The Effect of Prefrontal Cortex Stimulation on Antisocial and Aggressive Behavior: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for The Effect of Prefrontal Cortex Stimulation on Antisocial and Aggressive Behavior (NCT02427672), a randomized na study. The primary outcome is Change in Antisocial Behavior Inclinations at 24 Hours.

2. Clinical Question

3. Trial Design

This was a randomized, double-blind, parallel-group trial of prefrontal cortex stimulation for antisocial and aggressive behavior. The registry lists enrollment of 84 and a completed status. The study began in 2015-03, with primary completion in 2017-12. Its phase is listed as NA. The sponsor is the University of Pennsylvania.

Participants were assigned to anodal stimulation or sham stimulation. The active intervention was bilateral anodal tDCS of the dorsolateral prefrontal cortex. The sham condition used the same electrode placement, current intensity, and ramp time as the active condition, but stimulation lasted for 30 seconds. The brief study description says participants completed survey and laboratory measures during and after stimulation. Heart rate and skin conductance were also measured.

The registry lists two outcome measures and no posted secondary results. The primary outcome concerns change in antisocial behavior inclinations at an average of 24 hours after stimulation or sham, compared with baseline. The posted arm summaries include 39 participants for anodal stimulation and 42 for sham stimulation. The record does not explain the difference between the enrollment figure and the group counts reported for this outcome, or whether those counts represent everyone randomized, everyone assessed, or another analysis population.

Further details about eligibility criteria, the randomization procedure, allocation concealment, the exact blinding procedures, or the trial’s original sample-size justification are not reported in the registry record. The record also does not report the protocol’s prespecified statistical analysis plan.

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.

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.

6. Primary Endpoint

The registry lists the primary outcome as Change in Antisocial Behavior Inclinations at 24 Hours, measured over Baseline (an average of 15 minutes before receiving tDCS or sham) and on average, 24 hours following stimulation or sham.

The primary endpoint is change in antisocial behavior inclinations at an average of 24 hours after stimulation or sham, with baseline assessed an average of 15 minutes before the intervention. Participants responded to two hypothetical scenarios, one involving physical assault and one involving sexual assault. For each, they rated the likelihood that they would commit the described act on a scale from zero, meaning no chance at all, to ten, meaning 100 percent chance. The two responses were summed, producing a score from 0 to 20. A higher score indicates greater inclination to engage in the described antisocial acts.

This measure captures stated intentions in response to specific hypothetical situations, rather than observed behavior. It is used to quantify the study’s target construct in a consistent way across the two groups and assessment times. That makes it possible to report group-level scores and compare the posted results. The endpoint is limited to the scenarios and self-reported responses described in the registry; it should not be treated as a direct measure of every form of antisocial or aggressive behavior.

The registry lists the outcome as a mean with standard error as its dispersion measure. It does not report separate results for the two scenarios or describe how missing responses, if any, were handled.

7. Results Posted in the Registry

• Anodal Stimulation: mean 1.41 versus 3.05 on control; difference -1.64 (95% CI -3.12 to -0.16), standardized effect d = -0.47; z-test p = 0.030.

8. Statistical Interpretation

9. Statistical Methods Explained

What does a mean difference describe?

A mean is the arithmetic average of observations in a group. For this continuous outcome, the registry reports a mean score for each intervention group. The comparison is expressed as the anodal group mean minus the sham group mean, yielding the reported mean difference of -1.64 points. A negative estimate means the anodal group’s reported mean was lower. The mean difference keeps the result in the original score units, which makes it possible to relate the contrast to the endpoint’s 0-to-20 scale.

A mean difference describes the separation between group averages, not the range of individual responses. Two groups can have the same average while containing very different distributions of individual scores. The posted summary does not provide those distributions, so the group averages cannot indicate how consistently participants responded.

What is a standard error?

The arm summaries report standard errors of 0.33 for anodal stimulation and 0.68 for sham stimulation. A standard error describes the statistical uncertainty in an estimated mean, rather than the spread of individual scores. It is affected by both variation among observations and the amount of information contributing to the estimate. It should not be read as a typical participant’s score difference from the group mean. The registry does not report standard deviations for the two arms.

What does the confidence interval add?

A confidence interval gives a range of values that are compatible with the observed data under the interval’s statistical assumptions. For the reported mean difference, the 95% confidence interval runs from -3.121 to about -0.159. The interval is centered near the point estimate, but its width shows that the exact size of the group contrast is uncertain. A confidence interval is not a guarantee that the true value lies within the displayed limits, nor is it a range containing 95% of individual participant outcomes.

How should the p value be read?

The comparison has an unadjusted p value of 0.03. In general, a p value measures how unusual data at least as incompatible with a specified null hypothesis would be if that null model and its assumptions were correct. It does not quantify the probability that the result occurred by chance, and it is not a measure of effect size. The registry does not report the exact test or model used for the sponsor’s analysis, so the p value should be read as the posted unadjusted result rather than as evidence about an undocumented procedure.

Why does randomization matter?

In general, random assignment can make groups comparable on average with respect to measured and unmeasured characteristics, supporting an interpretation of between-group differences as related to assignment. It does not ensure that groups are identical in a particular trial, especially with limited enrollment, and it does not remove uncertainty from outcome measurement or missing data. The record identifies the study as randomized, but does not report enough detail to assess its randomization implementation or the analysis population.

Why does the score’s bounded range matter?

The outcome has a fixed range from 0 to 20, and the group means are near the lower end of that scale. In general, bounded outcomes can have distributions that are asymmetric or concentrated near a boundary. Such features may affect whether a statistical model’s assumptions are appropriate. The registry does not provide a distribution plot, individual-level observations, or a detailed model description, so the shape of the outcome data cannot be assessed from the reported means and standard errors alone.

What can recalculation establish?

Simple unadjusted re-calculations from posted summary statistics can describe a contrast under the assumptions of that calculation. They do not replace a sponsor’s prespecified analysis or reveal whether that analysis adjusted for baseline, handled missing values in a particular way, or followed the protocol. The discrepancy indicator is false, so there is no reported discrepancy between the posted result and the recalculated comparison. Even so, the sponsor’s detailed analysis method is not reported in the registry record, and the summary should not be mistaken for a complete statistical analysis plan.

10. Confidence Intervals and Precision

The reported mean difference is -1.64 points, with a 95% confidence interval from -3.121 to about -0.159. The point estimate gives the single best estimate in the posted comparison, while the interval displays a range of values compatible with the data under the calculation’s assumptions. Its negative limits indicate that the interval lies on the side of lower mean scores in the anodal group. The upper limit is rounded to three decimal places to comply with the display precision.

The interval is important because the point estimate alone can give a false impression of certainty. Although the estimate is -1.64 points, values closer to zero and values farther from zero remain compatible with the data. The interval does not show the full range of individual participant scores, and it does not mean that 95% of participants experienced a change within those limits. It concerns the uncertainty in the estimated group contrast.

The arm-level standard errors were 0.33 for anodal stimulation and 0.68 for sham stimulation. They describe precision of the group means, not the spread of participant-level scores. The registry does not report standard deviations or individual data, limiting assessment of variability and outcome distribution. It also does not report enough detail about the analysis model, baseline adjustment, or missing-data handling to evaluate how those choices might affect the interval.

Precision and importance are different considerations. The confidence interval describes statistical uncertainty on the score scale, while whether a difference is practically meaningful requires context not reported in the registry record. The results concern this specific self-reported endpoint and assessment timing.

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 figures are participants per arm, not total events. They are illustrations based on the observed effect, not the trial’s own design calculation. The assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning row uses the stated fraction of the observed effect as the effect to detect.

For planning at 100% of the observed effect, the display gives 71 participants per arm for 80% power and 95 participants per arm for 90% power. For planning at 75% of the observed effect, it gives 126 participants per arm for 80% power and 169 participants per arm for 90% power. For planning at 50% of the observed effect, it gives 283 participants per arm for 80% power and 379 participants per arm for 90% power.

In general, power is the probability of detecting an effect at least as extreme as the one being planned for, under the assumptions of the calculation, if that effect is present. The 80% and 90% columns therefore describe different target probabilities for a future study to detect its assumed effect. A higher target power generally requires more participants when other assumptions stay fixed. Likewise, smaller effects are harder to distinguish from random variation and require more participants, as the planning rows illustrate.

This is not observed power. It is a planning illustration based on the observed effect, and it does not establish that the trial was originally designed with these targets or assumptions. The original design assumptions and sample-size justification are not reported in the registry record. The curve reflects the planning relationship between assumed effect size and required participants per arm; it should be read as a planning aid rather than as evidence about the trial’s achieved power.

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 = -1.640; pooled standard deviation σ = 3.482.
2. n = 2 × (1.96 + 0.842)² × 3.482² / -1.640² = 70.7, rounded up to 71 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 <- -1.64                      # observed difference in means
sigma <- 3.48167462980792                     # 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(2427672)
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 = 71 (80% power), 95 (90% power)
 75% of observed effect: n per arm = 126 (80% power), 169 (90% power)
 50% of observed effect: n per arm = 283 (80% power), 379 (90% power)
power.t.test: 71.7 
Simulated power at n = 71 per arm: 0.799 (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

Multiplicity arises when multiple outcomes, comparisons, time points, or analyses are tested. In general, testing many hypotheses can increase the chance of at least one apparently notable result, so a prespecified analysis plan may define a primary outcome and specify how other tests will be handled. The registry lists two outcome measures, but reports no posted secondary results and no analyses in the record. The primary endpoint is identified, yet the registry does not describe whether any multiplicity adjustment was planned or applied. The reported p value is unadjusted.

Missing outcome data can also affect interpretation. If some participants do not contribute an endpoint measurement, the results may depend on why the data are missing and how the analysis handles them. The registry does not report the number of missing primary endpoint observations, reasons for missingness, imputation methods, or sensitivity analyses. The posted group counts are 39 for anodal stimulation and 42 for sham stimulation, but the record does not explain how these relate to enrollment or the analysis population. It is therefore not possible to determine from the registry whether the comparison follows an intention-to-treat approach, a complete-case approach, or another rule.

The record does not report a protocol-defined analysis population, treatment of protocol deviations, or whether participants were analyzed according to randomized assignment. It also does not report a statistical analysis plan or details of any interim analyses. These omissions do not demonstrate that such procedures were absent; they mean that they are not reported in the registry record. As a result, the posted summaries support a description of the reported endpoint comparison, but do not permit a full audit of outcome selection, multiplicity control, or missing-data assumptions.

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 5% reporting threshold.

Most frequent non-serious adverse event terms

The serious adverse event figures report zero affected participants in both groups, with 39 at risk in the anodal stimulation group and 42 at risk in the sham stimulation group. No serious adverse event terms are listed. These registry counts indicate that no serious adverse events were recorded as affecting participants in either group in the posted safety results. They do not establish that no event of any kind occurred.

The record also lists other adverse events as affecting 39 participants in the anodal group and 39 in the sham group, with 39 and 42 at risk, respectively. These are counts of affected participants as recorded, not a description of event types, severity, duration, or causal relationship to stimulation. The registry does not provide detailed terms for those other adverse events in the listed summary.

Safety counts depend on what was collected and reported. The record does not provide further detail about ascertainment procedures, follow-up completeness, or the relationship of an event to the intervention. The figures should therefore be read as registry-reported counts, not as a comprehensive account of all possible harms.

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

The result describes a lower average score on the antisocial behavior inclinations measure in the anodal stimulation group than in the sham group at the posted assessment. The estimated mean difference was -1.64 points, and the 95% confidence interval ranged from -3.121 to about -0.159. These statistics quantify a group contrast on the study’s self-reported, scenario-based scale and indicate uncertainty around its magnitude.

The measure asks participants how likely they would be to commit acts described in hypothetical physical and sexual assault scenarios. It is a measure of stated inclination in those scenarios, not direct observation of behavior. The result does not establish how participants behaved outside the study, whether any difference persisted after the assessment at an average of 24 hours, or whether the same pattern would apply to other forms of aggression or antisocial behavior.

The registry does not report a clinically meaningful threshold for the score or enough information to translate the group contrast into a practical interpretation. It also does not provide detailed results for other outcomes, separate scenario scores, or an account of missing data and the analysis population. The result should not be generalized beyond the outcome, groups, and assessment described without further evidence.

In general, a randomized comparison can help estimate differences associated with assignment, but confidence in interpretation also depends on implementation, measurement, analysis, and follow-up. Relevant details about those features are not reported in the registry record. The posted estimate is therefore best understood as a statistical summary of the recorded comparison, rather than a complete account of the intervention’s effects or broader consequences.

16. Why This Trial Matters Statistically

This trial is statistically interesting because it connects an experimental intervention with an outcome that is difficult to observe directly. The primary measure uses participants’ responses to hypothetical scenarios, then combines the two responses into a score. That approach makes a quantified group comparison possible, while also requiring careful interpretation: the score measures stated inclinations in those situations, not behavior itself.

The study uses a randomized, double-blind, parallel-group design and compares active stimulation with a sham condition. In general, randomization and blinding can support a fairer comparison by reducing some sources of systematic difference and expectation. The registry’s brief design description gives the framework, while limited reporting of implementation and analysis details constrains how fully the comparison can be evaluated.

The posted mean difference is expressed in the endpoint’s own score units and is accompanied by a confidence interval. This makes both direction and uncertainty visible. The interval communicates that the estimated difference is not known precisely, and its width matters alongside the p value. A statistically notable result does not by itself settle questions about the magnitude’s practical meaning, the validity of the measure, or applicability beyond the study conditions.

The record also illustrates why sample-size planning should be separated from observed results. The planning figures use fractions of the observed effect and specified assumptions; they do not reveal the trial’s original design rationale or achieved power. More complete reporting of the protocol, analysis plan, missing outcomes, and outcome distributions would help readers assess the evidence more comprehensively.

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 outcome is based on self-reported likelihood of committing acts in two hypothetical scenarios. The registry does not report whether responses correspond to behavior in real settings, and the result should not be interpreted as a direct behavioral outcome. The combined score may also obscure differences between the physical assault and sexual assault scenarios because separate scenario results are not posted.

The outcome is bounded from 0 to 20, while the posted group means are close to the lower end of that range. Without individual-level data or distribution summaries, it is not possible to assess whether scores clustered near the lower boundary, whether distributions were asymmetric, or how well the assumptions behind the comparison fit the observed data.

The registry describes the endpoint as change from baseline at an average of 24 hours, but does not report the detailed analysis model or explain how baseline measurements were incorporated. It also does not report missing outcome counts, reasons for missingness, or the analysis population. The relationship between the enrollment figure and the numbers contributing to the primary summaries is not explained.

Further details about eligibility, intervention fidelity, the blinding procedure, and the protocol’s statistical plan are not reported in the registry record. The active-arm description is incomplete in the record. There are no posted secondary results, and the registry does not explain whether any multiplicity procedures were planned. These reporting limitations make it difficult to assess robustness or generalizability beyond the reported comparison and endpoint.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: The Effect of Prefrontal Cortex Stimulation on Antisocial and Aggressive Behavior — NCT02427672.
• Registry record last updated 2019-08-28; status last verified 2019-08.
• Results first posted 2019-08-28.
• 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

The registry record describes a completed, randomized, double-blind, parallel-group trial sponsored by the University of Pennsylvania. It compared bilateral anodal tDCS of the dorsolateral prefrontal cortex with sham stimulation. Enrollment is listed as 84; the record gives study dates of 2015-03 for start and 2017-12 for primary completion.

The primary outcome was change in antisocial behavior inclinations at an average of 24 hours, measured with summed responses to two hypothetical scenarios. The reported group means were 1.41 for anodal stimulation and 3.05 for sham stimulation. The mean difference was -1.64, with a 95% confidence interval from -3.121 to about -0.159 and an unadjusted p value of 0.03.

The record lists two outcome measures, no posted secondary results, and no analyses in its analysis listing. It does not report the detailed analysis plan, missing-data handling, or the trial’s original sample-size assumptions. Serious adverse events were recorded as affecting zero participants in either group.