An Evaluation of Low Level Laser Light Therapy for Autistic Disorder: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for An Evaluation of Low Level Laser Light Therapy for Autistic Disorder (NCT03379662), a randomized na study. The primary outcome is Mean Change From Baseline to Study Endpoint in the Aberrant Behavior Checklist (ABC) Irritability & Agitation Subscale Score..

2. Clinical Question

3. Trial Design

The registry describes a randomized, parallel-group, quadruple-masked evaluation of Erchonia HLS Laser against Placebo Laser. It lists the phase as NA and the status as completed. Erchonia Corporation is named as the sponsor. The record lists enrollment of 40 and reports arm counts of 21 for Erchonia HLS Laser and 19 for Placebo Laser. The dates recorded for study start and primary completion are 2017-07-02 and 2017-10-28.

Both devices were administered 8 times across 4 weeks, for 5 minutes at each session, to the skull at the base of the brain and temporal areas. The record describes the placebo device as the comparator but does not report further details about how it was designed or how similarity between devices was maintained. It labels masking as quadruple; which roles were masked and how masking was assessed are not reported in the registry record.

The primary outcome was mean change from baseline to the 4-week study endpoint in the Aberrant Behavior Checklist (ABC) Irritability Subscale score. The posted outcome is a continuous measure summarized by a mean and standard deviation. The registry record lists one outcome measure and no posted analyses. Details of allocation implementation, analysis populations, missing-data procedures, or the trial’s statistical analysis plan are not reported in the registry record.

4. Participant Flow and Accounting

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

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.

6. Primary Endpoint

The registry lists the primary outcome as Mean Change From Baseline to Study Endpoint in the Aberrant Behavior Checklist (ABC) Irritability & Agitation Subscale Score., measured over Baseline and 4 weeks (Study Endpoint).

The primary endpoint is mean change from baseline to the 4-week study endpoint in the ABC Irritability Subscale score. The subscale contains 15 items addressing aggression, self-injury, tantrums, agitation, and unstable mood in individuals with developmental disorders. Each item is rated from 0, meaning not at all a problem, to 3, meaning the problem is severe in degree. Item scores are summed to a total score from 0 to 45, with higher scores indicating greater severity.

The endpoint is used to represent change in the specific set of behaviors covered by the subscale over the intervention period. A negative change means the score decreased from baseline and is defined in the record as positive for improvement; a positive change means the score increased and is defined as negative for improvement. The registry’s stated criterion for study success is detection of a minimum mean difference of -8.5 points between the test and placebo groups in change in the subscale score.

This endpoint is a score-based measure, not a count of events. The record does not report individual item results or other measures of change that would clarify how the total score changed across its component behaviors.

7. Results Posted in the Registry

• Erchonia HLS Laser: mean -14.81 versus 0.37 on control; difference -15.18 (95% CI -17.99 to -12.37), standardized effect d = -3.20; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: it is a score that can take values across a numerical scale. The registry reports a mean and standard deviation for each arm. The mean gives the group’s average change, while the standard deviation describes how spread out the participant-level changes are around that average. General explanation: these summaries make it possible to describe the overall direction and variability of changes, but they do not show the shape of the underlying observations.

What does the mean difference represent?

The comparison is the Erchonia HLS Laser mean change minus the Placebo Laser mean change. The posted arm means are -14.81 and 0.37, respectively, and the resulting unadjusted difference is -15.18 points. The negative sign follows the subtraction order and the score’s direction: a lower change value in the Erchonia group reflects a greater decrease in the score than the placebo group’s average change. The sign alone does not indicate whether the difference meets every clinical or research criterion; the registry states its own threshold separately.

The comparison is unadjusted. That means it is based on the posted group summaries without a reported adjustment for other variables. The registry record does not report an adjusted estimate or describe covariates used in an analysis. The arm comparison should therefore be interpreted as a summary contrast, not as evidence that any particular adjusted model was used.

What does the p-value say?

The posted unadjusted p-value is <0.001. General explanation: a p-value summarizes how compatible the observed data are with a specified no-difference model, under the assumptions of the test used. A small p-value is not the probability that the no-difference model is true, and it does not measure the size or importance of an effect. The test specification and the sponsor’s analysis are not reported in the registry record, so the p-value is best read as part of the posted unadjusted comparison rather than as a full description of the analysis plan.

Why do dispersion and allocation matter?

Standard deviations describe variation among observations. The posted standard deviations are 6.4 for Erchonia HLS Laser and 1.38 for Placebo Laser. General explanation: variability affects how precisely a group mean and the between-group contrast can be estimated; greater spread generally makes it harder to distinguish a mean from the variation around it when other features are held constant. The group summaries do not show whether values are symmetric, clustered, or influenced by individual observations.

The registry labels the design randomized and parallel. Random allocation is intended, in general, to reduce systematic differences between groups at the start of a trial. It does not guarantee that groups will be alike in every characteristic, especially in a trial with limited enrollment. The record does not report the randomization sequence, allocation concealment procedures, or baseline characteristics, so their implementation and balance cannot be assessed from the registry summaries.

What does the confidence interval add?

The 95% confidence interval for the unadjusted mean difference is -17.99 to -12.37. General explanation: a confidence interval gives a range of values compatible with the observed data under the calculation’s assumptions and expresses estimation uncertainty. It is not a range containing 95% of individual outcomes, nor does it account for every possible source of bias or uncertainty. The interval’s width depends on factors such as the variability in the observations and the amount of information available.

For a continuous measure, a comparison of means ordinarily relies on assumptions about how the estimate’s uncertainty is calculated. The posted summaries include a pooled standard deviation of 4.739, and the comparison includes standard errors of 0.317 and 1.397 for the placebo and Erchonia groups, respectively. These are part of the recalculated unadjusted comparison; they do not identify the sponsor’s analysis method. The registry record does not report the test procedure or a statistical analysis plan.

Why can over-dispersion matter?

General explanation: over-dispersion occurs when observed variation is greater than a statistical model allows. If a model underestimates variation, standard errors can be too small and intervals too narrow, making results appear more precise than they are. Over-dispersion is particularly relevant to models for counts or other outcomes whose variance is modeled directly. This primary endpoint is a continuous score, and the registry record does not report an over-dispersion assessment or a model-based analysis. The differing arm standard deviations are a feature of the posted summaries, but by themselves they do not establish over-dispersion.

The comparison also reports a standardized effect size, d = -3.203. General explanation: a standardized effect expresses a difference relative to a measure of variability, allowing effects measured on different scales to be described on a common scale. It does not replace the score-unit mean difference, and its interpretation depends on the calculation and context. No adjusted or sponsor-reported effect-size analysis is listed in the registry record.

Because no analyses are posted, the registry does not clarify whether the shown comparison was the prespecified primary analysis, whether any other analyses were performed, or how participants with missing outcome data were handled. No interim-analysis plan, multiplicity procedure, or analysis-population definition is reported in the registry record. Those omissions limit the ability to reconstruct the full analysis process from the posted summaries.

10. Confidence Intervals and Precision

The unadjusted mean difference is -15.18 points, with a 95% confidence interval from -17.99 to -12.37. The interval gives a measure of precision for the estimated group contrast under the calculation used: values across that range are compatible with the data and its assumptions. Because both interval endpoints are negative, the interval places the estimated difference in the direction of a lower mean change in the Erchonia HLS Laser group than in the Placebo Laser group.

Precision of a group contrast is different from the spread of individual outcomes. The standard deviations are 6.4 for Erchonia HLS Laser and 1.38 for Placebo Laser, describing variability within each arm. The confidence interval instead concerns uncertainty around the difference between group means. Neither statistic tells how much individual participants’ scores changed or how many experienced a particular change.

The p-value is reported as <0.001, but it does not indicate the precision or practical importance of the result on its own. The interval is more informative about the range of estimates compatible with the calculation. Its interpretation remains conditional on the analysis method and assumptions; those details are not reported in the registry record. The interval also does not address possible bias, missing data, or the relevance of the 4-week result beyond the measured endpoint.

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.

For this continuous endpoint, the planning figures mean participants per arm, not total events. The convention for time-to-event outcomes is different: those figures refer to total events. The planning illustration uses a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It uses the observed effect as its reference and considers effects of 100%, 75%, and 50% of that observed effect.

The 80% power column means the illustrative number of participants per arm for a design with an 80% chance of detecting the chosen effect under the stated assumptions, if that effect and those assumptions hold. The 90% power column gives the corresponding planning number for a 90% chance. These are design concepts, not guarantees that a future study will detect an effect. Smaller effects need more participants to detect under otherwise similar assumptions.

At 100% of the observed effect, the illustration lists 2 participants per arm for 80% power and 3 for 90% power. At 75% of the observed effect, it lists 3 per arm for 80% power and 4 for 90% power. At 50% of the observed effect, it lists 7 per arm for 80% power and 9 for 90% power. These figures are planning illustrations computed from the observed effect, not the trial’s own design justification; the trial’s original sample-size assumptions are not reported in the registry record. This is not observed power.

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 = -15.180; pooled standard deviation σ = 4.739.
2. n = 2 × (1.96 + 0.842)² × 4.739² / -15.180² = 1.5, rounded up to 2 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 <- -15.18                      # observed difference in means
sigma <- 4.73919602331117                     # 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(3379662)
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 = 2 (80% power), 3 (90% power)
 75% of observed effect: n per arm = 3 (80% power), 4 (90% power)
 50% of observed effect: n per arm = 7 (80% power), 9 (90% power)
power.t.test: 2.9 
Simulated power at n = 2 per arm: 0.429 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

13. Multiplicity, Missing Data and Analysis Populations

The registry lists one outcome measure and no secondary outcomes posted. It lists no analyses. The primary outcome is mean change from baseline to the 4-week study endpoint in the ABC Irritability Subscale score. The record does not report whether additional outcomes or analyses were planned but not posted, or whether any multiplicity adjustment was considered.

Multiplicity refers, in general, to the consequences of making several statistical comparisons or testing several outcomes. When many questions are examined, the chance of finding at least one apparently unusual result can increase unless the analysis plan accounts for that. The available registry record does not describe a multiplicity strategy, so it is not possible to assess whether the posted p-value was adjusted or how other analyses may have been handled.

Missing-data methods are not reported in the registry record. The record does not say whether all enrolled participants contributed endpoint scores, how missing measurements were treated, or whether a sensitivity analysis was performed. Analysis populations, such as which participants were included in the primary analysis, are also not reported. Although the arm summaries list counts of 21 and 19, the record does not explain the relationship between those counts and any analysis population.

The record does not report interim analyses, stopping rules, or the statistical analysis plan. These details matter because they clarify which analyses were planned, how decisions were made, and how deviations or incomplete measurements were addressed. Without them, interpretation is limited to the reported group summaries and unadjusted comparison rather than a reconstruction of the full statistical process.

14. Safety Results

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

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

The registry reports 0 serious adverse events and 0 other adverse events in the Erchonia HLS Laser group, with 0 deaths. It reports the same figures in the Placebo Laser group. The listed numbers at risk are 21 for Erchonia HLS Laser and 19 for Placebo Laser for both serious and other adverse events.

These figures mean that the registry record reports no affected participants for the listed event categories in either arm. They should not be read as proof that no adverse events occurred outside the definitions, collection procedures, or reporting period used for the record. The registry does not report further detail about event collection, severity grading, relatedness, or the time window used for these counts. Zero reported events also does not establish that the interventions are free of risk.

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

The posted results describe mean changes in an ABC Irritability Subscale score over the period from baseline to the 4-week study endpoint. The Erchonia HLS Laser group’s mean change was -14.81, compared with 0.37 in the Placebo Laser group. The recalculated, unadjusted mean difference was -15.18 points, with a 95% confidence interval of -17.99 to -12.37 and an unadjusted p-value of <0.001. By the score direction specified in the registry, negative change indicates a decrease in measured severity.

The registry’s stated success criterion is a minimum mean difference of -8.5 points. The posted point estimate is beyond that criterion, but interpretation should still account for the confidence interval, the analysis details that are not reported, and the fact that the endpoint is a score over a 4-week period. A score difference does not by itself describe each participant’s experience, and the group average cannot show the full distribution of individual changes.

The record does not report secondary outcomes or analyses, an analysis population, missing-data methods, or the statistical analysis plan. It also does not provide results beyond the 4-week endpoint. The available results therefore do not establish whether the observed score pattern persists over time, how it relates to outcomes not measured by this subscale, or how broadly it applies beyond the trial population.

These statistics describe the registry results; they do not constitute medical advice or a complete assessment of benefits and harms. The safety record lists no serious adverse events, other adverse events, or deaths in either group, but event-collection details are not reported. The posted figures should be understood with these limits rather than as a definitive statement about treatment effects or safety.

16. Why This Trial Matters Statistically

This trial is statistically notable because it reports a randomized, parallel comparison of a device intervention with a placebo device and uses a defined continuous score as its primary outcome. Randomized allocation and masking are design features intended, in general, to support a fair comparison. The registry identifies the trial as quadruple-masked, although which roles were masked and how masking was implemented are not reported.

The outcome has a clear score direction: negative change indicates a reduction in severity, and the record states a minimum mean difference of -8.5 points as its success criterion. The posted group means and unadjusted contrast can therefore be interpreted against a specified benchmark rather than by direction alone. The confidence interval also helps distinguish the point estimate from its estimation uncertainty.

At the same time, statistical interpretation depends on information beyond an effect estimate and p-value. The registry lists no analyses, no secondary outcomes, and does not report the analysis plan, handling of missing measurements, or analysis populations. This leaves important questions about how the posted comparison relates to the planned analysis unanswered. The registry’s concise safety figures also lack details about collection and reporting.

The sample-size illustration is based on the observed effect and is not the original design rationale. Its small planning figures should not be taken as evidence that the original design had those assumptions or that a future study with similar enrollment would reliably reproduce the result. The trial matters statistically because it offers an interpretable primary comparison while also illustrating why transparent reporting of analysis methods, uncertainty, and outcome handling is essential.

17. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The record reports a 4-week primary endpoint but no results beyond that timeframe. It therefore does not show whether the group-level score changes continued, diminished, or changed after the study endpoint. The population description is limited to children and adolescents aged five (5) to seventeen (17) years with autistic disorder; additional eligibility criteria and participant characteristics are not reported in the registry record.

Only one outcome measure is listed, with no secondary outcomes posted and no analyses listed. The registry does not report the statistical analysis plan, the test used for the unadjusted comparison, adjustment for other variables, missing-data procedures, or the analysis populations. It also does not report baseline scores or other baseline characteristics, which limits assessment of group comparability from the posted summaries.

The arm summaries provide means and standard deviations but not individual observations or a fuller description of score distributions. The confidence interval and p-value are presented for an unadjusted comparison, but the registry does not describe the calculation method. Masking is labeled quadruple, yet the masked roles and procedures are not specified. The record also does not describe allocation concealment or the placebo device’s design beyond its administration schedule and location.

Safety reporting gives counts for serious adverse events, other adverse events, and deaths, but does not report event-collection methods, severity, relatedness, or the relevant observation period. These limitations do not negate the posted summaries; they define what can and cannot be inferred from the registry record.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: An Evaluation of Low Level Laser Light Therapy for Autistic Disorder — NCT03379662.
• Registry record last updated 2021-05-27; status last verified 2021-05.
• Results first posted 2021-05-27.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

21. Record Summary

The registry describes a completed randomized, parallel-group, quadruple-masked trial comparing Erchonia HLS Laser with Placebo Laser in children and adolescents with autistic disorder. Both devices were administered 8 times across 4 weeks, for 5 minutes per session. The primary outcome was mean change from baseline to the 4-week endpoint in the ABC Irritability Subscale score.

The posted mean changes were -14.81 for Erchonia HLS Laser and 0.37 for Placebo Laser. The unadjusted mean difference was -15.18, with a 95% confidence interval of -17.99 to -12.37 and an unadjusted p-value of <0.001. The registry lists no analyses and no secondary outcomes. It reports 0 serious adverse events, 0 other adverse events, and 0 deaths in each arm. Details of the statistical analysis plan, missing-data handling, and analysis populations are not reported in the registry record.