Theta Burst Transcranial Magnetic Stimulation of Fronto-parietal Networks: Modulation by Mental State: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Theta Burst Transcranial Magnetic Stimulation of Fronto-parietal Networks: Modulation by Mental State (NCT04010461), a non-randomized na study. The primary outcome is 2-back Minus 1-back Blood Oxygen Level-Dependent (BOLD) Activation, Voxelwise in FPN.

2. Clinical Question

The study focuses on whether applying theta burst stimulation during a controlled mental state is associated with different network changes than applying stimulation when mental state is uncontrolled. The target is the dlPFC and its associated fronto-parietal network (FPN), a network described in the registry as supporting cognitive control. The primary endpoint is the FPN BOLD activation contrast between the 2-back and 1-back conditions, measured during fMRI 60 minutes after TMS.

The study is not a randomized comparison. Its listed arms represent different stimulation locations and mental-state conditions, and the registry explicitly warns against treating them as like-for-like controls. The record identifies a crossover model, but details about the order of conditions and the way participants moved between conditions are not reported in the registry record. Accordingly, the clinical question is about the pattern of measured network activity across the listed conditions, not a randomized estimate of a treatment effect.

3. Trial Design

This completed study is registered as NCT04010461 and is titled “Theta Burst Transcranial Magnetic Stimulation of Fronto-parietal Networks: Modulation by Mental State.” The sponsor is the University of Michigan. The registry lists the study as non-randomized, single-masked, and crossover, with phase listed as not applicable. Enrollment is recorded as 53. The study start date is 2019-11-11 and primary completion is recorded as 2022-03-29.

The planned participant group was healthy volunteers. The registry summary describes screening and assessment, a baseline fMRI scan followed by TMS, and experimental TMS sessions followed by fMRI scans. It describes a total of five visits, including the screening and assessment visit and later experimental visits. Psychological assessments and cognitive measures were also described; the summary notes that some were conducted by teleconference because of Covid. These are registry descriptions of the study plan, not details about the completion of each participant’s visits.

The conditions named in the arm descriptions are dlPFC stimulation at rest, vertex stimulation at rest, and dlPFC stimulation during the n-back working memory task. The device intervention is TMS, and the behavioral intervention is the n-back task. Although the registry calls the design crossover, the sequence of conditions, the interval between sessions, any washout procedure, and the handling of possible order or carryover effects are not reported in the registry record. The identity of the person or group masked in the single-masked design is also not reported.

The primary endpoint is continuous: mean FPN BOLD activation, expressed in arbitrary units, for the 2-back minus 1-back contrast. The registry lists 8 outcome measures and 14 analyses, but does not provide numerical results for the primary endpoint in the information summarized by the record. It also labels the comparison non-randomized and warns that the arms are not a like-for-like control comparison. Those design features limit how confidently observed differences can be attributed to the stimulation condition alone.

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: Of 59 participants who were screened, 6 were ineligible and 53 were enrolled. With each treatment, regardless of the sequence, an MRI was performed.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Of the 40 participants, image data from 3 failed quality control.

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 2-back Minus 1-back Blood Oxygen Level-Dependent (BOLD) Activation, Voxelwise in FPN, measured over 60 minutes after TMS during fMRI.

The primary endpoint is the mean 2-back minus 1-back BOLD activation, assessed voxelwise in the fronto-parietal network. BOLD is a functional MRI signal related to changes in blood oxygenation. Participants performed the n-back working memory task under high-load 2-back and low-load 1-back conditions; the endpoint is the contrast between those conditions rather than a measure from either condition alone. The assessment timeframe is 60 minutes after TMS during fMRI.

The registry describes the FPN using BOLD change during the n-back task. It says that the individual-level analysis estimated a general linear model with regressors for the 2-back and 1-back conditions, after convolution with a hemodynamic response function. The resulting contrast estimate was then used in group-level analyses. The registry describes extracting eigenvalues from second-level estimates using an FPN mask. These eigenvalues are in arbitrary units, and larger values indicate more BOLD signal.

This endpoint is used to characterize task-related brain activity in the network of interest after stimulation. It is a physiological imaging measure, not a direct measure of a participant’s clinical status or everyday cognitive function. The registry also lists other outcomes, including whole-brain BOLD activation, cerebral blood flow in the FPN, reaction time, and d-prime in the 2-back task. Numerical group estimates and uncertainty for the primary endpoint are not reported in the registry record, so its magnitude and precision cannot be described from the record.

7. Why No Re-analysis Is Shown

8. Statistical Interpretation

9. Statistical Methods Explained

The registry describes a continuous primary outcome: mean FPN BOLD activation for the 2-back minus 1-back contrast, measured 60 minutes after TMS during fMRI. The endpoint is reported in arbitrary units and uses the mean as its summary measure, with standard deviation as the stated measure of dispersion. A mean describes the central value of a set of measurements; a standard deviation describes the spread of individual measurements around that mean. Neither summary alone indicates how precisely a group difference is estimated. The group estimates and uncertainty statistics for this endpoint are not reported in the registry record.

How is the imaging contrast formed?

The registry says that the n-back task included 2-back and 1-back conditions, representing high and low working-memory loads. At the participant level, a general linear model was used to estimate BOLD change. The model included regressors for both task conditions after convolution with a hemodynamic response function. In general, a general linear model relates measured observations to specified predictors, allowing the estimated contribution of each predictor to be summarized. The 2-back minus 1-back beta estimate represents the contrast of interest. It is not simply a raw difference between two group averages.

The record then describes a group-level, second-level analysis of normalized images of the individual contrast estimates. Mean frame displacement was included as a covariate of no interest. In general, a covariate of no interest is included to account for a factor relevant to the measurements but not itself the scientific target. The registry says a fronto-parietal network mask was used and that eigenvalues from the second-level estimates were extracted for analysis. The extracted values are described as arbitrary units, with larger values indicating more BOLD signal. Details of model diagnostics, assumptions checks, and the exact group-level contrast estimates are not reported in the registry record.

What does a confidence interval describe?

In general, a confidence interval expresses the uncertainty around an estimated quantity under the assumptions of the statistical method used. A narrower interval indicates greater precision than a wider interval for the same quantity and method. It does not, by itself, establish that a difference is important or free of bias. No confidence intervals for the primary endpoint are reported in the registry record, so the precision of the estimated contrast cannot be assessed from these registry results.

What does the crossover label imply?

In general, crossover studies expose participants to more than one condition and may use within-participant comparisons. Such comparisons can account for stable differences between participants, but they require attention to treatment order, time effects, and carryover from an earlier condition. The registry labels this study crossover, but the condition sequence, any washout approach, and the analysis treatment of order or carryover are not reported in the registry record. The design label therefore does not establish which specific crossover methods were used.

Allocation is listed as non-randomized, and the registry warns that the arms are not a like-for-like control comparison. Non-random allocation can leave differences between conditions entangled with other differences in timing, context, or participant state. Statistical adjustment can address measured factors included in a model, but it cannot automatically remove unmeasured differences. The registry describes adjustment for mean frame displacement in the imaging model; it does not report other adjusted factors or establish that this covariate resolves the concerns arising from non-randomized allocation.

How should the planning illustrations be understood?

The registry includes assumptions for planning illustrations based on the observed effect: a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The target effect is expressed as a stated fraction of the observed effect. For non-time-to-event outcomes, the illustration is expressed as participants per arm; time-to-event illustrations use total events. These are planning illustrations, not observed participant counts and not evidence of the study’s actual power. The record says they are not the trial’s own design. No sample-size justification for the original study is reported in the registry record.

More generally, statistical power is the probability that a specified analysis will detect an effect of a specified size under stated assumptions. A planning calculation based on an observed effect does not show that the completed study had that power, and it may depend strongly on the estimated effect used. No numerical planning estimates are stated in the registry record for this analysis. The registry’s general assumptions do not fill in unreported details about the original design or the analyses that were ultimately performed.

The registry identifies 8 outcome measures and 14 analyses. A count of analyses does not indicate which outcome or comparison each analysis addresses, whether models were prespecified, or how results were selected for reporting. Those details, along with model assumptions and a complete statistical analysis plan, are not reported in the registry record. Accordingly, the methods description can explain the stated imaging workflow and general statistical concepts, but cannot reconstruct every analytic decision or independently evaluate the numerical results.

10. Confidence Intervals for Each Arm

No two-arm comparison is shown for this trial, but each arm's mean can be given with a t-based 95% confidence interval computed from the posted mean, spread and number of participants.

R code and output

arm <- c("TMS to dlPFC, Without a Concurrent Task (Passive)", "TMS to Vertex, Without Concurrent Task (Control)", "TMS to dlPFC, During Task (Active)")
n   <- c(37, 37, 37)
m   <- c(0.74, 0.75, 0.58)
sp  <- c(0.54, 0.45, 0.39)
sd  <- sp      # posted standard deviations
for (i in seq_along(n)) {
  se <- sd[i] / sqrt(n[i]); h <- qt(0.975, n[i] - 1) * se
  cat(sprintf("CARM|%s|%d|%.3f|%.3f|%.3f|%.3f\n", arm[i], n[i], m[i], sd[i], m[i] - h, m[i] + h))
}

CARM  TMS to dlPFC, Without a Concurrent Task (Passive)  37  0.740  0.540  0.560  0.920
CARM  TMS to Vertex, Without Concurrent Task (Control)  37  0.750  0.450  0.600  0.900
CARM  TMS to dlPFC, During Task (Active)  37  0.580  0.390  0.450  0.710

11. Multiplicity, Missing Data and Analysis Populations

The registry lists 8 outcome measures and 14 analyses. Multiple outcomes or analyses can create a multiplicity concern: when many hypotheses are tested, the chance of at least one apparently notable result can increase. In general, a prespecified approach may address this by defining a primary comparison, adjusting inference across a family of tests, or clearly distinguishing confirmatory from exploratory analyses. The registry record does not report whether any multiplicity adjustment was used, which analyses were considered confirmatory, or how the 14 analyses relate to the listed outcomes.

The record identifies a primary endpoint, but numerical estimates for it are not reported in the registry record. It also does not report a complete analysis plan, the timing of any plan finalization, or whether analyses changed after data collection. These omissions prevent assessment of whether the reported analysis set matches prespecified decisions. The presence of several outcome measures does not, on its own, show that the study used or failed to use an appropriate multiplicity strategy.

Missing data are relevant because the primary endpoint description says that, of 40 participants, image data from 3 failed quality control. The reasons for those failures, the distribution across study conditions, and the method used to handle the missing image data are not reported in the registry record. The record also states enrollment of 53, but does not give a participant flow explaining how that enrollment relates to the primary endpoint population. It is therefore not possible to determine from the registry how many participants contributed usable data to each analysis.

The analysis populations are not fully described. The registry does not report whether all available observations, only participants completing all conditions, or another defined population was used for each analysis. Nor does it report a missing-data sensitivity analysis. These details matter in a crossover study because incomplete condition measurements may affect within-participant comparisons. The information available supports noting the image quality-control exclusions and the difference between the enrollment and endpoint population counts, but not inferring how missing observations influenced estimates.

12. 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 non-serious adverse event terms

The registry lists four safety groups: Baseline Measurement; dlPFC stimulation without a concurrent task; vertex stimulation without a concurrent task; and dlPFC stimulation during the task. The reported numbers at risk for serious and other adverse events are 47 at baseline, 41 for dlPFC stimulation at rest, 43 for vertex stimulation at rest, and 40 for dlPFC stimulation during the task. The registry reports 0 serious adverse events in each group and reports 4, 2, 0, and 1 other adverse events, respectively, in the same listed order.

These are counts as recorded for the listed groups, not comparative risk estimates. The registry does not give event descriptions in the registry record, and the counts alone do not identify whether an event was caused by TMS, the task, or another factor. The group denominators differ, and the record does not explain the relationship between these safety populations or the primary endpoint population. No rates or between-condition safety comparisons should be inferred from the counts without additional information.

A reported count of 0 serious adverse events means none were recorded in the listed group in this registry entry; it does not establish that no event could occur or that follow-up was complete for every participant. The registry does not report additional detail about the event collection process, duration of safety follow-up, or attribution procedures. The figures should therefore be read as registry-reported safety counts, with those limitations.

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

The registry record establishes what the investigators set out to study: whether mental state during theta burst stimulation is associated with task-related activity in the fronto-parietal network. It specifies a primary imaging endpoint based on the 2-back minus 1-back BOLD contrast and describes a participant-level and group-level imaging workflow. It also records a completed, non-randomized crossover design and identifies the stimulation conditions of interest.

It does not, in the information summarized for this analysis, report the primary endpoint’s numerical estimates or uncertainty. As a result, the evidence available in the registry record does not establish the direction or size of any difference between the listed conditions, how consistent the measurements were, or how precisely an effect was estimated. The study’s stated hypothesis cannot be treated as a result. The record’s description of the outcome and methods is not enough to determine whether the data supported that hypothesis.

Even if a difference in BOLD activation were reported, the endpoint would need to be interpreted within its scope. It measures a contrast in brain signal during a specified task and post-stimulation timeframe. It is not itself a direct measure of clinical benefit, everyday function, or the effect of TMS in people with neuropsychiatric conditions. The registry describes the participant group as healthy volunteers, so results from this study would not automatically apply to other populations.

The non-randomized allocation and the registry’s caution that the arms are not like-for-like comparisons also constrain causal interpretation. The crossover label does not resolve these limitations without details about condition order, carryover, and analysis. The registry does not report those details. Thus, neither a definitive causal effect nor a clinical implication can be inferred from the design description alone.

The safety counts are limited registry entries and do not supply event descriptions or causal attribution. The study record can inform readers about the outcome definitions, design labels, participant counts, and reported safety counts, but it cannot support a conclusion about the primary result’s magnitude or practical meaning without the unreported outcome estimates and further methodological detail.

14. Why This Trial Matters Statistically

This study is statistically interesting because it frames a neuroscience question around state-dependent stimulation: the mental activity occurring during stimulation may be relevant to measured network response. The design places stimulation location and task engagement in the same experimental context, while the primary endpoint focuses on a task-related contrast in the fronto-parietal network. This makes the distinction between the scientific question and the statistical comparison especially important.

The crossover label raises questions about repeated observations, condition order, and possible carryover. The non-randomized allocation adds a separate concern: a measured difference between arms may not isolate the stimulation condition from other differences. The registry explicitly warns that the arms are not a like-for-like control comparison. Clear reporting of the sequence, analysis population, and model would be needed to understand how these features affected the comparisons.

The endpoint also highlights a common issue in imaging studies: an outcome can be technically defined and biologically motivated while still requiring careful interpretation. The BOLD contrast is expressed in arbitrary units and characterizes activity under a specific task and timeframe. Its statistical magnitude and precision would need to be reported before readers could evaluate the strength of evidence. The registry description gives the analysis framework, but numerical primary results are not reported in the registry record.

Finally, the gap between enrollment of 53 and the primary endpoint population description of 40, including 3 image datasets that failed quality control, makes participant flow and missing-data methods consequential. The registry does not explain that flow or the analytic handling of those data. These are not merely administrative details: they affect which observations inform the estimand and how robust an estimate may be. The study therefore illustrates why design labels, endpoint definitions, analytic details, and complete results all matter when interpreting clinical research.

15. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The main limitation for interpreting the primary endpoint is that numerical results are not reported in the registry record. Without estimates and measures of uncertainty, the result’s direction, size, and precision cannot be assessed. The endpoint is defined in arbitrary units, and the record does not report a threshold for judging the practical importance of a change.

The study is non-randomized, and the registry cautions that the arms are not a like-for-like control comparison. This limits straightforward causal attribution. Although the design is listed as crossover, the record does not report condition order, washout procedures, or how possible carryover and period effects were handled. It also does not identify who was masked under the single-masked design.

The participant counts require care. Enrollment is 53, while the primary endpoint description refers to 40 participants and notes that image data from 3 failed quality control. The record does not report a full participant flow, reasons for the image failures, or how missing observations were handled. It is also unclear from the registry information whether the same participants contributed to every outcome and analysis.

The record lists 8 outcome measures and 14 analyses but does not report the multiplicity strategy, complete statistical analysis plan, or which analyses were confirmatory. It does not provide model diagnostics or enough detail to evaluate assumptions. The safety entries give counts but not event descriptions, follow-up detail, or causal attribution. Finally, the study population is healthy volunteers, which limits direct application to populations with clinical conditions. These limitations concern what can be concluded from the registry record and do not establish that the study procedures or analyses were inadequate.

16. Related Tutorials

17. Related Statistical Calculators

18. Sources

• ClinicalTrials.gov: Theta Burst Transcranial Magnetic Stimulation of Fronto-parietal Networks: Modulation by Mental State — NCT04010461.
• Registry record last updated 2023-10-06; status last verified 2023-09.
• Results first posted 2023-10-06.
• 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.

19. Record Summary

NCT04010461 is a completed, non-randomized, single-masked crossover study sponsored by the University of Michigan. The registry lists enrollment of 53 healthy volunteers and describes theta burst TMS to the dlPFC at rest, stimulation to the vertex at rest, and dlPFC stimulation during the n-back working memory task.

The primary endpoint is mean FPN BOLD activation for the 2-back minus 1-back contrast, measured 60 minutes after TMS during fMRI. The registry describes a general linear model, normalized group-level imaging analyses, adjustment for mean frame displacement, and extraction of eigenvalues within an FPN mask. It notes that larger eigenvalues indicate more BOLD signal.

For the primary endpoint, the registry refers to 40 participants and reports that image data from 3 failed quality control. Numerical primary-outcome results are not reported in the registry record. The record lists 8 outcome measures and 14 analyses and cautions that the non-randomized arms are not a like-for-like control comparison. Reported serious adverse-event counts are 0 in each listed group; other adverse-event counts are also recorded, without event descriptions in the information.