A Phase III Trial of e-TNS for the Acute Treatment of Migraine: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Phase III Trial of e-TNS for the Acute Treatment of Migraine (NCT03465904), a randomized na study. The primary outcome is Pain Freedom at 2 Hours.

2. Clinical Question

3. Trial Design

This was a Phase III randomized, double-blind, sham-controlled trial with a parallel-group model. The phase field is recorded as NA, while the study title identifies it as a Phase III trial. Allocation is recorded as randomized, and masking as quadruple. The registry lists Cefaly Technology as the sponsor and the study status as completed. The recorded enrollment is 607.

Participants were assigned to a Verum or Sham Cefaly® Abortive Program device. Both arm descriptions specify 2-hour external trigeminal nerve stimulation for an early-stage migraine attack. The study objective describes use of the device at home. The posted primary outcome counts use denominators of 259 for Verum and 279 for Sham. Those are the denominators attached to the primary outcome, not a reconstruction of the full enrollment or a statement about why some enrolled participants may not appear in those counts.

The registry records a start date of 2018-04-10 and a primary completion date of 2019-01-11. It does not report the original sample-size justification, the planned number of participants in each arm, the randomization procedure, or the specific methods used to maintain and evaluate masking. Further details about eligibility criteria, treatment adherence, follow-up procedures, and analysis populations are not reported in the registry record.

The design supports a comparison between the assigned device programs under the trial conditions. It does not, by itself, provide information about how the result would generalize to populations, settings, or uses not described in the registry. The reported outcome counts and statistical contrasts should therefore be interpreted alongside the limited detail available about the trial conduct and analysis.

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 Pain Freedom at 2 Hours, measured over 2 hours.

The primary endpoint is pain freedom at 2 hours. The registry defines it as a change from a moderate or severe migraine headache at baseline, Grade 2 or 3, to no headache, Grade 0, at 2 hours after the e-TNS session began. It is recorded as a participant count, so the posted values describe how many participants in each analysis group met the endpoint.

This endpoint focuses on a concrete symptom state at a specified follow-up time. In general, a binary endpoint makes the outcome for each participant interpretable as meeting or not meeting a defined criterion. Comparing the proportions who meet that criterion between randomized groups gives a direct estimate of the difference in endpoint frequency. It does not describe the full trajectory of headache symptoms between baseline and the assessment, nor does it by itself measure every aspect of a migraine attack.

The distinction between pain freedom and pain relief matters. Pain freedom requires no headache at assessment, whereas pain relief is a separate secondary outcome. The primary endpoint also applies to the stated assessment time; it should not be read as evidence about later symptom status. The registry lists other outcomes, including later pain outcomes and migraine-associated symptoms, but those address different questions and should not be substituted for the primary endpoint.

The record does not report further details about how baseline severity was assessed, how participants with missing assessments were handled, or the precise analysis population. Those details would help clarify how closely the posted counts correspond to the endpoint definition for all randomized participants.

7. Results Posted in the Registry

• Verum: 25.5% (66/259) versus 18.3% (51/279) on control; risk difference 7.2 percentage points (95% CI 0.2 to 14.2), risk ratio 1.39 (1.01–1.93); unadjusted two-proportion z-test p = 0.043.

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.

Pain Relief at 2 Hours

• Endpoint type: Binary: the number of participants with the event, compared as proportions.
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Verum: 69.5% (180/259) versus 55.2% (154/279) on control; risk difference 14.3 percentage points (95% CI 6.2 to 22.4), risk ratio 1.26 (1.10–1.44); unadjusted two-proportion z-test p = <0.001.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Verum than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

Percentage of Patients With Absence of Photophobia, Phonophobia, Nausea, Vomiting at 2 Hours

• Endpoint type: Binary: the number of participants with the event, compared as proportions.
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Verum: 42.5% (110/259) versus 34.1% (95/279) on control; risk difference 8.4 percentage points (95% CI 0.2 to 16.6), risk ratio 1.25 (1.00–1.55); unadjusted two-proportion z-test p = 0.044.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the proportion with the event is statistically higher for Verum than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

Use of Rescue Medication Between 2 and 24 Hours

• Endpoint type: Binary: the number of participants with the event, compared as proportions.
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Verum: 39.2% (82/209) versus 44.3% (105/237) on control; risk difference -5.1 percentage points (95% CI -14.2 to 4.1), risk ratio 0.89 (0.71–1.10); unadjusted two-proportion z-test p = 0.279.
• Interpretation:
  • The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Verum and the control. The interval gives the range of effects that remain compatible with the data.

The secondary outcomes extend the primary question beyond pain freedom at 2 hours. They include pain relief at that time, absence of migraine-associated symptoms, rescue medication use between 2 and 24 hours, and sustained pain outcomes at 24 hours. These outcomes describe related but distinct experiences and time periods. They should be read as complementary measures, not as substitutes for the primary endpoint.

Across the outcomes with posted numerical comparisons, the pattern is not uniform. Pain relief and the combined absence-of-symptoms outcome have positive unadjusted risk differences favoring Verum, while the rescue-medication comparison has a negative point estimate and a confidence interval that includes no difference. Numerical results for the sustained pain outcomes are not reported in the registry record. The secondary estimates therefore do not all point in the same direction, and their precision varies.

The primary endpoint result is consistent with some of the posted secondary comparisons, but that does not independently confirm the primary finding. Pain relief, symptom absence, and rescue medication are different outcomes with different denominators and timeframes. A participant could meet one endpoint but not another, and the registry record does not provide participant-level data to examine how these outcomes overlap.

The secondary comparisons are unadjusted, and the registry record does not report a multiplicity strategy. In general, testing many outcomes creates more opportunities for nominally small p-values even when there is no true difference for some outcomes. This means unadjusted secondary findings carry less weight than a clearly prespecified primary comparison, particularly when the full analysis plan and outcome hierarchy are not reported. They are useful for describing the pattern of posted results, but should not be treated as separate definitive conclusions.

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

• Pain Relief at 2 Hours
• Percentage of Patients With Absence of Photophobia, Phonophobia, Nausea, Vomiting at 2 Hours
• Use of Rescue Medication Between 2 and 24 Hours
• Sustained Pain Freedom at 24 Hours
• Sustained Pain Relief at 24 Hours

9. Statistical Interpretation

10. Statistical Methods Explained

The main outcome is binary: each participant either met the pain-freedom definition at 2 hours or did not. For this kind of outcome, a group proportion is the number meeting the criterion divided by the number included in that group's outcome denominator. The registry reports counts and denominators, as well as comparison estimates. The posted primary proportions are 0.255 for Verum and 0.183 for Sham.

What does a risk difference express?

A risk difference subtracts the comparison-group proportion from the intervention-group proportion. It is an absolute contrast: it describes the difference in the probability of the endpoint between groups, on the proportion scale. The posted risk difference is 0.072. A value of zero would mean equal observed proportions; a positive value means the endpoint proportion is higher in the Verum group for the direction used in this comparison. This estimate is unadjusted and comes from the posted group summaries.

How does a risk ratio differ?

A risk ratio divides one group's endpoint proportion by the other group's proportion. It is a relative contrast rather than an absolute one. The posted risk ratio is 1.394, with a confidence interval from 1.008 to 1.927. Relative and absolute measures answer different questions, so considering both can give a fuller description of the comparison. Neither measure alone establishes the importance of the endpoint to patients or resolves limitations in the trial record.

What does the p-value tell the reader?

The unadjusted p-value for the primary comparison is 0.043. In general, a p-value is calculated under a null hypothesis and a statistical model, and indicates how compatible the observed data are with that model. A smaller p-value is not a measure of effect size, and it does not give the probability that a treatment effect is real. It also does not account automatically for multiple outcomes, analytic choices, or missing data. The registry record does not report a detailed analysis plan that would show how these issues were addressed.

Why are confidence intervals useful?

A confidence interval gives a range of values that are compatible with the data under the method used to calculate it. For the primary risk difference, the interval is 0.002 to 0.142. It conveys uncertainty around the point estimate and shows that the estimate is relatively close to the no-difference value at its lower end. The interval does not guarantee that the true value lies within its limits, nor does it reflect every possible source of uncertainty, such as bias or incomplete outcome data.

Why might over-dispersion matter?

Over-dispersion is relevant when the variability in data is greater than a statistical model expects. In general, using a model that fails to allow for extra variability can make uncertainty appear too small. The posted primary outcome is a binary participant count, and no dispersion estimate is reported for it. The registry record does not describe a model-based analysis or report whether over-dispersion was assessed. It is therefore appropriate to explain the concept generally, but not to claim that over-dispersion affected this trial's result.

What can be inferred from the posted analysis?

The record gives group counts and unadjusted comparisons for the primary outcome. These allow the reported risk difference, relative measures, confidence intervals, and p-value to be interpreted as summaries of the posted data. The record does not report adjustment for baseline characteristics, the precise test or interval method, an analysis population definition, or a method for handling missing outcome data. Those omissions limit the degree to which an independent reader can reproduce or evaluate the analysis from the registry record alone.

The registry also lists multiple secondary outcomes. In general, when many outcomes are examined, the chance of observing at least one nominally unusual result can increase unless the analysis plan accounts for multiplicity. No multiplicity adjustment is reported in the registry record. This does not invalidate the descriptive secondary results, but it is a reason to distinguish exploratory or unadjusted findings from a result supported by a prespecified multiplicity strategy.

11. Confidence Intervals and Precision

The primary risk-difference estimate is 0.072, with a 95% confidence interval from 0.002 to 0.142. The interval is the main indication of statistical precision: it shows that the observed estimate is compatible with a range of positive differences, including values close to zero as well as larger values. Its lower limit is close to the no-difference value, so the posted data do not pin down the effect size narrowly.

In general, a confidence interval reflects sampling uncertainty under the method used to calculate it. It is not a guarantee that the true effect falls within the limits, and it does not incorporate every possible source of uncertainty. The registry record does not report enough detail to assess the interval method or whether the analysis accounted for missing outcomes, covariates, or other features of the trial.

The relative-scale estimate is 1.394, with a 95% confidence interval from 1.008 to 1.927. Its lower limit is also close to the null value for a ratio. The risk difference and risk ratio describe the same group comparison on different scales; each has a confidence interval that conveys uncertainty on its own scale.

The unadjusted p-value of 0.043 is consistent with a result near the conventional threshold, but it should not replace the interval as a description of precision. A threshold-based interpretation alone would hide the range of effect sizes compatible with the data. The confidence interval also cannot indicate whether any particular effect size is meaningful to patients, because the registry does not report a threshold for clinical importance.

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 participants and not total events. They are planning illustrations calculated from the observed effect, rather than the trial's original design assumptions. The registry record does not report the trial's own sample-size justification or its original planning assumptions.

The stated illustration assumes a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It considers effects set to the stated fraction of the observed effect. The rows for planning for 100% of the observed effect, 75% of the observed effect, and 50% of the observed effect show how the estimate changes when the target effect is varied. For each target, the figures are given separately for participants per arm for 80% power and participants per arm for 90% power.

In general, power is the chance that a study will detect an effect of the specified size under the assumptions used for planning. The 80% column is the number of participants per arm estimated for an 80% chance of detecting that target effect at the stated significance level; the 90% column describes the corresponding planning target for a 90% chance. These are prospective planning quantities, not evidence about what the completed trial was capable of detecting.

Smaller effects require more participants to detect, because they are harder to distinguish from ordinary sampling variation. The illustrations are anchored to an observed effect, which is itself uncertain; they should not be treated as a validated design recommendation. This is not observed power. The original trial design rationale, including any assumptions about expected effect size or attrition, is not reported in the registry record.

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, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.183; treatment proportion p₁ = 0.255; average p̄ = 0.219.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.5847 = 1.1460.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.5825 = 0.4902.
4. n = (1.1460 + 0.4902)² / (0.0720)² = 516.0, rounded up to 516 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
p0 <- 0.182795698924731                          # control proportion
p1 <- 0.254826254826255                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^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 (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(3465904)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 516 (80% power), 691 (90% power)
 75% of observed effect: n per arm = 891 (80% power), 1,192 (90% power)
 50% of observed effect: n per arm = 1,941 (80% power), 2,598 (90% power)
power.prop.test: 516 
Simulated power at n = 516 per arm: 0.805 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-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 a primary endpoint and several secondary outcomes, making multiplicity relevant. When multiple outcomes are tested, the chance of obtaining at least one apparently unusual result can rise. In general, a prespecified strategy may control this issue by defining an outcome hierarchy or adjusting the testing procedure. The registry record does not report whether such a strategy was used, so the posted secondary p-values should be understood as unadjusted.

The primary comparison has an unadjusted p-value of 0.043. The record does not say whether the primary hypothesis was tested with a prespecified procedure, whether any interim analyses occurred, or how any testing across outcomes was handled. Those details are not reported in the registry record. The primary result can still be described as posted, but the available information does not establish how it fits into a complete family of planned analyses.

The registry does not report the approach to missing data, the definition of the primary analysis population, or whether participants were analyzed according to their randomized assignment. The primary outcome denominators are 259 for Verum and 279 for Sham; other outcomes have their own denominators. Differences between denominators do not by themselves explain why observations are absent or establish how missingness might affect the estimates.

Further information about exclusions, protocol deviations, missing assessments, and sensitivity analyses would help assess the robustness of the results. Without those details, it is not possible to determine from the registry record whether missing data could have changed the comparisons or whether the analysis included all randomized participants. These are reporting limitations, not evidence that a particular problem occurred.

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.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: appendicitis leading to appendectomy (0.3%).

The serious adverse-event figures are counts alongside the group sizes at risk for serious events. The Verum group lists 0 serious adverse events among 298 at risk; the Sham group lists 1 among 303 at risk. Deaths are recorded as 0 in each group. The serious event term listed is appendicitis leading to appendectomy, with 0.3% reported.

Other adverse events are reported separately: 22 among 259 at risk in Verum and 8 among 279 at risk in Sham. These are counts, not adjusted comparisons. The registry record does not provide event-level details, severity classifications for the non-serious events, timing, or attribution to the device or study procedures. The serious event term does not establish that the event was caused by the intervention.

These figures are descriptive safety information. They do not, on their own, establish a comparative safety profile: the counts are limited, and the registry record does not report a statistical analysis of adverse events or further details about ascertainment and follow-up. Absence of a recorded death or a small number of serious events should not be interpreted as proof that no safety risks exist.

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

The posted primary result describes a higher observed proportion meeting the pain-freedom definition at 2 hours in the Verum group than in the Sham group. The unadjusted risk difference is 0.072, and its confidence interval ranges from 0.002 to 0.142. The estimate is therefore compatible with a small positive difference as well as with a larger one. It is a comparison of groups in this trial, not a guarantee of an outcome for an individual.

The result concerns a specific device program, comparator, population context, endpoint definition, and assessment time. It does not establish how outcomes would differ at other times, with other approaches to treatment, or in groups not described by the registry record. The trial title and objective concern acute migraine treatment, but the posted endpoint does not capture all dimensions of a migraine attack or longer-term outcomes.

The confidence interval communicates sampling uncertainty, while other limitations remain. The registry record does not report the complete statistical analysis plan, missing-data methods, analysis populations, or multiplicity procedures. These gaps limit assessment of how sensitive the result may be to analytic choices and incomplete outcome information. The unadjusted p-value is not a measure of the probability that the result is true or of the magnitude of any benefit.

The secondary results address additional symptoms and medication use, but they do not all show the same direction of estimate, and the registry does not provide numerical results for every listed outcome. Unadjusted secondary findings should be treated as supportive context rather than as a series of definitive conclusions. Safety counts are also descriptive and do not establish causation or rule out uncommon risks.

Overall, the registry results provide a statistical comparison for the primary endpoint and descriptive information about selected secondary and safety outcomes. They do not, by themselves, determine clinical importance or support individual medical decisions.

17. Why This Trial Matters Statistically

This trial illustrates why a clinical result should be read through both its effect estimate and its uncertainty. The primary risk difference gives an absolute-scale comparison, while the confidence interval shows how much uncertainty remains around that estimate. A p-value near a conventional threshold cannot replace either quantity, because it does not describe the range or size of effects compatible with the data.

The endpoint is binary and tied to a defined assessment time. This makes the primary comparison straightforward to describe, but it also narrows the question: pain freedom at 2 hours is not the same as sustained relief, absence of associated symptoms, or reduced use of rescue medication. Keeping these outcomes distinct is important when interpreting a trial with multiple clinical measures.

The record also illustrates the importance of reporting analysis details. The registry gives counts, denominators, and unadjusted comparisons, but does not report the full plan for missing data, analysis populations, or multiplicity. Those details affect how confidently a reader can evaluate the reported estimates and how secondary findings should be weighed.

Finally, planning illustrations based on an observed effect can demonstrate how assumptions about target effect size influence prospective sample-size requirements. They are not a substitute for the trial's original design rationale and cannot be used to describe the completed study's observed power. Clear separation of planning assumptions, observed results, and inferential uncertainty is central to sound biostatistical interpretation.

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 record leaves important aspects of trial conduct and analysis unspecified. It does not report detailed eligibility criteria, baseline characteristics, the randomization procedure, or how masking was maintained and assessed. These omissions make it difficult to evaluate the population represented by the outcome counts or to judge the operational details of the comparison.

The primary outcome denominators are 259 for Verum and 279 for Sham, while the enrollment field records 607. The registry does not explain the relationship between enrollment and the analysis denominators or why denominators differ across outcomes. The missing-data approach, analysis population, exclusions, and handling of protocol deviations are not reported. No conclusion about the reasons for these denominator differences can be drawn from the record alone.

The statistical analysis plan is not described in enough detail to establish the exact methods used for the posted estimates, confidence intervals, and p-values. Adjustment for baseline variables, interim analyses, multiplicity handling, and the planned hierarchy of outcomes are not reported. The posted comparisons are unadjusted, which limits what can be inferred about analyses beyond the group summaries.

Numerical results are not reported in the record for every listed secondary outcome. Safety information is also limited to summary counts and a serious-event term; details about event timing, attribution, and ascertainment are not reported. These limitations constrain interpretation of the breadth and robustness of the results, but they do not establish that a specific bias or trial-conduct problem occurred.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: A Phase III Trial of e-TNS for the Acute Treatment of Migraine — NCT03465904.
• Registry record last updated 2024-12-11; status last verified 2024-11.
• Results first posted 2019-07-01.
• 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, quadruple-masked, parallel-group, sham-controlled Phase III study of the Verum and Sham Cefaly® Abortive Program devices for acute migraine treatment. The phase field is recorded as NA. Enrollment is 607, and the primary endpoint is pain freedom at 2 hours.

The posted primary counts are 66 of 259 for Verum and 51 of 279 for Sham. The unadjusted risk difference is 0.072, with a 95% confidence interval from 0.002 to 0.142 and an unadjusted p-value of 0.043. Secondary outcomes and adverse-event counts provide additional descriptive information, but the registry record does not report a complete statistical analysis plan, missing-data methods, or multiplicity procedures.