status as completed. The recorded start date is 2019-05-01, and primary completion is dated 2024-09-26. Although the masking level is listed as triple, the registry record does not report which roles were masked or how masking was maintained. Allocation procedures beyond randomization, sequence generation, concealment, and any stratification details are not reported in the registry record.

The factorial design can, in principle, support questions about the separate contributions of tDCS and exercise and whether their combination behaves differently from what would be expected from their separate effects. Those are different statistical questions from comparing each of the four arm means. The registry record does not report a factorial model or an interaction analysis, so the design alone does not establish which of these questions was used for inference.

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: 116 subjects were enrolled and randomized

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.

Population: Baseline participants for randomized subjects

6. Primary Endpoint

The registry lists the primary outcome as Conditioning Pain Modulation (CPM), measured over 6 weeks.

The primary endpoint is Conditioned Pain Modulation (CPM), reported as a mean on the Numeric Pain Scale, which ranges from 0 to 10. The trial first identified a temperature that elicited a pain rating of 6. That temperature was applied for 30s, with pain rated at 10, 20, and 30s; the average rating was the test-stimulus score.

After 5 minutes, participants immersed the left hand in 10-12°C water for 30s while the same pain-6 temperature was applied again. Pain was rated at the same time points, and the average was the conditioned-stimulus score. CPM was calculated as the test-stimulus average minus the conditioned-stimulus average. By the registry's definition, a positive value indicates better endogenous pain inhibition and a negative value indicates worse inhibition.

CPM is used as a laboratory measure of pain-modulating response: it compares pain ratings in the presence and absence of a conditioning stimulus. It is therefore a mechanistic endpoint, not by itself a measure of everyday functioning or a direct estimate of a participant's overall pain experience. Higher Numeric Pain Scale scores indicate worse pain, but the CPM direction has its own interpretation because it is a difference between two averages. The reported time point is 6 weeks.

7. Why No Re-analysis Is Shown

8. Statistical Interpretation

9. Statistical Methods Explained

Statistical interpretation depends on distinguishing a summary of observed data from an estimate of a treatment contrast. The posted CPM results are means by arm, each accompanied by a 95% confidence interval. A mean describes the center of the recorded values on the endpoint's scale. A confidence interval expresses uncertainty about the estimated mean under the assumptions of the method used. It is not a range expected to contain most individual participants' results, and it does not show that the underlying value is fixed within the interval.

What does the factorial structure allow?

In general, a factorial design assigns participants across combinations of intervention factors. Here, the factors are tDCS, active or sham, and exercise, active or sham. The four combinations allow researchers to ask more than one kind of question. A main-effect question concerns the average contrast for one factor across the levels of the other factor. An interaction question asks whether the contrast for one factor differs according to the level of the other factor. The interaction is not simply another name for a comparison of one arm against another.

These questions require explicit contrasts and a statistical model appropriate to the design and endpoint. Arm means alone do not provide the uncertainty for every possible contrast, especially when the comparisons involve combinations of arms. The registry record does not report the model, the factorial contrasts, or an interaction test for the posted primary outcome. As a result, the arm summaries should be read descriptively rather than as a complete analysis of the factorial questions.

How should the confidence intervals be read?

In general, a confidence interval is constructed by a procedure that, under its assumptions, would cover the target quantity at the stated rate across repeated applications. The 95% label refers to the procedure's long-run coverage property, not a claim that 95% of individual observations fall between the endpoints. It also does not tell the probability that a fixed parameter lies in the specific interval after the data have been observed.

For each arm, the interval gives a range of values compatible with the observed mean and the assumptions of its interval method. The interval's width reflects precision: wider intervals indicate less precise estimation than narrower intervals on the same scale. Precision is not the same as clinical importance, and interval overlap is not a formal test of a between-arm contrast. The registry record does not identify the method used to calculate these intervals, so the assumptions behind them are not reported in the registry record.

Why is a direct contrast different from comparing means?

A treatment contrast is an estimate of the difference or other specified relationship between groups, with uncertainty calculated for that contrast. Merely looking at two arm means does not supply the contrast's standard error or confidence interval. In general, the uncertainty in a contrast depends on the variability and dependence structure of the estimates, as well as the analysis model. No contrast estimate or p-value for CPM is posted in the registry record, and the recorded analysis count is zero.

The registry also flags the absence of values for a two-arm comparison for this continuous endpoint because such a comparison is missing or not estimable. Therefore, claims about statistical significance or the size and precision of a specific intervention effect cannot be made from the arm means alone. This does not negate the descriptive information in the reported means; it sets a boundary on what those summaries answer.

What does over-dispersion mean in general?

Over-dispersion is a general issue for outcomes whose variability is greater than a model assumes. When it is present and not handled appropriately, standard errors can be too small and confidence intervals too narrow. Its relevance depends on the outcome and statistical model. The primary endpoint is continuous, and the registry record does not report a model or a dispersion assessment. There is therefore no basis to claim that over-dispersion was present or that a particular adjustment was used.

What can sample-size planning illustrations establish?

In general, a planning calculation describes how many participants might be needed under stated assumptions to target a chosen power for a specified effect and significance level. It is not a measure of the power actually achieved after a trial, and it does not show whether the trial was adequately powered for every outcome or contrast. The registry record does not report its own sample-size justification or the assumptions used in its design. Any planning illustration based on the observed effect is separate from the trial's original design rationale and should not be called observed power.

For this factorial trial, planning for a particular contrast would require defining the estimand and using assumptions appropriate to that contrast. A calculation based on one arm's mean or a selected fraction of an observed effect does not automatically describe the power of a factorial interaction test. The posted record does not provide a trial-design calculation or a reported statistical analysis plan for CPM.

10. Multiplicity, Missing Data and Analysis Populations

The trial has a factorial design and the record identifies a primary endpoint, CPM, at 6 weeks. It also describes temporal slow pain summation as a measure of central sensitization in the study summary. However, the registry lists two outcome measures and zero posted analyses, and the primary outcome information does not provide a complete account of all tested hypotheses, model terms, or planned comparisons.

Multiplicity arises when several outcomes, time points, contrasts, or analyses are examined. In general, a larger family of tests increases the chance of at least one apparently notable result by chance if no adjustment or prespecified testing strategy is used. The registry record does not report a multiplicity adjustment, a hierarchy of tests, or whether any outcomes or analyses were designated exploratory. It is therefore not possible to determine how multiplicity was handled.

The arm counts associated with the posted primary outcome are 28, 28, 30, and 30. The record does not state whether those counts represent all randomized participants, participants with available 6-week measurements, or the analysis population for a particular model. It does not report an intention-to-treat definition, a per-protocol population, or another analysis-population rule.

Missing data methods are also not reported in the registry record. There is no description of the amount or pattern of missing CPM measurements, reasons for missingness, imputation, or sensitivity analyses. The arm summaries alone do not reveal whether missing values were excluded or handled by another procedure. The record does not report interim analyses, stopping rules, or a statistical analysis plan. Those omissions limit assessment of prespecification and robustness; they do not establish that a particular practice was or was not used.

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.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: allergic reaction (3.3%).

The registry reports serious adverse events and other adverse events separately for each arm. Serious adverse events were recorded for 0 participants in the active tDCS and active exercise arm, 0 in the sham tDCS and active exercise arm, 0 in the active tDCS and sham exercise arm, and 1 in the sham tDCS and sham exercise arm. Deaths were recorded as 0 in each arm. The listed serious-event term is allergic reaction, reported as 3.3%.

These figures are event counts in the registry record, not a comparison adjusted for exposure, follow-up, or participant characteristics. A zero count means no serious adverse event was recorded for that arm in the posted data; it does not establish that the underlying risk is zero. The record does not provide detail about event timing, severity grades, relatedness to an intervention, or event-level narratives. The listed allergic-reaction percentage should be read as the registry's report, not recalculated from arm counts.

Other adverse events were reported for 23 participants in the active tDCS and active exercise arm, 21 in the sham tDCS and active exercise arm, 18 in the active tDCS and sham exercise arm, and 28 in the sham tDCS and sham exercise arm. These totals do not by themselves identify the types, duration, or seriousness of those events. Arm-level adverse-event counts are descriptive and do not establish that an intervention caused or prevented an event.

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

The posted results establish that the registry contains CPM means and 95% confidence intervals for four randomized intervention combinations at 6 weeks. The means range from a negative value in the sham tDCS and sham exercise arm to positive values in the other arms. Under the registry's scoring rule, positive CPM indicates better endogenous pain inhibition and negative CPM indicates worse inhibition. The intervals describe uncertainty around the arm means, rather than the distribution of individual responses.

These summaries do not establish that one intervention combination is superior to another. A direct comparison requires an estimated contrast and its uncertainty, and none is reported for the primary endpoint. In particular, arm means do not provide a formal test of the average tDCS effect, the average exercise effect, or an interaction between tDCS and exercise. The record notes that values for a two-arm comparison of this continuous endpoint are missing or not estimable.

The outcome is mechanistic. It operationalizes pain modulation through ratings under a test stimulus and a conditioning stimulus. It is not interchangeable with a participant's overall pain, functional ability, quality of life, or long-term course. The registry record does not report a clinically meaningful threshold for CPM or link the posted arm means to a clinical threshold. The result therefore cannot be classified as clinically important based on the recorded information alone.

The record also does not support a claim about the effect of treatment in all people with fibromyalgia. It does not report detailed participant characteristics in the outcome information, a full analysis population, missing-data methods, or adjusted analyses. The registry's adverse-event counts are likewise descriptive and do not establish causality. These limits do not erase the value of the observed summaries; they define the scope of conclusions that those summaries can support.

In short, the posted data describe arm-specific CPM estimates and their stated precision, alongside adverse-event counts. They do not include the inferential comparisons needed to answer whether the intervention factors or their combination changed CPM relative to a comparator.

13. Why This Trial Matters Statistically

This trial is statistically notable for its factorial structure. Rather than assigning participants only to a single active treatment or a single control, the design combines active or sham tDCS with active or sham exercise. That structure can support separate questions about each intervention and whether their joint effect differs from the pattern expected from their individual effects. Correctly distinguishing those questions is important: four arm summaries are not a substitute for reporting the factorial contrasts and interaction estimate.

The endpoint also illustrates the need to understand measurement direction before interpreting a mean. CPM is calculated by subtracting the conditioned-stimulus average from the test-stimulus average. In this trial's definition, positive values indicate better endogenous pain inhibition, even though higher scores on the underlying Numeric Pain Scale indicate worse pain. A difference score can therefore have a direction that should not be confused with the direction of its component scale.

The reported confidence intervals offer a useful view of precision for each arm mean. Yet precision around an individual mean does not answer whether a treatment contrast is estimated precisely. Readers need the contrast, its confidence interval, and the analysis method to evaluate that question. The absence of those items in the registry record makes the descriptive results interpretable, while leaving the comparative treatment questions unresolved.

The trial further highlights why mechanistic endpoints should be kept distinct from patient-centered outcomes. CPM is an experimentally elicited measure of pain modulation. It can address a biological or functional mechanism, but a CPM result by itself does not show a change in daily symptoms or functioning. Clear reporting should connect mechanistic and clinical outcomes without treating them as interchangeable.

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.

The principal limitation for interpreting this trial's posted primary result is that arm means are available without a reported direct comparison or factorial analysis. The randomized factorial design invites questions about the separate tDCS and exercise effects and their interaction, but the registry record does not report estimates or uncertainty for those contrasts. The record lists zero analyses and identifies two-arm comparison values as missing or not estimable for the continuous endpoint.

The outcome information gives arm counts and confidence intervals but does not identify the method used to calculate the intervals. The registry record also does not report baseline CPM values, adjustment for baseline, the analysis population, or how missing observations were handled. Without this information, it is difficult to assess whether the displayed means correspond to all randomized participants or a subset with available measurements.

Important design and reporting details are not reported in the registry record, including the randomization sequence method, allocation concealment, which people were masked, the statistical analysis plan, sample-size justification, multiplicity strategy, and any interim analyses. The record describes the study as completed, but does not provide further detail in the posted primary outcome information about adherence, deviations from assigned interventions, or reasons for withdrawal.

The primary outcome is a laboratory measure with a specified scoring direction, not a direct measure of daily pain impact. A clinically meaningful CPM threshold is not reported in the registry record. Although the study summary mentions temporal slow pain summation, the posted primary result is CPM; the details and results for other outcomes cannot be inferred from that mention. These limitations constrain both causal interpretation and generalization beyond the reported summaries.

15. Related Tutorials

16. Related Statistical Calculators

17. Sources

• ClinicalTrials.gov: Optimized tDCS for Fibromyalgia: Targeting the Endogenous Pain Control System — NCT03371225.
• Registry record last updated 2025-12-10; status last verified 2025-11.
• Results first posted 2025-12-10.
• 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

NCT03371225 is a completed randomized, triple-masked factorial trial sponsored by Spaulding Rehabilitation Hospital. It enrolled 116 participants and studied tDCS and exercise in fibromyalgia, using active and sham combinations. The record lists the phase as NA.

The primary endpoint is CPM at 6 weeks, measured with the Numeric Pain Scale-based test and conditioning procedure. Group means and 95% confidence intervals are reported for the four arms. The record does not post an inferential comparison for the continuous outcome; it lists zero analyses and says values for a two-arm comparison are missing or not estimable.

Serious adverse events and other adverse events are reported by arm, with no deaths listed. The registry record does not report the statistical model, missing-data approach, analysis populations, multiplicity strategy, or sample-size justification. The available result is therefore best read as a set of arm-specific descriptive estimates rather than a complete comparative analysis.