Effect of Omega-3 Fatty Acid on Cortical Function in ADHD: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Effect of Omega-3 Fatty Acid on Cortical Function in ADHD (NCT01883817), a randomized phase 3 study. The primary outcome is Attention-Deficit Hyperactivity Disorder Symptom Ratings Using the ADHD Rating Scale (ADHD-RS-IV).

2. Clinical Question

The clinical question is whether the average ADHD-RS-IV score at the 10-week assessment differed between participants assigned to DHA Omega-3 and those assigned to placebo. The score ranges from 0 to 54, and higher scores indicate more severe ADHD symptoms. The posted group means were 46.1 for DHA Omega-3 and 47.1 for placebo. The unadjusted mean difference, expressed as DHA Omega-3 minus placebo, was -1.0.

This comparison is about the groups' average measured scores, not about whether every participant's symptoms changed in the same way. The registry record does not report baseline scores, individual changes, or the number of participants with a clinically meaningful change. It also does not state whether the posted values represent endpoint scores, change from baseline, or an adjusted analysis. The stated timeframe is 10 weeks, so the result addresses the recorded short-term assessment rather than longer-term outcomes.

There is an important population-description ambiguity. The trial title, condition, and brief summary concern ADHD, while the primary outcome's population text names depressive disorders and is truncated. These descriptions do not establish which participants contributed to the reported outcome. The record does not resolve this ambiguity, so interpretation should stay tied to the posted group results and avoid treating the population details as fully specified.

3. Trial Design

The registry describes a completed Phase 3 trial with randomized allocation, quadruple masking, and a parallel-group model. Enrollment was 30. The study started in 2013-09, and primary completion was recorded as 2017-03-03. The sponsor was the University of Cincinnati. These design features describe how the trial was registered; they do not by themselves establish how successfully allocation was concealed, how masking was maintained, or how participants were followed.

Participants were assigned to DHA Omega-3 or placebo. The DHA regimen was 1,200 mg/day, divided into 600 mg twice daily, for 10 weeks. The placebo consisted of corn/soy oil capsules similar in shape and color to the DHA capsules, also given for 10 weeks. The registry labels the trial quadruple masked but does not identify which four groups of people were masked or describe the practical procedures used to maintain masking.

The reported primary outcome was ADHD-RS-IV symptom rating at 10 weeks. The group-level results list 16 participants for DHA Omega-3 and 14 for placebo. The record states an enrollment of 30, but does not explain the relationship between enrollment and participants included in the outcome results, including whether all enrolled participants posted an outcome measure. It does not report participant flow, withdrawals, adherence, protocol deviations, or reasons for any exclusions.

The registry record lists one outcome measure and no secondary outcomes posted. The analysis count is listed as zero, even though group outcome values are present. The record does not provide a complete statistical analysis plan, a description of the analysis population, or an account of how missing observations were handled. The original trial's sample-size justification and design assumptions are not reported in the registry record. The planning figures associated with the observed effect are separate illustrations and should not be read as the trial's planned enrollment target.

The primary outcome population description is incongruent with the ADHD focus and is truncated after referring to a biological criterion. This leaves uncertainty about the intended population for the outcome measure. No information in the registry resolves whether the text is an error, describes a subgroup, or reflects some other population definition, so none of those possibilities can be assumed.

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

Analysis population for the primary outcome, as defined in the registry: Adolescents with a current Diagnostic and Statistical Manual of Mental Disorders, 4th edition, Text Revision diagnosis of Major Depressive Disorder or Depressive Disorder not otherwise specified, a Childhood Depression Rating Scale-Revised (CDRS-R) Version raw score of \>40, and at least one biological parent with bipolar I disorder.

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 Attention-Deficit Hyperactivity Disorder Symptom Ratings Using the ADHD Rating Scale (ADHD-RS-IV), measured over 10 weeks.

The primary outcome is the ADHD Rating Scale Version IV (ADHD-RS-IV) symptom rating at 10 weeks. This is a continuous score on a scale from 0 to 54, with higher values indicating more severe ADHD symptoms. A continuous rating preserves information across the range of symptom severity rather than reducing a participant's result to a simple category. Comparing average scores between randomized groups can therefore describe the direction and size of a group-level difference.

The registry reports the outcome as a mean with standard error. The mean is the arithmetic average of the recorded scores in an arm. The standard error describes the precision of that estimated average; it is not the spread of individual participant scores. The posted standard errors were 6.6 for DHA Omega-3 and 8.5 for placebo. These values alone do not describe the full range of individual responses.

A rating scale is used to make symptom assessment more structured and comparable across participants, provided the scale is administered and scored consistently. The record identifies the scale and its score direction, but does not describe who completed it, who rated the participants, or what procedures were used to standardize ratings. It also does not report a threshold for interpreting a change as clinically important.

The registry records a 10-week timeframe but does not clarify whether the means are final scores or changes from baseline. Baseline values, repeated measurements, and the instrument's assessment schedule are not reported in the registry record. The primary outcome population description also names depressive-disorder criteria rather than clearly specifying an ADHD population, and its wording is incomplete. These gaps limit interpretation of exactly who contributed to the measure and what aspect of score change the group means represent.

7. Results Posted in the Registry

• DHA Omega-3: mean 46.10 versus 47.10 on control; difference -1.00 (95% CI -22.09 to 20.09), standardized effect d = -0.03; z-test p = 0.926.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary measure is continuous, and the registry reports an arm mean and standard error for each group. A mean gives the central average score for the participants represented by that arm's result. The standard error quantifies how precisely that mean is estimated from the observed participants. It should not be interpreted as the typical distance between one participant's score and another's; that is a different quantity, commonly described by a standard deviation.

What does the mean difference represent?

The reported comparison is the DHA Omega-3 mean minus the placebo mean. Its estimate was -1.0. This direction is useful because the score's direction is defined: higher scores indicate more severe symptoms. A negative group difference therefore means the DHA group's posted average was lower. The estimate is a contrast between group averages, not a statement about each person's outcome, and it does not by itself establish that assignment caused a difference. Randomization supports a causal comparison when the design and analysis are carried out as intended, but details about implementation, follow-up, and analysis are not reported in the registry record.

How should the confidence interval be read?

A confidence interval gives a range of values that are reasonably compatible with the observed data under the method used to construct it. The reported interval for the unadjusted mean difference runs from -22.09 to 20.09. Its inclusion of zero means that the data do not clearly separate a negative difference from no difference or a positive difference at the confidence level associated with the interval. The interval is wide, so the estimate is not precise. A confidence interval is not a range containing a specified proportion of individual outcomes, and it is not a probability statement about the fixed true effect after the data have been observed.

The registry does not identify a confidence level in the outcome record. The comparison and interval are unadjusted, and the registry does not describe an adjustment for baseline score or other covariates. The analysis method used by the trial investigators is not reported. This interpretation describes the posted summary comparison rather than attributing a particular model to the trial.

What does the p-value add?

The unadjusted p-value was 0.926. In general, a p-value measures how compatible the observed data are with a null hypothesis under a statistical model and its assumptions. A large p-value does not prove that groups are the same and does not quantify the size or importance of an effect. It also does not tell readers the chance that the observed finding is due to chance. Here, the p-value and the interval both indicate that the data provide little precision about the direction and size of the group difference. Neither statistic can replace consideration of the estimate, interval, study design, and missing reporting details.

Why do standard errors matter?

Standard errors describe uncertainty in estimated averages. They depend on the amount of information available and the variation in the data. In general, a small sample can leave estimates uncertain, especially when outcomes vary across participants. The registry reports arm sizes of 14 for placebo and 16 for DHA Omega-3, alongside standard errors of 8.5 and 6.6, respectively. These arm-level figures help readers understand the basis of the group summaries, but no participant-level distribution is reported. The standard errors should not be mistaken for standard deviations or interpreted as ranges for individual scores.

In general, continuous outcomes can be analyzed using different approaches, including comparisons of final scores, changes from baseline, or models that account for repeated measurements or baseline values. Those approaches may answer slightly different questions and can produce different estimates. The record does not state which analysis was prespecified or used by the investigators, whether the reported averages are endpoint values or changes, or whether repeated measurements were collected. It is therefore not appropriate to infer a model from the reported summaries alone.

What are the limits of an unadjusted recalculation?

A recalculated comparison from posted summary statistics is a simple unadjusted reanalysis. It does not reproduce an analysis that might have used participant-level data, covariate adjustment, repeated measurements, or a prespecified missing-data method. The registry's discrepancy flag is false, so there is no stated disagreement between the sponsor's result and the recalculated comparison. Even so, a simple calculation cannot fill in unreported features of the analysis plan. The number of trial analyses is listed as zero, which makes the statistical analysis record especially limited despite the posted arm-level results.

In general, over-dispersion matters when observed variability is greater than a model assumes: standard errors may then be too small and inference overly confident if the model fails to account for that variability. That concept is most relevant to outcomes and models with a variance assumption that can be checked. The posted primary outcome is a continuous score, but the registry does not give the participant-level data or analysis model needed to assess distributional assumptions, outliers, or unusual variance. No claim about over-dispersion in this trial can be made from the arm summaries.

Likewise, statistical significance and clinical importance are distinct concepts. A small p-value would not, on its own, demonstrate an important change, while a non-small p-value does not rule one out. A threshold for a meaningful score change is not reported in the registry record. There is also no reported analysis of individual responder status. The mean difference should therefore be interpreted as a group-level estimate, with its interval, rather than as a direct measure of how participants experienced the intervention.

10. Confidence Intervals and Precision

The estimated unadjusted difference in mean ADHD-RS-IV score was -1.0 for DHA Omega-3 minus placebo. The reported confidence interval extends from -22.09 to 20.09. This interval is the most direct indicator of the uncertainty surrounding the point estimate: it spans values favoring a lower score in the DHA group, no difference, and values favoring a lower score in the placebo group. Since lower scores correspond to less severe symptoms, the interval does not establish a single direction of difference.

The interval is wide relative to the point estimate. That means the observed data are compatible with a range of possible group differences, not just a value close to zero. The estimate should not be described as precise merely because the point estimate is numerically near zero. Precision is about the range of values consistent with the data, and the interval includes both substantial negative and positive values.

The arm means were 46.1 for DHA Omega-3 and 47.1 for placebo; the corresponding standard errors were 6.6 and 8.5. These standard errors reflect uncertainty in the arm averages. They are not standard deviations and do not reveal how scores were distributed among individual participants. The group sizes were 16 and 14, and the record does not give participant-level results that would allow assessment of distributional shape or the influence of extreme scores.

A confidence interval does not establish equivalence. Equivalence requires a prespecified margin defining differences small enough to be treated as practically alike, along with an appropriate analysis. The registry does not report such a margin or an equivalence objective. The broad interval and unadjusted p-value of 0.926 are consistent with uncertainty, not proof that the interventions produce the same score.

There is also uncertainty about the population and analysis underlying the estimate. The primary outcome population description is incomplete and does not align clearly with the ADHD trial description. Baseline values, outcome missingness, and the handling of missing data are not reported. These issues do not change the numerical interval, but they limit how confidently readers can connect it to a clearly defined population and analysis procedure.

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 an illustration based on the observed effect, not a record of the trial's original enrollment calculation. The displayed figures are participants per arm, not total events. They assume a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. The original trial's sample-size assumptions and justification are not reported in the registry record.

The column for 80% power gives the number of participants per arm that the illustration estimates would be needed to have an 80% chance of detecting the specified effect under its assumptions, if that effect were real and the assumptions held. The 90% power column expresses the corresponding planning target for a 90% chance. Power is a property of a planned design under specified assumptions; it is not a probability that the study's conclusion is correct.

The displayed planning scenarios consider 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect. As the effect to detect becomes smaller, more participants are needed to distinguish it from random variation with the same power and significance level. The numeric planning values should be read in that context: they are hypothetical design illustrations based on the observed estimate, rather than observed participant counts or evidence that the completed study had a particular power.

This is not observed power. The illustrations do not establish what the trial was designed to detect, and they cannot resolve the uncertainty in the observed result. The curve, where it presents the planning relationship, should be read as a visual counterpart to those assumptions: smaller target effects require larger planned groups. These figures are not a substitute for a prospectively justified sample-size calculation using an effect considered important before results are known.

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 = -1.000; pooled standard deviation σ = 29.034.
2. n = 2 × (1.96 + 0.842)² × 29.034² / -1.000² = 13,233.2, rounded up to 13,234 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                      # observed difference in means
sigma <- 29.0344007785838                     # 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(1883817)
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 = 13,234 (80% power), 17,716 (90% power)
 75% of observed effect: n per arm = 23,526 (80% power), 31,495 (90% power)
 50% of observed effect: n per arm = 52,933 (80% power), 70,862 (90% power)
power.t.test: 13234.1 
Simulated power at n = 13,234 per arm: 0.801 (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 several outcomes, time points, subgroups, or statistical comparisons are examined. Testing many hypotheses can increase the chance of at least one apparently notable result unless the analysis plan accounts for the number and structure of comparisons. The registry lists one outcome measure and no secondary outcomes posted. This means the posted record offers little information about a broader family of outcome tests, but it does not establish that no additional analyses were conducted or considered.

The registry does not report a multiplicity adjustment, a hierarchy of outcomes, or a prespecified testing strategy. The unadjusted p-value should therefore be read as an unadjusted result, not as a family-wise adjusted result. The record also lists zero analyses. That listing leaves the relationship between the outcome values and any formal analysis plan unclear; it should not be interpreted as proof that investigators performed no analysis.

Missing-data handling is not reported in the registry record. There is no account of how many participants lacked a 10-week score, whether any observations were excluded, or whether the analysis used imputation or another method. The group counts associated with the outcome are 14 for placebo and 16 for DHA Omega-3, but the record does not provide participant flow or explain whether these counts include every randomized participant. Without those details, readers cannot assess whether missingness could have affected the comparison.

The analysis population is also not specified clearly. The registry does not say whether the primary comparison followed an intention-to-treat principle, included only participants who completed treatment, or used another population definition. The outcome's population description names depressive-disorder criteria and is truncated, whereas the trial description concerns ADHD. That inconsistency increases uncertainty about exactly which population the reported outcome represents.

Finally, the record does not describe interim analyses, stopping rules, protocol deviations, or the original statistical analysis plan. These details are not reported in the registry record. No conclusion about their presence or absence should be inferred from the posted result alone.

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.

The adverse-event summary reports zero participants affected by serious adverse events in the placebo group, with 14 at risk, and zero in the DHA Omega-3 group, with 16 at risk. The number affected by other adverse events is also recorded as zero in each group, with the same respective at-risk counts. Deaths are recorded as zero in both groups. No serious adverse-event terms are listed.

These are counts in a small study, and zero recorded events does not demonstrate that an event cannot occur or that the groups have identical safety profiles. The figures describe what the registry record reports during the trial, not the full range of possible risks. The record does not provide event definitions, collection procedures, severity grading, timing, or information about events after the treatment period. It also does not provide longer-term safety follow-up.

The adverse-event summary should be read alongside the trial's limited size and 10-week intervention timeframe. A lack of recorded events in this record cannot establish the absence of uncommon events or events that were not captured. These counts describe the posted adverse-event data only and do not support medical advice or a general safety conclusion.

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

The result means that the posted average ADHD-RS-IV score was 46.1 in the DHA Omega-3 group and 47.1 in the placebo group at the stated 10-week timeframe. The estimated unadjusted difference was -1.0, with a confidence interval from -22.09 to 20.09 and an unadjusted p-value of 0.926. Taken together, these statistics describe a point estimate near zero with substantial uncertainty about the direction and size of the difference.

It does not mean that the groups have been shown to be equivalent. The interval includes zero and a wide range of negative and positive differences, and the registry does not report an equivalence margin or equivalence analysis. It also does not mean that an effect is absent simply because the p-value is 0.926. The p-value is not a probability that the treatment works or does not work, and it cannot replace the estimate and interval.

The result does not establish a conclusion about brain activation. Although brain activation appears in the study hypothesis, the registry's posted primary result is a symptom rating. Brain-activation results are not reported in the registry record, and no secondary outcomes are posted. The symptom score cannot stand in for an unreported brain measure.

The result also does not establish a treatment effect on change from baseline. The record does not clarify whether the reported means are final scores or changes, and it supplies no baseline group values. Nor does it identify a clinically meaningful score difference. The mean comparison is a group-level statistic and does not show whether individual participants improved, worsened, or remained unchanged.

Finally, the registry's description of the outcome population is incomplete and inconsistent with the ADHD focus. Details of missing outcomes, participant flow, analysis population, and analysis model are also absent. The posted result can be described accurately as an uncertain unadjusted comparison of group means, but broader claims about the trial population, individual response, or outcomes beyond the recorded measure are not supported by the registry record.

16. Why This Trial Matters Statistically

This trial is statistically informative as an example of why an estimate must be read together with its uncertainty. The point estimate of -1.0 is close to zero, but the confidence interval from -22.09 to 20.09 is broad. Focusing only on the point estimate could make the evidence appear more definitive than it is; focusing only on the p-value could wrongly suggest that a large effect has been ruled out. The interval shows that the data leave substantial uncertainty about direction and size.

The small arm sizes, 14 for placebo and 16 for DHA Omega-3, are relevant to the precision of the comparison. The standard errors and interval help quantify that uncertainty, while the lack of participant-level data prevents readers from evaluating the score distributions or potential outliers. This illustrates why sample size is not the only statistical consideration: outcome variability, analytic choices, missingness, and the definition of the target population also matter.

Another statistical issue is the distinction between the study's motivating hypothesis and the posted endpoint. The hypothesis mentions brain activation and symptom reduction, while the registry reports a symptom-rating outcome and no secondary results. Statistical interpretation must remain tied to the actual posted measure, rather than extending findings to an unreported biological outcome.

The population text also matters. A randomized comparison is meaningful only in relation to a clearly defined analysis population. The mismatch between the ADHD trial description and the depressive-disorder wording in the primary outcome record prevents a fully clear account of who the result represents. Transparent reporting of population criteria, baseline data, participant flow, missing-data methods, and the analysis plan would make the estimate easier to evaluate.

Finally, the planning illustration demonstrates the dependence of sample-size requirements on the effect one aims to detect. Smaller target effects require more participants under a fixed set of planning assumptions. Those calculations are not evidence about the power of the completed trial, but they emphasize why a prospective design rationale should be distinguished from a calculation based on the observed result.

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 registry record leaves several trial-specific limitations unresolved. The outcome population description is truncated and names depressive-disorder criteria, whereas the trial title and summary concern ADHD. This discrepancy prevents a confident reading of the exact population represented by the primary outcome results. The incomplete phrase about a biological criterion cannot be interpreted beyond the words recorded.

Important details about the primary score are absent. The record does not say whether the group means are final scores or changes from baseline, and baseline values are not posted. It does not state who rated participants, how ratings were collected, or whether assessors were kept masked in practice. The stated timeframe is 10 weeks, but the assessment schedule and any additional outcome time points are not described.

The registry does not give participant flow, withdrawals, adherence, exclusions, or reasons for missing outcomes. Although arm-level results list 14 participants for placebo and 16 for DHA Omega-3, the record does not explain how these numbers relate to enrollment or whether all randomized participants were analyzed. The missing-data method and analysis-population definition are not reported.

The statistical analysis plan, model, baseline adjustment, and any multiplicity procedure are not reported in the registry record. Nor are protocol deviations, interim analyses, or stopping rules. The record lists no secondary outcomes and zero analyses, despite the posted primary outcome summaries, leaving the analysis history incompletely documented.

The adverse-event summary records zero affected participants for serious and other adverse events and zero deaths in each arm, but does not describe event collection, definitions, timing, or follow-up beyond the treatment period. These limitations mean that the posted safety counts should not be generalized beyond the events and observation captured in the registry.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Effect of Omega-3 Fatty Acid on Cortical Function in ADHD — NCT01883817.
• Registry record last updated 2022-03-16; status last verified 2022-02.
• Results first posted 2022-03-16.
• 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

NCT01883817 is a completed, randomized, quadruple-masked, parallel-group Phase 3 study sponsored by the University of Cincinnati. Enrollment was 30. The trial compared DHA Omega-3, described as 1,200 mg/day for 10 weeks, with a corn/soy oil placebo given over 10 weeks. The primary outcome was ADHD-RS-IV symptom score at 10 weeks, with higher scores indicating more severe symptoms.

The posted means were 46.1 for DHA Omega-3 and 47.1 for placebo. The unadjusted mean difference was -1.0, with a confidence interval from -22.09 to 20.09 and an unadjusted p-value of 0.926. The interval is broad and does not establish a clear direction or size of difference. The registry reports zero serious adverse events, zero other adverse events, and zero deaths in both groups.

Interpretation is limited by the incomplete and incongruent outcome population description, and by the lack of reported baseline results, participant flow, missing-data methods, analysis-population definition, and statistical analysis plan. Brain-activation results are not reported in the registry record.