Bright Light Therapy for Treatment of Sleep Problems Following Mild Traumatic Brain Injury: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Bright Light Therapy for Treatment of Sleep Problems Following Mild Traumatic Brain Injury (NCT02374918), a randomized na study. The primary outcome is Sleep Quality - Pittsburgh Sleep Quality Index (PSQI).

2. Clinical Question

3. Trial Design

The registry describes NCT02374918 as a completed, randomized, double-masked, parallel-group study sponsored by the University of Arizona. Its title concerns bright light therapy for sleep problems following mild traumatic brain injury. The registry records enrollment of 77 and gives the study start as 2014-12 and primary completion as 2019-09. It does not report the original sample-size justification or detailed design assumptions in the registry record.

Four device interventions are listed: mTBI wavelength-1 bright light, mTBI wavelength-2 bright light, HC wavelength-1 bright light, and HC wavelength-2 bright light. For each mTBI group, the arm description specifies 30 minutes of daily light exposure for 6 weeks. For each HC group, it records 30 minutes of light exposure without specifying a repeated treatment schedule. The wavelength values are not reported in the registry record.

The primary outcome is a continuous PSQI sleep-quality score measured post 6-week intervention. The registry reports results for the two mTBI arms: 18 participants in wavelength-2, with a mean of 1.28 and standard deviation of 0.67; and 17 in wavelength-1, with a mean of 1.35 and standard deviation of 0.7. The PSQI was not administered to the HC arms, so the posted primary-outcome comparison concerns only the two mTBI groups.

The record lists 10 outcome measures and no posted secondary results. It records no statistical analyses in its analysis listing. The detailed masking procedures, randomization implementation, allocation concealment, analysis population definitions, and handling of missing outcome data are not reported in the registry record.

4. Participant Flow and Accounting

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

Before assignment: No pre-assignment criteria were needed after enrollment but before study group assignment for the Effect Localization Arm. For the Treatment Arm, participants went through a screening visit before study group assignment and were excluded based on the inclusion/exclusion criteria.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: The PSQI was not administered to the HC wavelength-2 and HC wavelength-1 arms of this 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 Sleep Quality - Pittsburgh Sleep Quality Index (PSQI), measured over Post 6-week intervention.

The primary endpoint is overall sleep quality measured with the Pittsburgh Sleep Quality Index (PSQI) subscale, assessed post 6-week intervention. The registry description says that this measure is derived from question 6 of the assessment and uses a Likert scale from 0 to 3. A score of 0 represents “very good” sleep quality and is the better outcome; a score of 3 represents “very bad” sleep quality and is the worse outcome. Thus, lower scores indicate better reported sleep quality on this measure.

A mean is a way to describe the average score in a group. The registry reports a mean and standard deviation for each mTBI arm. The standard deviation describes variation in individual scores around the group mean; it is not the uncertainty interval for the difference between group means. The reported measure is a specific self-reported sleep-quality item, not a general measure of all sleep features, cognition, mood, or activity.

The record names these other areas in the study purpose, but it does not post secondary results for them. The PSQI was not administered to the HC wavelength-1 or HC wavelength-2 arms. The available primary outcome therefore supports a comparison of the two mTBI wavelength groups at the stated post-intervention time, rather than a comparison with the HC groups or a change-from-baseline analysis.

7. Results Posted in the Registry

• mTBI Wavelength-1 Bright Light: mean 1.35 versus 1.28 on control; difference 0.07 (95% CI -0.38 to 0.52), standardized effect d = 0.10; z-test p = 0.763.

8. Statistical Interpretation

9. Statistical Methods Explained

What does a group mean describe? A mean is the arithmetic average of recorded outcome scores in a group. For this endpoint, the mean summarizes PSQI overall sleep-quality scores at post 6-week intervention. The registry reports a mean of 1.28 in the mTBI wavelength-2 group and 1.35 in the mTBI wavelength-1 group. Because the score runs from 0 for “very good” to 3 for “very bad,” lower group means correspond to better reported sleep quality on this item. A group mean does not show the full distribution of individual responses or establish that every participant had a score close to the mean.

What does the standard deviation describe? The standard deviation measures how dispersed participant scores are around their group mean. The posted standard deviations are 0.67 for wavelength-2 and 0.7 for wavelength-1. These values describe observed within-group variability. They are not standard errors, confidence limits, or estimates of the treatment contrast. Two groups can have similar means while individual scores vary within each group, and the spread helps convey that distinction.

What is a mean difference? A mean difference subtracts one group’s mean from the other according to a stated direction. The registry reports wavelength-1 relative to wavelength-2, with an estimate of 0.07. A positive value in this direction means the reported wavelength-1 mean was higher. For this scale, higher scores represent worse sleep quality. This direction describes the numerical contrast; it does not by itself establish a causal effect or a reliable population difference. Interpretation depends on the uncertainty around the estimate and the study design and analysis.

What does a confidence interval add? A confidence interval gives a range of values compatible with the observed data under the method’s assumptions. In general, narrower intervals represent greater precision, while wider intervals indicate more uncertainty. The interval for this mean difference includes zero and covers values on either side of zero. Zero corresponds to no difference between the group means. Because the interval includes zero and values in both directions, the result does not precisely identify which group would have a higher mean in the population. A confidence interval is not a range containing a fixed proportion of individual participant scores.

How should the p-value be understood? The posted unadjusted p-value is 0.763. In general, a p-value describes the compatibility of the data with a null model, such as no difference, assuming that model and the test’s assumptions. It is not the probability that the null hypothesis is true, and it does not quantify clinical importance. The label “unadjusted” means the posted value is not reported as adjusted for multiple comparisons. The registry does not report an analysis plan or a multiplicity strategy, so it is not possible to establish from the record whether this was the only planned primary comparison or how other outcomes were intended to be considered.

What is the role of randomization? Random allocation is intended, in general, to make treatment groups comparable on average with respect to factors measured and unmeasured at baseline. The record classifies the study as randomized, double-masked, and parallel-group. Those design labels do not reveal how allocation was generated, concealed, or implemented. Details of those procedures are not reported in the registry record. Nor does the record specify which people were masked or how masking was maintained. The result can therefore be described using the registry’s design classifications, but the operational details cannot be assessed from the record.

What can be inferred from the reported comparison? The posted means and their comparison describe the PSQI endpoint in the two mTBI arms at the stated time. They are not a baseline-adjusted estimate or a within-person change unless the registry explicitly defines them that way; it does not. The registry states the endpoint was measured post 6-week intervention, and no baseline values are posted for this measure. The outcome was not administered to the HC arms, so the primary result is not a four-group comparison. A causal interpretation also depends on the conduct of the randomized design, outcome completeness, and analysis decisions, details that are not fully reported.

What does the absence of posted analysis detail mean? The registry lists no analyses and no posted secondary results, while providing a primary outcome comparison. The original statistical plan, analysis population, treatment of missing observations, and any covariate adjustment are not reported in the registry record. This limits assessment of whether the posted analysis matches the prespecified plan and whether all randomized participants were included. The registry status is completed, but completion does not supply those missing analytical details.

General statistical interpretation distinguishes the size of an observed estimate, its precision, and the strength of evidence against a null model. The mean difference is the estimate; the confidence interval expresses uncertainty; and the p-value is one summary of compatibility with a null model. None alone answers every question about importance or generalizability. For this trial, the registry reports a small numerical difference, a p-value of 0.763, and an interval spanning zero, while key details needed for a fuller audit are not reported in the registry record.

10. Confidence Intervals and Precision

The mean difference is reported as 0.07 for wavelength-1 relative to wavelength-2. Its confidence interval extends below and above zero. In statistical terms, zero is the value corresponding to no difference between the group means, so an interval crossing zero indicates that the data do not precisely distinguish a positive difference from a negative one. The interval is broad enough to allow multiple possible underlying contrasts, including a result near no difference.

A confidence interval is an uncertainty summary for an estimate, calculated under a statistical method and its assumptions. In general, it reflects both the observed data and the amount of information available. It should not be confused with the range of individual participant scores, which is described in part by the group standard deviations. Nor does a confidence interval assign a probability to the true value after the data have been observed.

The registry reports the group standard deviations as 0.67 and 0.7 and the outcome group sizes as 18 and 17. Those summaries indicate that participant scores varied within each arm, while the estimated separation of the group means was small relative to the scale’s 0-to-3 range. The unadjusted p-value is 0.763, consistent with substantial uncertainty about whether the population means differ. The record does not report an adjusted estimate or a separate analysis of precision.

Precision should be distinguished from importance. A narrow interval could estimate even a small contrast precisely, while a wide interval can leave uncertainty about both direction and size. Here, the interval includes zero and values in either direction, so the posted result does not support a precise claim about the population difference. Its interpretation is limited to the reported PSQI outcome and the two mTBI groups at post 6-week intervention.

11. Planning a Similar Trial: Sample Size

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

The planning figures are illustrative calculations based on the observed mean difference, not the trial’s own original design assumptions. The registry record does not report the original sample-size justification. These figures are participants per arm, not total events. The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation; the effect to detect is the stated fraction of the observed effect. The record also distinguishes time-to-event planning tables, which use total events, from other tables, which use participants per arm. This comparison is continuous, so the figures are participants per arm.

The 80% power column gives the planned participants per arm for a hypothetical study designed to have an 80% chance of detecting the chosen effect under the stated assumptions, if that effect is the true one and the model assumptions hold. The 90% power column gives the corresponding planning number for a higher target chance of detection. For 100% of the observed effect, the figures are 1,502 participants per arm for 80% power and 2,011 participants per arm for 90% power. For planning for 75% of the observed effect, the figures are 2,671 and 3,575 participants per arm, respectively. For planning for 50% of the observed effect, they are 6,008 and 8,043 participants per arm.

Smaller effects are harder to distinguish from random variation, so planning to detect a smaller fraction of the observed effect requires more participants under these assumptions. These are planning illustrations, not observed power, and they do not establish what the trial’s original design targeted. The curve should be read in the same planning context: it represents hypothetical sample-size requirements under stated assumptions, not observed trial outcomes.

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 = 0.070; pooled standard deviation σ = 0.685.
2. n = 2 × (1.96 + 0.842)² × 0.685² / 0.070² = 1,501.9, rounded up to 1,502 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 <- 0.0700000000000001                      # observed difference in means
sigma <- 0.684709626577042                     # 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(2374918)
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 = 1,502 (80% power), 2,011 (90% power)
 75% of observed effect: n per arm = 2,671 (80% power), 3,575 (90% power)
 50% of observed effect: n per arm = 6,008 (80% power), 8,043 (90% power)
power.t.test: 1502.9 
Simulated power at n = 1,502 per arm: 0.797 (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 10 outcome measures but posts no secondary results. It records no analyses in its analysis listing, while reporting a primary PSQI comparison. The statistical analysis plan, including whether multiple comparisons were anticipated and how they would be handled, is not reported in the registry record. The posted p-value is explicitly unadjusted, so it should be understood as the value reported for this comparison without a stated multiplicity adjustment. The record does not establish whether other planned tests were conducted or how conclusions were to account for them.

Missing outcome data can affect both the precision and potential validity of a comparison. The primary outcome group sizes are reported as 18 for wavelength-2 and 17 for wavelength-1, while overall enrollment is recorded as 77. The registry does not explain the difference between the enrollment figure and the outcome denominators. It does not report how many randomized participants lacked PSQI data, why any data were unavailable, whether imputation was used, or whether complete-case or another approach was applied. Those details are not reported in the registry record.

The record also does not define the analysis population. It is not stated whether the reported comparison includes all randomized participants, only participants who completed the intervention, or another subset. No intention-to-treat designation, per-protocol definition, or handling of treatment discontinuation is posted. Without those details, readers cannot determine exactly which participants contributed to the result or assess the consequences of missing observations.

The PSQI was not administered to either HC group. This is a design and outcome-availability limitation for this endpoint, rather than an unreported value that can be recovered from the posted mTBI comparison. No primary PSQI comparison against the HC groups can be made from these results. The record does not provide a baseline PSQI result or a change-from-baseline analysis. These gaps limit interpretation of the endpoint comparison and make it important to keep claims tied to the reported groups, measure, and time point.

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 5% reporting threshold.

The registry reports serious adverse event counts of 0 in each listed group. The corresponding numbers reported at risk are 17 for mTBI wavelength-1, 18 for mTBI wavelength-2, 22 for HC wavelength-1, and 20 for HC wavelength-2. The registry also reports 0 other adverse events in each group and 0 deaths in each group. These are the safety figures recorded for the listed groups.

A count of zero reported events means that no events of that category were recorded in the registry results for the stated group and at-risk count. It does not establish that no event could occur, and it does not rule out events that were not captured or reported. The registry does not provide event terms for serious adverse events, because none are listed, or additional detail on ascertainment, follow-up duration, severity grading, or causal attribution. These details are not reported in the registry record.

The safety counts cover all four listed intervention groups, including the HC arms, whereas the PSQI primary outcome was not administered to the HC groups. The safety findings should therefore be kept separate from the sleep-quality comparison. They describe reported adverse-event counts, not comparative estimates of risk or evidence about the primary endpoint.

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

The posted result describes the average PSQI overall sleep-quality score in the two mTBI wavelength groups at post 6-week intervention. The mean was 1.28 in wavelength-2 and 1.35 in wavelength-1, on a scale where lower scores represent better reported sleep quality. The reported difference of 0.07 is numerically small, and its confidence interval includes zero. The unadjusted p-value of 0.763 also does not provide clear evidence of a difference between the group means.

This does not establish that the two wavelength groups are identical. The interval allows values on either side of no difference, and the reported outcome group sizes are limited. A non-significant result is not proof of equivalence or proof that an effect is absent. An equivalence or non-inferiority conclusion would require an appropriate design and a prespecified margin, neither of which is reported in the registry record.

The result is also not a comparison of bright light with no light, usual care, or no intervention. Both mTBI groups received recorded daily light exposure for 6 weeks; the comparison is between the two wavelength-labelled groups. The wavelength values themselves are not reported in the registry record. The result does not address the HC groups for PSQI, because that measure was not administered to them.

The endpoint is a specific overall sleep-quality item derived from question 6 of the PSQI. It does not by itself summarize all aspects of sleep or the study’s other stated interests in cognitive functioning, mood, and activity. The registry does not post secondary results, baseline PSQI scores, or change-from-baseline estimates. Accordingly, the posted comparison cannot establish how scores changed over time or what occurred on other outcomes.

The record supports a cautious description of an uncertain mean difference on one reported measure at one stated time point. It does not establish clinical importance, explain individual responses, or support conclusions beyond the two mTBI groups and endpoint actually reported. Missing-data handling and analysis-population details are not reported in the registry record, further limiting assessment of how broadly the estimate represents the randomized groups.

16. Why This Trial Matters Statistically

This trial illustrates why an estimated effect, its precision, and a test result need to be considered together. The registry reports a mean difference of 0.07, an unadjusted p-value of 0.763, and a confidence interval that includes zero. The estimate conveys the observed direction and size of the contrast; the interval shows that the result remains uncertain; and the p-value summarizes compatibility with a no-difference model under the analysis assumptions. None of these measures alone establishes equivalence or clinical importance.

It also illustrates the value of identifying exactly which population and outcome support a comparison. The registry lists four intervention groups, but the primary PSQI measure was not administered to the HC groups. The reported sleep-quality contrast therefore concerns only the two mTBI bright-light groups. Without this distinction, readers might mistakenly assume the primary outcome includes all listed arms.

The outcome scale’s direction matters: lower scores are better, so the numerical ordering of the means has a clear descriptive interpretation. Yet a descriptive difference does not settle whether the underlying groups differ. The interval crossing zero and the unadjusted p-value indicate that the result is not precise evidence of a group separation. This is a useful example of why a numerical ordering should not be treated as a definitive finding.

Finally, the registry’s missing analysis details matter statistically. The original sample-size justification, analysis population, missing-data approach, and multiplicity strategy are not reported in the registry record. These are not cosmetic details: they affect how readers assess precision, selection, and the context for interpreting a p-value. The posted planning illustrations can inform hypothetical future planning but do not reconstruct the trial’s original design or imply observed power.

17. Limitations

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

Several trial-specific limitations constrain interpretation of the posted primary result. The PSQI was not administered to the HC wavelength-1 or HC wavelength-2 groups. Consequently, the primary outcome cannot be used to compare the mTBI groups with those HC arms. The reported analysis is limited to wavelength-1 versus wavelength-2 among the mTBI groups.

The endpoint is a single overall sleep-quality measure derived from question 6 of the PSQI, scored from 0 to 3. It does not represent every dimension of sleep. Although the brief study summary names cognitive functioning, mood, activity, and sleep as areas of interest, the registry record posts no secondary results. The available result therefore does not describe outcomes in those other domains.

The registry reports outcome group sizes of 18 and 17, but does not explain how these groups relate to the enrollment figure of 77. It does not state the analysis population, the amount or reasons for missing PSQI data, or the method used to address missing values. Baseline PSQI scores and change-from-baseline results are also not posted. This prevents readers from assessing the reported post-intervention means in relation to baseline values or from evaluating the effect of missing observations.

Further details are absent about the original sample-size justification, randomization implementation, masking procedures, analysis plan, and multiplicity approach. The listed interventions identify wavelength groups but do not give the wavelength values. These reporting gaps limit assessment of the protocol and interpretation beyond the specific posted comparison. The limitations do not change the arithmetic description of the reported means, but they narrow what can be concluded from them.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Bright Light Therapy for Treatment of Sleep Problems Following Mild Traumatic Brain Injury — NCT02374918.
• Registry record last updated 2021-06-24; status last verified 2021-06.
• Results first posted 2021-06-24.
• 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

NCT02374918 is a completed, randomized, double-masked, parallel-group study sponsored by the University of Arizona. It concerns bright light therapy for sleep problems following mild traumatic brain injury and records enrollment of 77. The primary outcome is PSQI overall sleep quality, measured post 6-week intervention on a scale from 0 to 3, where lower is better.

The registry reports a mean of 1.28 (standard deviation 0.67) for mTBI wavelength-2 and 1.35 (standard deviation 0.7) for mTBI wavelength-1. The reported mean difference for wavelength-1 relative to wavelength-2 is 0.07, with an unadjusted p-value of 0.763 and a confidence interval that includes zero. The PSQI was not administered to the HC groups.

The registry reports zero serious adverse events, zero other adverse events, and zero deaths in each listed group. It does not post secondary results or analysis details sufficient to assess missing-data handling, the analysis population, or the original design assumptions.