Naloxone, Hypoglycemia and Exercise: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Naloxone, Hypoglycemia and Exercise (NCT03149770), a randomized phase 2 study. The primary outcome is Change in Symptom Score.

2. Clinical Question

The rationale in the registry record is that exercise may be followed by an impaired counterregulatory response to hypoglycemia. The study asks whether giving intranasal naloxone during exercise is associated with a difference in that subsequent response, assessed using symptom scores. It is a question about a measured response under the study conditions, not a direct measure of longer-term awareness, daily-life events, or clinical outcomes.

The record describes this as a phase 2 trial and identifies its overall objective as evaluating intranasal naloxone in people with type 1 diabetes. The primary endpoint is the difference in symptom scores collected during a hypoglycemic clamp on Day 2. The record does not report a separate primary question about safety or a long-term outcome.

3. Trial Design

The registry describes NCT03149770, titled “Naloxone, Hypoglycemia and Exercise,” as a completed phase 2 randomized, quadruple-masked crossover trial sponsored by the University of Minnesota. The reported enrollment is 30. The record gives a start date of 2017-09-18 and a primary completion date of 2022-05-01.

The two listed sequences were Naloxone then placebo and Placebo then Naloxone. In a crossover design, treatment comparisons are made within a sequence in which participants receive more than one treatment condition. This can make the within-participant comparison relevant to interpretation, but the registry record does not describe the analysis model, the handling of sequence or period effects, or whether any washout was used. Those details should not be assumed.

The registry calls the study quadruple-masked but does not specify which roles were masked. The posted outcome summaries list 28 observations for Naloxone and 26 for Placebo. These are treatment-group outcome counts in the record; they should not be added or interpreted as a count of distinct participants in a crossover study. The record does not explain the difference between those counts.

The study summary describes administration during acute exercise on Day 1 and measurement during a hypoglycemic clamp on Day 2. The primary outcome is Change in Symptom Score. The registry does not report the original sample-size justification, detailed eligibility criteria, allocation procedures beyond randomization, or a statistical analysis plan.

4. Participant Flow and Accounting

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

Overall Study

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 Change in Symptom Score, measured over Day 2.

The primary endpoint is Change in Symptom Score, measured on Day 2 during a hypoglycemic clamp after intranasal treatment during exercise on Day 1. The registry describes the measure as a mean on a symptom-score scale from 0-72. A higher score represents a better outcome. It does not provide further information about the questionnaire’s items or how the change in score was calculated beyond describing the primary comparison as naloxone versus saline.

Symptom scores provide a way to quantify participants’ reported symptoms during the controlled hypoglycemic assessment. They are relevant to the stated study question because the registry’s rationale concerns the counterregulatory response to hypoglycemia after exercise. The endpoint therefore captures a response during the study assessment, rather than measuring longer-term awareness or events outside the clamp.

The posted group summaries report means and standard deviations: 25.0 with a standard deviation of 12.0 for Naloxone, and 21.0 with a standard deviation of 13.0 for Placebo. The posted comparison expresses the mean difference as Naloxone minus Placebo. The registry record does not report a confidence interval for each group mean or a separate primary endpoint analysis model.

7. Results Posted in the Registry

• Naloxone: mean 25.00 versus 21.00 on control; difference 4.00 (95% CI -2.69 to 10.69), standardized effect d = 0.32; z-test p = 0.241.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary measure is continuous: it is a symptom score summarized by a mean and standard deviation. A mean describes the average score in a group, while a standard deviation describes how dispersed individual observations are around that group average. The posted means are 25.0 for Naloxone and 21.0 for Placebo; the corresponding standard deviations are 12.0 and 13.0. These summaries describe the observed treatment-group data but do not, by themselves, describe uncertainty about the comparison.

The reported contrast is a mean difference, Naloxone minus Placebo. Its estimate is 4.0 score points. A positive value means the posted average is higher for Naloxone than for Placebo under this direction of subtraction. Since the scale description says a higher score represents a better outcome, that direction has a straightforward descriptive interpretation. It should not be treated as a conclusion about the effect without considering the interval estimate, design, and analysis details.

A confidence interval expresses uncertainty about an estimated quantity under the assumptions of the method used to construct it. The posted interval for the mean difference is -2.688 to 10.69. Because it spans zero, it includes no difference as well as differences in either direction. A confidence interval is not a guarantee that the true value lies in the interval, nor does it assign a probability to a specific value being true. Its interpretation also depends on whether the analysis appropriately reflects the trial design.

The unadjusted p-value is 0.241. In general, a p-value describes how unusual data at least as incompatible with a specified null hypothesis would be if that null and the test assumptions held. It does not measure the probability that the null hypothesis is true, the probability that the observed result occurred by chance, or the size of an effect. Here, the registry does not report the test or model used, and it records no analysis entries. The p-value therefore should be read as an unadjusted posted statistic rather than as a fully documented model result.

The distinction between a crossover design and an independent-groups analysis matters. In general, crossover observations from the same participant are related. A suitable analysis may need to account for that relationship, as well as any period or sequence features relevant to the design. The registry record identifies randomized sequences but does not state how the posted comparison handled within-participant correlation or sequence and period. It is not possible from the record to determine whether the comparison was based on paired observations or another method.

General statistical context: when observations are more variable than a model assumes, standard errors and confidence intervals can be too small if that extra variation is ignored. This is one reason the analysis model matters. There is no information in the registry record about over-dispersion, model diagnostics, or adjustments for variation beyond the stated standard deviations. No claim about such features can be made for this trial.

The record reports means and standard deviations rather than medians or other summaries. These statistics are useful for describing a continuous measure, but they do not show the full distribution of scores. Nor does the record provide participant-level data, subgroup summaries, or a description of how incomplete observations were treated. Those omissions limit independent assessment of distributional features and the assumptions used in the comparison.

The crossover sequences also make the reported arm counts important to interpret carefully. In general, treatment-period observations in a crossover trial are not equivalent to separate groups of unrelated participants. The registry lists 28 observations for Naloxone and 26 for Placebo but does not explain the unequal counts, whether they reflect missing measurements, or how the analysis handled them. The posted treatment-group summaries should therefore be understood as reported, without inferring a particular missing-data or paired-analysis procedure.

Finally, the registry reports no analysis entries and no posted secondary outcomes. It does not describe multiplicity adjustments, prespecified analysis populations, an intention-to-treat approach, or the original sample-size assumptions. The sample-size planning illustration uses stated assumptions and the observed effect; it is not evidence of the original trial design or of the probability that this trial would detect an effect.

10. Confidence Intervals and Precision

The mean difference is 4.0 score points, with a confidence interval from -2.688 to 10.69. The interval communicates uncertainty around the estimated difference more fully than the point estimate alone. It includes negative values, zero, and positive values, so the posted result does not narrowly distinguish between lower, unchanged, or higher mean scores under Naloxone relative to Placebo.

The interval’s endpoints are expressed in score points on the symptom measure. The lower endpoint is below zero, while the upper endpoint is above zero. That span means the direction of the underlying difference is uncertain in the posted summary. The estimate is also not precise enough to identify a single, well-defined magnitude of difference. The registry record does not state what difference would be considered important, so the interval cannot be judged against a reported clinical-importance threshold.

The standard deviations, 12.0 for Naloxone and 13.0 for Placebo, describe variability in the scores within the treatment groups. They are not confidence limits and should not be substituted for the interval around the difference. The comparison interval is the relevant measure of precision for the contrast reported.

Precision depends on the analysis as well as the observed data. Because the registry record does not describe the statistical model or how the crossover structure was handled, the interval should be interpreted as the interval accompanying the posted comparison, not as confirmation that all design features were incorporated. The record also does not explain the difference between treatment-group outcome counts or report a separate interval for a crossover-adjusted estimate.

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. They are illustrations computed from the observed effect, not the trial’s original design assumptions. The stated assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, a normal approximation, and an effect to detect defined as a stated fraction of the observed effect. The registry record does not report the original sample-size justification or the assumptions used to plan the trial.

For planning for 100% of the observed effect, the figures are 154 participants per arm for 80% power and 205 participants per arm for 90% power. For planning for 75% of the observed effect, they are 273 participants per arm for 80% power and 365 participants per arm for 90% power. For planning for 50% of the observed effect, they are 613 participants per arm for 80% power and 820 participants per arm for 90% power.

In general, power is the chance that a study would meet its specified statistical decision rule if the effect being planned for were the true effect and the assumptions held. The 80% and 90% columns describe different target probabilities for detecting the specified effect under the planning assumptions. Smaller effects require more participants to detect with the same target power, which is reflected in the increasing planning figures as the assumed fraction of the observed effect gets smaller.

These figures are planning illustrations, not observed power. They use the observed effect as their starting point and do not establish what the trial was designed to detect. Because the trial is described as crossover, the equal-allocation, two-arm normal-approximation illustration should not be mistaken for documentation of a crossover-specific design calculation.

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 = 4.000; pooled standard deviation σ = 12.491.
2. n = 2 × (1.96 + 0.842)² × 12.491² / 4.000² = 153.1, rounded up to 154 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 <- 4                      # observed difference in means
sigma <- 12.490765819966                     # 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(3149770)
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 = 154 (80% power), 205 (90% power)
 75% of observed effect: n per arm = 273 (80% power), 365 (90% power)
 50% of observed effect: n per arm = 613 (80% power), 820 (90% power)
power.t.test: 154 
Simulated power at n = 154 per arm: 0.799 (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. Multiplicity, Missing Data and Analysis Populations

The registry record lists one primary outcome and reports no posted secondary outcomes. It also records no analysis entries. The record therefore does not provide a complete statistical analysis plan, a list of all analyses conducted, or a description of which results were prespecified.

Multiplicity arises when several outcomes, comparisons, subgroups, or analytic choices are considered. In general, repeated testing can increase the chance of a false-positive finding if the analyses are interpreted without accounting for that multiplicity. The registry record does not state whether any multiplicity adjustment was planned or used. With no reported secondary outcome results or analysis entries, it is not possible to assess the full range of analyses conducted or whether selective reporting affected the posted comparison.

The record also does not describe the analysis population. It does not say whether analyses were based on all randomized participants, participants who completed both treatment conditions, or another defined set. Although the trial is described as randomized and crossover, the registry does not explain how participants with incomplete observations were handled.

Missing-data methods are not reported in the registry record. The treatment-group outcome counts differ, but the record does not identify why, how many measurements were missing, whether missingness occurred in one or both periods, or whether any imputation or sensitivity analysis was used. Those details matter because incomplete outcomes can affect both the estimate and its uncertainty, particularly when paired observations are part of the design.

Accordingly, the posted estimate and unadjusted p-value can be described, but the registry does not support a full evaluation of multiplicity control, analysis populations, or missing-data assumptions. These are reporting limitations rather than evidence that a particular procedure was or was not used.

14. 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 serious adverse event figures separately by treatment group. For Naloxone, 0 participants were affected by serious adverse events among 28 at risk; for Placebo, 0 were affected among 26 at risk. Deaths are reported as 0 in each group. No serious adverse event terms are listed.

For other adverse events, 4 participants were affected in the Naloxone group and 2 in the Placebo group. These are counts of participants affected as reported in the registry, not counts of distinct event types. The record does not list the terms for these other adverse events, their severity, timing, relationship to treatment, or whether any participant experienced more than one event.

These figures describe the safety information posted in the registry. A zero recorded count for serious adverse events or deaths does not establish that no such events could occur, and the other adverse-event counts do not by themselves establish a treatment-related difference. The registry record does not provide further detail needed to interpret event characteristics or comparative safety statistically.

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

The posted results show a higher mean symptom score under Naloxone than under Placebo, with a mean difference of 4.0 score points. The score definition says that higher values represent a better outcome. However, the confidence interval, from -2.688 to 10.69, includes differences in either direction. The estimate therefore remains uncertain in magnitude and direction.

The unadjusted p-value of 0.241 is another summary of the comparison, but it does not state the probability that naloxone is effective or ineffective. It does not measure the clinical importance of the observed difference, and it should not be interpreted without knowing the test and analysis assumptions. The registry record does not report those details or a sponsor analysis entry.

The result concerns a symptom score during a controlled hypoglycemic clamp on Day 2 after treatment during exercise on Day 1. It does not directly show what happens to symptoms or counterregulatory responses in other settings, over longer periods, or in populations not described by the record. The registry’s rationale discusses hypoglycemia awareness, but the primary endpoint is the score collected during the clamp, not a direct long-term awareness outcome.

The trial’s randomized crossover design is relevant, but the registry does not explain whether the posted comparison accounts for within-participant observations, sequence, or period. It also does not explain why the treatment-group outcome counts differ or how missing observations were treated. Those gaps limit what can be concluded from the posted summary.

In short, the record documents a positive point estimate alongside an interval compatible with both lower and higher scores under Naloxone. It does not establish a definitive direction or magnitude of difference, and it does not support claims about outcomes beyond the measured endpoint and study setting.

16. Why This Trial Matters Statistically

This trial raises a useful statistical issue: the design is crossover, while the posted results are expressed as treatment-group means and a mean difference. In a crossover study, observations from the same participant may be related. The statistical analysis needs to reflect the design to estimate uncertainty appropriately. The registry identifies the treatment sequences but does not say how the comparison handled that dependence or any sequence or period effects.

The posted estimate is interpretable as a descriptive contrast, but the missing analysis details make it difficult to know exactly what inferential procedure produced the confidence interval and unadjusted p-value. The record also lists different outcome counts for the two treatments without explaining why. These are not minor presentation details: they affect how readers assess the precision and potential bias of the comparison.

The interval is particularly important because the point estimate alone might appear to suggest a favorable direction for Naloxone on the symptom score. The interval spans negative and positive values, so that direction is not firmly established by the posted result. Looking at uncertainty alongside the estimate prevents a single summary value from being treated as a conclusive finding.

The planning illustration offers another statistical lesson. Its participant counts depend on the assumed fraction of the observed effect, the target power, and the stated planning assumptions. It is not a record of the original design rationale and is not observed power. This distinction matters when interpreting how informative a completed trial is and what a future study might require.

Overall, the study is a setting in which the clinical question, crossover structure, endpoint timing, analysis transparency, and precision all need to be considered together. The posted numbers can be described, while the registry’s omissions place limits on stronger statistical conclusions.

17. 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 limitation in interpreting the posted comparison is that the registry record does not describe the analysis model. Although the study is identified as a randomized crossover trial, the record does not state whether the comparison accounts for within-participant correlation, treatment sequence, or period. It also does not identify the statistical test underlying the unadjusted p-value.

The outcome counts are 28 for Naloxone and 26 for Placebo, but the record does not explain the difference. It does not report the amount, timing, or reasons for missing measurements, or how incomplete crossover observations were handled. The original sample-size assumptions and justification are also not reported, so the planning illustration should not be treated as evidence of the planned design.

The endpoint is a symptom score during a hypoglycemic clamp on Day 2. The registry does not provide questionnaire details beyond the score range and direction, or report a threshold for a clinically important difference. It also does not report secondary outcomes or analysis entries, limiting assessment of other outcomes and analytic choices.

The record gives limited detail about masking roles, allocation procedures, eligibility criteria, and the conduct of the study beyond its stated randomized, quadruple-masked crossover design and treatment sequences. It does not report whether any protocol deviations or sensitivity analyses occurred. These omissions do not establish that a procedure was absent; they mean it is not reported in the registry record.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Naloxone, Hypoglycemia and Exercise — NCT03149770.
• Registry record last updated 2024-04-16; status last verified 2024-03.
• Results first posted 2024-04-16.
• 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.

21. Record Summary

NCT03149770 is a completed phase 2 randomized, quadruple-masked crossover trial sponsored by the University of Minnesota. It enrolled 30 people with type 1 diabetes and compared treatment sequences of Naloxone then placebo and Placebo then Naloxone.

The primary outcome was Change in Symptom Score during a Day 2 hypoglycemic clamp after treatment during exercise on Day 1. The posted mean difference, Naloxone minus Placebo, was 4.0 score points, with a confidence interval from -2.688 to 10.69 and an unadjusted p-value of 0.241. The interval includes differences in either direction.

The registry record does not report the crossover analysis details, missing-data handling, original sample-size justification, or analysis entries. The posted comparison is therefore best interpreted as a summary of the recorded endpoint with important statistical details unresolved.