Evaluation of an Oral Cannabidiol (CBD)-Terpene Formulation on Sleep Physiology in Participants With Insomnia: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Evaluation of an Oral Cannabidiol (CBD)-Terpene Formulation on Sleep Physiology in Participants With Insomnia (NCT05233761), a randomized phase 2 study. The primary outcome is Percentage of Time Spent in the Combination of Slow Wave Sleep (SWS) and Rapid Eye Movement (REM) Sleep.

2. Clinical Question

3. Trial Design

This was a randomized, double-blind, placebo-controlled, phase 2 crossover study of Defined CBD in participants with insomnia. The registry lists an enrollment of 125 and a completed trial. The recorded start date was 2022-02-18, and the primary completion date was 2022-07-02.

In a crossover design, participants receive more than one study condition at different times, so comparisons may use information from the same participants under both conditions. The registry describes two treatment sequences, A/B and B/A, and says each participant was assessed during a four-week period on CBD-terpenes and a four-week period on placebo. The registry record does not describe a washout period or give details about sequence allocation beyond the sequence labels, so those features are not reported in the registry record.

Both treatments were taken orally as two capsules with water one hour before bedtime, on a minimum of four nights per week during each four-week treatment period. The active formulation was described as containing 300 mg CBD and 8 mg terpenes in total; placebo contained neither CBD nor terpenes. The trial was double-blind, but the specific people who were masked and the procedures used to maintain masking are not reported in the registry record.

The analysis of the primary outcome excluded six participants because of protocol deviations, including inadequate reporting of treatment use and/or insufficient sleep-data collection. The registry’s posted outcome groups each contain 56 participants. The record does not explain how the enrollment figure, exclusions, and analysis-group figures relate at the participant level, and no additional reconciliation should be inferred.

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.

Treatment Period A

Reasons for not completing this period:

Treatment Period B

Analysis population for the primary outcome, as defined in the registry: Data from six participants \[four participants from Group 1 (A/B) and two participants from Group 2 (B/A)\] were excluded from the final data analysis due to protocol deviations (e.g. due to a lack of reporting whether or not they took the study treatment, and/or insufficient sleep data collection).

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 Percentage of Time Spent in the Combination of Slow Wave Sleep (SWS) and Rapid Eye Movement (REM) Sleep, measured over Participants were assessed for treatment with CBD-terpenes and placebo, each for a treatment period of four weeks. Participants took the treatment (CBD-terpenes or Placebo) for at least four nights per week over the entire four week treatment period..

The primary endpoint was the percentage of total sleep time spent in slow wave sleep (SWS) and rapid eye movement (REM) sleep combined. It is a continuous measure: its value is a mean on a percentage-of-total-sleep-time scale. The registry says the endpoint was quantified with a non-invasive wrist-worn Whoop sleep-tracking device.

The endpoint combines two sleep stages rather than treating either stage alone as the primary measure. In general, a combined measure can represent a prespecified aspect of sleep physiology while reducing the focus on any single component. That general rationale does not establish why this particular combination was selected; the endpoint’s rationale beyond its stated role as the primary measure is not reported in the registry record.

The posted mean was 43.0 for Defined CBD and 41.8 for placebo. The registry gives a mean difference of 1.3 in its sponsor-reported analysis and an unadjusted recalculation of 1.2 from the posted summary statistics. These values describe the group-level outcome on the stated scale; they are not a measure of each participant’s experience or a direct assessment of every aspect of sleep. The record does not report a clinically meaningful threshold for interpreting a difference in this endpoint.

7. Results Posted in the Registry

• Defined CBD: mean 43.00 versus 41.80 on control; difference 1.20 (95% CI 0.09 to 2.31), standardized effect d = 0.40; z-test p = 0.034.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is continuous, and the registry identifies its summary as a mean with standard error. The sponsor-reported analysis is a two-sided t-test of final values, reported as a mean difference. A t-test compares means while accounting for the variability in the observed data under the assumptions of the specified test. A two-sided test considers departures in either direction rather than only a prespecified increase or decrease.

What does the mean difference describe?

The posted mean for Defined CBD is 43.0 and the posted mean for placebo is 41.8. The sponsor-reported mean difference is 1.3; the unadjusted recalculation from the summary statistics is 1.2. Because the endpoint is expressed as a percentage of total sleep time, a difference in this outcome is interpreted on that percentage scale. The estimate summarizes the contrast between treatment conditions; it does not show how every participant’s outcome changed.

The two reported estimates are close, but they arise from different descriptions of the analysis. The sponsor’s result is the registry-reported trial analysis. The recalculation is an unadjusted calculation from the posted summary values. It can be a useful check on the reported contrast, but it is not a substitute for the trial’s full analysis, particularly in a crossover study where observations from a participant under different conditions may be correlated.

What does the confidence interval contribute?

A confidence interval conveys uncertainty around an estimated difference. In general, a wider interval indicates less precision, while a narrower interval indicates greater precision, given the analysis and its assumptions. The sponsor-reported 95% confidence interval ranges from 0.1 to 2.5. Its lower limit is above zero, so the interval does not include a zero difference. This does not indicate whether the full range is clinically important: the registry does not report a meaningful-difference threshold for the endpoint.

The recalculated comparison has its own interval based on the posted summary statistics. That recalculation is unadjusted, and should not be read as a reproduction of all possible features of the sponsor’s crossover analysis. The registry does not report the treatment-period and sequence terms, paired-data handling, or other model details needed to evaluate that distinction fully.

How should the p-value be read?

The sponsor-reported two-sided p-value is 0.035. In general, a p-value describes how unusual results at least as incompatible with a specified null hypothesis would be if that hypothesis and the model assumptions were true. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of an effect. The reported value is below the conventional 0.05 threshold, but the registry does not state whether any multiplicity adjustment was applied.

The record lists 16 analyses and four outcome measures, including three posted secondary outcomes. When many outcomes or comparisons are examined, the chance of at least one nominally small p-value can increase. That general concern does not show that the primary result is false; it means the analysis plan and multiplicity approach are relevant context. The multiplicity approach is not reported in the registry record.

Why does crossover structure matter?

In general, a crossover study can compare conditions within the same participant, which may reduce the influence of stable differences between participants. It also requires attention to period effects, treatment sequence, carryover, and the correlation between repeated observations. The registry identifies the study as crossover and describes A/B and B/A sequences, but does not report whether or how these features were included in the sponsor’s statistical model. It also does not report a washout period. No particular crossover model or washout procedure should be assumed.

The posted arm means and simple recalculation do not provide the within-participant covariance or enough detail to reconstruct a paired treatment estimate. The sponsor-reported t-test of final values is the method stated in the results. The record does not explain how that test relates to the crossover design or whether the analysis used additional terms not captured by the brief description.

What do standard errors and spread indicate?

The posted standard error is 0.4 for each group mean. In general, a standard error describes the estimated uncertainty of a sample mean, not the spread of individual observations. The registry also gives a pooled standard deviation for the recalculation, but the individual-level distribution is not described in the record. A mean and its standard error therefore cannot show the full range of participant outcomes or whether the measure’s distribution was symmetric.

For continuous outcomes, assumptions about the distribution and the analysis model affect inference. The registry does not report diagnostic checks, transformations, robust methods, or sensitivity analyses for the primary outcome. This is a reporting limitation; it does not establish that any particular assumption was violated.

What is not specified?

The registry record does not report the original sample-size justification, the planned statistical analysis in sufficient detail to assess all model choices, interim analyses, or a multiplicity strategy. It also does not describe missing-data methods beyond stating that six participants were excluded from the final primary analysis for protocol deviations. These omissions limit independent evaluation of how the posted analysis was planned and how robust the result is to alternative analysis choices.

10. Confidence Intervals and Precision

The sponsor-reported estimate is a mean difference of 1.3, with a 95% confidence interval from 0.1 to 2.5. The interval is centered around a positive contrast and does not include zero. The corresponding two-sided p-value is 0.035. These statistics describe uncertainty under the sponsor-reported analysis; they do not quantify clinical importance or the probability that the result will be replicated.

In general, a confidence interval gives a range of values compatible with the observed data and the analysis model at the stated confidence level. Its width is informative about precision: a broad interval leaves more uncertainty about the size of the contrast, while a narrow interval constrains it more tightly. Here, the interval extends from a small positive difference to a larger positive difference on the percentage-of-total-sleep-time scale. The registry does not provide a threshold for deciding which values in that range would be clinically meaningful.

The recalculation based on posted summary statistics gives a mean difference of 1.2 and an interval whose lower limit is above zero. Its calculation is unadjusted and does not reproduce any unreported crossover-model features. The sponsor’s analysis, rather than the recalculation, is the registry’s reported trial analysis; the record does not flag a discrepancy.

Precision is also affected by analysis-population and missing-data decisions. The primary-outcome description says six participants were excluded for protocol deviations, including treatment-use reporting gaps and/or insufficient sleep data. The registry does not report sensitivity analyses to show how different missing-data assumptions might affect the estimate or interval. Thus, the confidence interval captures uncertainty under the reported analysis, not every possible source of uncertainty about the result.

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. The registry record does not report the original sample-size justification or its design assumptions. The figures are participants per arm, not total events. They use a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect.

For planning at 100% of the observed effect, the illustration gives 98 participants per arm for 80% power and 131 participants per arm for 90% power. At 75% of the observed effect, it gives 174 participants per arm for 80% power and 233 participants per arm for 90% power. At 50% of the observed effect, it gives 391 participants per arm for 80% power and 524 participants per arm for 90% power.

In plain language, the 80% power column describes the number of participants per arm estimated to provide an 80% chance of detecting the selected effect under the stated assumptions, if that effect and the assumptions were true. The 90% column uses a higher target chance of detection and therefore requires more participants per arm for each listed effect. Smaller effects need more participants to distinguish them from random variation, which is why the illustrated requirements rise as the selected fraction of the observed effect gets smaller.

These are planning calculations, not observed power and not a claim about the trial’s actual power. They are not a retrospective verdict on whether the trial was adequate, and they should not be treated as the original crossover-design sample-size plan. The assumptions are an illustration based on the observed effect and a two-arm equal-allocation setup; the record does not report a trial-specific justification incorporating its crossover structure.

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 = 1.200; pooled standard deviation σ = 2.993.
2. n = 2 × (1.96 + 0.842)² × 2.993² / 1.200² = 97.7, rounded up to 98 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 <- 1.2                      # observed difference in means
sigma <- 2.99332590941915                     # 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(5233761)
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 = 98 (80% power), 131 (90% power)
 75% of observed effect: n per arm = 174 (80% power), 233 (90% power)
 50% of observed effect: n per arm = 391 (80% power), 524 (90% power)
power.t.test: 98.6 
Simulated power at n = 98 per arm: 0.795 (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 registry reports the sponsor’s primary comparison as a two-sided t-test of final values. It gives a mean difference of 1.3, a 95% confidence interval from 0.1 to 2.5, and a p-value of 0.035. The simple unadjusted recalculation from the posted group summary statistics gives a mean difference of 1.2. The registry does not flag a discrepancy, so the recalculation is broadly consistent with the sponsor’s reported contrast.

The recalculation is not an independent reconstruction of the full analysis. It uses posted summary statistics and does not recover unreported details such as paired observations, treatment sequence, period effects, or other model terms. The registry’s description of the sponsor analysis is brief and does not explain how the t-test was applied in relation to the crossover design. Accordingly, the sponsor-reported result remains the relevant account of the trial analysis, while the recalculation serves as a simple unadjusted comparison rather than a replacement for it.

The sponsor labels the analysis as superiority. That label identifies the stated comparison framework; it does not by itself establish clinical importance. The record does not report a clinically meaningful threshold for the primary outcome.

14. Multiplicity, Missing Data and Analysis Populations

The registry identifies four outcome measures, three posted secondary outcomes, and 16 analyses. These counts indicate that the record includes more than the primary comparison. The record does not report a multiplicity strategy, such as whether the primary and secondary tests were considered together or whether any adjustment was applied. The sponsor-reported p-value should therefore be read as the result for the stated comparison, without assuming it accounts for the full set of analyses.

In general, testing multiple outcomes or contrasts can increase the chance that at least one result appears statistically notable by chance. A prespecified hierarchy or adjustment can address that issue, but the record does not say whether such a plan was used. The absence of that information is a limitation in assessing the strength of evidence across the whole set of results; it does not change the reported estimate for the primary comparison.

The primary outcome description says data from six participants were excluded from the final analysis because of protocol deviations. Examples include lack of reporting about whether study treatment was taken and/or insufficient sleep-data collection. The record does not describe imputation, a missing-data model, or sensitivity analyses. It does not report whether the exclusions were considered separately by treatment sequence or whether missingness differed by treatment period.

Analysis-population details are limited. The posted primary-outcome groups each list 56 participants, while the registry reports enrollment of 125 and also describes six exclusions from the final analysis. The record does not reconcile these figures at the participant level, so no additional participant accounting should be inferred. The safety populations have different at-risk counts from the primary-outcome groups.

The record does not report an interim-analysis plan, the original sample-size justification, or a complete statistical analysis plan. It also does not describe crossover-specific handling of within-participant correlation, period effects, sequence, or carryover. These items are not reported in the registry record; their absence from the record does not establish that they were not considered by the investigators.

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 lists serious adverse events and other adverse events separately for the safety groups. For Defined CBD, 99 participants were listed as at risk, with zero serious adverse events and zero other adverse events; deaths were zero. For placebo, 88 participants were listed as at risk, with zero serious adverse events and zero other adverse events; deaths were zero.

These figures describe the recorded safety data in the registry. The at-risk counts differ between the treatment groups and are not the same as the 56 participants listed in each primary-outcome group. The record does not explain the relationship between these safety and efficacy populations, and their counts should not be combined or treated as interchangeable.

Zero recorded events means no events were reported in the listed categories for these safety populations. It does not establish that no symptoms or events occurred outside the registry’s reported categories, nor does it determine how often an event might occur in a larger or different population. The record does not provide further detail on event definitions, collection procedures, or the duration of safety follow-up beyond the treatment-period descriptions.

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

The posted primary-outcome means are 43.0 for Defined CBD and 41.8 for placebo, for the percentage of total sleep time spent in SWS and REM combined. The sponsor-reported mean difference is 1.3, with a 95% confidence interval from 0.1 to 2.5 and a two-sided p-value of 0.035. These results describe the measured sleep-physiology outcome under the registry’s stated analysis.

The result does not by itself establish that the difference is clinically important. The registry does not report a threshold for a meaningful change in this measure, nor does the endpoint represent every dimension of sleep or insomnia. The result also does not establish an effect on outcomes that were not measured or reported in the record.

The crossover design means participants were assessed during both treatment conditions, but the registry’s results description does not explain in detail how repeated measurements, periods, or treatment sequences were handled. The simple recalculation is unadjusted and cannot resolve those modeling questions. Missing-data handling is also limited to the statement that six participants were excluded for protocol deviations involving treatment reporting and/or sleep-data collection.

The listed p-value is nominal; the registry does not report whether it was adjusted for the 16 analyses or the other outcome measures. This limits conclusions about the result in the context of all analyses. The observed estimate and interval should not be taken as a guarantee that a future study would produce the same value.

The safety record lists zero serious adverse events and zero other adverse events for each treatment group’s stated at-risk population, and zero deaths. These are registry-reported counts, not proof that all possible harms are absent. Overall, the results are specific to this trial’s participants, treatment schedule, device-based endpoint, and reported analysis. They should not be generalized beyond those data without additional evidence.

17. Why This Trial Matters Statistically

This trial is statistically notable because it combines a crossover design with an outcome measured repeatedly across two treatment periods. In general, crossover studies can use within-participant comparisons, but statistical interpretation depends on how the analysis handles repeated observations, treatment sequence, periods, and possible carryover. The registry identifies the crossover structure but gives limited detail about how those features entered the sponsor’s analysis.

The primary outcome is a continuous device-measured sleep-physiology measure, reported as the mean percentage of total sleep time spent in SWS and REM combined. The result is expressed on a clear scale and accompanied by a confidence interval, allowing readers to consider both the estimated contrast and its uncertainty. The absence of a reported threshold for clinical importance means statistical separation from zero cannot settle whether the difference matters in practice.

The record also illustrates why results require attention to data availability and multiplicity. Six participants were excluded from the final primary analysis for specified protocol deviations, while the missing-data method is not described. The registry lists 16 analyses and multiple outcomes but does not report a multiplicity plan. These details shape how confidently the single p-value can be interpreted in the broader set of tests.

Finally, the simple recalculation provides a check on the reported mean contrast, but cannot substitute for a complete account of the crossover model. Clear reporting of analysis populations, missing-data handling, model specification, and multiplicity would make the estimate easier to evaluate independently.

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 registry provides limited detail about the statistical analysis for a crossover study. It identifies a two-sided t-test of final values, but does not report whether the sponsor’s model accounted for paired measurements, period, sequence, or carryover. A washout period is not described. These aspects cannot be evaluated from the posted analysis description.

The primary analysis excluded six participants because of protocol deviations, including lack of treatment-use reporting and/or insufficient sleep-data collection. The registry does not report imputation, sensitivity analyses, or a detailed account of missingness by treatment or sequence. The potential influence of these exclusions on the estimate is therefore not assessable from the record.

The record lists 16 analyses, four outcome measures, and three posted secondary outcomes, but does not report whether the analysis plan addressed multiplicity. The clinical meaning of the primary-outcome difference is also uncertain because no meaningful-difference threshold is reported. The primary measure relies on a wrist-worn sleep-tracking device; the registry does not report validation details or measurement-error analyses for this endpoint.

The registry gives an enrollment of 125, lists 56 participants in each primary-outcome group, and reports six exclusions from the final analysis, but does not reconcile these figures at the participant level. Safety at-risk counts differ from the primary-outcome group counts. The original sample-size justification, interim analyses, and detailed analysis plan are not reported in the registry record. These reporting limitations do not prove that the methods were inadequate, but they restrict independent assessment of design and robustness.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Evaluation of an Oral Cannabidiol (CBD)-Terpene Formulation on Sleep Physiology in Participants With Insomnia — NCT05233761.
• Registry record last updated 2025-09-11; status last verified 2025-08.
• Results first posted 2025-09-11.
• 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

NCT05233761 is a completed randomized, double-blind, phase 2 crossover study of Defined CBD versus placebo in participants with insomnia. The registry lists enrollment of 125, a start date of 2022-02-18, and a primary completion date of 2022-07-02.

The primary endpoint was the percentage of total sleep time spent in SWS and REM combined, measured with a non-invasive wrist-worn Whoop device. Posted means were 43.0 for Defined CBD and 41.8 for placebo. The sponsor-reported mean difference was 1.3, with a 95% confidence interval from 0.1 to 2.5 and a two-sided p-value of 0.035. Six participants were excluded from the final primary analysis for protocol deviations.

The registry reports zero serious adverse events, zero other adverse events, and zero deaths in each listed safety group. Crossover-specific model details, missing-data methods, multiplicity handling, the original sample-size justification, and a threshold for clinical importance are not reported in the registry record.