Development of a Resiliency Training Program for Parents of Children With Autism Spectrum Disorder: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Development of a Resiliency Training Program for Parents of Children With Autism Spectrum Disorder (NCT02995408), a randomized na study. The primary outcome is Distress.

2. Clinical Question

The study had developmental aims as well as a pilot comparison. Its first phase used focus group interviews to identify parents’ concerns, unmet support and resource needs, and areas where education or skill training might be useful; it also sought feedback on the 3RP. The later phase aimed to develop and assess the feasibility and acceptability of the virtual program and to test it in a pilot wait-list control trial. The registry repeats the label “Phase II” for these later aims.

The comparison therefore addresses a specific statistical question: how the groups’ posted distress outcome differs over the stated assessment period. It does not, by itself, describe every aspect of the program’s feasibility, acceptability, or development. Those findings are not reported in the registry record.

3. Trial Design

The registry describes a randomized, parallel-group study with no masking. The study is marked completed, and its enrollment is 64. Its listed phase is NA. The registry identifies Massachusetts General Hospital as the sponsor and lists Stress as the condition.

Two groups are described: an experimental 3RP treatment group and a wait-list control group. The experimental intervention was adapted for parents of children with ASD and included relaxation response elicitation, stress awareness, and adaptive strategies. It was intended to be virtual and to consist of 8 sessions over 8 weeks. The wait-list group’s description says that it participated in the program starting 3 months later. Further detail about how the groups were assigned, how the intervention was delivered in practice, or how adherence was assessed is not reported in the registry record.

The recorded study start is 2016-12, and the recorded primary completion is 2018-06. The primary outcome is distress, assessed with a single-item scale. Its specified timeframe is change between baseline at week 0 and post intervention at week 12. The posted group summaries give an analyzed sample size of 20 for the experimental group and 22 for the wait-list group. These are the group sizes for the posted outcome summaries; the registry does not explain how they relate to the enrollment figure or why participants are not represented in those summaries.

The registry describes both program development and a pilot comparison. It does not report the original design assumptions for the randomized trial, a sample-size justification, or the target number of participants for the endpoint analysis. It also does not state whether the trial was intended to provide a definitive efficacy estimate. The study’s stated pilot and development aims are important context when interpreting the size and precision of the posted comparison.

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

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: Note 13 individuals were randomized but never completed the baseline survey or any intervention. (7 immediate and 6 waitlist)

6. Primary Endpoint

The registry lists the primary outcome as Distress, measured over change between baseline (week 0) to post intervention (week 12).

The primary endpoint is distress measured using the Visual Analogue Scale-Distress. It is a one-item scale asking respondents to rate their distress from 0 to 10; higher scores indicate more distress. The registry defines the primary outcome as a mean and specifies its timeframe as change between baseline at week 0 and post intervention at week 12.

A brief self-rating can capture a participant’s own assessment of distress directly, which is relevant to a program designed around parents’ psychosocial needs. A continuous score also allows a group mean and a difference in means to be reported. These statistics describe average values; they do not show how every participant responded or whether participants’ experiences were alike.

The scale’s range and direction help interpret the sign of the posted values: a lower score represents less reported distress on this measure. The experimental group’s posted mean is -1.35 and the wait-list group’s is -0.36. These are the values reported for the endpoint; the registry does not provide additional information about the scale’s validation, measurement properties, or a threshold for an important change.

There is a wording distinction to keep in mind. The endpoint description refers to change from baseline, while the sponsor’s analysis is labeled “Mean Difference (Final Values).” The registry does not explain how those labels relate to one another. The posted comparison can be described as a difference in means, but the record does not fully clarify whether the sponsor’s contrast is based on change scores or final values.

7. Results Posted in the Registry

• Experimental: 3RP Treatment: mean -1.35 versus -0.36 on control; difference -0.99 (95% CI -2.57 to 0.59), standardized effect d = -0.38; z-test p = 0.221.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry’s reported analysis is a two-sided t-test comparing the experimental and wait-list groups. A t-test evaluates whether the observed difference in group means is large relative to the variability and uncertainty in those means, under the test’s assumptions. “Two-sided” means that differences in either direction are considered, rather than testing only for a difference favoring one group.

What does a mean difference describe?

A mean difference is the experimental-group mean minus the comparator-group mean. The posted means are -1.35 for the experimental group and -0.36 for the wait-list group, and the recalculated contrast is -0.99. Because higher values on the distress scale indicate more distress, a negative value means the experimental group’s posted average is lower. This arithmetic describes the contrast; it does not establish why the groups differ.

The registry’s primary endpoint is described as change between baseline and week 12. However, the sponsor’s analysis is labeled “Mean Difference (Final Values).” A difference in final values and a difference in changes are distinct estimands: the former compares group values at the final assessment, while the latter compares how much the groups changed from baseline. The registry does not explain whether the reported analysis used change scores, final values, or another approach. That uncertainty in the endpoint-to-analysis description limits how specifically the estimate can be interpreted.

How should the p-value be read?

The recalculated unadjusted p-value is 0.221, and the sponsor’s posted analysis reports p = .23. In general, a p-value measures how unusual results at least as incompatible with a null model as the observed result would be if that model and the test assumptions held. It is not the probability that the null model is true, and it does not measure the size or practical importance of a difference. A p-value above a chosen threshold is not proof of equivalence or proof that there is no effect.

The sponsor describes its analysis as a two-sided t-test and reports a 95% confidence interval. The recalculated comparison uses the posted group means, standard deviations, and sample sizes as an unadjusted summary-statistic analysis. It is not an adjustment for baseline values, covariates, or other features of the study. The registry does not report whether the sponsor’s analysis used adjustment, how the analysis population was selected, or how incomplete outcome data were handled.

Why does variability matter?

The standard deviation describes how spread out individual measurements are around a group mean. The posted standard deviations are 2.5 and 2.74. In general, greater within-group variability makes a mean difference harder to estimate precisely when sample sizes stay the same. It increases uncertainty in the average contrast and can widen a confidence interval. A group mean and standard deviation do not reveal the distribution’s shape or whether unusual observations influenced the summary.

In general, over-dispersion means that observed variability is greater than a statistical model assumes. If a model underestimates variability, its standard errors may be too small and its intervals too narrow. The posted endpoint is continuous and the sponsor reports a t-test; the registry does not report an over-dispersion assessment or a separate model for over-dispersion. This general concept should not be taken to mean that over-dispersion was found in this trial.

What do the reported estimate and recalculation contribute?

The sponsor’s posted estimate is -0.99, with a 95% confidence interval from -2.63 to 0.65 and p = .23. The unadjusted recalculation also gives a mean difference of -0.99 and p = 0.221. Its interval is not identical to the sponsor’s posted interval. The record marks the discrepancy indicator as false; the sponsor analysis therefore does not take precedence under the stated discrepancy convention. Both accounts point to substantial uncertainty, and the sponsor’s result remains the registry’s own reported analysis.

Recalculation from summary statistics is useful for checking or contextualizing a posted contrast, but it cannot reproduce an analysis that depends on participant-level data, adjustments, or modeling choices absent from the record. It should not be treated as a replacement for the sponsor’s analysis. Neither version supplies information about individual trajectories, baseline balance, or reasons for missing endpoint observations.

Finally, the study’s randomized parallel structure identifies the intended comparison between assigned groups, but the registry does not report enough about implementation and analysis details to assess all assumptions. Allocation concealment, adherence, analysis population, missing-data methods, and any prespecified covariate adjustment are not reported in the registry record. The methods should therefore be understood at the level documented: a reported two-sided t-test and a separate unadjusted recalculation from the posted summaries.

10. Confidence Intervals and Precision

A confidence interval describes a range of values compatible with the data and the method used to calculate it. In general, a 95% confidence procedure would cover the true value in 95% of repeated studies conducted under the same conditions and assumptions. It is not a statement that there is a 95% probability that this particular interval contains the true effect.

The sponsor reports a mean difference of -0.99, with a 95% confidence interval from -2.63 to 0.65. The interval crosses zero, so it includes both a negative contrast and a positive contrast as well as no difference. On the distress scale, that means the posted data do not estimate the direction and size of the group difference precisely. The point estimate alone is not an adequate summary of that uncertainty.

The recalculated unadjusted interval also includes zero. Its endpoints are not identical to the sponsor’s reported endpoints, but the overall interpretation is similar: the plausible values span both directions. The record does not identify a reason for the difference in interval calculation, and the discrepancy indicator is false. The sponsor’s analysis is the registry’s own reported result; the recalculation is a simple unadjusted analysis of summary statistics.

Precision depends on the amount of information available and on variability. The endpoint analysis includes 20 experimental participants and 22 wait-list participants, with standard deviations of 2.5 and 2.74. The interval’s breadth is consistent with an estimate that leaves substantial uncertainty. The registry does not report a clinical or practical threshold for interpreting differences on this scale, so the interval cannot be classified against such a threshold from the posted record.

Confidence intervals do not address every source of uncertainty. They do not account for unreported choices about missing data, the analysis population, or the distinction between change and final values. The interval is best read as precision for the reported comparison under its analysis assumptions, rather than as a complete measure of uncertainty about all aspects of the program.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The sample-size figures are planning illustrations based on the observed effect, not the trial’s original design calculations. They give participants per arm, not total participants or total events. The registry’s planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each row considers an effect equal to the stated fraction of the observed effect.

The 80% power column gives the number of participants per arm that the illustration estimates would be needed to have an 80% chance of detecting the specified effect under those assumptions, if that effect were the true one. The 90% power column uses a higher target chance of detection and therefore gives a larger planning requirement for the same effect. These are design-planning quantities, not descriptions of what happened in this trial.

The illustration lists 111 participants per arm for 80% power and 149 per arm for 90% power when planning for 100% of the observed effect. For 75% of the observed effect, it lists 197 per arm for 80% power and 264 per arm for 90% power. For 50% of the observed effect, it lists 443 per arm for 80% power and 593 per arm for 90% power. Smaller effects require more participants to detect under the same assumptions, because they are harder to distinguish from random variation.

These figures are not observed power. They do not describe the achieved power of the completed trial, and they should not be read as a recommendation for a future study without considering its objectives and design. The registry does not report the original sample-size justification or the assumptions used when planning this trial. The illustrations are anchored to the observed effect, which is uncertain in this pilot comparison; they should therefore be treated as examples of how sample requirements change with the effect targeted.

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 = -0.990; pooled standard deviation σ = 2.629.
2. n = 2 × (1.96 + 0.842)² × 2.629² / -0.990² = 110.7, rounded up to 111 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- -0.99                      # observed difference in means
sigma <- 2.62873353537402                     # 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(2995408)
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 = 111 (80% power), 149 (90% power)
 75% of observed effect: n per arm = 197 (80% power), 264 (90% power)
 50% of observed effect: n per arm = 443 (80% power), 593 (90% power)
power.t.test: 111.6 
Simulated power at n = 111 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.

13. Analyses Reported by the Sponsor

The sponsor’s posted analysis is a two-sided t-test for the mean difference in final values. It reports an estimate of -0.99, a 95% confidence interval from -2.63 to 0.65, and p = .23. The recalculated unadjusted analysis, based on the posted group summary statistics, gives the same mean difference of -0.99 and a p-value of 0.221. Its confidence interval is not identical to the sponsor’s interval.

The record marks the discrepancy indicator as false. Accordingly, the sponsor’s analysis is not displaced by the recalculation under the stated convention. The recalculation is a simple, unadjusted check using summary statistics; it cannot reproduce unreported participant-level choices or adjustments. The sponsor’s analysis remains the reported trial analysis, while the recalculation provides a separate view of the contrast from the posted means, standard deviations, and group sizes.

Both analyses indicate considerable uncertainty: the sponsor’s interval includes zero, and the recalculated interval does as well. The p-values are close, but neither should be interpreted in isolation as establishing whether the difference is important. The registry’s outcome description refers to change from baseline, whereas the sponsor’s analysis label refers to final values. The record does not clarify this distinction or provide further detail about the sponsor’s analysis population and missing-data handling.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists three outcome measures, but no secondary outcome results are posted. The registry record therefore does not allow a reader to assess the other listed measures or determine how their results relate to the distress comparison. The details of those measures and their analysis results are not reported in the registry record.

When several outcomes or comparisons are tested, the chance of at least one apparently unusual result can increase. In general, multiplicity methods are used to address that issue, depending on the study’s aims and analysis plan. The registry does not report whether any adjustment for multiple outcomes or analyses was planned or performed, nor does it describe a hierarchy among outcomes beyond identifying distress as primary. The reported p-value is therefore discussed as posted; the record does not establish whether it was adjusted for multiplicity.

The registry lists three analyses overall, while the posted primary comparison is described as a two-sided t-test. Details of the other analyses are not reported in the registry record. The study’s protocol, prespecified statistical analysis plan, interim analyses, and any rules for selecting among analyses are also not reported in the registry record. No assumptions about those procedures can be made from the posted information.

The record does not describe how missing outcome values were handled, whether all randomized participants were included in the analysis, or whether the analysis followed an intention-to-treat or other population definition. The posted endpoint summaries include 20 participants in the experimental group and 22 in the wait-list group, while overall enrollment is 64. The registry does not explain the difference between those counts or identify the reasons for it. The adverse-event risk sets have other group counts, but those do not establish which participants contributed to the distress analysis.

These omissions matter because missingness and analysis-population choices can affect both the estimate and its uncertainty. Without participant flow, reasons for missing assessments, or the stated analysis strategy, it is not possible to determine from the registry record whether the posted comparison represents all randomized participants or how sensitive it is to incomplete data.

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 events for 0 of 25 participants at risk in the experimental group and 0 of 26 participants at risk in the wait-list control group. It also reports 0 other adverse events in each group, with 25 and 26 participants at risk, respectively. No deaths are reported in either group, and no serious-event terms are listed.

These are event counts and risk-set sizes as reported in the registry. Zero reported events means that no events of the listed types were recorded in those groups in this record; it does not establish that the risk is zero or that no unreported events occurred. The registry does not provide further detail about how adverse events were defined, collected, or monitored.

The adverse-event risk-set counts differ from the endpoint-analysis group sizes of 20 and 22. The record does not explain this distinction, so the safety counts should not be substituted for the distress outcome denominators or treated as proof that the same participants contributed to both summaries. These figures describe reported safety events and do not resolve the uncertainty in the primary outcome comparison.

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

The posted distress means are lower in the experimental group than in the wait-list group, and the unadjusted estimated mean difference is -0.99. The scale is oriented so that higher scores indicate more distress. This is the direction of the observed contrast, but the confidence interval is broad and includes zero. The data therefore do not provide a precise estimate of the direction or size of the group difference.

The sponsor reports p = .23, while the recalculated unadjusted p-value is 0.221. These values do not establish that the groups are identical, and they do not show that a difference is absent. They indicate that the reported comparison does not provide strong statistical evidence against a null difference under the stated test. Statistical evidence and practical importance are separate questions; the registry gives no threshold for a meaningful change on this scale.

The study also had aims related to program development, feasibility, and acceptability. The posted distress comparison alone does not answer those questions. Feasibility and acceptability results are not reported in the registry record. Nor do the results establish what the program would do in a different population, setting, or delivery format.

The randomized, parallel design describes an intended group comparison, but the registry does not provide details on allocation procedures, adherence, missing-data handling, or the analysis population. No masking was listed. In addition, the outcome is described as change from baseline while the sponsor’s test is labeled as a comparison of final values. These limitations make it important to avoid treating the estimate as an unambiguous causal effect.

The most direct reading is that the posted group averages differ by -0.99, with considerable uncertainty in the sponsor’s interval. The finding should not be extended beyond the distress measure and the recorded comparison, and it should not be framed as proving benefit, lack of benefit, or equivalence. Further detail about the analysis and the developmental aims is not reported in the registry record.

17. Why This Trial Matters Statistically

This trial is statistically informative because it illustrates the difference between an observed point estimate and the precision of that estimate. The experimental group’s posted distress mean is lower, and the estimated mean difference is -0.99. Yet the sponsor’s 95% confidence interval ranges from -2.63 to 0.65. A directional point estimate alone would hide how broadly the underlying difference remains uncertain.

The study also illustrates why a pilot comparison should be read in the context of its aims. The registry describes development of a program and assessment of feasibility and acceptability, as well as a pilot wait-list comparison. It does not report a definitive sample-size justification for the trial. Planning illustrations based on the observed effect show how sample requirements increase when targeting smaller effects, but they cannot turn the pilot estimate into a precise one.

Another statistical lesson is the importance of clear outcome and analysis definitions. The registry’s primary endpoint refers to change from baseline, while the sponsor’s analysis label refers to final values. Those descriptions may represent different ways to compare groups, and the record does not explain their relationship. A reader needs the estimand and analysis method to understand exactly what a reported contrast represents.

Finally, the registry record leaves important analysis details unresolved: missing-data procedures, analysis populations, multiplicity handling, and results for secondary outcomes are not reported. Recognizing these absences is part of interpreting the evidence responsibly. The study’s posted result is a useful description of one pilot comparison, but uncertainty and incomplete reporting constrain broader conclusions.

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 endpoint analysis includes 20 participants in the experimental group and 22 in the wait-list control group, compared with overall enrollment of 64. The registry does not explain how these counts relate or why the endpoint summaries include fewer participants. Reasons for missing outcome assessments and their handling are not reported in the registry record.

The primary outcome is described as change from baseline at week 0 to post intervention at week 12, but the sponsor’s analysis is labeled “Mean Difference (Final Values).” The relationship between the outcome definition and the reported analysis is not explained. The record also does not describe baseline group values or any adjustment for baseline distress.

The registry lists no masking. It does not provide details on allocation concealment, adherence to the virtual sessions, intervention completion, or the support received by the wait-list group before it began the program. These details are not reported in the registry record and should not be inferred from the group descriptions.

The distress outcome is a one-item 0-to-10 scale. The registry does not report further information about its measurement properties, the distribution of scores, or a threshold for a meaningful change. The posted group means and standard deviations cannot show individual response patterns.

Only the primary distress comparison is available in detail; secondary results are not posted. The protocol, original sample-size justification, missing-data strategy, analysis-population definition, and multiplicity approach are also not reported in the registry record. These limitations restrict assessment of robustness and the range of conclusions that can be drawn from the posted comparison.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Development of a Resiliency Training Program for Parents of Children With Autism Spectrum Disorder — NCT02995408.
• Registry record last updated 2024-03-12; status last verified 2024-03.
• Results first posted 2024-03-12.
• 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

NCT02995408 is a completed randomized, parallel-group study with no masking, sponsored by Massachusetts General Hospital. It enrolled 64 participants and compared an adapted virtual Relaxation Response Resiliency Program for parents of children with ASD with a wait-list control group. The registry lists the study phase as NA and the condition as Stress.

The primary outcome was distress on a single-item 0-to-10 scale, with higher scores indicating more distress. The registry describes change from week 0 to week 12. Posted endpoint summaries include 20 experimental participants and 22 wait-list participants. The recalculated unadjusted mean difference is -0.99, with p = 0.221; the sponsor reports -0.99, a 95% confidence interval from -2.63 to 0.65, and p = .23.

The estimate is uncertain, and the interval includes zero. Secondary results, the original sample-size justification, missing-data handling, and analysis-population details are not reported in the registry record.