Brain Response Associated With Parent-based Treatment for Childhood Anxiety Disorders: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Brain Response Associated With Parent-based Treatment for Childhood Anxiety Disorders (NCT03585010), a randomized na study. The primary outcome is Change From Baseline Anxiety Severity on the Pediatric Anxiety Rating Scale (PARS) at Week 12..

2. Clinical Question

The trial record describes a randomized, single-masked, parallel study of parent-based treatment for childhood anxiety disorders. The interventions listed are SPACE, Parent Educational Support, and Cognitive-Behavioral Therapy. The group descriptions specify parent sessions for SPACE and PES, and child sessions for CBT. The listed intervention descriptions give 12 sessions for each of these treatments.

The central outcome addressed by the posted results is change in anxiety severity on the Pediatric Anxiety Rating Scale (PARS) at week 12. The registry record reports mean change and standard deviation for four groups. The comparisons use Phase 1 SPACE as the reference. The posted figures therefore describe these specific group summaries and contrasts; they do not, by themselves, resolve whether effects differed by study phase or whether each listed comparison represents an otherwise equivalent randomized contrast.

The record’s stated research aims also include examining brain circuitry and its association with anxiety change. The posted primary and secondary outcome information is about anxiety severity, and brain-circuitry results are not reported in the registry record. Accordingly, the results address the reported anxiety-scale outcome rather than the neural mechanisms named in the study summary.

3. Trial Design

The registry record identifies NCT03585010 as a completed randomized, single-masked, parallel study sponsored by Yale University. It records enrollment of 214. The recorded start date is 2018-08-24, and the primary completion date is 2024-03-31. The study phase is listed as not applicable.

Three behavioral interventions are named: Supportive Parenting for Anxious Childhood Emotions (SPACE), Parent Educational Support (PES), and Cognitive-Behavioral Therapy (CBT). The arm descriptions specify 12 sessions with parents for Phase 1 SPACE, Phase 1 PES, and Phase 2 SPACE. Phase 2 CBT is described as 12 sessions with the child. The posted primary outcome results list two SPACE groups, one PES group, and one CBT group, distinguished by phase labels.

The primary outcome is change from baseline in PARS anxiety severity at 12 weeks. The registry describes the measure as clinician-administered, with total scores from 0-35 and higher scores indicating more severe anxiety. The primary outcome population is participants with anxiety-severity measurements recorded at both baseline and 12 weeks. The secondary outcome listed is change from baseline in anxiety severity on the Multimodal Anxiety Scale for Children (MASC) at week 12.

The posted mean-difference comparisons use Phase 1 SPACE as the reference group. They contrast it with Phase 1 PES, Phase 2 SPACE, and Phase 2 CBT. The record describes the overall study as randomized and parallel, but details about allocation procedures, the specific masking arrangement, and how the phase-labelled groups entered each comparison are not reported in the registry record. The original design assumptions, including any planned sample-size justification, are not reported in the registry record.

The registry lists two outcome measures and one posted secondary outcome, while the analysis count is recorded as zero. Those record entries do not explain the statistical procedures used to produce the posted group summaries and comparisons. Details of the analysis plan, adjustment strategy, and analysis populations beyond the primary outcome’s recorded-measurement description are not reported in the registry record.

4. Participant Flow and Accounting

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

Before assignment: Of 104 participants enrolled in Phase 1, 78 met inclusion criteria and were randomized to treatment; 26 were excluded (11 did not meet criteria, 6 could not complete scan, and 9 dropped before randomization). Of 205 participants enrolled in Phase 2, 136 met inclusion criteria and were randomized to treatment; 69 were excluded (27 did not meet criteria, 26 did not complete scan, 14 dropped out before randomization, and 2 did not complete assessment.)

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: All participants for whom anxiety severity was recorded at Baseline and 12 weeks.

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 From Baseline Anxiety Severity on the Pediatric Anxiety Rating Scale (PARS) at Week 12., measured over Baseline and 12 weeks.

The primary endpoint is change from baseline to week 12 in anxiety severity measured by the Pediatric Anxiety Rating Scale (PARS). The record describes PARS as a clinician-administered measure for children and adolescents. Total scores range from 0-35; higher scores indicate more severe anxiety. The outcome is reported as a mean, with standard deviation describing variation among participants.

A change score expresses how much a participant’s recorded score differs between the two measurement times. In the posted group results, the mean changes are negative in all four groups. Given the scale direction, a negative change corresponds to a lower mean severity score at week 12 than at baseline. This describes the direction of the recorded score change, not the cause of that change.

The endpoint is relevant to the study’s stated focus on childhood anxiety because it measures anxiety severity directly. Using a clinician-administered scale provides a structured way to record symptom severity, while the baseline-to-week-12 change expresses movement over the stated treatment period. A mean summarizes the group’s average change; the standard deviation gives information about the spread of individual recorded changes around that mean. Neither group mean nor standard deviation shows the full range of participant responses.

The primary outcome population is described as all participants for whom anxiety severity was recorded at baseline and 12 weeks. How missing measurements were handled, whether other analysis populations were used, and whether the change score was adjusted for other variables are not reported in the registry record. The secondary anxiety outcome uses MASC, but its numerical results are not included in the posted outcome details.

7. Results Posted in the Registry

• Phase 1: Parent Educational Support (PES): mean -6.29 versus -11.82 on control; difference 5.53 (95% CI 2.31 to 8.75), standardized effect d = 0.79; z-test p = <0.001.
• Phase 2: Supportive Parenting for Anxious Childhood Emotions (SPACE): mean -8.47 versus -11.82 on control; difference 3.35 (95% CI 0.50 to 6.20), standardized effect d = 0.49; z-test p = 0.021.
• Phase 2: Cognitive Behavioral Therapy (CBT): mean -6.54 versus -11.82 on control; difference 5.28 (95% CI 2.52 to 8.04), standardized effect d = 0.82; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

All four primary-outcome summaries are means of a continuous change score. A continuous measure can take values along a scale rather than being limited to categories. For PARS, the registry reports mean change from baseline to week 12 and a standard deviation for each group. The mean describes the average change; the standard deviation describes how dispersed individual recorded changes are around that average. A mean alone can conceal meaningful variation among participants.

What does a mean difference represent?

General statistical explanation: a mean difference compares the average outcome in one group with the average in another. Here, the posted contrasts use Phase 1 SPACE as the reference and give differences for Phase 1 PES, Phase 2 SPACE, and Phase 2 CBT. The reported contrasts are positive because the comparison groups’ mean changes are less negative than the reference mean change. The estimate describes the difference between group averages; it does not describe the difference for each individual.

The posted reference mean is -11.82. The comparison-group means are -6.29 for Phase 1 PES, -8.47 for Phase 2 SPACE, and -6.54 for Phase 2 CBT. The associated posted mean differences are 5.53, 3.35, and 5.28, respectively. These contrasts are unadjusted re-calculations from posted summary statistics, and the record indicates no discrepancy. Each should be understood as a summary-statistic contrast rather than as a fully described model-based adjusted effect. The statistical model and any covariate adjustment are not reported in the registry record.

Why report standard deviations?

General statistical explanation: a standard deviation conveys variability within a group, while the standard error conveys uncertainty in an estimate such as a mean. The posted group standard deviations are 7.45 for Phase 1 SPACE, 6.51 for Phase 1 PES, 6.52 for Phase 2 SPACE, and 5.68 for Phase 2 CBT. The standard errors listed for the group means are 1.193, 1.133, 0.828, and 0.752, respectively. The standard deviation and standard error answer different questions: one concerns spread among recorded observations, and the other concerns precision of an estimated mean.

The comparisons also report pooled standard deviations and standardized effect-size estimates. General statistical explanation: a standardized effect expresses a mean difference relative to a measure of variation, which can help compare effects measured on different scales. It does not replace the original scale’s units or explain the practical meaning of a change. The registry record does not describe a threshold for interpreting the size of a PARS change as clinically important.

How should the p-values be read?

General statistical explanation: a p-value describes how compatible the observed data are with a specified null model, assuming that model and its assumptions. It is not the probability that the null hypothesis is true, nor does it measure the size or practical importance of an effect. The posted unadjusted p-values are < 0.001 for Phase 1 PES versus Phase 1 SPACE, 0.021 for Phase 2 SPACE versus Phase 1 SPACE, and < 0.001 for Phase 2 CBT versus Phase 1 SPACE. They are unadjusted; whether the investigators used another inferential procedure is not reported in the registry record.

A p-value should be considered alongside the estimate and its confidence interval. The estimate conveys the direction and scale of the contrast; the interval conveys uncertainty under the calculation method. Neither one alone establishes a causal explanation. The registry labels the study randomized, but the posted comparisons’ phase structure and any phase-specific randomization details are not reported in the registry record. This limits conclusions about how directly each contrast maps to a randomized treatment comparison.

What do the analysis counts and outcome entries tell us?

The registry record lists two outcome measures, one posted secondary outcome, and zero analyses. These administrative entries do not substitute for a statistical analysis plan. The primary endpoint specifies participants with recorded PARS scores at baseline and 12 weeks, but the record does not state how missing scores were handled, whether all randomized participants were included in an analysis, or whether any imputation or sensitivity analysis was used. Details of outcome ascertainment and analysis beyond the stated measure and time point are not reported in the registry record.

The secondary outcome is change in MASC anxiety severity at week 12. Its numerical results are not reported in the registry record. The brain-circuitry questions in the study summary likewise have no corresponding results among the posted outcomes described in the registry record. Consequently, interpretation of the numerical results is confined to the posted PARS group summaries and contrasts.

10. Confidence Intervals and Precision

The posted comparisons include confidence intervals, which describe uncertainty around estimated mean differences. General statistical explanation: a confidence interval is calculated using a method that, under its assumptions, produces intervals that cover the target value at the stated rate over repeated samples. It is not a guarantee that the particular interval contains the true value, and its width reflects both the estimate’s uncertainty and the calculation method.

For Phase 1 PES compared with Phase 1 SPACE, the estimated mean difference is 5.53 and the interval extends from 2.305 to 8.755. For Phase 2 SPACE compared with Phase 1 SPACE, the estimate is 3.35; the interval is entirely above zero, extending from a lower bound of 0.504 to 6.196. For Phase 2 CBT compared with Phase 1 SPACE, the estimate is 5.28 and the interval extends from 2.516 to 8.044. Each interval is for the reported mean difference, not for an individual participant’s change.

The intervals provide more information than the point estimates alone. They indicate that the estimates are not known without uncertainty, and their endpoints show a range of values compatible with the stated interval method. All three posted intervals lie above zero. This observation should be read with the unadjusted nature of the comparisons and the absence of a reported multiplicity procedure in mind. The registry record does not specify the confidence-interval construction method, whether intervals were adjusted, or whether the analysis incorporated additional covariates.

The group standard deviations also show that recorded changes vary within each group. A confidence interval for a group mean or mean difference is not the same as the distribution of individual outcomes. Nor does a narrower interval by itself establish greater clinical importance. No clinically meaningful PARS difference threshold is reported in the registry record, and no confidence intervals for the individual group means are posted in the registry record.

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 illustrate how the required number per arm would change under different assumed effect sizes and target power levels. The entries are based on the observed effect, with scenarios using 100% of that effect, 75% of the observed effect, and 50% of the observed effect.

The planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. For each assumed effect size, the 80% power column gives the planned participants per arm for a design that would have an 80% chance of detecting that assumed effect under the stated assumptions, if the model and assumptions hold. The 90% power column gives the corresponding per-arm planning figure for a 90% chance under those assumptions. These are design-planning interpretations, not guarantees for a future study.

The listed scenarios demonstrate the general relationship between effect size and required sample size: smaller effects need more participants. For example, planning for 50% of the observed effect requires larger per-arm figures than planning for 100% of the observed effect in each listed comparison. The exact per-arm figures depend on which comparison and effect fraction are being considered; they are displayed in the planning entries and should not be treated as observed enrollment counts.

This is not observed power. It is a planning illustration calculated from the observed effect, not the trial’s original design assumptions. The original sample-size justification and planned design assumptions are not reported in the registry record. The planning figures also do not account for any unreported design features, missing outcome data, multiplicity adjustment, or phase-specific structure.

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 = 5.530; pooled standard deviation σ = 7.036.
2. n = 2 × (1.96 + 0.842)² × 7.036² / 5.530² = 25.4, rounded up to 26 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 <- 5.53                      # observed difference in means
sigma <- 7.03588577020894                     # 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(3585010)
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 = 26 (80% power), 35 (90% power)
 75% of observed effect: n per arm = 46 (80% power), 61 (90% power)
 50% of observed effect: n per arm = 102 (80% power), 137 (90% power)
power.t.test: 26.4 
Simulated power at n = 26 per arm: 0.794 (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

Three primary-outcome mean-difference comparisons are posted, each using Phase 1 SPACE as the reference. The corresponding p-values are labelled unadjusted. The registry record does not report whether the investigators planned or applied a multiplicity procedure. When several comparisons are examined, multiplicity can affect the chance of obtaining one or more nominally small p-values under a broader null hypothesis. General statistical explanation: adjustment procedures can address that issue, but their choice depends on the questions and analysis plan. No particular procedure should be inferred.

The primary endpoint population is described as participants with anxiety-severity data recorded at baseline and 12 weeks. This tells the reader which records define the outcome population, but it does not explain what happened to participants with missing measurements. The method for handling missing data, the number of missing PARS observations, and any sensitivity analyses are not reported in the registry record. It is therefore not possible to determine from these registry entries whether the reported summaries reflect complete cases only or another approach.

The record does not describe an intention-to-treat population, a per-protocol population, or another formal analysis population. It also does not report whether all randomized participants were included in the posted comparisons or whether any exclusions were made. The broad study enrollment is recorded as 214, while the outcome summaries give group-specific recorded counts; no account of participant flow or reasons for differences in available outcome data is reported.

The registry describes the study as randomized and parallel, but the posted comparisons span Phase 1 and Phase 2 groups. Details of the phase-specific allocation, any stratification, and the analysis model are not reported in the registry record. There is also no reported adjustment for baseline PARS score or other covariates. These omissions matter when judging how directly the raw change-score contrasts represent the intended randomized comparisons.

The record lists one secondary outcome, MASC change at week 12, but its numerical results are not reported in the registry record. Brain-circuitry analyses described in the study summary are also not reported in the registry record. Without fuller outcome and analysis reporting, the extent of selective reporting or the complete family of analyses cannot be assessed.

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 registry’s adverse-event entries report zero serious adverse events in each listed group: SPACE, PES, and CBT. The corresponding serious-event at-risk counts are 113 for SPACE, 37 for PES, and 64 for CBT. The record also reports zero other adverse events in each group, with the same at-risk counts, and zero deaths in each group.

These are counts in the registry record, not evidence that no unrecorded events occurred. The record does not provide event descriptions, definitions, ascertainment procedures, follow-up completeness, or an explanation of how the adverse-event at-risk counts relate to the phase-specific efficacy groups. No serious adverse-event terms are listed. The figures should therefore be read as the registry’s posted counts rather than as a detailed assessment of safety.

Zero reported events does not establish that risk is absent. In general, when an event is not observed, the data still have limited ability to rule out uncommon events, particularly when the available observation group is limited. The record does not provide enough detail to quantify such uncertainty. No percentages or between-group safety comparisons are posted among these registry entries.

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

The posted results describe average change in a clinician-rated anxiety scale over the baseline-to-week-12 period. Mean PARS scores declined in all four listed groups, with group mean changes of -11.82 for Phase 1 SPACE, -6.29 for Phase 1 PES, -8.47 for Phase 2 SPACE, and -6.54 for Phase 2 CBT. The reported contrasts indicate that the mean changes in the three comparison groups were less negative than the Phase 1 SPACE mean change.

Those findings do not, on their own, establish why the scores changed. The registry identifies the study as randomized, but the posted comparisons include groups labelled as different phases, and details of the relationship between those phases are not reported in the registry record. A difference between posted means can reflect the contrast as recorded, but it should not be interpreted beyond the design and analysis details available.

The results concern PARS anxiety severity, not every aspect of childhood anxiety, functioning, or well-being. The scale’s score range and direction are reported, but a clinically important change threshold is not reported in the registry record. The group mean changes also do not show how many participants improved, remained unchanged, or worsened; individual response distributions are not reported in the registry record.

The study summary refers to whether parent-based treatment engages child brain circuitry and whether changes in circuitry are associated with changes in anxiety. The posted outcome information does not include brain-circuitry measurements or analyses linking them with anxiety change. The numerical PARS results cannot establish a neural mechanism or explain how any score change occurred.

The absence of reported serious adverse events in the listed groups is a description of the registry entries, not proof that adverse effects cannot occur. The record does not provide detailed adverse-event collection information. Similarly, statistical significance based on unadjusted p-values does not establish clinical importance, and the reported confidence intervals do not remove uncertainty. The most defensible reading is limited to the posted group-level changes and contrasts, with the design, analysis, and reporting gaps kept in view.

16. Why This Trial Matters Statistically

This trial is statistically interesting because it reports continuous change scores and compares several treatment groups against a single reference group. That structure makes it important to distinguish group means, mean differences, and within-group variability. A large average change within one group is not the same question as a difference between groups, and neither tells the reader how uniformly participants changed.

The phase labels are also important to interpretation. The reported comparisons include Phase 1 PES versus Phase 1 SPACE, as well as Phase 2 SPACE and Phase 2 CBT versus Phase 1 SPACE. The registry record describes randomization but does not report the phase-specific allocation or analysis details needed to fully assess how these comparisons map onto the study design. Calling a study randomized does not, by itself, explain every contrast in a posted results record.

The unadjusted p-values and confidence intervals illustrate why effect estimates and uncertainty should be read together. The estimates convey the scale and direction of each contrast, while the intervals show uncertainty under the method used. Because a multiplicity procedure is not reported, the inferential status of several comparisons considered together remains unclear. The registry’s missing-data and analysis-population details also matter: the primary outcome is defined for participants with measurements at both time points, but the handling of unavailable measurements is not described.

Finally, the trial summary’s mechanistic aims and the posted anxiety-scale results are not interchangeable. Understanding whether brain circuitry changed, and whether that change tracked anxiety, requires corresponding measures and analyses. Those results are not reported in the registry record. Distinguishing the stated research aims from the available outcome evidence is central to a statistically careful reading.

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.

Several trial-specific reporting gaps constrain interpretation. The registry records four phase-labelled groups, but the relationship between Phase 1 and Phase 2, how participants were allocated within each phase, and whether the three posted contrasts were prespecified randomized comparisons are not reported in the registry record. The broad designation of randomized, parallel allocation does not answer those questions.

The primary outcome is defined for participants with PARS measurements at baseline and week 12. The count of missing measurements, participant flow by group, reasons for missingness, and methods for handling missing data are not reported in the registry record. The record also does not describe the analysis population beyond the recorded-measurement criterion or state whether an intention-to-treat analysis was used.

Statistical methods beyond the posted summaries and unadjusted comparisons are not reported in the registry record. In particular, the model, any covariate adjustment, confidence-interval method, and multiplicity procedure are not described. The original sample-size justification and planned design assumptions are not reported. The available planning illustration is based on observed effects and should not be mistaken for the trial’s original design rationale.

The posted numerical results focus on PARS. Although MASC is listed as a secondary outcome, its numerical result is not reported in the registry record. The study summary also describes brain-circuitry aims, but corresponding measurements and analyses are not reported in the registry record. The absence of those results prevents assessment of the stated mechanistic questions.

Finally, the adverse-event entries give zero serious and other events and zero deaths, but do not describe collection methods, definitions, follow-up completeness, or the relationship between safety and efficacy group counts. These record-level limitations do not negate the posted summaries; they define the boundaries of what can be concluded from them.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Brain Response Associated With Parent-based Treatment for Childhood Anxiety Disorders — NCT03585010.
• Registry record last updated 2026-04-22; status last verified 2026-04.
• Results first posted 2026-04-22.
• 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

NCT03585010 is recorded as a completed randomized, single-masked, parallel study sponsored by Yale University, with enrollment of 214. The study concerns parent-based treatment for childhood anxiety disorders and lists SPACE, Parent Educational Support, and Cognitive-Behavioral Therapy. The primary outcome is change in PARS anxiety severity from baseline to week 12.

The posted PARS summaries give mean changes for Phase 1 SPACE, Phase 1 PES, Phase 2 SPACE, and Phase 2 CBT. Three unadjusted mean-difference comparisons use Phase 1 SPACE as the reference. Each comparison’s confidence interval is above zero, but the record does not report multiplicity adjustment, missing-data methods, or enough phase-specific design detail to resolve all interpretation questions.

The registry also lists MASC change as a secondary outcome, but its numerical result is not reported in the registry record. Brain-circuitry results are not reported in the registry record. Adverse-event entries report zero serious events, zero other events, and zero deaths in each listed safety group.