Dimethyl Fumarate for Obstructive Sleep Apnea: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Dimethyl Fumarate for Obstructive Sleep Apnea (NCT02438137), a randomized phase 2 study. The primary outcome is Mean Change in Apnea Severity as Measured by the Respiratory Disturbance Index (RDI).

2. Clinical Question

3. Trial Design

This was a randomized, double-masked, parallel-group Phase 2 clinical trial sponsored by the University of Michigan. Its status is recorded as completed. The registry lists an enrollment of 65 participants and dates the study start to 2015-05 and primary completion to 2016-04. The stated purpose was to assess dimethyl fumarate as a treatment for obstructive sleep apnea among people unable, unwilling, or uneager to use positive airway pressure therapy.

The intervention was oral dimethyl fumarate, and the comparator was placebo. The arm description lists a starting dimethyl fumarate dose of 120 mg twice a day, followed after 7 days by a maintenance dose of 240 mg twice a day, with slower dose escalation possible. Placebo was taken twice a day with breakfast and dinner for 4 months. The registry record does not establish whether every participant followed the same dose-escalation schedule.

For the primary endpoint, the record says 50 participants had both completed the study and produced interpretable Month 4 polysomnography: 35 in the dimethyl fumarate group and 15 in the placebo group. It also reports that 14 participants withdrew or were lost to follow-up, 51 completed study activities, and one participant’s Month 4 polysomnography was uninterpretable. These figures describe different stages of participation and outcome availability; the primary outcome is not based on all 65 randomized participants.

The registry record does not report the planned allocation ratio, the original sample-size justification, detailed eligibility criteria, or a full statistical analysis plan. Those details should not be inferred from the observed group sizes or from the analyses posted after the trial.

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:

Analysis population for the primary outcome, as defined in the registry: 65 participants were randomized. 14 participants withdrew from the study or were lost to followup. 51 completed study activities. 50 (35 DMF and 15 placebo) both completed the study and had an interpretable Month 4 PSG. One participant's Month 4 PSG was uninterpretable, thus the RDI from this participant could not be included in the final analysis.

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

Population: 65 participants were randomized and included in baseline analyses. 14 participants withdrew from the study or were lost to followup. 51 participants completed study activities. 50 participants (35 DMF and 15 placebo) who both completed the study and had an interpretable Month 4 PSG were included in the final analyses.

6. Primary Endpoint

The registry lists the primary outcome as Mean Change in Apnea Severity as Measured by the Respiratory Disturbance Index (RDI), measured over Month 0 to Month 4.

The primary endpoint was mean change in apnea severity, measured by the respiratory disturbance index, from Month 0 to Month 4. RDI is the number of apneas, hypopneas, and respiratory-related arousals per hour of sleep. It is measured using polysomnography, the sleep study named in the registry record. A change score describes how the measure differed between the baseline and follow-up assessments for a participant.

RDI is used in this study as a numerical measure of sleep-disordered breathing severity. The unit, respiratory events per hour, gives the result a direct interpretation as a rate during sleep. A group mean summarizes the average change in that measure among participants included in the analysis. The standard deviation describes how dispersed individual changes were around that group mean; it is not a measure of uncertainty in the mean itself.

The posted endpoint summary includes participants with interpretable Month 4 polysomnography. The record reports 35 such participants in the dimethyl fumarate arm and 15 in the placebo arm. That distinction matters because the endpoint describes this available-outcome group, not necessarily the experience of all randomized participants. The registry record does not report a primary-outcome result for the participant whose Month 4 polysomnography was uninterpretable.

7. Results Posted in the Registry

• Dimethyl Fumarate (Tecfidera®) Capsules: mean -3.11 versus 10.20 on control; difference -13.31 (95% CI -21.20 to -5.42), standardized effect d = -1.03; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The registry posts both a sponsor-reported regression analysis and group summaries that permit an unadjusted recalculation. They answer related but not identical statistical questions. The sponsor’s result is a linear regression coefficient for treatment effect, reported as -11.3 with p = 0.012. The recalculation compares the posted mean change in the two groups directly. Since the discrepancy flag is true, the sponsor’s own analysis takes precedence; the recalculation is useful as a transparent comparison of the posted summary statistics, not as a replacement for the sponsor’s analysis.

What does a group mean describe?

For a continuous outcome such as RDI change, the mean is the arithmetic average of the observed participant values in a group. The posted mean changes are -3.11 in the dimethyl fumarate group and 10.2 in the placebo group. The standard deviations are 12.9 and 13.1, respectively. A standard deviation describes variation among individual observations around the group mean. It does not describe how certain the estimated mean is; that uncertainty depends on both the variation and the number of observations.

General statistical explanation: a mean difference expresses the contrast between two group averages in the outcome’s original units. The unadjusted recalculation is -13.31 respiratory events/hour, with dimethyl fumarate treated as the first group and placebo as the comparison group. Its negative sign expresses the direction of that contrast under this ordering. It does not by itself establish why the groups differed or whether the magnitude matters clinically.

What does the confidence interval add?

The unadjusted recalculation has a 95% confidence interval from -21.2 to -5.422. General statistical explanation: a confidence interval describes the uncertainty around an estimate under the statistical procedure used to construct it. A narrower interval indicates greater precision than a wider interval on the same scale. The interval belongs to the unadjusted recalculation, not the sponsor’s regression estimate. The registry does not report a confidence interval for the sponsor’s coefficient.

How should the p-values be understood?

The recalculated unadjusted comparison has p < 0.001, while the sponsor’s reported regression analysis has p = 0.012. General statistical explanation: a p-value measures how inconsistent the data are with a specified null model, under the assumptions of the analysis. It is not the probability that the null hypothesis is true, nor does it quantify the size or clinical importance of an effect. The two p-values accompany different analyses and should not be treated as competing measurements from an identical model.

The sponsor’s coefficient is identified as a treatment-effect coefficient from linear regression. The registry record does not report the model’s covariates, diagnostics, handling of missing data, or other specification details. No adjustment method can be reconstructed from the coefficient and p-value alone. The sponsor’s result should therefore be quoted as reported, without attributing its difference from the simple recalculation to a particular modeling choice.

What is the role of the standardized effect?

The unadjusted recalculation also reports a pooled standard deviation of 12.96 and a standardized effect, d = -1.027. General statistical explanation: a standardized effect expresses a group contrast in standard-deviation units, making the effect dimensionless. It can be useful for planning calculations that need a standardized input, but it does not replace the original-unit estimate. Its interpretation depends on the data and assumptions used to calculate it; it should not be mistaken for a separate clinical endpoint.

The planning illustrations use fractions of the observed effect and state assumptions of a two-sided significance level of 0.05, equal allocation between arms, and a normal approximation. They are forward-looking planning calculations, not a description of the trial’s original design or of the sponsor’s regression model. The trial’s own design assumptions and sample-size justification are not reported in the registry record. General statistical explanation: over-dispersion means that observations vary more than a chosen model allows; when present, it can make model-based uncertainty estimates unreliable unless the model accounts for it. The registry record does not report whether over-dispersion was assessed, and the endpoint’s standard deviations alone do not establish that it occurred.

10. Confidence Intervals and Precision

The recalculated unadjusted mean difference is -13.31 respiratory events/hour, with a 95% confidence interval from -21.2 to -5.422. This interval gives a range of values compatible with the unadjusted estimate under the interval’s statistical procedure. Its endpoints are both negative, so the interval places the unadjusted contrast in the direction of a lower mean change in the dimethyl fumarate group relative to placebo.

General statistical explanation: a confidence interval conveys precision, not certainty that the true effect lies within the particular interval. Its width reflects the information and assumptions used in the calculation. The group standard deviations, 12.9 and 13.1, describe variability among observed changes, while the confidence interval describes uncertainty around the between-group estimate. These are related but distinct aspects of the results.

The confidence interval belongs to a simple, unadjusted recalculation from the posted group summaries. It is not the interval for the sponsor’s linear regression coefficient. The registry reports that coefficient as -11.3 with p = 0.012, but reports no confidence limits for it. The sponsor analysis takes precedence because the posted analysis differs from the unadjusted recalculation. The interval should therefore be used to understand the precision of the recalculated comparison, not to assign precision to the sponsor’s estimate.

The sample available for the primary outcome was 35 dimethyl fumarate participants and 15 placebo participants, rather than all 65 randomized participants. This imbalance in available endpoint observations and the loss of outcome data can affect precision and may also affect how representative the analyzed participants are. The registry record does not provide a missing-data analysis or a confidence interval for the sponsor’s model, so those sources of uncertainty cannot be evaluated from the posted information.

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 participants per arm, not total event counts. The registry’s planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The calculations use the observed effect or a stated fraction of it as the effect to detect. They are planning illustrations based on the observed result, not the trial’s original design assumptions; the original sample-size justification is not reported in the registry record.

The 80% power column gives the planned number of participants per arm under those assumptions for an 80% chance of detecting the specified effect if that effect is the true one. The 90% power column gives the corresponding number per arm for a 90% chance. These are prospective design targets for hypothetical studies, not statements about the certainty of the result in this completed trial.

The estimates are 15 participants per arm for 80% power and 20 for 90% power when planning for 100% of the observed effect. For 75% of the observed effect, the corresponding figures are 27 and 36 participants per arm. For 50% of the observed effect, they are 60 and 80 participants per arm. Smaller effects need more participants to detect under the same planning assumptions.

These figures are not observed power. They should not be read as a retrospective measure of whether the completed trial was adequately powered, nor as a claim about the trial’s original planned enrollment. The assumptions, including equal allocation, are part of the planning illustration and need not match the observed endpoint counts.

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 = -13.310; pooled standard deviation σ = 12.959.
2. n = 2 × (1.96 + 0.842)² × 12.959² / -13.310² = 14.9, rounded up to 15 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 <- -13.31                      # observed difference in means
sigma <- 12.9586521932903                     # 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(2438137)
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 = 15 (80% power), 20 (90% power)
 75% of observed effect: n per arm = 27 (80% power), 36 (90% power)
 50% of observed effect: n per arm = 60 (80% power), 80 (90% power)
power.t.test: 15.9 
Simulated power at n = 15 per arm: 0.775 (20000 replicates)

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

13. Analyses Reported by the Sponsor

The sponsor’s posted analysis uses linear regression and reports a treatment-effect coefficient of -11.3 with p = 0.012. The registry does not report a confidence interval for this coefficient or the details of the model specification. Its adjustment variables, missing-data handling, and diagnostic results are not reported in the registry record.

The unadjusted recalculation from the posted group summaries gives a mean difference of -13.31 respiratory events/hour, with a 95% confidence interval from -21.2 to -5.422 and p < 0.001. This calculation uses the reported mean changes and standard deviations for the analyzed groups; it is not the same analysis as the sponsor’s regression. Because the discrepancy flag is true, the sponsor’s own analysis takes precedence when stating the trial’s reported inferential result.

Both estimates are negative, but they should not be blended into a single estimate or treated as if they came from one method. The recalculation helps readers see what a direct comparison of posted summaries yields. The sponsor result is the trial analysis recorded by the sponsor. The registry does not explain the difference between the two estimates, so no specific cause should be assigned.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists one secondary outcome: mean change in serum cytokine levels, described as a mean difference of log-transformed values. It records two outcome measures overall. The posted analysis information identifies one analysis, the linear regression treatment-effect analysis for the primary endpoint. The registry record does not describe a multiplicity adjustment, a hierarchy among endpoints, or a plan for interpreting multiple comparisons.

General statistical explanation: multiplicity arises when several outcomes, comparisons, or analyses are examined. Without an appropriate plan, repeated testing can increase the chance of findings that appear noteworthy by chance. Whether and how this concern applies depends on the prespecified analysis plan and the analyses actually conducted. Those details are not reported in the registry record, so the presence or absence of a multiplicity adjustment cannot be established.

The record does not provide a posted result for the listed secondary cytokine outcome in the information available for this analysis. That outcome should not be interpreted as having no effect or as having been unmeasured merely because a result is not listed. The registry record does not report its estimate, uncertainty, or analysis details.

Missing outcome data are directly relevant to the primary endpoint. The registry states that 65 participants were randomized, 14 withdrew or were lost to follow-up, 51 completed study activities, and 50 both completed the study and had interpretable Month 4 polysomnography. One participant’s Month 4 polysomnography was uninterpretable. The primary outcome description is based on those 50 interpretable assessments, with 35 in the dimethyl fumarate arm and 15 in the placebo arm.

The registry record does not report whether the sponsor used imputation, a model-based approach to missing outcomes, or another method to address missingness. It also does not state whether the posted regression used the same 50 participants as the mean summaries. The analysis population beyond the endpoint description is not reported in the registry record. Consequently, the available-case results cannot establish how the missing outcomes might have affected the estimate.

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 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: myocardial infarction (4.8%), pneumonia (2.3%).

The registry lists serious adverse events for 44 participants at risk in the dimethyl fumarate group and 21 at risk in the placebo group. One participant in each group was recorded as affected by a serious adverse event. The record lists zero deaths in both groups. These denominators differ from the primary endpoint analysis counts, so the safety figures should not be conflated with the 35 and 15 participants whose Month 4 polysomnography was interpretable.

The registry also lists other adverse events affecting 27 of the 44 participants at risk in the dimethyl fumarate group and 7 of the 21 at risk in the placebo group. The posted serious-event terms include Myocardial Infarction at 4.8% and Pneumonia at 2.3%. The record does not make clear in this summary which group each term corresponds to, so those percentages should not be assigned to an arm.

These are counts recorded in the registry, not a complete characterization of an individual participant’s experience or the cause of an event. The registry information does not establish whether events were judged related to study treatment. Comparisons of these counts should be interpreted cautiously, particularly because the numbers at risk differ between groups. No medical conclusion should be drawn from these figures alone.

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

The posted primary endpoint results describe mean change in RDI from Month 0 to Month 4 among participants with interpretable follow-up polysomnography. The observed group means were -3.11 respiratory events/hour for dimethyl fumarate and 10.2 respiratory events/hour for placebo. The unadjusted recalculation estimates a mean difference of -13.31, with a 95% confidence interval from -21.2 to -5.422. The sponsor’s reported regression result is -11.3 with p = 0.012, and that sponsor analysis takes precedence over the recalculation.

These results describe the analyzed participants and the measured time period. They do not establish what happened to participants without interpretable follow-up polysomnography, or how including those participants through another method would affect the estimate. The registry does not report a confidence interval for the sponsor’s regression coefficient or sufficient model details to reconstruct the sponsor analysis.

The endpoint is a numerical sleep-study measure: apneas, hypopneas, and respiratory-related arousals per hour. The posted group contrast is not, by itself, an assessment of every aspect of obstructive sleep apnea or of participants’ broader health. The registry record does not report results beyond the primary endpoint and the single listed secondary outcome in the information. The study’s Month 0 to Month 4 comparison does not establish effects at other follow-up times.

The trial result should not be read as a guarantee that a similar result would occur in a different group of participants, in a different study, or under a different analysis. Nor does a p-value alone describe clinical importance. The registry record’s missing information about the original sample-size justification, detailed analysis plan, and handling of missing data limits how fully the statistical result can be assessed.

17. Why This Trial Matters Statistically

This trial illustrates why a clinical result should be read together with its analysis population. Although 65 participants were randomized, the primary RDI comparison uses 50 participants with interpretable Month 4 polysomnography. The registry also reports 14 withdrawals or losses to follow-up, 51 participants completing study activities, and one uninterpretable Month 4 study. Those distinctions affect what the endpoint estimate represents and how confidently it can be generalized to all randomized participants.

It also illustrates the difference between a sponsor-reported model and a direct recalculation from group summaries. The posted sponsor coefficient is -11.3 with p = 0.012, while the unadjusted recalculation is -13.31 with p < 0.001 and a 95% confidence interval from -21.2 to -5.422. Because the estimates differ, the sponsor analysis takes precedence, while the recalculation remains useful for understanding the raw group contrast. The registry does not explain the discrepancy, which makes careful labeling of each analysis important.

The trial also provides a practical example of uncertainty: group standard deviations describe the spread of individual changes, while a confidence interval describes uncertainty around a group contrast. The interval available is for the recalculation, not the sponsor model. Keeping those quantities distinct prevents an unadjusted precision estimate from being mistakenly attributed to a different analysis.

Finally, the planning illustrations show how required sample size depends on the effect targeted. Under the stated assumptions, planning for a smaller fraction of the observed effect requires more participants per arm. Those calculations are not the trial’s original justification and are not evidence of observed power. Together, these points emphasize the importance of matching conclusions to the precise population, endpoint, analysis, and uncertainty that the registry reports.

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 primary endpoint analysis includes 50 participants with interpretable Month 4 polysomnography, rather than all 65 randomized participants. The registry reports withdrawals or loss to follow-up, a smaller number completing study activities, and one uninterpretable follow-up study. It does not report a missing-data method or show how conclusions would change under alternative assumptions about missing outcomes.

The posted group sizes for the primary endpoint are 35 for dimethyl fumarate and 15 for placebo. The registry does not report the planned allocation ratio or explain the difference between these analyzed counts. The safety denominators are 44 and 21, which are not the same as the endpoint counts. The record does not provide enough detail to determine how each analysis population was defined beyond the endpoint description and safety counts.

The sponsor’s regression estimate is reported without a confidence interval or detailed model specification. The unadjusted recalculation differs from that analysis, and the registry does not explain the discrepancy. As a result, the recalculated confidence interval should not be used to describe the precision of the sponsor’s coefficient.

The study’s original sample-size justification, detailed statistical plan, multiplicity handling, and analysis of the listed secondary outcome are not reported in the registry record. The primary endpoint timeframe is Month 0 to Month 4; longer-term outcomes are not reported in the information. Detailed eligibility criteria beyond the stated study purpose are also not reported in the registry record. These gaps restrict assessment of generalizability and of how the analyses were planned and conducted.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Dimethyl Fumarate for Obstructive Sleep Apnea — NCT02438137.
• Registry record last updated 2017-05-31; status last verified 2017-04.
• Results first posted 2017-05-31.
• 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

The registry describes a completed, randomized, double-masked, parallel-group Phase 2 trial sponsored by the University of Michigan. It enrolled 65 participants and compared oral dimethyl fumarate with placebo for obstructive sleep apnea. The primary endpoint was mean change in respiratory disturbance index from Month 0 to Month 4.

For 50 participants with interpretable Month 4 polysomnography, the mean changes were -3.11 respiratory events/hour in the dimethyl fumarate group and 10.2 in the placebo group. The sponsor reported a linear regression treatment-effect coefficient of -11.3 with p = 0.012. An unadjusted recalculation differs and is presented separately; the sponsor’s analysis takes precedence. Missing outcome data, limited model details, and unreported original design assumptions constrain interpretation.