Accelerated TMS to a Novel Brain Target in MDD and PTSD: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Accelerated TMS to a Novel Brain Target in MDD and PTSD (NCT03114891), a randomized na study. The primary outcome is Percent Change in Depression Severity of TMS at fMRI-guided Brain Target vs Standard Brain Target.

2. Clinical Question

3. Trial Design

The registry describes a randomized, double-masked crossover trial sponsored by the University of Pennsylvania. Its status is completed, and the enrollment field reports 50. The listed conditions are post-traumatic stress disorder and major depressive disorder. The phase is recorded as NA.

The study compared TMS at an individualized fMRI-guided brain target with stimulation at a standard target. The fMRI-guided target was created using participants’ individualized resting connectivity data, with a cortical site in the left prefrontal cortex selected to influence the subgenual anterior cingulate cortex. The standard target was identified by measuring 6cm anterior of the hand knob. The descriptions refer to two daily intermittent theta-burst stimulation sessions about 10 minutes apart, on 10 consecutive weekdays.

The four reported arm descriptions represent different sequences of target and video/task conditions across the first and second rounds. The primary outcome, however, is explicitly defined as change from baseline to after the first round. The posted results give a mean and standard deviation for each of the four sequence groups, and three comparisons against the group whose first round was fMRI-guided target/video. Thus, the posted primary-outcome comparisons are between first-round groups; they are not reported as a paired estimate using both periods of the crossover.

The registry lists the start date as 2017-04-20 and primary completion as 2021-12-01. It does not report further details about the masking procedures, sequence generation, or how the crossover periods were handled analytically.

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 the 87 subjects screened for the study, 37 did not start treatment (19 were deemed ineligible,15 withdrew, 3 lost to follow up) and 50 enrolled in the study (assigned to an intervention group).

First Treatment Round

Reasons for not completing this period:

3 Week Break

Reasons for not completing this period:

Second Treatment Round

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 Percent Change in Depression Severity of TMS at fMRI-guided Brain Target vs Standard Brain Target, measured over Before and after the first round of two weeks of TMS treatment (two daily iTBS sessions over 10 consecutive weekdays).

The primary endpoint is percent change in depression severity, measured with the Montgomery-Asberg Depression Rating Scale (MADRS), from baseline to after the first round of TMS. The MADRS is clinician-rated and contains 10 items, each rated on a 0-6 scale, for a maximum total score of 60. Higher total scores indicate more severe depression.

The registry defines the change as a percent decrease from baseline. A positive value therefore indicates that the post-treatment MADRS score was lower than baseline, while a negative value indicates that it was higher. Larger positive values represent greater symptom reduction by this measure. The endpoint is reported as a mean with standard deviation for each arm.

Using a continuous rating scale retains information about the degree of change rather than reducing the result to a yes/no category. This makes it possible to describe average change and its variability across participants. The endpoint is specifically limited to the first round, so these estimates do not themselves describe the full crossover sequence or later-round change. The registry does not report the formula used to calculate each participant’s percent change, nor does it provide a separate outcome definition for the two listed diagnoses.

7. Results Posted in the Registry

• First Round: 6cm Target/Video, Second Round: fMRI-guided Target/Task: mean 24.94 versus 49.11 on control; difference -24.17 (95% CI -50.82 to 2.48), standardized effect d = -0.75; z-test p = 0.075.
• First Round: fMRI-guided Target/Task, Second Round: 6cm Target/Video: mean 36.47 versus 49.11 on control; difference -12.64 (95% CI -38.11 to 12.83), standardized effect d = -0.43; z-test p = 0.331.
• First Round: 6cm Target/Task, Second Round: fMRI-guided Target/Task: mean 42.56 versus 49.11 on control; difference -6.55 (95% CI -29.12 to 16.02), standardized effect d = -0.23; z-test p = 0.570.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: each participant’s percent change in MADRS severity contributes to a group mean. The registry reports the mean and standard deviation for each first-round sequence group. A mean describes the group’s average endpoint value. A standard deviation describes how dispersed individual values were around that mean; it is not the uncertainty of the mean itself and is not a range containing every participant’s result.

What does a mean difference represent?

Each posted comparison uses the first-round fMRI-guided target/video group as the reference. The mean difference expresses the comparison group’s mean relative to that reference. A negative estimate indicates a lower mean percent decrease in the comparison group, consistent with the endpoint’s direction where a higher positive value represents greater reduction in MADRS score. The estimate is in the endpoint’s units, percentage of change. The three reported estimates are -24.17, -12.64, and -6.55.

In general, a mean difference summarizes the contrast between group averages; it does not describe how every participant differed. It can be influenced by variation within each group, and a mean alone does not show the distribution’s shape. The posted standard deviations offer information about variability, but individual-level data and distribution plots are not part of the registry record.

What does a confidence interval add?

In general, a confidence interval describes uncertainty around an estimated contrast under a specified statistical procedure. It gives a range of values that are compatible with the data and method, rather than a guarantee that the true value lies in that particular interval. The reported intervals extend from -50.82 to 2.482, from -38.11 to 12.83, and from -29.12 to 16.02. Each range contains zero, the value corresponding to no mean difference.

The confidence level and the method used to construct these intervals are not reported in the registry record. The record also does not state whether the comparisons were adjusted for covariates or whether the crossover structure was included in the calculation. The comparisons are presented as unadjusted mean differences. These limitations matter because analysis choices affect the interpretation and precision of an interval.

How should the p-values be read?

In general, a p-value describes how unusual data at least as incompatible with a specified null model would be if that model and the analysis assumptions were true. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of an effect. The reported unadjusted p-values are 0.075, 0.331, and 0.57. They should be considered alongside the estimates and intervals, rather than treated as a standalone decision rule. The registry does not report a prespecified threshold for these endpoint comparisons or an adjustment for making multiple comparisons.

The record reports no formal analysis records, although it does post group summaries and comparison estimates. Details such as the specific model, degrees of freedom, missing-data handling, and analysis population are not reported in the registry record. No assumption about those procedures can be made from the means, standard deviations, intervals, and p-values alone.

Why does variability matter?

In general, greater dispersion within groups can make an average contrast less precise, especially when group sizes are limited. Over-dispersion means that observed variability is larger than a chosen model expects; if present and ignored, standard errors and inferential results may be unreliable. The registry record does not report an over-dispersion assessment or a model that addresses it. The relatively large standard deviations compared with the mean differences are a reason to focus on uncertainty, but they do not by themselves establish a particular distribution or model failure.

The outcome is bounded in its underlying MADRS score, but the percent-change calculation and its possible range are not described in enough detail to infer a suitable distribution. The record does not report residual checks, transformations, robust methods, or a nonparametric analysis. In general, these are among the issues an analysis plan can address for continuous outcomes, but no such plan is reported.

The trial is described as a crossover, but the primary endpoint is measured after the first round. A crossover design can in general use within-participant comparisons across periods, while also needing to consider period, sequence, and possible carryover effects. The posted primary estimates instead compare the first-round groups. The registry does not report a full crossover analysis, a carryover assessment, or an explanation of why the first-round result was selected for this endpoint. It is therefore safest to interpret the displayed comparisons as first-round group contrasts and not assume that within-participant crossover information was used.

10. Confidence Intervals and Precision

The reported confidence intervals are broad relative to their point estimates, and all three include zero. The first comparison has an estimate of -24.17 and an interval from -50.82 to 2.482. The second estimate is -12.64, with an interval from -38.11 to 12.83. The third estimate is -6.55, with an interval from -29.12 to 16.02. These intervals show that the posted data do not pin down a single precise value for any contrast.

For each comparison, the interval includes possible negative differences and values on the positive side of zero. In the endpoint’s direction, a negative difference means a smaller average percent decrease in the comparison group than in the reference group; a positive difference would mean a larger average decrease. Because zero is also within each range, the data are compatible with little or no average difference under the reported analysis. The intervals should not be interpreted as proving equivalence: no equivalence margin or equivalence analysis is reported.

Arm sizes are 12, 11, 10, and 12, and the reported standard deviations range from 25.42 to 37.97. These summaries help explain why the estimates warrant caution, but they do not identify the exact source of uncertainty. Confidence-interval level and construction method are not reported in the registry record. There are no confidence limits listed for the individual arm means, so the stated intervals apply to the mean differences, not to each group mean. Overall, the point estimates suggest differences in the observed averages, while their intervals indicate limited precision and leave substantial uncertainty about the size and direction of the underlying contrasts.

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 estimates are expressed as participants per arm for 80% power and participants per arm for 90% power. They are not total event counts: this is a continuous-outcome illustration, not a time-to-event calculation. The planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, a normal approximation, and an effect to detect set at the stated fraction of the observed effect. The registry’s own original design assumptions are not reported.

The 80% power column describes the planned per-arm size for a hypothetical study with an 80% chance of detecting the selected effect under those assumptions, if that effect and the model assumptions were correct. The 90% power column applies the same idea with a higher target chance of detection. These are planning targets, not observed power.

The rows describe planning for 100%, 75%, and 50% of the observed effect. Smaller effects require more participants because a smaller signal is harder to distinguish from random variation. Estimates differ by comparison because the observed effects used in the illustrations differ. They should not be read as the original trial’s enrollment rationale, as a guarantee of a future result, or as evidence that the trial had a particular probability of success. The displayed figures are hypothetical design calculations based on the observed summaries.

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 = -24.170; pooled standard deviation σ = 32.016.
2. n = 2 × (1.96 + 0.842)² × 32.016² / -24.170² = 27.5, rounded up to 28 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 <- -24.17                      # observed difference in means
sigma <- 32.0157322934478                     # 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(3114891)
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 = 28 (80% power), 37 (90% power)
 75% of observed effect: n per arm = 49 (80% power), 66 (90% power)
 50% of observed effect: n per arm = 111 (80% power), 148 (90% power)
power.t.test: 28.5 
Simulated power at n = 28 per arm: 0.792 (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 reports three primary-outcome comparisons against the first-round fMRI-guided target/video group, with unadjusted p-values. It does not report a multiplicity adjustment, a hierarchy among the comparisons, or a prespecified strategy for interpreting them together. When several comparisons are considered, the chance of at least one chance finding can increase; in general, multiplicity procedures are used to manage that issue. Whether an adjustment was planned or considered by the investigators is not reported in the registry record.

The registry lists one outcome measure and no secondary outcomes. It also lists zero analysis records. The posted summaries and comparisons do not, by themselves, establish what analyses were prespecified, which were exploratory, or whether additional analyses were conducted outside the registry record. A statistical analysis plan, hypothesis-testing framework, and endpoint-specific significance threshold are not reported.

Missing-data details are also not reported. The record does not state how many endpoint observations were missing, how missing values were handled, or whether all randomized participants were included in each analysis. The listed group sizes are available for the posted outcome summaries, but no flow of participants through the periods or reasons for missing observations are given. Consequently, it is not possible to assess from the registry record whether missingness could have affected the estimates.

The analysis population is not specified: the record does not say whether the primary results use an intention-to-treat, per-protocol, or other population. It also does not describe adherence criteria or exclusions from analysis. Since this is a crossover trial but the endpoint is after the first round, the record does not clarify how sequence allocation, period effects, or possible carryover were addressed in any broader analysis. These absences limit assessment of the inferential framework, not just interpretation of the numerical results.

14. 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 reports serious adverse event and death counts separately for four exposure groups. For fMRI-guided target/video, 23 were at risk; serious adverse events were reported for 0, and deaths were 0. For 6cm target/video, 24 were at risk; serious adverse events were 0, and deaths were 0. For fMRI-guided target/task, 21 were at risk; serious adverse events were 0, and deaths were 0. For 6cm target/task, 24 were at risk; serious adverse events were 0, and deaths were 0.

These are group-level registry counts, not a comparison designed to establish safety differences. The record also lists other adverse events affecting 0, 7, 2, and 0 participants in those same groups, respectively. Those counts are distinct from the serious-event counts. The record does not provide event descriptions in the posted serious-event terms, and it does not explain how adverse events were attributed, collected, or managed. Zero reported serious events in these groups should be read as a registry result, not as proof that no risk exists.

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

The primary endpoint describes the average percent change in MADRS score from baseline to after the first round. The reference group’s mean was 49.11, and the other group means were 24.94, 36.47, and 42.56. Under the endpoint definition, positive values indicate reduced MADRS scores. These are observed group summaries; they do not establish that TMS caused the changes.

The three posted differences compare first-round sequence groups against fMRI-guided target/video. Their estimates are negative, but each confidence interval includes zero. The findings therefore leave uncertainty about whether the underlying mean differences are negative, close to zero, or positive. The intervals also allow differences that could be appreciable in either direction. The data do not demonstrate that the targets are equivalent, because no equivalence margin or equivalence test is reported.

The comparisons combine target and video/task arrangements, so they do not isolate the effect of brain target while holding all other features constant across every contrast. The outcome is measured after the first round, rather than being reported as a full within-person crossover estimate. The record also does not report separate effects for participants with post-traumatic stress disorder and those with major depressive disorder. These aspects limit how broadly the contrasts can be interpreted.

The results do not establish whether one target is clinically preferable, whether either approach produces a treatment benefit, or whether findings apply to people outside the enrolled study population. The registry describes the stimulation use as experimental. Interpretation should remain focused on the posted endpoint, its group averages, and the uncertainty in the comparisons. The record does not report a no-TMS comparison for this primary outcome, so within-group reductions cannot be separated from other explanations using these results alone.

16. Why This Trial Matters Statistically

This trial raises a statistical question that is common in clinical research: how much can a small set of group summaries tell us when the observed averages differ but variability is substantial? The arm means provide a clear descriptive picture, while the broad confidence intervals show that the data leave considerable uncertainty about the corresponding population contrasts. Reporting both the point estimates and their uncertainty is essential; a ranking of means alone would give an incomplete account.

The crossover label also matters. A crossover design can in general support within-participant comparisons, but the posted primary endpoint is defined after the first round and the reported comparisons are between first-round groups. A reader should not assume that all information from both rounds contributed to these estimates. The registry does not report a full crossover analysis or details on period and carryover effects. This distinction helps align the interpretation with the actual posted estimand.

The randomized sequences include combinations of target and video/task conditions. That makes the contrast structure important: differences in the endpoint cannot be attributed to target alone from these comparisons without further analysis or design details. The record also lacks a reported multiplicity strategy, missing-data approach, and analysis population, all of which affect how confidently the numerical estimates can be interpreted.

Finally, the planning illustrations make explicit that sample requirements depend on the effect size targeted. Planning around a fraction of an observed effect is a useful demonstration, but it is not the trial’s original design rationale and does not remove uncertainty in the estimated effect. Together, these points make the record useful for understanding the endpoint and the limits of its estimates, while underscoring the need to distinguish descriptive findings from causal or confirmatory conclusions.

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 primary results are based on small reported first-round groups, with arm sizes of 12, 11, 10, and 12. The standard deviations are substantial, and all three confidence intervals include zero. The estimates are therefore imprecise, and the registry record does not provide individual-level results that would allow assessment of distribution shape, outliers, or the influence of particular observations.

The comparison groups differ in both stimulation target and video/task arrangement. The posted mean differences do not isolate a target effect independently of those combinations. The endpoint is measured after the first round, and the record does not provide a full crossover analysis, period-specific results, or a carryover assessment. The relation between first- and second-round outcomes is consequently not described by the primary estimates.

Important analysis details are absent from the registry record: the confidence-interval level and method, the statistical model, covariate adjustment, missing-data handling, the analysis population, and any multiplicity plan. The registry lists no secondary outcomes and no analysis records, which limits the ability to compare the posted results with a prespecified analytical framework. Diagnostic subgroup findings are also not reported, so the combined results cannot show whether patterns differ by condition.

The record reports a total enrollment field of 50, but it does not describe participant flow through treatment rounds or explain the difference between enrollment and the group sizes shown for the primary endpoint. Eligibility criteria, baseline characteristics, adherence, and reasons for missing data are not reported in the information available. These gaps limit assessment of representativeness and possible selection effects. The safety counts are also reported without event details or a fuller account of collection and attribution.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Accelerated TMS to a Novel Brain Target in MDD and PTSD — NCT03114891.
• Registry record last updated 2023-05-06; status last verified 2023-04.
• Results first posted 2023-05-06.
• 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.

21. Record Summary

NCT03114891 is a completed randomized, double-masked crossover study sponsored by the University of Pennsylvania. The registry lists enrollment of 50, with post-traumatic stress disorder and major depressive disorder as conditions. The study compared TMS at an individualized fMRI-guided target with a standard target identified 6cm anterior of the hand knob, in sequences that also included video or task conditions.

The primary outcome was percent change in MADRS depression severity after the first round of TMS. The four arm means were positive, while the three posted mean differences against the fMRI-guided target/video group were negative and had confidence intervals that included zero. The registry reports zero serious adverse events and zero deaths in each listed exposure group. Detailed analysis plans, missing-data methods, and a full crossover analysis are not reported in the registry record.