Inositol and Omega-3 Fatty Acids in Pediatric Mania: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Inositol and Omega-3 Fatty Acids in Pediatric Mania (NCT01396486), a randomized phase 4 study. The primary outcome is Improvement in Mania Symptoms by Change in Young Mania Rating Scale (YMRS).

2. Clinical Question

The record describes a 12-week trial and states that the study was intended to evaluate omega-3 fatty acids versus inositol, the combination versus the individual treatment combinations, and side effects. The posted primary outcome is a continuous measure: the mean change in YMRS score. The arm-level means and pairwise comparisons address the symptom-change question, but they do not by themselves establish which treatment caused any observed differences. The registry record does not report a more detailed primary-outcome population definition or a formal analysis plan.

3. Trial Design

The registry lists this study as a randomized, quadruple-masked, Phase 4 trial, with a start date of 2012-02-03, primary completion on 2019-04-11, and status completed. The listed enrollment is 69. The brief description characterizes the study as a 12-week trial in children ages 5-12 years old with bipolar spectrum disorders. Massachusetts General Hospital is listed as sponsor.

Three treatment combinations are described: Omega-3/Placebo, Placebo/Inositol, and Omega-3/Inositol. Their descriptions identify combination omega-3 and placebo treatment, combination placebo and inositol treatment, and combination omega-3 and inositol treatment, respectively. The primary outcome results report a mean and standard deviation for each arm. The reported outcome sample sizes are 19 for Omega-3/Placebo, 16 for Placebo/Inositol, and 17 for Omega-3/Inositol. These are outcome-specific figures and should not be treated as a reconciliation of the enrollment figure.

There is a design-label tension in the record: allocation is listed as randomized and three arms are described, while the model is listed as single-group. The record does not explain this label or how the study's design was encoded. It also does not report treatment doses, the precise randomization procedure, the masking roles, or the original design assumptions. Those details should not be inferred from the masking and allocation labels alone.

4. Participant Flow and Accounting

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

Before assignment: While 69 subjects enrolled in the study, only 61 were randomized. Of the 8 subjects who enrolled but were not randomized, 3 were found ineligible, 3 withdrew, and 2 were lost to follow-up.

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 Improvement in Mania Symptoms by Change in Young Mania Rating Scale (YMRS), measured over Baseline to endpoint (12 weeks or last observation carried forward if dropped prior to week 12).

The primary endpoint is improvement in mania symptoms measured as change in the Young Mania Rating Scale (YMRS) from baseline to endpoint. Endpoint is defined as 12 weeks or the last observation carried forward if a participant dropped out before week 12. The result is reported as a mean change, with standard deviation describing the spread of individual changes within each treatment arm.

The YMRS contains 7 items scored from 0 to 4 and 4 items scored from 0 to 8, with total scores ranging from 0-60. Questions refer to the last week. Higher scores signify more severe manic symptoms; therefore, a negative change represents a decrease in score and points in the direction of symptom improvement. The posted mean changes are -4.8 for Omega-3/Placebo, -6.4 for Placebo/Inositol, and -10.2 for Omega-3/Inositol.

As a continuous measure, change in score can retain information about the degree of change rather than reducing results to a binary category. It is relevant to the stated study purpose of evaluating change in mania symptoms. The registry record does not report a threshold for a clinically important change, or a separate definition of response or remission. Thus, mean change describes average score movement, not the proportion of participants reaching a particular clinical state.

7. Results Posted in the Registry

• Placebo/Inositol: mean -6.40 versus -4.80 on control; difference -1.60 (95% CI -6.34 to 3.14), standardized effect d = -0.22; z-test p = 0.508.
• Omega-3/Inositol: mean -10.20 versus -4.80 on control; difference -5.40 (95% CI -10.96 to 0.16), standardized effect d = -0.64; z-test p = 0.057.

8. Statistical Interpretation

9. Statistical Methods Explained

What does a mean change represent?

The primary endpoint is continuous: each participant's change in YMRS score is summarized by an arm mean. A negative mean indicates that scores decreased on average from baseline to endpoint. The standard deviation describes how dispersed individual change scores are around that arm's mean. It is not the standard error and does not directly tell how precisely the mean is estimated. General explanation: a mean is useful for describing the average direction and size of change, while the spread and sample size help determine how uncertain that average is.

What is a pairwise mean difference?

The posted comparisons set Omega-3/Placebo as the reference and compare its mean change with each of the other arm means. The difference for Placebo/Inositol is -1.6; the difference for Omega-3/Inositol is -5.4. In this orientation, a negative estimate means the compared arm had a more negative mean change than the reference arm. Since more negative change corresponds to a larger average score decrease, the signs describe direction, not proof of a treatment advantage. The differences are in YMRS units.

General explanation: a pairwise comparison reduces a multi-arm study to a specified contrast between two arms. Each contrast answers only that particular comparison; it does not compare every possible pair or establish an overall treatment ranking. The posted comparison estimates are unadjusted recalculations from the arm summary statistics, rather than a reported adjusted analysis. The registry record lists zero analyses, and it does not report an analysis model or covariate adjustment.

Why are confidence intervals useful?

A confidence interval gives a range of estimates compatible with the observed data under the method used to construct it. The first interval extends from -6.338 to 3.138, and the second from -10.96 to 0.161. Both include zero, the value corresponding to no mean difference. General explanation: an interval that includes zero does not show that the true difference is zero; rather, it indicates that the data do not precisely distinguish zero from some positive or negative differences at the stated confidence level. Interval width is an important guide to precision.

The calculations use pooled standard deviations and standard errors reported for the pairwise comparisons. General explanation: pooling estimates a common within-arm spread for a two-arm comparison, while the standard error describes the uncertainty of the estimated difference. These calculations assume a continuous outcome and use the posted summary statistics. The registry record does not report whether the study's own analysis used the same approach, nor does it report a model for repeated measurements or baseline adjustment.

What does a p-value convey?

The unadjusted p-values are 0.508 for Placebo/Inositol versus Omega-3/Placebo and 0.057 for Omega-3/Inositol versus Omega-3/Placebo. General explanation: a p-value measures how unusual data at least this inconsistent with a specified no-difference model would be, if that model and the statistical assumptions held. It is not the probability that the null hypothesis is true, and it does not measure clinical importance. These values are unadjusted, and the registry record does not report multiplicity handling.

How should the analysis structure be understood?

The outcome is reported as mean and standard deviation, with arm-level sample sizes. The endpoint definition permits last observation carried forward for participants who dropped out before week 12. General explanation: carrying the last observed value forward treats that earlier measurement as the endpoint value; this can be problematic if symptoms would have changed after dropout, and the resulting estimate can depend on assumptions about missing outcomes. The registry record does not report how many outcomes were missing, how many participants dropped out, or whether any sensitivity analyses assessed the effect of missing data.

The record lists three arms but gives two pairwise comparisons against Omega-3/Placebo. General explanation: multiple comparisons can increase the chance of a nominally notable finding when several hypotheses are tested. The record does not report a formal multiplicity strategy, a prespecified hierarchy, or an overall test. The reported comparison results should therefore be interpreted as the specific unadjusted contrasts they represent, not as a complete account of an undocumented analysis plan.

10. Confidence Intervals and Precision

The interval for Placebo/Inositol versus Omega-3/Placebo is -6.338 to 3.138 around a mean difference of -1.6. It spans negative and positive values and includes zero. This indicates substantial uncertainty about the direction and size of the difference: the data are compatible with the compared arm having a more negative change, with little or no difference, or with a less negative change. The unadjusted p-value is 0.508.

The interval for Omega-3/Inositol versus Omega-3/Placebo is -10.96 to 0.161 around a mean difference of -5.4. It also includes zero, while extending further into negative values. Its estimate points toward a larger average score decrease in the combination arm, but the interval does not exclude no difference. The unadjusted p-value is 0.057. Neither interval should be interpreted as a range containing every individual participant's change; it concerns uncertainty in the arm contrast.

General explanation: wider intervals indicate less precision, while narrower intervals indicate more precision under the statistical method used. Precision is affected by the amount of variability and the number of observations. The reported standard deviations are 7.9, 6.4, and 9.0, and the outcome-specific arm sample sizes are 19, 16, and 17. The registry record does not report confidence intervals for the individual arm means or a separate adjusted analysis. The posted contrasts therefore provide limited precision for distinguishing treatment-combination differences.

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 sample-size figures are planning illustrations for a two-arm comparison, expressed as participants per arm. They are not total event counts. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation; the effect to detect is the stated fraction of the observed effect. The original trial's own design assumptions are not reported in the registry record.

The 80% power column gives the planned number of participants per arm for a design with an 80% chance of detecting the specified effect under those assumptions, if the effect and assumptions are correct. The 90% power column gives the corresponding per-arm number for a 90% chance. These are design probabilities under a hypothetical repeated-sampling framework, not probabilities that a result is true. This is not observed power.

For Placebo/Inositol versus Omega-3/Placebo, the illustration based on 100% of the observed effect lists 323 participants per arm for 80% power and 433 for 90% power. At 75% of the observed effect, the figures are 575 and 769 per arm; at 50%, they are 1,292 and 1,730 per arm. For Omega-3/Inositol versus Omega-3/Placebo, the corresponding figures are 39 and 52 per arm at 100%, 69 and 92 per arm at 75%, and 154 and 206 per arm at 50%.

The curve should be read as illustrating how the planning requirement changes with the effect size being targeted. Smaller effects require more participants to detect under otherwise unchanged assumptions. These figures are based on observed effects from this trial and are not the trial's original enrollment rationale or evidence about the design'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 = -1.600; pooled standard deviation σ = 7.257.
2. n = 2 × (1.96 + 0.842)² × 7.257² / -1.600² = 322.9, rounded up to 323 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 <- -1.6                      # observed difference in means
sigma <- 7.25672102261069                     # 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(1396486)
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 = 323 (80% power), 433 (90% power)
 75% of observed effect: n per arm = 575 (80% power), 769 (90% power)
 50% of observed effect: n per arm = 1,292 (80% power), 1,730 (90% power)
power.t.test: 323.9 
Simulated power at n = 323 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

The registry record lists two posted outcome measures and zero analyses. It does not report a statistical analysis plan, a prespecified testing hierarchy, an overall test across arms, or any adjustment for multiple comparisons. The two reported pairwise comparisons are unadjusted. Because the study describes three treatment combinations and more than one outcome measure, the multiplicity strategy is important context for interpreting nominal p-values, but it is not reported in the registry record.

General explanation: when several hypotheses are tested, the probability of at least one apparently unusual result can increase even if none of the underlying effects is real. Adjustment methods or a prespecified ordering can address that issue in different ways. Without information about the planned family of tests or its handling, the unadjusted p-values should be understood as results for the specific contrasts, not as multiplicity-controlled evidence.

The endpoint timeframe allows the last observation carried forward if a participant dropped out before week 12. The registry record does not report the number of missing endpoint values, the number or timing of dropouts, reasons for missingness, or the analysis population used. It does not report whether the endpoint was analyzed for all randomized participants, only participants with observed outcomes, or another defined population. It also does not describe sensitivity analyses or alternative approaches to missing data.

General explanation: missing outcomes can affect comparisons when the probability of missingness or the unobserved outcome values differ across participants or treatment arms. Carrying a last observation forward is one way to assign an endpoint value, but it relies on assumptions that may not hold. The registry record's endpoint description tells readers that this method was part of the endpoint definition; it does not provide enough detail to assess how missingness affected the reported estimates. The outcome population field is blank, and the trial's original analysis assumptions are not reported.

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 serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: agitated/irritable (5.3%).

The serious adverse event figures report the number at risk and the number affected in each arm. Omega-3/Placebo lists 20 at risk and 1 affected; Placebo/Inositol lists 19 at risk and 1 affected; Omega-3/Inositol lists 22 at risk and 0 affected. Deaths are listed as 0 in each arm. The most frequently listed serious-event term is Agitated/Irritable, at 5.3%.

These are descriptive counts. They do not establish whether an event was caused by a treatment, and the record does not provide details about event timing, severity beyond the serious-event classification, or the criteria used to attribute an event. The at-risk denominators differ from the outcome-specific sample sizes, and the registry record does not explain the difference. The figures should be read within each arm as posted rather than combined into an overall total.

The separate other-adverse-event counts are 13 affected among 20 at risk for Omega-3/Placebo, 12 among 19 for Placebo/Inositol, and 10 among 22 for Omega-3/Inositol. They are not a substitute for the serious-event figures. The record provides no event-level descriptions for these other adverse events in the registry record.

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

The posted results describe average decreases in YMRS score from baseline to endpoint in all three arms. The mean change is -4.8 for Omega-3/Placebo, -6.4 for Placebo/Inositol, and -10.2 for Omega-3/Inositol. The pairwise estimate for Placebo/Inositol compared with Omega-3/Placebo is -1.6; for Omega-3/Inositol compared with Omega-3/Placebo it is -5.4. The confidence intervals for both contrasts include zero, so the posted comparisons do not precisely distinguish a difference from no difference.

These results do not establish that any treatment combination caused the observed within-arm changes. Nor do they establish a definitive ranking of the combinations. A within-arm decrease can reflect many influences, and the registry record does not report an analysis that separates treatment effects from other changes over time. The posted pairwise contrasts are unadjusted recalculations from summary statistics, not a reported adjusted sponsor analysis.

The outcome is a scale score, not a direct count of participants who improved by a clinically meaningful amount. A higher score indicates more severe symptoms, but the registry record does not report a threshold for clinically important change, response, or remission. The mean and standard deviation do not show the distribution of individual outcomes or how many participants improved, worsened, or stayed similar.

Safety counts are descriptive and do not establish causation. The registry record also lacks information about missing outcomes, analysis populations, and multiplicity handling. These gaps limit how much can be concluded from the posted summaries. The results should be read as estimates of mean change and selected pairwise differences, with uncertainty, rather than as a stand-alone basis for treatment decisions.

16. Why This Trial Matters Statistically

This trial is statistically interesting because it reports three treatment combinations while its model is labeled single-group. The record also identifies randomized allocation and quadruple masking. Those entries do not align transparently, and the registry record does not explain the design label. This makes it especially important to describe the arm-level results and pairwise contrasts as recorded rather than assume an analysis structure that is not documented.

The outcome is continuous and uses a symptom scale with an explicit direction: higher YMRS scores indicate greater severity. That makes interpretation of negative change straightforward, but mean change alone can conceal variation among participants. The standard deviations are substantial relative to the mean changes, and the comparison intervals remain broad enough to include no difference. This is a useful reminder that a more negative arm mean is not equivalent to a precise between-arm effect.

The comparison of combination treatment with the reference arm has an estimate of -5.4 and an unadjusted p-value of 0.057, while its confidence interval includes zero. Reading the point estimate, interval, and p-value together is more informative than treating a single threshold as decisive. The record's lack of a reported multiplicity strategy and analysis plan further argues for a cautious interpretation of these unadjusted comparisons.

The sample-size illustrations also demonstrate how strongly planning depends on the effect targeted: smaller assumed effects lead to larger participant requirements under the stated assumptions. Since these illustrations use observed effects rather than the original trial design assumptions, they are useful for understanding planning sensitivity, not for judging whether the completed study was adequately designed.

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 details unreported. It does not give treatment doses, the detailed randomization process, who was masked, or an explanation of the single-group model label alongside the three listed arms. It also does not report the original sample-size justification or the trial's original statistical analysis assumptions. These omissions make it difficult to reconstruct the intended design and analysis solely from the registry entry.

The outcome population field is blank, and the record lists zero analyses. It does not identify the analysis population, describe baseline values by arm, or report an adjusted analysis. The posted pairwise comparisons are unadjusted recalculations from summary statistics. Multiplicity handling is not reported, despite the presence of multiple treatment combinations and outcome measures.

The endpoint definition includes last observation carried forward for participants who dropped out before week 12, but the number of missing outcomes and the reasons for dropout are not reported. No sensitivity analyses are reported. Consequently, the effect of missing data on the arm means and pairwise differences cannot be assessed from the registry record.

The outcome-specific sample sizes and adverse-event at-risk counts differ, and the record does not explain why. The safety information is presented as arm-level counts and does not include detailed event descriptions, timing, or attribution. Finally, the primary outcome is a mean change score, without a reported clinically important threshold or responder definition. These limitations do not invalidate the posted numbers, but they restrict the conclusions that can be drawn from them.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Inositol and Omega-3 Fatty Acids in Pediatric Mania — NCT01396486.
• Registry record last updated 2020-08-13; status last verified 2020-08.
• Results first posted 2020-04-21.
• 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 completed Phase 4 registry record describes a randomized, quadruple-masked study sponsored by Massachusetts General Hospital, with listed enrollment of 69. It concerns children ages 5-12 years old with pediatric bipolar spectrum disorders and compares Omega-3/Placebo, Placebo/Inositol, and Omega-3/Inositol.

The primary outcome is mean change in YMRS score from baseline to 12 weeks, or last observation carried forward for participants who dropped out before week 12. Posted mean changes are negative in all arms. The two unadjusted pairwise comparisons against Omega-3/Placebo have confidence intervals that include zero. The record does not report the analysis plan, multiplicity approach, analysis population, or missing-data counts, and lists zero analyses.