Sleep Length and Circadian Regulation in Humans: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Sleep Length and Circadian Regulation in Humans (NCT00843843), a randomized na study. The primary outcome is Dim Light Melatonin Onset (Hours).

2. Clinical Question

3. Trial Design

This is a completed, randomized, single-masked crossover study sponsored by Rush University Medical Center. The registry lists an enrollment of 16 and gives the study start as 2008-03 and primary completion as 2014-02. The phase is recorded as NA. A crossover design means participants are assigned to experience more than one condition in sequence, so comparisons can potentially use information from within the same participant. The registry’s arm labels describe 9 Hour Sleep and 3 Hour Nap and 6 Hour Sleep, and the arm descriptions list the two conditions in opposite orders.

The registry does not report the randomization procedure, the masking target, the sequence allocation counts, or the detailed timing of each study period. It also does not report whether a washout period was used, how long each condition lasted, or how the effects of sequence and period were handled in the analysis. Those details matter in a crossover study because the order of conditions, changes over time, and persistence of an earlier condition can influence the comparison.

Outcome summaries list 12.0 participants for each sleep condition. The registry does not explain how these counts relate to the enrolled 16 participants, whether every participant contributed data under both conditions, or whether any participants were excluded from an outcome analysis. The bright light box is listed as the device intervention, while the arm labels identify sleep schedules. How the device exposure was integrated with the sleep schedules is not reported in the registry record. Psychomotor Vigilance is listed as a secondary outcome, measured after short or long nights. The registry records the study as completed but does not report its original statistical design assumptions or detailed analysis plan.

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 Dim Light Melatonin Onset (Hours), measured over 12 days from baseline to final dim light melatonin onset.

Dim Light Melatonin Onset, reported in hours, is the primary endpoint. The registry describes it as a gold-standard marker of circadian timing. In general, melatonin onset measured under dim-light conditions is used to characterize the timing of the body’s circadian system while reducing the influence of bright light on the measurement itself. The registry describes the endpoint as a mean and gives a standard deviation as its measure of spread.

The stated timeframe is 12 days from baseline to final dim light melatonin onset. This wording indicates the period covered by the outcome assessment, but does not specify the individual measurement schedule or the precise calculation used to arrive at each participant’s endpoint. Those details are not reported in the registry record.

The reported means are 1.93 hours for 9 Hour Sleep and 0.8 hours for 3 Hour Nap and 6 Hour Sleep. The comparison is expressed as a mean difference, with the latter condition compared with the former. A difference in this marker describes a difference in measured circadian timing; by itself it does not establish why the timing differs, whether the difference is meaningful to participants, or whether it represents a response to bright light. The registry’s research summary proposes that sleep restriction may reduce the body clock’s response to bright light, but the posted endpoint is a timing marker rather than a direct measure of that response.

7. Results Posted in the Registry

• 3 Hour Nap and 6 Hour Sleep: mean 0.80 versus 1.93 on control; difference -1.13 (95% CI -1.89 to -0.37), standardized effect d = -1.19; z-test p = 0.004.

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.

Psychomotor Vigilance

• 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:
  • 3 Hour Nap and 6 Hour Sleep: mean 221.16 versus 215.15 on control; difference 6.01 (95% CI -20.45 to 32.47), standardized effect d = 0.18; z-test p = 0.656.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between 3 Hour Nap and 6 Hour Sleep and the control. The interval gives the range of effects that remain compatible with the data.

Psychomotor Vigilance is the listed secondary outcome, measured in msec after short or long nights. Across the registry’s posted outcomes, the primary circadian timing comparison and the vigilance comparison do not give equally clear statistical evidence. The primary estimate is separated from zero by its posted confidence interval, while the secondary interval includes zero and spans differences in either direction. The broad secondary uncertainty means the results do not establish a consistent change across both circadian timing and vigilance measures.

The secondary outcome is relevant because vigilance is a behavioral measure that can complement a marker of circadian timing. The two outcomes address different aspects of the research question, however, and should not be expected to produce identical estimates. A pattern in one outcome cannot substitute for direct evidence about the other. The registry’s research summary discusses the body clock’s response to bright light, while Psychomotor Vigilance measures performance; neither outcome alone fully captures every element described in the summary.

The registry lists one secondary outcome and no reported analyses for it. The posted comparison has an unadjusted p-value, meaning the record does not indicate that the result has been adjusted to account for multiple testing. In general, when multiple outcomes or comparisons are examined, the chance of obtaining at least one apparently notable result can increase. Prespecified outcome hierarchies, multiplicity adjustments, or other planned interpretation rules can address this concern, but those plans are not reported in the registry record.

Accordingly, the secondary result should be regarded as supportive descriptive information, not as a separate definitive conclusion. Its uncertainty and its unadjusted status reduce the weight it can carry in interpreting the study. The registry does not report whether other secondary measures were planned but not posted, how outcome selection was handled, or whether the analysis was prespecified. Those omissions limit assessment of how the secondary finding fits into the full set of analyses.

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

• Psychomotor Vigilance

9. Statistical Interpretation

10. Statistical Methods Explained

Dim Light Melatonin Onset and Psychomotor Vigilance are continuous outcomes: each is measured on a numerical scale, rather than classified into categories. For a continuous outcome, a mean describes the average observed value in a condition. A standard deviation describes how spread out individual observations are around that mean. In general, the mean summarizes the center of the recorded values, whereas the standard deviation describes variation among those values; neither measure alone describes the full distribution.

What does the mean difference represent?

The primary comparison is expressed as the mean difference for 3 Hour Nap and 6 Hour Sleep relative to 9 Hour Sleep. The reported estimate is -1.13 hours. The negative sign indicates that the mean in the first-named comparison condition is lower than the mean in the reference condition, as reflected by the posted values of 0.8 and 1.93 hours. This is a difference in the recorded outcome summaries. It is not a percentage change, and it should not be interpreted as a within-person change unless the analysis is known to have estimated that quantity.

The secondary comparison is expressed in the same direction, with Psychomotor Vigilance means of 221.2 msec and 215.2 msec. The reported mean difference is 6.01 msec. These estimates are stated in the outcome’s measurement units. The unit matters: the numerical size of an estimate has meaning only alongside the scale on which the outcome was measured.

What do standard deviations and standard errors tell us?

Standard deviations describe variation among participant measurements. For the primary outcome, the posted standard deviations are 0.98 and 0.92 hours. For Psychomotor Vigilance, they are 32.57 and 33.56 msec. These values describe the spread within each condition; they are not uncertainty intervals for the mean difference.

A standard error describes the uncertainty of an estimated quantity under a statistical model. In general, it is influenced by the amount of information and by the variability in the measurements. A comparison’s standard error is used in constructing a confidence interval and testing a hypothesis. In a crossover study, the uncertainty of a difference may depend on how measurements from the same participant are related. The registry does not report the paired covariance or the method used to account for repeated measurements, so the relationship between the posted standard deviations and the uncertainty of the comparison cannot be fully assessed from the registry record.

How should the confidence intervals and p-values be read?

A confidence interval gives a range of estimates compatible with the observed data and the assumptions of the analysis. For the primary mean difference, the posted interval is entirely negative. Under the reported comparison, that means the interval does not include a zero difference. The unadjusted p-value is 0.004. In general, a p-value is calculated under a null hypothesis and an analysis model; it is not the chance that the result is due to chance, and it does not measure the size or importance of an effect.

For Psychomotor Vigilance, the interval ranges from -20.45 to 32.47 msec and crosses zero. The unadjusted p-value is 0.656. This indicates considerable uncertainty about the direction and size of the difference under the reported comparison. It is not a formal demonstration of equivalence or absence of an effect. Equivalence requires an appropriate prespecified margin and analysis, neither of which is reported in the registry record.

What is special about the crossover design?

In general, crossover studies collect outcome information under multiple conditions for the same participants. When the analysis properly uses that pairing, each participant can serve as a partial control for stable personal characteristics. The comparison then depends on within-participant differences, not only on the means and standard deviations of condition summaries considered separately. A paired analysis needs information about the relationship between each participant’s measurements across conditions.

Crossover results can also be affected by period effects, sequence effects, and carryover. A period effect is a change associated with the time or study period in which a condition is received. A sequence effect concerns the order in which conditions are given. Carryover refers to an effect of an earlier condition that persists into a later period. These are general statistical considerations, not claims that any such effect occurred in this trial. The registry does not report how these issues were assessed or modeled, whether there was a washout period, or whether the posted comparison uses a paired analysis.

The registry labels the comparison as a mean difference and reports outcome counts of 12.0 for each condition. It does not report the analysis population, participant-level data, or a detailed statistical model. Without those details, the posted estimate and uncertainty can be described, but the assumptions underlying the inference cannot be independently evaluated in full. No discrepancy is recorded between the posted result and the comparison, but that does not fill in the unreported analytic details.

Over-dispersion is a general concern when a model’s assumed variability is smaller than the actual variability in the data. If not accounted for, uncertainty may be understated. It is not possible to determine from the registry record whether over-dispersion was relevant to these outcomes or whether any adjustment was used. The outcomes are continuous, and the registry reports means and standard deviations rather than event counts or rates.

11. Confidence Intervals and Precision

Precision concerns how narrowly the data locate an estimated comparison. A confidence interval makes that uncertainty visible by giving a range of values compatible with the estimate under the analysis assumptions. A narrower interval indicates greater precision; a wider interval leaves more uncertainty about the size and possibly the direction of a difference. The interval does not include every value that might be true, and its interpretation depends on the model and design being appropriate.

For the primary mean difference of -1.13 hours, the posted confidence interval is entirely negative. This supports a directional description of the reported comparison under its assumptions: the estimated mean is lower for 3 Hour Nap and 6 Hour Sleep than for 9 Hour Sleep. The interval’s width still matters for judging the range of plausible differences, and the registry does not report a threshold for judging which differences would be practically important. The posted p-value of 0.004 addresses a null-difference test, not the precision or clinical meaning of the estimate.

The secondary Psychomotor Vigilance interval extends from -20.45 to 32.47 msec, crossing zero and allowing differences in both directions. Its width indicates that the registry’s summary does not pin down the direction or magnitude with much precision. This uncertainty is consistent with the unadjusted p-value of 0.656, but the p-value alone is not a precision measure. Neither result establishes that the conditions are equivalent.

In general, precision depends on sample information, variability, and the analysis design. In a crossover study, precision can depend importantly on the within-participant relationship between measurements. The outcome counts and separate standard deviations do not reveal that relationship. Since the registry does not report the paired data or detailed analysis method, the confidence intervals should be read as the intervals posted for the comparison, with the underlying assumptions not fully assessable from the record.

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 event counts. The event-count convention for time-to-event outcomes does not apply to these continuous outcomes. The registry states that its planning illustration uses a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The target effect is a stated fraction of the observed effect. The trial’s own original design assumptions are not reported in the registry record.

Each planning row represents a different effect size to detect: 100% of the observed effect, 75% of the observed effect, or 50% of the observed effect. The 80% power column gives the number of participants per arm that the illustration estimates would be needed to detect that effect under the stated assumptions with 80% power. The 90% column gives the corresponding number per arm for 90% power. In general, greater power means a higher chance of detecting an effect of the specified size when that effect is present, provided the planning assumptions hold.

Smaller effects require more participants to detect than larger effects under otherwise unchanged assumptions. For the primary endpoint, planning for 75% of the observed effect gives 20 participants per arm for 80% power and 27 participants per arm for 90% power; planning for 50% gives 45 and 60 participants per arm, respectively. These are design illustrations, not observed enrollment requirements or results from the trial’s original planning. The corresponding Psychomotor Vigilance planning figures are much larger, reflecting the small observed comparison relative to its variability.

This is not observed power. It is a forward-looking calculation based on an effect estimate from the posted results and stated planning assumptions. It does not show the probability that the trial’s findings are true, and it does not remedy uncertainty about the crossover analysis, original design, or observed participant counts.

13. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = -1.130; pooled standard deviation σ = 0.950.
2. n = 2 × (1.96 + 0.842)² × 0.950² / -1.130² = 11.1, rounded up to 12 participants per arm for 80% power.

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

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- -1.13                      # observed difference in means
sigma <- 0.950473566176356                     # 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(843843)
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 = 12 (80% power), 15 (90% power)
 75% of observed effect: n per arm = 20 (80% power), 27 (90% power)
 50% of observed effect: n per arm = 45 (80% power), 60 (90% power)
power.t.test: 12.1 
Simulated power at n = 12 per arm: 0.794 (20000 replicates)

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

14. Multiplicity, Missing Data and Analysis Populations

The registry lists Dim Light Melatonin Onset as the primary outcome and Psychomotor Vigilance as a secondary outcome. It records two outcome measures and zero reported analyses, and the reported analyses list for the secondary outcome is empty. The posted comparisons include unadjusted p-values. Whether those analyses were prespecified, and whether any multiplicity procedure was planned or used, is not reported in the registry record.

Multiplicity is the general statistical issue that arises when several outcomes, time points, contrasts, or subgroups are tested. With more opportunities to test hypotheses, a nominal p-value can be less informative about the overall evidence unless the analysis plan accounts for the testing strategy. Possible strategies include defining a primary outcome in advance, using a testing sequence, or adjusting the threshold or inference for the family of comparisons. The registry identifies a primary outcome, but it does not describe any such procedures or explain how the secondary result was intended to be interpreted.

Missing-data methods and analysis populations are also not reported in the registry record. The record does not state whether all enrolled participants contributed outcome data, how missing observations were handled, or whether participants were analyzed according to assigned sequence or another population definition. The enrollment is 16, while the outcome summaries list 12.0 participants per condition. These counts alone do not explain participant flow or the amount and pattern of missing outcome data.

For a crossover design, it is also important to know how incomplete sequences or missing measurements in one condition were handled. The registry does not report whether participants with partial data were included, what assumptions were made about missingness, or whether sensitivity analyses were performed. Missingness can affect both the estimate and its uncertainty when the reason for absence is related to the outcome or condition.

The record does not report interim analyses, a detailed statistical analysis plan, model diagnostics, or subgroup analyses. These items should not be assumed either to have occurred or not to have occurred; their status is not reported in the registry record. As a result, the posted summary supports a description of the recorded estimates, but does not permit a full audit of multiplicity control, missing-data handling, or population selection.

15. 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 0% reporting threshold.

For 9 Hour Sleep, the registry lists 8 participants at risk for serious adverse events and 0 affected. It also lists 8 at risk for other adverse events and 0 affected. For 3 Hour Nap and 6 Hour Sleep, the corresponding figures are also 8 at risk and 0 affected for serious adverse events, and 8 at risk and 0 affected for other adverse events. No serious adverse event terms are listed.

These counts mean that the posted adverse-event summaries record no affected participants in the reported groups. They do not establish that an event is impossible, and the small numbers at risk limit how much can be learned about uncommon events. The registry does not explain the relationship between these safety counts and the 16 enrolled participants, or provide additional detail about how adverse events were collected, classified, or attributed.

Death counts are not reported in the registry record. A blank or unavailable death count should not be interpreted as a reported count of zero. The posted safety information is therefore limited to the listed adverse-event counts and terms, and does not support broader conclusions about safety.

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

The posted primary outcome comparison describes lower mean Dim Light Melatonin Onset in the 3 Hour Nap and 6 Hour Sleep condition than in the 9 Hour Sleep condition. The reported mean difference is -1.13 hours, and its confidence interval is entirely negative, with an unadjusted p-value of 0.004. This is a statistical description of the recorded outcome summaries under the comparison as posted.

It does not, on its own, establish that one sleep schedule caused the difference. The registry labels the study as randomized and crossover, but does not report enough detail to assess how participant pairing, sequence, period, or carryover were treated. The record also does not describe precisely how the bright light box was used alongside the sleep conditions. The primary endpoint measures circadian timing; it is not itself a direct measure of the body clock’s response to bright light, overall sleep health, or a participant’s quality of life.

The registry’s research summary names several possible applications of the research, including circadian rhythm sleep disorders and related effects on well-being and functioning. Those statements describe the motivation for the study, not outcomes established by the posted endpoint data. The record does not report disorder-specific clinical outcomes or a threshold for interpreting the measured difference as beneficial, harmful, or important.

The secondary vigilance comparison is uncertain and does not establish either a clear difference or equivalence. The posted safety counts show no affected participants among the listed at-risk groups, but the counts are limited and deaths are not reported in the registry record. Taken together, the findings are best understood as a small set of outcome summaries from a completed study, with an estimated difference in the primary circadian timing marker and substantial limitations in the detail available for evaluating its analysis and broader meaning.

17. Why This Trial Matters Statistically

This study illustrates why a clinical or physiological result cannot be interpreted from a p-value alone. The primary estimate has a direction, a unit, and a confidence interval; each answers a different question. The estimate describes the recorded difference in hours, the interval describes uncertainty about its size under the analysis assumptions, and the p-value summarizes evidence against a specified null model. None of these by itself determines whether a difference matters in practice.

The crossover structure makes study design and analysis especially important. In general, using measurements from the same participants can improve a comparison by accounting for stable individual differences. But the value of that design depends on appropriate handling of pairing, time period, sequence, and possible carryover. Marginal means and standard deviations do not reveal the within-participant relationship needed to assess that aspect of the analysis. The registry’s lack of detail on those methods shows why transparent reporting is essential alongside the numerical result.

The contrast between the primary and secondary outcomes also illustrates the distinction between an estimate and the strength of evidence around it. A secondary outcome can be relevant without providing a precise or conclusive result. Reporting the confidence interval and the unadjusted status helps readers avoid treating a single p-value as a full summary of evidence, especially where more than one outcome is recorded.

Finally, planning calculations based on an observed effect are not the same as the design assumptions used before a study begins. Such illustrations can show how required sample size changes as the target effect becomes smaller, but they cannot establish the trial’s original rationale or its achieved power. The registry does not report that original rationale. Together, these statistical considerations make the record useful as an example of the importance of design-specific analysis, precision, and complete reporting.

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.

Several limitations specific to this record constrain interpretation. The overall enrollment is 16, while the primary and secondary outcome summaries list 12.0 participants per condition. The registry does not explain this difference, identify the number with complete paired measurements, or describe exclusions and missing observations. That limits assessment of the population represented by the posted comparisons.

Although the study is labeled randomized, single-masked, and crossover, the registry does not report the randomization method, the masking target, sequence counts, period structure, or washout details. It does not describe how period and sequence effects or carryover were handled. Those are important features of a crossover comparison, and their absence prevents detailed evaluation of whether the reported estimates account for the design.

The bright light box is listed as the device intervention, but the arm labels describe sleep schedules. The exact light exposure timing and its relationship to the sleep conditions are not reported in the registry record. It is therefore not possible to determine from the record which aspects of the protocol correspond to the research summary’s question about sleep restriction and bright light.

The registry does not report a detailed statistical analysis plan, the primary outcome population, missing-data methods, multiplicity procedures, or a threshold for a meaningful change in the primary marker. It provides no participant-level data or paired covariance, so the crossover-specific uncertainty cannot be independently assessed. No interim-analysis information is reported in the registry record. These limitations do not negate the posted estimates, but they restrict how far they can be interpreted beyond their descriptive statistical content.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Sleep Length and Circadian Regulation in Humans — NCT00843843.
• Registry record last updated 2016-03-08; status last verified 2016-02.
• Results first posted 2016-03-08.
• 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

NCT00843843 is a completed randomized, single-masked crossover study sponsored by Rush University Medical Center, with enrollment of 16. It compares the registry-listed 9 Hour Sleep and 3 Hour Nap and 6 Hour Sleep conditions and lists a bright light box as the device intervention. The primary outcome is Dim Light Melatonin Onset (Hours), described as a gold-standard marker of circadian timing.

The primary posted comparison reports a mean difference of -1.13 hours, with a confidence interval entirely negative and an unadjusted p-value of 0.004. Psychomotor Vigilance is listed as a secondary outcome; its comparison is less precise and has an unadjusted p-value of 0.656. The registry records no affected participants in the adverse-event counts listed for either condition; death counts are not reported in the registry record.

Important details about the crossover analysis, participant flow, missing data, multiplicity, and original sample-size rationale are not reported in the registry record. The estimates therefore describe the posted results, while their design-specific assumptions and broader clinical meaning remain incompletely documented.