The Preventive Treatment of Migraine With Low-Dose Naltrexone and Acetaminophen Combination: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for The Preventive Treatment of Migraine With Low-Dose Naltrexone and Acetaminophen Combination (NCT03194555), a randomized phase 2 study. The primary outcome is Change in Monthly Migraine Days (MMD) From Baseline to the Last 28 Days of Treatment Period..

2. Clinical Question

3. Trial Design

This was a randomized, double-blind, parallel-group phase 2 study comparing a low-dose naltrexone and acetaminophen combination with placebo. The registry lists enrollment as 12 and the study status as completed. The recorded study start was 2017-08-25, and primary completion was 2018-07-26. The sponsor was Allodynic Therapeutics, Inc.

The brief summary describes the study as small and placebo-controlled, with an open-label extension for none-responders. The primary outcome timeframe, however, refers to the last 28 days of an 84-day double-blinded treatment period. Details of the open-label extension, including its procedures, participants, and outcomes, are not reported in the registry record.

The primary outcome was change in monthly migraine days from a 28-day baseline period to the last 28 days of treatment. The primary analysis population was modified intent to treat, defined in the registry as all randomized participants who took study drug. The posted arm summaries list 6 participants for the combination group and 6 for placebo. The registry does not report how many randomized participants did not take study drug, or whether any participants were excluded from the modified intent-to-treat population for other reasons.

The registry lists 13 outcome measures, 10 analyses, and five posted secondary outcomes. These include responder counts based on improvement in monthly migraine days, acute migraine medication treatment days, and change in HIT-6. The registry record does not provide arm descriptions beyond the treatment names. Dosing, adherence, allocation procedures, and the procedures used to maintain blinding are not reported in the registry record.

4. Participant Flow and Accounting

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

Overall Study

Analysis population for the primary outcome, as defined in the registry: Modified intent to treat (mITT) participants included all randomized participants who took study drug.

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: Baseline analysis population included all treated participants (all enrolled participants who took the study drug).

6. Primary Endpoint

The registry lists the primary outcome as Change in Monthly Migraine Days (MMD) From Baseline to the Last 28 Days of Treatment Period., measured over From the 28-day baseline period to the last 28 days of the 84-days double-blinded treatment period..

The primary endpoint was change in monthly migraine days, measured from the 28-day baseline period to the last 28 days of the 84-day double-blinded treatment period. It is a continuous outcome: each participant's monthly migraine-day measure can take a range of values, and the reported group summaries are means with standard deviations. The registry defines the primary analysis population as modified intent to treat, including randomized participants who took study drug.

Monthly migraine days provide a count-based way to describe headache frequency over a defined observation period. Comparing a follow-up period with baseline can describe how the measured frequency changed during treatment. Reporting a group mean gives a summary of the average change, while the standard deviation describes variation among individual observations around that mean. Neither summary alone shows the distribution of individual responses or establishes the precision of the between-group comparison.

The registry's endpoint description also defines qualifying migraine headaches as moderate or severe and lasting at least 30 minutes, according to the stated International Classification of Headache Disorders definition. The posted results give a mean change of -5.67 days with a standard deviation of 3.2 in the combination group, and -3.5 days with a standard deviation of 5.56 in the placebo group. The registry does not provide confidence limits for these arm-specific means. Its reported between-group analysis is labelled as a chi-squared analysis with a risk-difference effect measure, which is not the same form of summary as a comparison of continuous mean changes.

7. Why No Re-analysis Is Shown

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous because it is reported as a mean change in monthly migraine days. For a continuous endpoint, an analysis commonly compares group means or estimates a difference in means, with an uncertainty interval. The registry instead labels its reported analysis as chi-squared and its effect measure as risk difference. Those labels usually describe analysis of a categorical outcome, such as whether an event occurred, rather than a mean change. The record does not explain the basis for this choice or identify a categorical version of the primary endpoint. This mismatch is an important interpretive limitation.

What do the means and standard deviations describe?

The mean is the arithmetic average of observations in a group. Here, the recorded means are -5.67 days for the combination group and -3.5 days for placebo. The standard deviation describes how much individual observations vary around a group's mean; the posted values are 3.2 and 5.56, respectively. A standard deviation is not a confidence interval and does not directly quantify uncertainty in a comparison between groups. It describes dispersion among observations, while a confidence interval for an estimate also depends on the analysis and the amount of information available.

The outcome is a change from baseline, so interpretation depends on how the change was defined and measured. The registry specifies the baseline and follow-up periods but does not provide participant-level values or additional detail about calculation of the monthly measure. The negative group means are the recorded changes. The registry does not provide confidence intervals around the means, which limits assessment of their precision as group summaries.

How should a confidence interval be read?

In general, a confidence interval expresses uncertainty around an estimate under the assumptions of a statistical procedure. A narrow interval indicates greater precision than a broad interval, all else equal. The posted interval for the risk difference is -3.67 to 8.01 at the 95% level. It spans zero, so it includes values corresponding to no difference on that effect-measure scale, as well as values on either side. Because the registry does not explain the risk-difference analysis in relation to the continuous endpoint, this interval cannot be confidently interpreted as an interval for the difference in mean monthly migraine-day changes.

The reported p-value is 0.427. In general, a p-value is calculated under a null hypothesis and a specified statistical model; it is not the probability that the null hypothesis is true, nor does it measure the clinical importance of an effect. The registry does not report enough detail to determine the precise null model or assumptions underlying the chi-squared analysis. The p-value should therefore be read alongside the stated method and effect measure, not as a stand-alone test of the continuous mean endpoint.

Why does the endpoint-analysis mismatch matter?

A method should correspond to the type of outcome and the estimand being compared. A mean difference answers a question about average change. A risk difference answers a question about the difference in proportions meeting a defined binary condition. These are different quantities and generally require different data representations. The registry lists continuous mean and standard deviation summaries, but does not report a binary threshold for the primary outcome or explain how its risk difference was obtained. No recalculated two-arm continuous comparison is reported in the registry record.

In general, small group sizes can make estimates sensitive to individual observations and leave substantial uncertainty. The posted group summaries describe 6 participants per arm. The standard deviations show that observations varied within both groups, particularly in the placebo arm. Without participant-level data, assumptions and robustness cannot be checked independently. The record does not report a distributional assessment, an alternative analysis, or a sensitivity analysis.

What does randomization contribute?

Randomization is intended to make treatment assignment independent of participant characteristics on average, reducing systematic differences between groups. Double blinding is intended to reduce the influence of treatment knowledge on participants' experience and study assessment. These design features do not guarantee balance in a small trial, nor do they correct ambiguity in the endpoint analysis. The registry states that allocation was randomized and masking was double, but it does not report allocation concealment procedures or details of how masking was maintained.

What can planning illustrations tell readers?

In general, a sample-size calculation is a planning exercise based on assumptions about the effect to detect, variability, significance level, power, and allocation. The registry's planning assumptions describe a two-sided significance level of 0.05, equal allocation, and a normal approximation, using a fraction of the observed effect. Any resulting sample-size illustration is not an observed property of the completed study and is not observed power. The registry does not report the trial's own sample-size justification or enough information to treat a planning illustration as evidence that the study was adequately powered.

Statistical methods that would clarify the reported result—including the exact definition of the risk-difference outcome, the continuous endpoint comparison, model assumptions, and handling of missing observations—are not reported in the registry record. Accordingly, the posted estimate and test result can be described, but their direct interpretation as an analysis of the stated primary endpoint remains uncertain.

10. Confidence Intervals for Each Arm

No two-arm comparison is shown for this trial, but each arm's mean can be given with a t-based 95% confidence interval computed from the posted mean, spread and number of participants.

R code and output

arm <- c("Low-Dose Naltrexone and Acetaminophen Combination", "Placebo")
n   <- c(6, 6)
m   <- c(-5.67, -3.5)
sp  <- c(3.2, 5.56)
sd  <- sp      # posted standard deviations
for (i in seq_along(n)) {
  se <- sd[i] / sqrt(n[i]); h <- qt(0.975, n[i] - 1) * se
  cat(sprintf("CARM|%s|%d|%.3f|%.3f|%.3f|%.3f\n", arm[i], n[i], m[i], sd[i], m[i] - h, m[i] + h))
}

CARM  Low-Dose Naltrexone and Acetaminophen Combination  6  -5.670  3.200  -9.028  -2.312
CARM  Placebo  6  -3.500  5.560  -9.335  2.335

11. Analyses Reported by the Sponsor

The sponsor's posted analysis reports a risk difference of -2.17, a 95% confidence interval from -3.67 to 8.01, and p = 0.427, using a method labelled chi-squared. The primary endpoint is described as a continuous change in monthly migraine days, and the arm summaries are means and standard deviations. The registry does not explain how the sponsor's risk difference relates to those continuous summaries, or define the categorical quantity that was analyzed.

The registry record does not report a recalculated two-arm comparison of continuous mean changes. Therefore, there is no separate continuous-effect estimate to set against the sponsor's analysis. The arm means and standard deviations are descriptive summaries, not a replacement inferential analysis. The discrepancy flag is false, but that does not resolve the methodological mismatch in the labels or provide the missing analysis details. The sponsor's own analysis remains the reported inferential result; it should be quoted with its stated effect measure and method, while making clear that its connection to the continuous primary endpoint is not explained in the registry record.

12. Multiplicity, Missing Data and Analysis Populations

The registry lists 13 outcome measures, 10 analyses, and five posted secondary outcomes. The secondary outcomes include counts of participants exceeding 50% and 75% improvement thresholds in mean monthly migraine days, complete improvement in the last 28 days of the double-blinded treatment period, change in acute migraine medication treatment days, and change in HIT-6. Their names indicate that several outcomes and thresholds were considered, but results for those secondary outcomes are not reported in the record summarized for these results.

When multiple outcomes or analyses are examined, the chance of at least one apparently notable result can increase. In general, multiplicity procedures can address this issue through prespecified testing strategies or adjustments to inference. Whether such procedures were planned or used is not reported in the registry record. The record also does not report a statistical analysis plan, a hierarchy among outcomes, or whether secondary analyses were exploratory or confirmatory. It is therefore not possible to determine how the number of analyses was handled when interpreting the primary result.

The primary population is described as modified intent to treat, including randomized participants who took study drug. This differs from an analysis defined as all randomized participants, because participants who never took study drug would not meet the stated population definition. The registry does not report whether any randomized participants did not take study drug, or whether the analysis population differed from the randomized groups for any other reason.

Handling of missing outcome data is not reported in the registry record. The record does not specify how missing monthly migraine-day observations were treated, whether any imputation was used, or whether sensitivity analyses assessed the effect of missing data. The registry does not report interim analyses or a sample-size justification. These omissions limit assessment of whether the analysis population and statistical procedures were fully specified before results were known. They do not establish that a particular procedure was or was not used; they indicate that the relevant information is not reported in the registry record.

13. 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 non-serious adverse event terms

The registry reports zero serious adverse events in each group and zero deaths in each group. For other adverse events, the posted counts are 4 among 6 participants at risk in the combination group and 2 among 6 participants at risk in the placebo group. These counts describe the entries in the registry record; they do not establish the nature, severity, timing, or causal relationship of individual events.

No serious adverse event terms are listed. The record does not provide event-level descriptions or further information about how adverse events were collected or classified. A count of participants affected is not the same as a count of events if an individual can experience more than one event, and the registry does not clarify the counting detail for the other adverse events. With few participants in each group, these posted safety counts are limited summaries and cannot characterize uncommon events reliably.

In general, safety data from a small trial are most informative as a description of what was recorded during the study, rather than as a precise comparison of risks. The registry's figures should be read in that limited scope. They do not, on their own, establish whether the intervention caused or did not cause any event, and they are not a basis for medical advice.

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

The posted data describe mean changes in monthly migraine days during the specified treatment period. The combination group mean was -5.67 days, with a standard deviation of 3.2; the placebo group mean was -3.5 days, with a standard deviation of 5.56. These are group-level summaries for the stated modified intent-to-treat population. They do not show how each participant's outcome changed, how many individuals improved, or how consistently responses were distributed.

The registry's inferential result is a risk difference of -2.17, with a 95% confidence interval from -3.67 to 8.01 and p = 0.427. Because the endpoint is described as continuous but the analysis is labelled chi-squared and risk difference, the exact question addressed by that inferential result is unclear from the record. It should not be treated as an unambiguous test of the difference between the posted mean changes.

In general, a non-significant p-value does not demonstrate that two treatments are equivalent, and a confidence interval that includes zero does not establish that there is no meaningful difference. Conversely, the direction of the posted group means does not establish a causal effect. Randomization and double blinding support a comparative design, but the small group sizes and lack of a clearly described continuous-outcome analysis limit what can be concluded from the posted results.

The registry does not report the results for the listed secondary outcomes in the record, nor does it report missing-data methods, multiplicity procedures, or a statistical analysis plan. The record also does not provide participant-level data for independent analysis. As a result, the findings support a description of the recorded arm summaries and sponsor analysis, but not a definitive estimate of the comparative effect on monthly migraine days or a broad conclusion about treatment efficacy or safety.

15. Why This Trial Matters Statistically

This trial illustrates why the statistical method and the endpoint need to be read together. The primary outcome is defined as a continuous change in monthly migraine days, and the arm results are expressed as means with standard deviations. Yet the reported inferential analysis is labelled chi-squared and risk difference. Without an explanation of the categorical quantity analyzed, readers cannot confidently connect that estimate to the stated primary question. This is not merely a difference in terminology: a difference in means and a difference in risks answer distinct statistical questions.

The record also shows why descriptive results and inferential results should not be conflated. The posted arm means give a concise account of observed group averages, while standard deviations describe within-group spread. The reported confidence interval and p-value belong to the sponsor's stated analysis, but its form does not match the endpoint description. Each statistic has a role, and interpretation depends on knowing which quantity was estimated and under what assumptions.

With 6 participants per arm, the trial offers limited information for estimating average effects and variability. In general, small studies can be useful for generating evidence and examining procedures, but estimates may be imprecise and sensitive to individual observations. The registry's completed status and phase 2 designation describe the study record; they do not establish that its design or results support a definitive comparative conclusion.

Finally, the record lists several secondary outcomes while not reporting their results in the available outcome summary. Without a reported analysis plan, multiplicity approach, and missing-data methods, readers cannot fully assess the context in which the primary result was selected and interpreted. The statistical importance of this study is therefore as much about transparency and alignment of estimand, endpoint, and analysis as about the numeric summaries themselves.

16. 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 most important limitation for interpreting the primary result is that the endpoint is a continuous mean change, whereas the reported comparison is labelled as a chi-squared analysis with a risk-difference effect measure. The registry does not define the categorical outcome behind that analysis or explain how it relates to the monthly migraine-day endpoint. A continuous two-arm recalculation is not reported in the registry record, so the sponsor's inferential result cannot be checked against a matching comparison of means from the posted summaries.

The posted group sizes are 6 participants per arm. Such a small study provides limited precision, and the posted standard deviations indicate variability within both groups. The record does not provide individual-level observations, confidence intervals for the arm-specific means, distributional information, or sensitivity analyses. The confidence interval reported for the risk difference is broad and spans zero, but its interpretation is constrained by the uncertainty about the analyzed outcome.

The modified intent-to-treat population includes randomized participants who took study drug. The registry does not report whether any randomized participants were excluded from this population or how missing outcome measurements were handled. A statistical analysis plan, multiplicity procedure, sample-size justification, and interim-analysis information are not reported in the registry record. The record also does not report results for the listed secondary outcomes in this set of posted results, limiting assessment of the broader outcome profile.

Further design details are sparse. Dose and schedule, allocation concealment, blinding procedures, adherence, and details of the open-label extension described in the brief summary are not reported in the registry record. The safety information is limited to aggregate counts, with no serious adverse event terms listed and no event-level descriptions. These limitations restrict both statistical and clinical interpretation; they do not establish that unreported procedures were absent.

17. Related Tutorials

18. Related Statistical Calculators

19. Sources

• ClinicalTrials.gov: The Preventive Treatment of Migraine With Low-Dose Naltrexone and Acetaminophen Combination — NCT03194555.
• Registry record last updated 2024-04-10; status last verified 2024-03.
• Results first posted 2024-04-10.
• 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.

20. Record Summary

The registry describes a completed randomized, double-blind, parallel-group phase 2 study of a low-dose naltrexone and acetaminophen combination versus placebo for episodic migraine in adults. Enrollment was 12. The primary endpoint was change in monthly migraine days from a 28-day baseline period to the last 28 days of an 84-day double-blinded treatment period, analyzed in a modified intent-to-treat population of randomized participants who took study drug.

The posted mean changes were -5.67 days, with a standard deviation of 3.2, for the combination and -3.5 days, with a standard deviation of 5.56, for placebo. The reported analysis gives a risk difference of -2.17, a 95% confidence interval from -3.67 to 8.01, and p = 0.427. The registry does not explain how this chi-squared risk-difference analysis relates to the continuous primary endpoint. Serious adverse events and deaths were recorded as zero in both groups; other adverse events affected 4 participants in the combination group and 2 in placebo.