Using Transcranial Magnetic Stimulation (TMS) to Understand 'Negative' Symptoms of Schizophrenia: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Using Transcranial Magnetic Stimulation (TMS) to Understand 'Negative' Symptoms of Schizophrenia (NCT03648268), a randomized na study. The primary outcome is Change in Negative Symptom Severity.

2. Clinical Question

3. Trial Design

The registry describes a randomized, quadruple-masked, parallel-group study sponsored by Beth Israel Deaconess Medical Center. Its phase is listed as NA. The enrollment is 47, and the status is terminated. The recorded study start is 2019-05-02 and primary completion is 2023-12-22. The reason for termination is not reported in the registry record.

Four treatment arms are described: active and sham rTMS to the right dorsolateral prefrontal cortex, and active and sham rTMS to the cerebellum. Active cerebellar stimulation is described as using an intermittent theta-burst pattern at 100% of active motor threshold; active right dorsolateral prefrontal stimulation is described at 80% of active motor threshold. The record does not specify which roles were masked under the quadruple-masking designation.

The posted primary results compare the active and sham cerebellar arms. They do not provide corresponding primary results for the dorsolateral prefrontal arms. The primary outcome is continuous: change in PANSS negative symptom total from baseline to one week post treatment, reported as a mean and standard deviation. The observed group sizes for this outcome are 13 in the active cerebellar arm and 16 in the sham cerebellar arm.

The study description says the purpose was to learn about how TMS may affect negative symptoms. The record also lists changes in cerebellar-prefrontal functional connectivity and auditory hallucination severity as secondary outcomes. Further details on treatment duration, visit schedules beyond the stated outcome time frame, eligibility, and the reason for termination are not reported in the registry record.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Before assignment: 47 participants agreed to participate in the study following completion of the informed consent process. During subsequent study procedures, 18 consented participants were found ineligible to continue in the study and were not randomized to a treatment arm. Participants were randomized into "Active Cerebellum rTMS" and "Sham Cerebellum rTMS" arms but the study concluded before participants could be enrolled into the "Active DLPFC rTMS" and "Sham DLPFC rTMS"

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: Participants were randomized into "Active Cerebellum rTMS" and "Sham Cerebellum rTMS" arms but the study concluded before participants could be enrolled into the "Active DLPFC rTMS" and "Sham DLPFC rTMS"

6. Primary Endpoint

The registry lists the primary outcome as Change in Negative Symptom Severity, measured over Before treatment (Baseline) and 1 week post treatment.

The primary endpoint is change in the PANSS negative symptom total, measured from before treatment at baseline to one week after treatment. The total sums seven PANSS questions, N1 through N7. Each question is scored from 1 to 7, and the total for an individual ranges from 7 to 49. The registry states that higher scores indicate greater symptomology.

A change score expresses how the measured total differs between the stated time points. A negative group mean change therefore indicates that the score decreased on average over that interval; it does not by itself show why the score changed. The endpoint is relevant to the stated study question because the study aims to investigate negative symptoms, and the PANSS negative symptom total provides a defined measure of those symptoms.

The registry describes the outcome as a mean with standard deviation. This presents the average change in each group alongside a measure of participant-to-participant spread. It is important to distinguish the within-group mean changes from the between-group comparison: the latter estimates how much the average change differed between active and sham cerebellar stimulation. The posted results concern that comparison and the specified follow-up interval, not a broader claim about outcomes beyond it.

7. Results Posted in the Registry

• Active Cerebellum rTMS: mean -0.77 versus -0.50 on control; difference -0.27 (95% CI -1.78 to 1.24), standardized effect d = -0.13; z-test p = 0.726.

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Change in Cerebellar - Prefrontal Functional Connectivity

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Active Cerebellum rTMS: mean -0.15 versus 0.09 on control; difference -0.23 (95% CI -0.40 to -0.07), standardized effect d = -1.13; z-test p = 0.005.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the mean is statistically lower for Active Cerebellum rTMS than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

Change in Auditory Hallucination Severity

• Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
• Test: Unadjusted two-sample z-test for the difference in means, using the posted standard deviations.
• Result:
  • Active Cerebellum rTMS: mean -0.08 versus -0.18 on control; difference 0.10 (95% CI -0.41 to 0.61), standardized effect d = 0.15; z-test p = 0.699.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Active Cerebellum rTMS and the control. The interval gives the range of effects that remain compatible with the data.

The secondary outcomes cover two distinct domains: cerebellar-prefrontal functional connectivity and auditory hallucination severity. Their observed patterns differ. The connectivity contrast is negative and its reported confidence interval does not include zero, while the auditory hallucination severity contrast is positive and its interval includes zero. These findings should be read as outcome-specific estimates rather than as a single overall measure of the intervention.

Neither secondary measure is the registered primary endpoint of change in PANSS negative symptom total. A finding in functional connectivity does not establish a corresponding change in negative symptoms, and an auditory hallucination measure addresses a different symptom dimension. The primary result remains uncertain about the between-group difference in the negative symptom total; the secondary outcomes do not remove that uncertainty.

The registry reports unadjusted comparisons for the secondary outcomes and lists no reported analyses. When several outcomes are examined, the chance of at least one apparently unusual result can increase if no adjustment or prespecified hierarchy is used. The record does not say whether multiplicity was considered in the study plan or whether any correction was applied. Consequently, an unadjusted secondary p-value carries less weight as confirmatory evidence than a result interpreted under a clearly documented testing plan.

The record lists two secondary outcomes and gives no adjusted estimates or analysis details. Their results can be useful as descriptive signals for further study, but should not be treated as independently confirmed effects. A sound overall reading keeps the primary and secondary questions distinct, considers uncertainty for each estimate, and avoids selecting a single secondary result as a substitute for the primary outcome.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Change in Cerebellar - Prefrontal Functional Connectivity
• Change in Auditory Hallucination Severity

9. Statistical Interpretation

10. Statistical Methods Explained

What does a mean change describe?

A mean is an average across the observations in a group. Here, each observation is a participant’s change in PANSS negative symptom total between baseline and one week post treatment. A negative mean indicates that the group’s average score was lower at the later measurement. It does not mean that every participant’s score fell, and it does not show the pattern of individual responses.

The standard deviation describes how dispersed the observed changes are around the group mean. Larger spread means individual changes were more variable. The active and sham groups have standard deviations of 1.92 and 2.22, respectively. A standard deviation is not the same as a confidence interval: it characterizes the observed spread of participant-level values, whereas a confidence interval expresses uncertainty around an estimated quantity.

What is the between-group mean difference?

The comparison is expressed as the active cerebellar mean change minus the sham cerebellar mean change. The estimate is -0.27. This sign convention matters: a negative difference means the active group’s mean change was more negative than the sham group’s mean change. The contrast is not the same as either group’s change considered alone. It focuses on the difference between the two group averages.

The posted comparison is unadjusted. It is based on group summary statistics rather than a reported adjusted model. The registry lists no reported analyses, so it does not give a sponsor-reported model, covariate adjustment, or other analysis details to compare against the unadjusted estimate. No discrepancy is flagged in the registry record.

How should a confidence interval be read?

A confidence interval gives a range of values compatible with the estimate under the statistical method used. The primary interval runs from -1.778 to 1.238. Because it includes zero, the results are compatible with no average difference as well as with differences in either direction. The interval’s endpoints are not guaranteed bounds on the true effect, and the interval does not assign a probability to any particular value. Its breadth is a sign that the primary comparison is not estimated precisely.

What does the p-value add?

The unadjusted p-value for the primary comparison is 0.726. A p-value measures how unusual a result at least as far from a null value would be under a specified null model and the analysis assumptions. It is not an effect-size measure and does not indicate the probability that the null hypothesis is true. It should be read alongside the estimate and confidence interval, not in isolation. Since the registry does not report an analysis plan, it is not known whether this calculation matches the intended inferential procedure.

Why can over-dispersion matter?

Over-dispersion, in general, occurs when observations vary more than a statistical model expects. When a model assumes less variability than is present, its uncertainty estimates can be too small and its tests too optimistic. Conversely, appropriately representing extra variability can widen uncertainty. This is a general consideration rather than a reported feature of this trial: the registry does not report a model for over-dispersion, nor does the continuous mean comparison identify it as part of the posted analysis.

What is the role of randomization and masking?

Random allocation is intended, in general, to make comparison groups similar on average in factors that could affect outcomes. Masking is intended to reduce influences on care, measurement, or interpretation arising from knowledge of assignment. These are general design principles, not proof that groups were balanced or that masking was maintained in this study. The record identifies randomization and quadruple masking, but does not report the allocation procedure, the identities of masked roles, or checks on masking.

The four listed arms indicate that the study included two stimulation targets and active and sham procedures. The posted primary outcome results presented in the registry are limited to the cerebellar active-versus-sham contrast. The existence of other arms does not supply results for them, and no effect for the unreported dorsolateral prefrontal comparison can be inferred from the cerebellar findings.

11. Confidence Intervals and Precision

Precision concerns how narrowly the data estimate a quantity. The primary mean difference is -0.27, and its 95% confidence interval extends from -1.778 to 1.238. That interval is broad relative to the point estimate and includes zero. It therefore leaves substantial uncertainty about the size and direction of the average difference. The estimate alone should not be treated as a precise measure of a group contrast.

The primary group means are based on 13 active-arm participants and 16 sham-arm participants. The standard deviations of 1.92 and 2.22 indicate appreciable variation in individual changes relative to the estimated difference. Together, the group sizes and observed variability help explain why the interval provides limited precision. This description does not imply that any particular participant’s change can be predicted from the group averages.

The secondary connectivity estimate has a confidence interval from -0.4 to -0.07, while the auditory hallucination severity estimate has an interval from -0.407 to 0.607. These intervals have different locations and widths because they concern different measures and observed data. The apparent precision of one outcome does not transfer to another outcome or to the primary endpoint.

Confidence intervals describe statistical uncertainty under a calculation’s assumptions; they do not capture every source of uncertainty. The registry does not report missing-data methods, the analysis population, or the planned statistical model. Those unreported choices could matter to interpretation, but their effects cannot be determined from the record. The interval is therefore best read as precision for the posted unadjusted primary comparison, not as a complete account of uncertainty about the study.

12. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The planning figures are participants per arm, not total events. They are illustrations computed from the observed effect, using a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each row considers detecting the stated fraction of the observed effect: the full observed effect, 75% of it, or 50% of it. The original trial’s sample-size assumptions and justification are not reported in the registry record.

The 80% power column gives the planned number of participants per arm under those assumptions for a design with an 80% chance of detecting the specified effect if that effect were the true one. The 90% column gives the corresponding planning number for a design with a 90% chance under the same assumptions. These are prospective design quantities; they are not probabilities that the observed result is correct.

For the primary comparison, the listed figures rise as the effect to be detected becomes a smaller fraction of the observed effect. In general, smaller effects are harder to distinguish from sampling variation, so detecting them requires more participants when other assumptions are held fixed. The figures are sensitive to the observed effect used as their starting point, which may itself be uncertain. This is not observed power.

13. 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 = -0.270; pooled standard deviation σ = 2.092.
2. n = 2 × (1.96 + 0.842)² × 2.092² / -0.270² = 942.4, rounded up to 943 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 <- -0.27                      # observed difference in means
sigma <- 2.09198470357696                     # 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(3648268)
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 = 943 (80% power), 1,262 (90% power)
 75% of observed effect: n per arm = 1,676 (80% power), 2,243 (90% power)
 50% of observed effect: n per arm = 3,770 (80% power), 5,047 (90% power)
power.t.test: 943.3 
Simulated power at n = 943 per arm: 0.800 (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.

14. Multiplicity, Missing Data and Analysis Populations

The registry identifies one primary outcome and two secondary outcomes. The primary outcome is change in PANSS negative symptom total; the secondary outcomes are change in cerebellar-prefrontal functional connectivity and change in auditory hallucination severity. The record lists no reported analyses. It does not report a statistical analysis plan, a testing hierarchy, or a multiplicity adjustment. It is therefore not known whether the outcomes were intended to be tested as a family, whether one result was designated confirmatory, or how any multiple testing was addressed.

Multiplicity matters because looking at several outcomes can make an unadjusted result appear more compelling than it would under a plan that accounts for the number and structure of tests. The secondary p-values are explicitly unadjusted. The record does not establish whether the primary p-value was adjusted, and the posted comparison is described as unadjusted. The reader should not assume that a correction was or was not specified outside the registry record.

Missing-data handling is not reported in the registry record. The record does not explain whether all randomized participants contributed to each outcome, how unavailable follow-up measurements were treated, or whether any imputation or sensitivity analyses were used. The outcome-specific group sizes differ, but the registry does not explain why. No conclusion about reasons for missing observations or their likely influence is warranted from the reported summaries alone.

The analysis population is also not reported. The record does not say whether results were based on all randomized participants, participants who completed treatment, or another defined group. It does not provide details of adherence, protocol deviations, or exclusions from analysis. These omissions limit assessment of how closely the posted estimates reflect the randomized comparison. They also make it difficult to evaluate whether the analysis followed the original plan.

15. 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

For serious adverse events, the registry reports zero affected participants among 13 at risk in the active cerebellar group and zero among 16 at risk in the sham cerebellar group. Deaths are reported as zero in both groups. No serious adverse event terms are listed. These figures describe the posted safety counts in the two cerebellar arms; they do not establish that no serious events occurred outside the reported record or in other study arms.

Other adverse events affected 7 participants among 13 at risk in the active cerebellar group and 9 among 16 at risk in the sham cerebellar group. The registry does not provide event descriptions in these figures, severity classifications for these other events, or an assessment of whether they were related to stimulation. The counts should therefore be read as reported affected-participant figures, not as proof of causation or as a complete account of the nature of events.

Safety comparisons are limited by the posted group information and the lack of further detail. The record does not report timing, duration, or outcomes for individual events. The figures are descriptive and should not be used to infer comparative risk beyond the data recorded.

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

The posted primary result describes the average change in PANSS negative symptom total in the active and sham cerebellar groups over the interval from baseline to one week post treatment. The active group’s mean change was -0.77 and the sham group’s was -0.5; the estimated active-minus-sham difference was -0.27. The confidence interval ranges from -1.778 to 1.238, so the estimate does not pin down a clear direction or size for the average contrast.

This result does not establish that active cerebellar rTMS did or did not change negative symptoms. The data show an estimated difference with considerable uncertainty, not a definitive conclusion about benefit or lack of benefit. The unadjusted p-value of 0.726 does not measure the probability that the intervention works, nor does it prove the groups are equivalent. Equivalence would require a suitable design and prespecified margin, neither of which is reported in the registry record.

The result also does not answer whether stimulation of the right dorsolateral prefrontal cortex has an effect. Although that target and its active and sham arms are described, corresponding results are not posted in the reported outcomes. Nor do the secondary findings establish effects on symptoms beyond their specific measures or time frame. The outcome time frame does not support conclusions about durability or longer-term changes.

The registry reports a terminated study but does not give the reason. It does not report missing-data handling, analysis populations, or the planned statistical analysis. These gaps mean that the posted summaries cannot fully address possible selection, incomplete follow-up, or deviations from the planned methods. The most defensible interpretation stays close to the reported cerebellar comparison and its uncertainty, without extending the findings to other targets, populations, or outcomes.

17. Why This Trial Matters Statistically

This trial illustrates why a point estimate should be read together with its uncertainty. The primary estimated difference is negative, but the confidence interval extends across zero and covers values in both directions. A single estimate is not enough to characterize what the data can support. The interval communicates that the primary comparison is not precise enough to settle the direction of the average difference.

The record also demonstrates the importance of separating a registered primary question from secondary outcomes. Connectivity and auditory hallucination severity are meaningful but distinct measures. An unadjusted result on a secondary outcome does not automatically answer the primary symptom question, especially when the registry does not report a multiplicity plan or detailed analysis methods.

Finally, design labels and posted results answer different questions. Randomization and quadruple masking describe the stated design, while the available outcome data concern the active and sham cerebellar arms. The record lists additional arms but does not report results for them. Statistical interpretation depends on the actual comparison and data available, not simply on the full list of intended treatment groups.

For clinical researchers, this is a useful example of the limits of registry summaries: estimates can be described, but important context may be unavailable. Transparent reporting of analysis populations, missing-data methods, multiplicity decisions, and the reason for termination would help readers assess how the posted results relate to the planned study. Without those details, the conclusions should remain appropriately narrow.

18. 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 registry record has limitations specific to interpreting this trial. The study is marked terminated, but the reason is not reported. The record does not explain whether termination affected recruitment, follow-up, or the availability of outcome results. Enrollment is listed as 47, but the posted primary cerebellar comparison includes outcome groups of 13 and 16 participants. The record does not explain the difference between the enrollment figure and the group sizes contributing to this result.

Four arms are described, but the posted primary results concern only active versus sham cerebellar rTMS. Results for the active and sham right dorsolateral prefrontal arms are not included in the posted outcomes. The observed primary result therefore cannot be used to characterize every randomized comparison in the study.

The registry does not report participant characteristics, detailed eligibility criteria, the analysis population, missing-data procedures, or the prespecified statistical analysis. It also does not explain how the masking was implemented or identify who was masked. These omissions prevent assessment of baseline comparability, the handling of incomplete observations, and adherence to the intended analysis.

The primary confidence interval is broad, and the secondary comparisons are unadjusted. The registry does not report a multiplicity strategy. The secondary measures also assess different domains from the primary endpoint, limiting their use as substitutes for it. Finally, the posted outcomes concern baseline to one week post treatment; no longer-term outcome results are reported in this record.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Using Transcranial Magnetic Stimulation (TMS) to Understand 'Negative' Symptoms of Schizophrenia — NCT03648268.
• Registry record last updated 2026-06-25; status last verified 2026-06.
• Results first posted 2026-06-25.
• 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.

22. Record Summary

The registry record describes a randomized, quadruple-masked, parallel-group study of rTMS for negative symptoms in psychotic disorders. It lists active and sham stimulation to the cerebellum and right dorsolateral prefrontal cortex. The study is terminated, with enrollment of 47; the reason for termination is not reported.

The posted primary result compares active with sham cerebellar rTMS for change in PANSS negative symptom total from baseline to one week post treatment. The mean difference is -0.27, with a 95% confidence interval from -1.778 to 1.238 and unadjusted p = 0.726. The interval includes zero and allows for differences in either direction.

Two secondary outcomes are posted: cerebellar-prefrontal functional connectivity and auditory hallucination severity. The registry lists no reported analyses and does not report the analysis plan, missing-data methods, analysis population, or multiplicity approach. Interpretation is therefore limited to the posted summaries and their stated time frame.