Study of Outcome and Safety of Lithium, Divalproex and Risperidone for Mania in Children and Adolescents: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Study of Outcome and Safety of Lithium, Divalproex and Risperidone for Mania in Children and Adolescents (NCT00057681), a randomized phase 3 study. The primary outcome is Clinical Global Impressions-Bipolar Mania Improvement.

2. Clinical Question

3. Trial Design

The Treatment of Early Age Mania study was a Phase 3 randomized, parallel-group trial. Its registry title identifies lithium, divalproex, and risperidone as the treatments under study, and the record lists bipolar disorder as the condition. The trial was open-label, with no masking. Washington University School of Medicine is listed as sponsor.

The registry reports enrollment of 379 and a completed status. The recorded start is 2003-02, and primary completion is 2008-12. These dates describe the registry record; they do not establish how long an individual participant was followed. The arm descriptions state that each treatment was given for 8 to 16 weeks. The primary outcome was measured at Week 8.

The primary outcome summaries are based on participants completing 8 weeks, rather than necessarily every enrolled participant. The listed outcome counts are 72 for lithium, 67 for divalproex sodium, and 69 for risperidone. The registry does not report a participant-flow account explaining the relationship between enrollment and the week 8 outcome population, or reasons for missing outcome data.

Randomization supports comparison of assigned groups, but the open-label design matters when interpreting outcomes that involve clinical ratings. The registry record does not report details of the randomization procedure, allocation concealment, masking of outcome assessors, dose schedules, adherence, or treatment discontinuations. These details should not be inferred from the trial title or intervention descriptions.

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: CGI-BP mania improvement data were analyzed for all subjects completing 8 weeks of the 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 Clinical Global Impressions-Bipolar Mania Improvement, measured over Measured at Week 8.

The primary endpoint was Clinical Global Impressions-Bipolar Mania Improvement, measured at Week 8 and reported as a mean with a standard deviation. The registry describes the measure as capturing change in mania from baseline. Its ordered response labels run from 1, very much improved, through 4, no change, to 7, very much worse. Therefore, lower scores correspond to more improvement on the scale as defined in the record.

A clinician-rated global measure can summarize a participant’s overall clinical change in a way that is interpretable alongside specific symptom measures. The CGI-BP instrument also assesses depression and overall bipolar illness, but mania improvement was the primary outcome in this trial. The reported primary outcome specifically concerns the mania-improvement score; it should not be read as a measure of every aspect of bipolar illness or as a direct measure of long-term outcome.

The registry says that primary outcome data were analyzed for all subjects completing 8 weeks of the study. Consequently, the posted means describe that outcome population. They do not by themselves show how participants without a week 8 assessment were handled in an analysis, or whether another analysis population was used. Such analysis details are not reported in the registry record.

7. Results Posted in the Registry

• Randomized Medication - Divalproex Sodium: mean 2.73 versus 2.49 on control; difference 0.24 (95% CI -0.11 to 0.59), standardized effect d = 0.23; z-test p = 0.185.
• Randomized Medication - Risperidone: mean 1.70 versus 2.49 on control; difference -0.79 (95% CI -1.07 to -0.51), standardized effect d = -0.91; z-test p = <0.001.

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.

Modified Side Effects Form for Children and Adolescents

• 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:
  • Randomized Medication - Divalproex Sodium: mean 4.95 versus 5.11 on control; difference -0.16 (95% CI -1.30 to 0.98), standardized effect d = -0.05; z-test p = 0.782.
  • Randomized Medication - Risperidone: mean 3.70 versus 5.11 on control; difference -1.41 (95% CI -2.41 to -0.41), standardized effect d = -0.46; z-test p = 0.006.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Randomized Medication - Divalproex Sodium and the control. The interval gives the range of effects that remain compatible with the data.
  • The 95% confidence interval excludes no difference, so the mean is statistically lower for Randomized Medication - Risperidone than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

K-SADS Mania Rating Scale

• 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:
  • Randomized Medication - Divalproex Sodium: mean 26.31 versus 24.06 on control; difference 2.25 (95% CI -1.71 to 6.21), standardized effect d = 0.19; z-test p = 0.266.
  • Randomized Medication - Risperidone: mean 14.58 versus 24.06 on control; difference -9.48 (95% CI -12.79 to -6.17), standardized effect d = -0.94; z-test p = <0.001.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Randomized Medication - Divalproex Sodium and the control. The interval gives the range of effects that remain compatible with the data.
  • The 95% confidence interval excludes no difference, so the mean is statistically lower for Randomized Medication - Risperidone than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

The registry posts two secondary outcomes measured at Week 8: the Modified Side Effects Form for Children and Adolescents and the K-SADS Mania Rating Scale. Both are reported as group means and standard deviations, with unadjusted comparisons against lithium. Together, they add information about recorded side effects and mania ratings, but they address different features from the primary global improvement rating.

Across the posted outcomes, the risperidone group has lower mean values than the lithium group, while the divalproex sodium group’s mean is close to lithium on the side-effects measure and higher on the mania rating. These numerical patterns should not automatically be called favorable or unfavorable: the registry does not provide scoring-direction details for the secondary scales in the outcome descriptions. The primary CGI-BP measure does define its direction, but that interpretation should not be transferred to measures with different scoring rules.

The secondary results can be considered alongside the primary result as descriptive context, not as independent confirmation of it. The registry record does not report a multiplicity plan or adjustment. When several outcomes and comparisons are examined, unadjusted p-values carry less weight as confirmatory evidence because they do not account for the opportunity to observe chance findings across multiple tests. The record also lists no formal reported analyses for the secondary outcomes. Their means, intervals, and p-values are therefore best read as exploratory summary comparisons, with the same limitations around open-label assessment and week 8 outcome availability.

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

• Modified Side Effects Form for Children and Adolescents
• K-SADS Mania Rating Scale

9. Statistical Interpretation

10. Statistical Methods Explained

The outcome is continuous and reported as a mean with a standard deviation. A mean describes the group’s average score; it does not imply that every participant had that score. The standard deviation describes how dispersed individual scores were around the group mean. A larger standard deviation indicates more variation among recorded scores, while a smaller one indicates scores were more concentrated. Neither summary provides the full distribution of participant outcomes.

What does a mean difference express?

A mean difference subtracts the reference group mean from the comparison group mean. In these reported comparisons, lithium is the reference. A positive mean difference therefore means the comparison group’s mean is higher than lithium’s; a negative mean difference means it is lower. Because the primary scale labels lower scores as more improved, the sign can be interpreted using those labels. The estimate concerns averages, not the probability that a particular participant improves.

The divalproex sodium versus lithium estimate is 0.24. The risperidone versus lithium estimate is -0.79. These are unadjusted comparisons calculated from the posted group summaries. The registry record does not list a trial-reported analysis for the primary outcome. Thus, the comparisons should be understood as simple summary-statistic contrasts rather than as confirmation of the trial’s original analysis procedure.

What does a p-value convey?

A p-value describes how unusual data at least as incompatible with a no-difference model would be, if that model and the statistical assumptions were correct. It is not the probability that the no-difference model is true, nor the probability that a treatment works. The p-value for divalproex sodium versus lithium is 0.185; the p-value for risperidone versus lithium is < 0.001. The latter is stronger evidence against a no-difference model in this unadjusted comparison, but statistical evidence does not by itself establish clinical importance or eliminate possible bias.

When several outcomes or comparisons are examined, the chance of finding a small p-value somewhere can increase. This is the general issue of multiplicity. The registry lists a primary endpoint and secondary endpoints but does not report a multiplicity adjustment or a statistical plan specifying how multiple comparisons were addressed. The p-values should therefore be read as unadjusted, not as values corrected for multiple testing.

Why do the analysis population and design matter?

Randomization is intended to make treatment groups comparable at assignment, on average. However, the primary endpoint population is described as participants completing 8 weeks. If participants without a week 8 result differ from those with one, a completer-only summary may not represent all randomized participants. The registry record does not report reasons for missing week 8 results, an imputation method, or a sensitivity analysis. It is therefore not possible from these summaries to assess the effect of missing outcomes.

The trial was open-label. For a clinician-rated outcome, knowledge of assigned treatment could potentially influence ratings or participant reports. Whether outcome assessors were masked is not reported in the registry record. This is a design consideration, not evidence that a particular rating was biased.

Standard statistical comparisons also rely on assumptions about how observations vary and how the summary estimates behave. General statistical explanation: a normal approximation can be used to construct simple mean-comparison intervals, but it may not fully capture skewed scores, unusual observations, or other features of the data. The record supplies group means and standard deviations, not individual participant data or distribution plots that would permit those features to be checked. The posted estimates are consequently best read as summary-based comparisons with the stated uncertainty, rather than as a complete account of the underlying data.

What do standardized effects add?

A standardized effect expresses a mean difference in relation to the variability of the measure, which can help compare the relative size of effects measured on different scales. The posted standardized effects are 0.225 for divalproex sodium versus lithium and -0.908 for risperidone versus lithium. They do not replace the original scale units, and they do not establish clinical importance. Their interpretation depends on the same group summaries and unadjusted comparison framework.

Other analytic details that could affect interpretation—including the trial’s original statistical plan, baseline adjustment, interim analyses, subgroup analyses, and sensitivity analyses—are not reported in the registry record. The available calculations should not be treated as evidence that those methods were or were not used outside the registry information.

11. Confidence Intervals and Precision

A confidence interval expresses uncertainty around an estimated group difference. In general statistical terms, a 95% confidence interval is produced by a method that would cover the true parameter in 95% of repeated samples if its assumptions hold. It is not a range containing 95% of individual participant scores, and it is not a guarantee that the true difference lies within the particular interval.

For divalproex sodium versus lithium, the mean-difference estimate is 0.24 and the interval runs from -0.115 to 0.595. Because zero is within that interval, the result is compatible with no mean difference under this unadjusted calculation, as well as with differences in either direction. The interval does not support a precise conclusion about the direction of the group difference.

For risperidone versus lithium, the estimate is -0.79 and the interval runs from -1.074 to -0.505. The entire interval is below zero. This gives a more precise direction for the unadjusted group contrast than the divalproex comparison, though the interval still represents uncertainty about the size of the difference. Its interpretation remains tied to the recorded scale, the week 8 completer population, and the assumptions of the calculation.

These intervals quantify sampling uncertainty, not uncertainty from every source. They do not account for possible effects of open-label assessment, missing outcomes, or choices among multiple outcomes unless those factors are built into the analysis. The registry record does not report such adjustments. Precision should therefore be considered alongside the design and reporting limitations, not as a substitute for them.

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 sample-size figures are planning illustrations based on the observed effect, not a reconstruction of the trial’s original design. Because the outcomes are continuous, each figure refers to participants per arm, not total events. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The detectable effect is set to the stated fraction of the observed effect: 100%, 75%, or 50%.

The 80% power column gives the estimated participants per arm for a future study to have an 80% chance of detecting the specified effect under those assumptions, if that effect is real and the assumptions hold. The 90% power column uses a higher target chance of detection, so its planning figures are larger. These values depend on the effect size used in the calculation; they are not universal sample-size recommendations.

Planning for a smaller effect requires more participants per arm, because a subtler difference is harder to distinguish from sampling variation. The table and curve should therefore be read as scenarios tied to the observed effect and its stated fractions, rather than as proof that the observed effect will recur. They do not establish what sample size would be suitable under different assumptions, outcome definitions, or analysis plans. The trial’s own original sample-size assumptions are not reported in the registry record. These figures are 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 = 0.240; pooled standard deviation σ = 1.065.
2. n = 2 × (1.96 + 0.842)² × 1.065² / 0.240² = 308.9, rounded up to 309 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 <- 0.24                      # observed difference in means
sigma <- 1.06455809686735                     # 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(57681)
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 = 309 (80% power), 414 (90% power)
 75% of observed effect: n per arm = 550 (80% power), 736 (90% power)
 50% of observed effect: n per arm = 1,236 (80% power), 1,654 (90% power)
power.t.test: 309.8 
Simulated power at n = 309 per arm: 0.796 (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 a primary outcome and two secondary outcomes. It does not report a statistical analysis plan describing which comparisons were prespecified, how the family of tests was defined, or whether any adjustment for multiple outcomes or treatment comparisons was planned. The displayed p-values are unadjusted calculations. This means they do not incorporate a stated correction for multiplicity, and a small unadjusted p-value should not be interpreted as if it were the result of a multiplicity-controlled confirmatory procedure.

The registry record lists no reported analyses for the posted outcomes. It does not describe interim analyses, stopping rules, subgroup analyses, covariate-adjusted models, or sensitivity analyses. Those items are not reported in the registry record; their absence from the record should not be taken as proof that no such work occurred outside it.

The primary outcome description says that the analysis included subjects completing 8 weeks. The record does not explain the handling of participants without a week 8 measure, give reasons for missing outcome data, or describe an imputation approach. It also does not state whether a separate intention-to-treat analysis was performed. Thus, the results can be interpreted for the stated completer population, but the available information is insufficient to determine how missing outcomes might affect estimates for all randomized participants.

The group counts accompanying the primary outcome are 72, 67, and 69. These are outcome-specific counts and should not be treated as a participant-flow report. No detailed account of exclusions after randomization, protocol deviations, or completeness by outcome is reported. The safety at-risk counts differ from the primary outcome counts, and the record does not explain the relationship between those populations. These reporting gaps limit assessment of analysis population choices and comparability across outcomes.

15. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

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

Serious events with the highest arm-level rate: hospitalization (4.9%), event requiring intervention to prevent permanent impairment or damage (0.7%).

The registry lists serious adverse events by randomized medication group, with affected counts of 6 for lithium, 4 for divalproex sodium, and 5 for risperidone. The corresponding numbers at risk are 137, 139, and 103. These figures should be read as group-specific registry counts; they are not the week 8 outcome counts and should not be combined to make a total.

The record lists hospitalization at 4.9% and an event requiring intervention to prevent permanent impairment or damage at 0.7% among the top serious event terms. These are presented as event-term percentages, not as treatment-effect estimates. The registry also lists 0 other adverse events in each group, with the at-risk counts. Death counts are not reported in the registry record.

The summaries do not establish whether differences in serious-event counts are due to chance, exposure time, or other factors. No comparative safety analysis or detailed event-level account is reported. These figures describe the registry’s posted safety entries and are not, by themselves, a complete assessment of safety.

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

The primary outcome summaries show a lower mean week 8 mania-improvement score for risperidone than for lithium, with an unadjusted confidence interval entirely below zero. On the scale as described, lower scores correspond to greater improvement. The divalproex sodium mean was higher than the lithium mean, but its unadjusted confidence interval includes zero and does not establish a clear mean difference. These findings describe the posted data and should not be converted into advice about treatment choice.

The results do not show what an individual participant’s outcome would have been under a different assigned medication. Group averages can conceal variation in response, and the registry does not provide participant-level data. Nor does statistical significance establish clinical importance: the record does not report a threshold for a clinically meaningful change on the primary measure.

The outcome was measured at Week 8 among participants completing 8 weeks, while treatment descriptions span 8 to 16 weeks. The posted results therefore do not establish durability after treatment, longer-term outcomes, or results for participants without a week 8 assessment. Such follow-up findings and missing-data analyses are not reported in the registry record.

Interpretation is also bounded by the open-label design, the lack of a reported formal analysis plan, and the unadjusted nature of the comparisons. The intervals represent statistical uncertainty under the calculation assumptions; they do not resolve possible assessment effects, missing-data bias, or multiplicity. The posted results are evidence about the recorded group means in this trial, not a complete account of comparative benefits, harms, or applicability to every child or adolescent with bipolar disorder or symptoms of mania.

17. Why This Trial Matters Statistically

This trial illustrates why a randomized comparison and a statistical interpretation are related but distinct tasks. Random allocation creates a basis for comparing groups, yet interpretation still depends on who contributed outcome data, how the outcome was measured, and what analysis was performed. Here, the primary outcome population is described as participants completing 8 weeks, while detailed participant flow and missing-data methods are not reported.

It also shows why effect direction must be tied to the instrument. The primary scale explicitly labels lower values as greater improvement, so a negative mean difference for a comparison against lithium points toward a lower average score in that group. The same directional interpretation cannot automatically be applied to secondary measures whose scoring direction is not described in the registry record.

Finally, the example separates statistical precision from importance. Confidence intervals communicate uncertainty about the average contrast, while p-values summarize evidence under a model. Neither answers whether a difference is meaningful to patients, and neither addresses multiplicity unless the analysis accounts for it. Since the registry does not report the original statistical plan or adjustments, the unadjusted comparisons are informative summaries but have a narrower evidential role than a fully documented confirmatory analysis.

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.

Several trial-specific reporting limitations constrain interpretation. The primary analysis population is stated to include subjects completing 8 weeks, but the registry does not give reasons for missing week 8 outcome data or explain their treatment in analysis. The outcome means consequently do not establish results for all enrolled or randomized participants. Outcome counts are reported, but a detailed participant-flow account is not.

The trial was open-label, and whether outcome assessors were masked is not reported. Because the primary outcome is a clinical rating, knowledge of assigned treatment is a relevant design consideration. The available record does not permit assessment of whether or how this affected scoring.

The treatment descriptions give an 8 to 16 week duration, while the primary endpoint is measured at Week 8. The posted primary findings therefore concern that time point and do not provide evidence about longer-term outcomes. Dose information, adherence, discontinuations, and follow-up beyond the stated outcome are not reported in the registry record.

The registry does not provide a formal statistical analysis plan, adjusted treatment estimates, multiplicity handling, or sensitivity analyses. The posted comparisons are unadjusted summaries and may not reproduce the analysis approach used by investigators outside the registry. The secondary outcome descriptions also do not specify their score direction. Finally, the record does not give a clinically meaningful difference threshold for the primary scale, limiting conclusions about the practical importance of the mean contrast.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Study of Outcome and Safety of Lithium, Divalproex and Risperidone for Mania in Children and Adolescents — NCT00057681.
• Registry record last updated 2013-04-04; status last verified 2013-03.
• Results first posted 2013-03-27.
• 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 Treatment of Early Age Mania study was a completed Phase 3 randomized, open-label, parallel-group trial sponsored by Washington University School of Medicine. The registry reports enrollment of 379, a start of 2003-02, and primary completion in 2008-12. The interventions were lithium, divalproex sodium, and risperidone, described as treatment for 8 to 16 weeks.

The primary outcome was the mean Clinical Global Impressions-Bipolar Mania Improvement score at Week 8 among subjects completing 8 weeks. The unadjusted risperidone-versus-lithium comparison was -0.79, with a 95% confidence interval from -1.074 to -0.505 and p < 0.001. The divalproex-sodium-versus-lithium comparison was 0.24, with a 95% confidence interval from -0.115 to 0.595 and p = 0.185. These summary-based results do not replace a formal analysis plan, which is not reported in the registry record.