Cognitive Behavioral Therapy (CBT) for Anxiety Disorders in Autism: Adapting Treatment for Adolescents: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Cognitive Behavioral Therapy (CBT) for Anxiety Disorders in Autism: Adapting Treatment for Adolescents (NCT01177969), a randomized phase 1, phase 2 study. The primary outcome is Pediatric Anxiety Rating Scale..

2. Clinical Question

3. Trial Design

The registry describes a randomized, single-masked, parallel-group Phase 1/Phase 2 study sponsored by the University of South Florida. The study is marked completed and records enrollment of 33 participants. The registry lists cognitive-behavioral therapy and wait-list as the two behavioral interventions. Allocation was randomized; the identity of the person or people masked is not reported in the registry record.

The intervention involved 16 weekly sessions of about 90 minutes. Both the child and parent participated. The wait-list group did not receive active treatment during its stated 16-week period. The primary outcome was recorded post-treatment, at an average of 16 weeks after baseline. The start and primary completion dates are listed in the registry record, but the reasons for the study's timing or any changes to its conduct are not reported.

The primary outcome data include 19 participants in the cognitive-behavioral therapy group and 14 in the wait-list group. These are the outcome-group counts recorded for this measure; they should not be taken as a complete account of attendance, follow-up, or analysis-population rules. Those details are not reported in the registry record.

Although the study is identified as Phase 1 and Phase 2, the registry information does not describe separate phase-specific aims or analyses. The original sample-size justification, planned interim analyses, protocol deviations, and detailed statistical plan are not reported in the registry record. Accordingly, the displayed comparisons should be read as reported study analyses and straightforward re-calculations from the posted group summaries, not as a full reconstruction of the protocol.

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

Reasons for not completing this period:

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 Pediatric Anxiety Rating Scale., measured over Post-treatment, which is an average of 16 weeks after Baseline.

The primary endpoint was the Pediatric Anxiety Rating Scale, a clinician-rated measure of anxiety symptoms and their associated severity and impairment over the past week. It includes five items that are summed into a total score. The recorded scale range is 0 to 25, with higher scores indicating more severe anxiety symptoms. The registry reports the endpoint as a mean with standard deviation, at post-treatment, an average of 16 weeks after baseline.

A continuous scale can retain information about the degree of symptoms rather than reducing each participant's outcome to a yes-or-no category. Comparing group means is one way to describe the average score difference, while the standard deviations show how spread out individual scores were within each group. The scale's clinician rating also allows symptom severity and impairment to be assessed together, as described in the registry.

That summary does not show each participant's trajectory, the range of individual experiences, or whether a particular change was important to an individual. The record does not specify a threshold for a clinically meaningful difference, nor does it report a separate responder definition for this endpoint. The outcome therefore supports interpretation of group-level scores, not a claim that every participant experienced a similar result.

7. Results Posted in the Registry

• Wait-list: mean 14.04 versus 11.62 on control; difference 2.42 (95% CI 0.40 to 4.44), standardized effect d = 0.80; z-test p = 0.019.

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.

Anxiety Disorders Interview Schedule: Child and Parent Versions

• 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:
  • Wait-list: mean 4.04 versus 3.28 on control; difference 0.76 (95% CI -0.60 to 2.12), standardized effect d = 0.38; z-test p = 0.275.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Wait-list and the control. The interval gives the range of effects that remain compatible with the data.

The posted secondary outcome adds a separate perspective on anxiety-related symptoms, but its inferential pattern is less definite than the primary result. Its unadjusted interval includes no difference, and its registry-reported ANCOVA p-value is .25. The secondary endpoint therefore does not offer equally clear statistical evidence of a group contrast in these data. It should be interpreted as a different measure, not as a direct replication of the primary scale.

Across the endpoints, the primary result is the more statistically distinct signal, while the secondary result leaves substantial uncertainty about the group difference. This pattern is neither proof that the primary finding is false nor confirmation that it is robust. Different measures may capture different aspects of anxiety, and the registry does not report enough detail about the secondary measure's scoring or prespecified role to make stronger claims about how closely it should track the primary endpoint.

Unadjusted secondary results generally carry less weight when several outcomes may be examined, because multiple testing can increase the chance of chance findings. The registry lists two outcome measures and does not report a multiplicity adjustment or a hierarchy for interpreting them. That absence does not establish that no strategy was used; it means the approach is not reported in the registry record. The secondary result is best treated as contextual evidence, with attention to its uncertainty, rather than as an independent confirmatory test.

The registry does not describe whether the secondary analysis was prespecified, whether all planned secondary outcomes were posted, or how missing observations were handled. These limitations constrain comparisons across outcomes. The overall pattern is informative as a description of the posted endpoints, but it is not enough to settle whether the primary result would recur in a larger or different study.

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

• Anxiety Disorders Interview Schedule: Child and Parent Versions

9. Statistical Interpretation

10. Statistical Methods Explained

What does a mean difference describe? The primary outcome is continuous, and the registry reports a mean for each group. A mean difference expresses the distance between the two group averages in the scale's units. Here the re-calculated contrast is expressed as wait-list minus cognitive-behavioral therapy, so a positive value corresponds to a higher average score in the wait-list group. Because higher scores indicate more severe symptoms, the direction of the estimate is important for reading the comparison. The difference remains a group-level summary: it does not imply that each participant's score changed by that amount.

What is a standard deviation?

The standard deviation describes spread around the group mean. The primary outcome standard deviations are 3.26 for cognitive-behavioral therapy and 2.64 for wait-list. They help convey that participants' scores were not all identical, but they do not describe the full shape of the score distribution or identify individual outcomes. Standard deviation is different from the standard error, which describes the estimated uncertainty of a group mean. The registry's posted group summaries support estimates of mean uncertainty, but the record does not report confidence intervals for each arm's mean.

What does a confidence interval convey?

In general, a confidence interval is a range of values compatible with the estimate under the statistical method and assumptions used. Its width indicates precision: narrower intervals indicate less uncertainty in the estimate, while wider intervals indicate more. For the primary unadjusted difference, the posted interval is entirely above zero. That means the simple comparison's interval does not include no difference. This interpretation is tied to that unadjusted calculation; it is not the interval for the sponsor's ANCOVA result, which is not reported in the registry record.

How does the p-value fit in?

In general, a p-value measures how unusual data at least as discrepant as those observed would be under a specified null model. It is not the probability that the null hypothesis is true, nor does it measure the size or importance of an effect. The unadjusted primary comparison has p = 0.019, while the registry reports p = .04 for ANCOVA. The values differ because the latter is a separate model-based analysis. The record does not report enough ANCOVA detail to determine precisely how its estimate or uncertainty was obtained.

Why might an adjusted analysis differ?

In general, ANCOVA compares outcomes while accounting for one or more covariates. If the model includes baseline scores or other covariates, adjustment can change the estimated comparison and its uncertainty. The registry names ANCOVA, but does not list its covariates, coefficient estimate, confidence interval, or analysis population. It would therefore be inappropriate to assume which factors were included or to infer the magnitude of the adjusted effect from its p-value alone.

Why can small outcome groups make estimates uncertain?

In general, estimates from limited samples may vary noticeably from sample to sample. A small study can still produce an informative estimate, but uncertainty and the possibility of an unstable estimate deserve attention. The outcome groups contain 19 and 14 participants, and the confidence interval provides a more direct account of the uncertainty around the primary unadjusted difference than the p-value alone. It cannot, however, resolve issues such as representativeness, missing outcome data, or model assumptions.

What is over-dispersion, and is it established?

In general, over-dispersion means the observed variability is greater than a statistical model assumes. It can make standard errors too small if the model does not account for the extra variability. The primary outcome is analyzed as a continuous scale summarized by means and standard deviations; the registry does not report an over-dispersion assessment or a model diagnostic. It is therefore a general statistical consideration, not a finding about this trial.

How should the secondary test be viewed?

The secondary Anxiety Disorders Interview Schedule outcome is also continuous and is summarized by means and standard deviations. Its unadjusted mean-difference interval includes zero, and its sponsor-reported ANCOVA p-value is .25. In general, testing multiple outcomes can increase the chance of obtaining at least one apparently notable result by chance if no multiplicity strategy is used. The registry does not report whether such a strategy was planned or applied. The secondary result should consequently be treated as supportive or exploratory information rather than as a stand-alone confirmation of the primary comparison.

All statistical interpretations depend on assumptions and analysis decisions. The record does not report residual checks, missing-data methods, a detailed analysis plan, or the prespecified status of each analysis. General statistical concepts help explain what the posted summaries mean, but they cannot fill in those unreported trial-specific details.

11. Confidence Intervals and Precision

For the primary unadjusted comparison, the estimated wait-list mean is 2.42 units higher than the cognitive-behavioral therapy mean. Its confidence interval extends from 0.405 to 4.435. The interval is wholly above zero, so the simple unadjusted estimate is compatible with a positive difference across the interval's range. It also spans values that differ materially in size, which is a reminder that the estimate is not exact. The interval is more informative about uncertainty in the estimated difference than the p-value alone.

The interval describes uncertainty under the calculation and its assumptions. It is not a range containing every participant's outcome, and it does not show how much individual participants changed. It also does not represent the confidence interval from ANCOVA. The registry reports the ANCOVA p-value but not its adjusted estimate or interval, so precision for the sponsor's model-based contrast cannot be assessed from the record.

The secondary outcome's unadjusted confidence interval crosses zero. That range is compatible with no mean difference as well as differences in either direction, so it gives less precise evidence about the direction of the group contrast. This distinction is about uncertainty in an estimate, not whether the secondary measure is useful or whether its result changes the primary endpoint.

Both endpoints have outcome-group counts of 19 and 14. The size and width of an interval depend on the observed spread and the analysis method, not only on sample counts. The record does not report a clinically meaningful threshold for the primary scale, so the interval cannot be classified against a registry-defined threshold of importance. Precision is best read as the degree to which the estimated group difference is constrained by the data, rather than as a judgment about practical significance.

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 are participants per arm, not total events. They are illustrative calculations based on the observed effect, not a report of the study's original sample-size design. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The planning effect is a stated fraction of the observed effect. The original trial's own sample-size assumptions and justification are not reported in the registry record.

The 80% power column gives the number of participants per arm estimated to be needed, under those planning assumptions, for an 80% chance of detecting the specified effect if that effect were the true one. The 90% power column gives the corresponding number per arm for a 90% chance. These are design-planning quantities, not descriptions of the participants actually enrolled. The figures are shown for planning at 100%, 75%, and 50% of the observed effect. A smaller target effect requires more participants to distinguish it from random variation with the same power and significance level.

The calculations use the observed effect as their starting point, so they are sensitive to how accurately this small study estimated that effect. They should not be treated as a guarantee that a future study of the indicated size would reproduce the observed result. This is not observed power: it is a planning illustration for hypothetical future sample sizes, not a retrospective measure of how persuasive the completed trial's result is. The registry's original planning choices remain unreported.

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 = 2.420; pooled standard deviation σ = 3.016.
2. n = 2 × (1.96 + 0.842)² × 3.016² / 2.420² = 24.4, rounded up to 25 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 <- 2.42                      # observed difference in means
sigma <- 3.01555964955098                     # 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(1177969)
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 = 25 (80% power), 33 (90% power)
 75% of observed effect: n per arm = 44 (80% power), 59 (90% power)
 50% of observed effect: n per arm = 98 (80% power), 131 (90% power)
power.t.test: 25.4 
Simulated power at n = 25 per arm: 0.792 (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. Analyses Reported by the Sponsor

The registry reports a sponsor analysis using ANCOVA for the primary comparison, with p = .04. It does not report the adjusted mean difference, its confidence interval, or the covariates used in the model. As a result, the direction and magnitude of the adjusted estimate cannot be reconstructed from that p-value alone.

The simple re-calculation from the posted means and standard deviations gives an unadjusted mean difference of 2.42 units, a confidence interval from 0.405 to 4.435, and p = 0.019. This calculation does not adjust for covariates. It is therefore not an attempted reproduction of the ANCOVA, and the difference between the p-values should not automatically be treated as a contradiction. The methods answer related but distinct questions and can yield different uncertainty estimates.

The posted ANCOVA result is the registry's own analysis and should be read as such. Without model details, it is not possible to assess the effect of adjustment or independently verify the reported p-value. The re-calculation is useful as a transparent description of the group summaries, but it does not replace the sponsor's model-based analysis or establish which analysis was prespecified.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists a primary measure and a secondary measure, but a multiplicity strategy is not reported in the registry record. When several outcomes or analyses are tested, the chance of at least one apparently notable result can increase. In general, a prespecified hierarchy or an adjustment for multiple testing can address that concern, but neither should be presumed for this trial. The reported primary result should be distinguished from the less confirmatory secondary evidence, without claiming that a particular correction was or was not performed.

The record does not report how missing data were handled, whether outcomes were imputed, or whether analysis used complete cases. It also does not specify the analysis population, such as whether the reported groups include all randomized participants or only those with a post-treatment measurement. The recorded outcome counts are 19 and 14, but those numbers alone do not identify the number randomized to each group or explain any exclusions. Reasons for missingness and their possible relationship to outcomes are likewise not reported.

The registry names ANCOVA for both reported analyses but does not state its covariates, model specification, diagnostic checks, or whether baseline scores were incorporated. It does not report whether analysis followed an intention-to-treat principle, how deviations from assigned treatment were handled, or whether any sensitivity analyses were conducted. The original statistical plan and interim-analysis approach are not reported in the registry record.

These are reporting gaps, not evidence that a particular method was omitted or that a bias necessarily occurred. They limit independent assessment of how robust the estimates are to missing outcomes, analysis choices, and multiple testing. The posted findings can still be described accurately, but stronger conclusions about the full prespecified analysis strategy are not supported by the record.

16. 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 5% reporting threshold.

The registry records zero serious adverse events among 19 participants at risk in the cognitive-behavioral therapy group and among 14 at risk in the wait-list group. These are the serious-event figures posted for the two groups. The registry does not list serious adverse event terms.

These counts describe what is recorded for serious adverse events; they do not establish that no adverse experiences of any kind occurred. Other adverse events are also recorded as zero among the stated at-risk groups, but the record does not provide event descriptions. Death counts are not reported in the registry record. The outcome-group counts and safety at-risk counts should not be assumed to answer questions about all possible safety monitoring or follow-up.

With limited group sizes, a zero count does not demonstrate that an event is impossible or provide a precise estimate of rare-event risk. It is a description of the registry's reported event counts, not a guarantee of safety and not medical advice. The record does not report further detail about collection procedures, severity definitions, or the duration of safety follow-up beyond the information associated with the study.

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

The results describe a randomized comparison of adapted cognitive-behavioral therapy with a wait-list among adolescents with autism and anxiety. On the primary clinician-rated anxiety measure, the posted group means favor a lower average score in the therapy group, and the unadjusted interval for the mean difference is above zero. The registry's ANCOVA analysis also reports a p-value below 0.05. Together, these are evidence of a group difference in this study under the reported analyses.

That evidence does not establish that the therapy caused the entire observed difference, that every participant benefited, or that the estimated difference is clinically important. The registry does not report a clinically meaningful threshold, the adjusted ANCOVA estimate, or enough model detail to evaluate adjustment. The secondary measure is more uncertain and does not provide an equally clear contrast. Results on one measure should not be generalized to every aspect of anxiety or functioning.

The study enrolled 33 participants, with 19 and 14 in the primary outcome groups. A result from this scale and this population may not generalize to other ages, settings, or groups not represented in the record. The registry's description centers on adolescents with autism spectrum disorders and comorbid anxiety, but it does not provide enough detail to characterize all participant characteristics or eligibility limits.

The findings are not a substitute for individual clinical assessment and do not provide medical advice. They are a statistical account of outcomes posted for this trial. Missing-data procedures, multiplicity handling, and several features of the analysis plan are not reported in the registry record. Those gaps, along with the limited group sizes and incomplete reporting of the adjusted estimate, should temper claims beyond the observed group comparison.

18. Why This Trial Matters Statistically

This trial is statistically interesting because it compares an intervention adapted for adolescents with autism against a wait-list and reports both a clinician-rated primary outcome and a secondary anxiety measure. The outcome is continuous, so the posted summaries allow readers to consider means, variability, an estimated mean difference, and its confidence interval rather than relying only on a binary outcome or a significance label.

The trial also illustrates why statistical interpretation benefits from separating an unadjusted comparison from an adjusted analysis. The posted means yield a straightforward re-calculation, while the registry reports an ANCOVA p-value without the adjusted estimate or its model details. These analyses are not interchangeable. Reporting the model estimate and uncertainty would make the adjusted result easier to interpret and assess.

The contrast between the primary and secondary results is another useful lesson. A clear signal on one measure does not mean every related endpoint will show the same pattern. Multiple outcomes, uncertainty, and the distinction between statistical evidence and practical importance all matter. The record does not report a multiplicity strategy or a threshold for clinical importance, so conclusions should remain proportionate to what is documented.

Finally, the sample-size illustrations show how planning depends on the effect a future study aims to detect: smaller effects require larger groups under the same assumptions. Because those illustrations begin with an observed effect from a small study, they are planning examples rather than a replacement for prospective design work. The original sample-size justification is not reported, emphasizing the difference between a post hoc planning illustration and the trial's own design rationale.

19. 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 trial's recorded enrollment is 33, and the primary outcome groups contain 19 and 14 participants. These counts limit the amount of information available for estimating a group difference and make precision particularly important. The confidence interval describes uncertainty in the unadjusted estimate, but it cannot address whether the sample represents the broader population of adolescents with autism and anxiety.

The registry gives limited information about participant characteristics, eligibility criteria, treatment adherence, and follow-up beyond the outcome timeframe. It does not identify who was masked despite recording single masking. The ANCOVA model's covariates and adjusted estimate are not reported, restricting assessment of the sponsor's analysis. The original sample-size justification and prespecified analysis plan are also not reported.

Missing-data methods, analysis-population definitions, and any sensitivity analyses are not reported in the registry record. The number of outcome observations therefore cannot explain whether any randomized participants lacked measurements or how such cases were handled. A multiplicity strategy is also not reported, which matters when interpreting more than one outcome.

The wait-list comparison does not provide a comparison with another active treatment. The registry describes the wait-list as receiving no active treatment during 16 weeks; it does not give further details about contact or other care during that time. The outcome records focus on post-treatment scores, so the longer-term durability of any difference is not established by these results. Finally, the record does not provide a clinically meaningful threshold for the primary scale. These limitations constrain interpretation but do not by themselves invalidate the posted findings.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Cognitive Behavioral Therapy (CBT) for Anxiety Disorders in Autism: Adapting Treatment for Adolescents — NCT01177969.
• Registry record last updated 2014-07-01; status last verified 2014-06.
• Results first posted 2014-07-01.
• 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.

23. Record Summary

NCT01177969 is a completed randomized, single-masked, parallel-group Phase 1/Phase 2 study sponsored by the University of South Florida. It enrolled 33 participants and compared adapted cognitive-behavioral therapy with a wait-list for adolescents with autism and comorbid anxiety. The intervention was described as 16 weekly child-and-parent sessions of about 90 minutes each; the wait-list period was 16 weeks.

The primary outcome was the Pediatric Anxiety Rating Scale at post-treatment, an average of 16 weeks after baseline. The posted means were 11.62 for cognitive-behavioral therapy and 14.04 for wait-list. The unadjusted re-calculation indicates a mean difference of 2.42 units, with an interval from 0.405 to 4.435; the registry reports ANCOVA p = .04. The secondary outcome is less conclusive. Serious adverse event counts are recorded as zero in both groups, while death counts are not reported in the registry record.

Detailed analysis-plan, missing-data, multiplicity, and model information are not reported in the registry record. The findings describe the posted outcomes and should be interpreted with those limitations in mind.