Parent-Led Cognitive-Behavioral Teletherapy for Anxiety in Youth With ASD: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Parent-Led Cognitive-Behavioral Teletherapy for Anxiety in Youth With ASD (NCT04111874), a randomized na study. The primary outcome is 6-item Pediatric Anxiety Rating Scale.

2. Clinical Question

3. Trial Design

The registry describes a randomized, single-masked, parallel-group behavioral study. Participants were assigned to low-intensity therapist assistance (LTA) or standard therapist assistance (STA), with parent-led cognitive-behavioral teletherapy in both arms. The recorded enrollment is 87. The registry lists the study as completed, with a start date of 2019-07-30 and primary completion on 2022-12-31. The phase is recorded as NA.

The arms differ in the amount of therapist contact described in the registry: LTA involved four 30-minute supportive video calls, whereas STA involved ten 60-minute supportive video calls. Both schedules are described as occurring over the 12 weeks of treatment. The registry does not describe additional intervention components in enough detail to compare them, and the identity of the masked party is not reported in the registry record. Random allocation supports a planned between-arm comparison, but it does not by itself establish that the posted outcome groups remained comparable after allocation.

The primary endpoint is the 6-item Pediatric Anxiety Rating Scale, with post-treatment scores reported. The registry also lists Clinical Global Impression-Severity as a secondary outcome. Although the endpoint timeframes mention baseline and follow-up assessments, the posted primary and secondary results are post-treatment values. Results for the other listed time points are not reported in the registry record.

Arm-level outcome counts are 31.0 for LTA and 33.0 for STA. These are the numbers associated with the posted post-treatment outcome summaries, not a statement about why other enrolled participants may not appear in those summaries. Reasons for the difference between recorded enrollment and outcome counts, the analysis population, and handling of missing observations are not reported in the registry record. The registry record lists no reported analyses.

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: Results for the post-treatment assessment

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.

Population: All participants (87) were randomly assigned to either the LTA or STA groups

6. Primary Endpoint

The registry lists the primary outcome as 6-item Pediatric Anxiety Rating Scale, measured over Baseline (before treatment), post-treatment (on average 12 weeks), 3 month follow up; Post-treatment scores reported..

The primary endpoint is the 6-item Pediatric Anxiety Rating Scale, a clinician-rated measure of child anxiety severity throughout the past week. Each item is scored from 0 to 5, producing a total score from 0 to 30. Higher scores correspond to greater anxiety severity. The registry identifies the reported population as participants assessed post-treatment, on average 12 weeks after treatment began.

A continuous score preserves more gradation than a simple yes-or-no outcome. Comparing the arm means describes the average score in each group, while the standard deviations describe variation among the individual scores within each group. These are different features: similar averages can coexist with substantial spread among participants.

This measure is used to quantify anxiety severity in a consistent way across participants and arms. A clinician rating is not the same as a participant’s own report, and the registry description does not specify further rating procedures. The score provides an outcome for comparing the two therapist-assistance schedules, but interpretation depends on the scale definition, the timing of measurement, and uncertainty in the estimated difference.

Only post-treatment scores are reported in the registry results. Baseline and 3 month follow up are mentioned in the timeframe, but corresponding results are not reported in the registry record. The record also does not report a threshold for a clinically important change, so the score difference alone cannot establish whether the observed contrast represents a meaningful change for an individual youth.

7. Results Posted in the Registry

• Low-Intensity Therapist Assistance (LTA): mean 11.35 versus 10.26 on control; difference 1.09 (95% CI -1.27 to 3.45), standardized effect d = 0.23; z-test p = 0.366.

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.

Clinical Global Impression-Severity

• 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:
  • Low-Intensity Therapist Assistance (LTA): mean 2.83 versus 2.59 on control; difference 0.24 (95% CI -0.29 to 0.77), standardized effect d = 0.22; z-test p = 0.372.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Low-Intensity Therapist Assistance (LTA) and the control. The interval gives the range of effects that remain compatible with the data.

The registry lists Clinical Global Impression-Severity as a secondary outcome, and the posted post-treatment comparison follows the same broad direction as the primary outcome: the LTA mean is higher than the STA mean. The unadjusted comparison does not establish a clear between-arm difference. This directional consistency is descriptive, but it should not be treated as independent confirmation of the primary result. The measures assess related clinical concepts, and their results are subject to uncertainty and the same limitations of summary-statistic recalculation.

The registry record identifies one posted secondary outcome, while it lists three outcome measures overall. Results for the other time points named in the secondary timeframe are not reported in the registry record. The record lists no reported analyses. Consequently, it is not possible to tell from the registry whether secondary outcomes were prespecified for formal testing, whether all planned outcomes are represented in the posted results, or how missing outcome information was handled.

Unadjusted secondary results carry less weight when multiple outcomes or comparisons are considered because repeated testing increases the opportunity to observe an apparently notable result by chance. General statistical context: multiplicity procedures can control the overall error rate across a defined family of tests, but their choice depends on which hypotheses were planned and how they relate. No such procedure is reported in the registry record. The secondary result therefore serves as supporting descriptive context rather than a confirmatory test.

Because the secondary endpoint does not replace the primary endpoint, it should not be used to override the uncertainty in the primary comparison. A coherent direction across endpoints may be informative, but it does not remove imprecision, establish causation, or answer whether the differences matter clinically. The registry record does not report an analysis integrating the primary and secondary measures, so no combined conclusion is warranted.

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

• Clinical Global Impression-Severity

9. Statistical Interpretation

10. Statistical Methods Explained

For a continuous endpoint, an arm mean is the arithmetic average of the observed scores in that arm. It gives a compact description of the group’s central value, but it does not imply that every participant had a score near that average. The standard deviation describes the spread of scores around the mean. A larger standard deviation indicates more variability within that group; it is not the uncertainty of the mean difference itself.

What does the mean difference represent?

The primary comparison is a difference between two arm means. The reported contrast is LTA minus STA, so positive values indicate a higher observed mean in LTA and negative values indicate a higher observed mean in STA. On this endpoint, higher scores correspond to greater anxiety severity. The recalculated estimate is 1.09 points. This estimate describes the observed difference in average post-treatment scores; it does not establish that the assigned therapist-assistance level produced that difference.

A mean difference keeps the outcome in its original score units, which makes it possible to relate the estimate to the scale. A standardized effect instead expresses a difference relative to a measure of score variability. That can help compare effects across measures with different units, but it is less directly interpretable in the scale’s original points. The registry record does not report a sponsor-selected standardized effect as an analysis result, so the interpretation centers on the score-unit mean difference and its confidence interval.

Why is there uncertainty around the estimate?

Each arm’s mean is based on a sample, and another sample of participants could produce different averages. A confidence interval conveys uncertainty around the estimated contrast under the calculation’s assumptions. It is not a range containing every participant’s score, nor is it a guarantee about the true difference. The interval for the primary contrast extends from -1.273 to 3.453, so it includes zero. In general, an interval that includes zero does not provide clear evidence of a nonzero difference at the corresponding conventional two-sided significance level. It also does not prove the true difference is zero.

The reported unadjusted p-value is 0.366. In general, a p-value describes how unusual data at least as discrepant as those observed would be under a specified null hypothesis and statistical model. It is not the probability that the null hypothesis is true, the chance that the finding occurred by chance, or a measure of clinical importance. The registry record does not report the sponsor’s model or test for this outcome; the posted p-value is an unadjusted recalculation from summary statistics.

Why might a simple calculation differ from a trial analysis?

A recalculation from arm means, standard deviations, and outcome counts is an unadjusted comparison. It does not account for baseline values, additional covariates, site or therapist effects, repeated measurements, clustering, or missing-data procedures unless those are explicitly included in the calculation. The registry record does not report whether the trial’s own analysis used any of these approaches. Therefore, the recalculated estimates should be read as a basic summary-statistic comparison, not as a reconstruction of an undocumented analysis plan.

General statistical context: an adjusted analysis can improve precision or address measured differences, but adjustment is not automatically better in every situation. Its validity depends on the model, variables, data completeness, and prespecification. Repeated observations on the same participant are also statistically related, so treating them as independent can understate or misstate uncertainty. No claim can be made about whether such considerations applied to the sponsor’s analysis because it is not reported in the registry record.

Why does over-dispersion matter in some outcomes?

General statistical context: for count outcomes, over-dispersion means the observed variability is greater than a model’s simplest assumptions allow. If it is ignored, uncertainty estimates can be too narrow and apparent evidence can be overstated. The primary endpoint is a continuous scale score, not an event count, so over-dispersion is not the central issue in this comparison. Its relevance would depend on the outcome type and analysis model, neither of which should be inferred beyond the endpoint description.

The reported standard deviations are 5.36 for LTA and 4.17 for STA. They describe variability in the observed post-treatment scores. The arm outcome counts, 31.0 and 33.0, describe the samples contributing to those summaries. The registry does not provide individual scores, distributions, or a missing-data analysis, so the summary statistics cannot show whether there were outliers, skew, ceiling effects, or differences in score distributions beyond the means and standard deviations.

What do the planning calculations mean?

The planning figures are illustrations based on fractions of the observed effect and assumptions stated in the registry-derived planning description. They use a two-sided significance level of 0.05, equal allocation between arms, and a normal approximation. The figures are participants per arm, not total events. They show how the required planning sample size changes when the target effect is set to 100%, 75%, or 50% of the observed effect. Smaller target effects require more participants to detect under the same assumptions. These calculations are separate from evidence about the actual trial’s original design, whose sample-size assumptions are not reported in the registry record.

11. Confidence Intervals and Precision

The primary mean difference is 1.09 points, with a 95% confidence interval from -1.273 to 3.453. The interval describes uncertainty in the estimated difference, not the range of individual scores. Its lower end is below zero and its upper end is above zero. Accordingly, the posted summary statistics are compatible with an average difference favoring either arm as well as with little or no average difference.

The interval is fairly broad relative to the point estimate: it allows contrasts notably smaller and larger than the estimate itself. That means the observed estimate should not be read as a precise measurement of the difference between the therapist-assistance schedules. The standard deviations also show meaningful variation in individual scores within each arm, but they do not by themselves determine whether an estimated difference is precise; precision depends on sample size and the variability of the measure.

General statistical context: a confidence interval is constructed by a method that has a stated long-run coverage property when its assumptions hold. It is not correct to say there is a particular probability that the fixed true effect lies inside this specific interval. Instead, the interval gives a range of values reasonably compatible with the data and calculation method. The registry record does not report the sponsor’s inferential method, so the interval should be understood as the unadjusted recalculation associated with the posted summaries.

The interval does not identify which differences would be important to patients or clinicians. A clinically meaningful threshold is not reported in the registry record. Therefore, statistical uncertainty can be described, but the practical importance of values within the interval cannot be classified from these results alone. The interval’s inclusion of zero is not evidence of equivalence, and the point estimate alone is not enough to establish a meaningful advantage for either arm.

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 planning figures express sample size as participants per arm. They are not total event counts: this is a continuous outcome, and the planning description specifies per-arm participant counts for non-time-to-event outcomes. For illustration, planning for 100% of the observed effect corresponds to 303 participants per arm for 80% power and 405 participants per arm for 90% power. Planning for 75% of the observed effect corresponds to 538 participants per arm for 80% power and 720 participants per arm for 90% power. Planning for 50% of the observed effect corresponds to 1,210 participants per arm for 80% power and 1,619 participants per arm for 90% power.

The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The target effect is the stated fraction of the observed effect. In plain terms, the 80% column describes a planning size intended to give an 80% chance of detecting an effect of that target size under those assumptions if that effect is real; the 90% column uses a higher detection probability under the same assumptions. Smaller effects are harder to distinguish from random variation, so planning for a smaller effect requires more participants.

These are illustrations based on the observed effect, not evidence about the assumptions used to design the trial. The original sample-size justification and design assumptions are not reported in the registry record. This is not observed power: it is a prospective planning calculation under stated assumptions, not a measure of how likely the completed study was to detect its effect after seeing the results.

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 = 1.090; pooled standard deviation σ = 4.783.
2. n = 2 × (1.96 + 0.842)² × 4.783² / 1.090² = 302.3, rounded up to 303 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 <- 1.09                      # observed difference in means
sigma <- 4.78292122910999                     # 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(4111874)
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 = 303 (80% power), 405 (90% power)
 75% of observed effect: n per arm = 538 (80% power), 720 (90% power)
 50% of observed effect: n per arm = 1,210 (80% power), 1,619 (90% power)
power.t.test: 303.2 
Simulated power at n = 303 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.

14. Multiplicity, Missing Data and Analysis Populations

Multiplicity arises when researchers evaluate more than one outcome, time point, subgroup, or comparison. General statistical context: with repeated testing, the chance of at least one apparently positive result can increase even when none of the tested effects is real. Researchers may address this through a prespecified hierarchy, adjustment procedure, or a clear distinction between confirmatory and exploratory analyses. The registry record does not report a multiplicity strategy, and it lists no reported analyses. It is therefore not possible to determine whether the unadjusted secondary comparison was part of a formal testing family or whether any adjustment was used in the trial’s own analysis.

The outcome descriptions mention baseline, treatment-period assessments, post-treatment, and 3 month follow up, but the posted results are post-treatment scores. Results at the other listed times are not reported in the registry record. The absence of posted values does not establish that those observations were not collected, nor does it reveal why results are absent. The registry record does not report a complete outcome-by-timepoint accounting.

Missing-data handling is not reported in the registry record. In general, missing outcome values can affect both the estimated group means and the uncertainty around comparisons, especially if the chance of missingness is related to participant characteristics or outcomes. The available summaries do not identify how many observations were missing, the reasons for missingness, or whether any imputation or sensitivity analysis was performed. No mechanism of missingness should be assumed.

The analysis population is also not reported in the registry record. The outcome counts are 31.0 for LTA and 33.0 for STA, but those counts alone do not establish whether the analysis included all randomized participants, only participants with observed post-treatment values, or another population. The registry record does not report adherence-based exclusions, protocol deviations, or an intention-to-treat analysis. These details matter because the interpretation of a randomized comparison depends partly on how participants are retained in the analysis and how departures from the assigned intervention are handled.

These gaps limit what can be inferred from the posted results. The recalculated comparisons can describe the reported group summaries, but they cannot establish whether the trial’s own prespecified inferential framework led to the same estimates or conclusions. A complete account of multiplicity, missing observations, and analysis populations is not reported in the registry record.

15. 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 reports serious adverse event figures for both therapist-assistance arms. In LTA, 48 participants were listed as at risk, with 0 serious adverse events and 0 other adverse events reported; deaths were 0. In STA, 39 participants were listed as at risk, with 0 serious adverse events and 0 other adverse events reported; deaths were 0. No serious-event terms are listed.

These figures are counts in the registry record, not evidence that no adverse events of any kind occurred outside the recorded categories or reporting period. The event counts and the at-risk counts are not the post-treatment endpoint sample sizes; the registry does not explain the difference between these denominators. It also does not provide detail about event definitions, collection procedures, follow-up completeness, or whether events were judged related to the intervention. The reported zeros should therefore be read narrowly as the posted counts, not as proof of safety or a basis for comparing risk between arms.

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

The posted results describe post-treatment anxiety scores in two randomized arms that both involved parent-led cognitive-behavioral teletherapy, with different levels of therapist assistance. The primary score mean was higher in LTA than STA, and the recalculated mean difference was 1.09 points. Its confidence interval includes zero and spans values in both directions. The results therefore leave substantial uncertainty about the size and direction of the population-average difference.

These findings do not answer whether parent-led teletherapy is effective compared with no treatment, usual care, or another intervention, because those comparisons are not part of the posted results. They also do not establish that the two assistance schedules are equivalent. A failure to establish a clear difference is not the same as proving that the approaches produce the same outcomes. Equivalence would require a clinically justified margin and a suitable analysis, neither of which is reported in the registry record.

The mean score is a group-level summary. It does not show how individual participants changed, whether all participants improved or worsened, or how many experienced a meaningful change. The registry record does not report a clinically important difference threshold. It also does not post the baseline and follow-up values described in the timeframe, so the reported post-treatment comparison cannot show within-person change over time.

The estimates come from posted summaries and unadjusted recalculations. They are not a replacement for the trial’s complete analysis, which is not reported in the registry record. The results can be used to describe the recorded scores and their statistical uncertainty, but they do not support medical advice or a definitive conclusion about the benefits and risks of either schedule.

17. Why This Trial Matters Statistically

This comparison is statistically informative because it separates the intervention contrast from a simple treatment-versus-no-treatment question. Both arms received parent-led cognitive-behavioral teletherapy, while the therapist-support schedule differed. That distinction focuses attention on what the randomized comparison can address: the contrast between the two recorded levels of therapist assistance.

The continuous anxiety score also makes the uncertainty visible in the original scale units. The mean difference can be read alongside the scale’s 0 to 30 range and the fact that higher scores indicate greater severity. Its confidence interval, however, includes zero and extends across differences in either direction. The point estimate alone is not an adequate summary of the evidence; precision and the interval’s breadth are central to interpretation.

The registry record also illustrates why a completed trial’s observed effect should not automatically be treated as a dependable planning target. The sample-size illustrations show that planning for smaller fractions of the observed effect requires substantially more participants under the listed assumptions. Those calculations are planning illustrations, not evidence that the original design used those assumptions and not a measure of observed power.

Finally, the record emphasizes the distinction between a randomized design and a fully documented analysis. Randomization is important for planned comparisons, but interpretation also depends on which participants contribute outcomes, how missing data are handled, what analyses were prespecified, and how multiple outcomes are treated. Those details are not reported in the registry record. The posted summaries therefore support a careful description of the observed contrast, while leaving important analytic questions unresolved.

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.

The registry record does not report the sponsor’s analysis for the primary comparison, and it lists no reported analyses. The available estimates are unadjusted recalculations from group summaries. The record does not state whether the trial’s own analysis incorporated baseline values, repeated measures, therapist or site structure, or other covariates. These omissions prevent comparison with a prespecified model-based result.

Outcome results are posted for post-treatment, although the timeframe also names baseline and 3 month follow up. The record does not report the values at those other times, reasons for their absence, or whether they were collected. Without baseline results, the post-treatment means alone do not describe change from baseline. Without later results, they do not describe the persistence of the post-treatment scores.

The analysis population and missing-data procedures are not reported in the registry record. The outcome counts differ from the recorded enrollment, but the reason is not given. The record also does not provide individual-level data, score distributions, adherence information, or details about departures from assigned treatment. Those limits restrict assessment of selection, variability beyond the reported standard deviations, and sensitivity to missing observations.

The endpoint description gives the scale range and direction, but a clinically important threshold is not reported in the registry record. It is therefore not possible to determine from the mean difference alone whether the observed contrast would matter clinically. The registry also does not report the masked party or a multiplicity plan. These are limitations of interpretation rather than proof that the trial did not use procedures that were not recorded.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Parent-Led Cognitive-Behavioral Teletherapy for Anxiety in Youth With ASD — NCT04111874.
• Registry record last updated 2025-01-15; status last verified 2024-12.
• Results first posted 2025-01-15.
• 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 registry identifies a completed randomized, single-masked, parallel-group behavioral study of parent-led cognitive-behavioral teletherapy for anxiety in youth with ASD. It compares low-intensity therapist assistance with standard therapist assistance over 12 weeks. Recorded enrollment is 87.

The primary post-treatment endpoint is the 6-item Pediatric Anxiety Rating Scale. The LTA mean was 11.35 and the STA mean was 10.26; the recalculated unadjusted mean difference was 1.09, with a 95% confidence interval from -1.273 to 3.453 and an unadjusted p-value of 0.366. The interval includes zero and leaves uncertainty about the between-arm difference.

The registry also posts Clinical Global Impression-Severity as a secondary outcome, but reports no sponsor analyses. Missing-data handling, analysis populations, multiplicity procedures, and the trial’s original sample-size assumptions are not reported in the registry record. The posted results support a descriptive, cautious reading of the available post-treatment summaries, not a definitive treatment conclusion.