Physiologic Response to Glucagon at Varying Insulin Levels: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Physiologic Response to Glucagon at Varying Insulin Levels (NCT01483651), a randomized na study. The primary outcome is Area Under the Curve for Glucose Above Baseline.

2. Clinical Question

The study rationale describes a question about whether insulin levels affect glucagon’s ability to raise blood glucose. The trial measured a glucose-production response using a stable glucose isotope assay. Its posted results can be read as a comparison of response summaries under different insulin infusion conditions. They do not, by themselves, establish how responses would differ outside the study conditions or in other populations.

3. Trial Design

The registry describes a randomized, single-masked, crossover study. In a crossover design, participants receive multiple study conditions in a sequence, so observations under different conditions may come from the same participant. The arm descriptions list sequences in which low, medium, and high regular insulin infusion are administered in different orders, with glucagon administration at each insulin level. The registry does not specify who was masked.

The listed study conditions are low, medium, and high insulin infusion rates, with glucagon administered in each condition. The record gives the condition sequence descriptions but does not report the actual infusion rates, glucagon dose, duration between study visits, or any washout procedures. Those details are not reported in the registry record.

The registry lists enrollment of 11 and a completed study. Outcome summaries are posted for the three insulin conditions: the low condition has a reported mean based on 10 observations, the medium condition based on 9, and the high condition based on 10. The record does not explain why the outcome denominators differ or how those observations relate to the enrollment figure. They should not be treated as a documented account of participant flow.

The primary outcome was the area under the curve for glucose above baseline, assessed for 60 minutes after each glucagon administration. The record describes measurement of glucose appearance with dideuterated glucose and gas chromatography-mass spectrometry. It lists one outcome measure and no posted secondary outcomes. A detailed protocol, a description of the randomization procedure, and the original statistical analysis plan 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

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 Area Under the Curve for Glucose Above Baseline, measured over 60 minutes after each glucagon administration.

The primary endpoint is the area under the curve for glucose above baseline after glucagon administration. It is intended to summarize the glucose response over the 60 minutes following each administration, rather than representing a single glucose measurement at one time point.

The registry description says that the change in the rate of glucose appearance was assessed using the stable glucose isotope dideuterated glucose, measured by gas chromatography-mass spectrometry. The outcome is expressed in mg/kg glucose per mcg glucagon. The description explains that the underlying rate is measured over time, and that the time component cancels in the area calculation; the resulting area is also normalized per microgram of glucagon delivered.

Using an area-under-the-curve measure can capture the overall response across the stated observation period. Normalization per microgram of glucagon is intended to express the response relative to the delivered amount. These are general features of the measurement, not evidence that it captures every clinically relevant aspect of glucose control. The registry record does not report the calculation details, baseline definition, assay precision, or whether the endpoint was adjusted for other variables.

The reported summaries are means and standard deviations for the continuous endpoint in each insulin condition. The registry does not post a separate endpoint result for a different clinical outcome.

7. Results Posted in the Registry

• High Insulin Infusion Rate: mean 0.03 versus 0.62 on control; difference -0.59 (95% CI -0.80 to -0.38), standardized effect d = -2.47; z-test p = <0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The outcome is continuous and is reported as a mean with a standard deviation. A mean describes the central value of the measurements in a condition. A standard deviation describes how spread out the observed measurements are around that mean. It is a descriptive measure of variability, not a confidence interval for the mean and not a range containing all observations.

What does the mean difference express?

The registry reports a mean difference for high insulin infusion versus low insulin infusion. A mean difference expresses the contrast between the two condition means in the units of the endpoint, with direction determined by the comparison’s ordering. The reported estimate is -0.593. Its negative sign indicates a lower mean endpoint in the high insulin condition under the posted comparison’s direction. It is an estimate for this measured outcome, not a statement about every participant or every possible setting.

How should the p-value be read?

The unadjusted p-value is <0.001. In general, a p-value describes how incompatible the observed data, or data more extreme, would be with a specified null hypothesis under the assumptions of the statistical test. It is not the probability that the null hypothesis is true, nor does it measure the probability that the result happened “by chance.” The registry does not report the test used or its assumptions, so those details are not reported in the registry record. “Unadjusted” indicates that this p-value is presented without a reported multiplicity adjustment; the registry does not provide a broader testing plan.

Why does the crossover design matter?

In general, crossover studies compare conditions within participants, which can reduce the influence of stable differences between participants. However, measurements from one participant are usually not statistically independent. An analysis should account for this dependence when estimating uncertainty. Study sequence and period may also matter if responses differ by order or over time. The registry identifies a crossover design and lists different condition orders, but the analysis method for within-participant dependence, sequence, and period is not reported in the registry record. The posted comparison should therefore be understood as a registry result whose full model cannot be evaluated from the record.

What does the confidence interval add?

In general, a confidence interval gives a range of values compatible with the data and the method used to construct it, under repeated use of that method and its assumptions. It conveys estimation uncertainty in a way that a point estimate alone cannot. The interval posted for the mean difference lies entirely below zero. That is consistent with the direction of the estimate, but the interval’s interpretation depends on the unreported details of the analysis. A confidence interval is not a range of individual responses, and it does not account for uncertainties that the analysis did not include.

What does over-dispersion mean in general?

Over-dispersion is a concern when observed variability is greater than a statistical model expects. It is especially relevant to some count-data models, where excess variability can make standard errors too small if ignored. This trial’s primary endpoint is continuous and summarized with means and standard deviations, not a count outcome. The registry does not report an over-dispersion assessment or a model for the primary comparison. The general concept should not be treated as a finding about this trial.

What is not described?

The registry lists no posted analysis records. It does not state the statistical test or model, whether estimates were adjusted, how missing measurements were handled, which participants were included in each analysis, or how the crossover structure was incorporated. It also does not report an original sample-size justification or a detailed statistical analysis plan. These omissions limit assessment of whether the posted comparison follows the intended design and how robust its uncertainty estimate is. The displayed condition summaries and comparison remain useful descriptions of what is posted, but they do not fill in those undocumented methods.

10. Confidence Intervals and Precision

The posted high-versus-low mean difference is -0.593. Its confidence interval is reported with both limits below zero, so the interval excludes a zero difference. The interval gives a range of estimates compatible with the reported analysis, subject to the method’s assumptions. Its width conveys uncertainty around the estimated contrast; it does not show the spread of individual outcomes.

The p-value of <0.001 and the confidence interval address related but different questions. The p-value describes compatibility with a null hypothesis under a test’s assumptions, while the interval describes the range of effect estimates supported by the procedure. Neither quantity measures clinical importance by itself. The endpoint’s units and the study’s narrow measurement conditions are relevant when interpreting the mean difference.

Precision is also constrained by the small study enrollment and the condition-specific outcome denominators. The record lists an enrollment of 11 and reports 10 observations for low insulin, 9 for medium insulin, and 10 for high insulin. It does not explain the denominator differences. The confidence interval reflects the analysis used for the posted comparison, but the registry does not report enough methodological detail to assess its treatment of the crossover design, missing measurements, or other sources of uncertainty.

The interval should not be treated as covering all plausible results in every population or clinical setting. It quantifies uncertainty only as represented by the posted statistical comparison and its assumptions. No confidence intervals are posted for the medium-condition contrasts because those comparisons are not reported.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The sample-size values are planning illustrations based on the observed high-versus-low effect, not the trial’s original design calculations. For this continuous endpoint, the figures refer to participants per arm, not total events. The planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each row considers detecting a stated fraction of the observed effect. The trial’s own design assumptions and sample-size justification are not reported in the registry record.

The 80% power column gives the illustrated number of participants per arm for a design intended to have an 80% chance of detecting the selected effect under the stated assumptions, if that effect and those assumptions are correct. The 90% power column expresses the corresponding planning target with a higher chance of detection. These are planning concepts, not guarantees about a future study.

The rows for 100% of the observed effect list 3 participants per arm for 80% power and 4 participants per arm for 90% power. For 75% of the observed effect, the corresponding figures are 5 and 7 participants per arm. For 50% of the observed effect, they are 11 and 14 participants per arm. Smaller effects require more participants under these assumptions, which is why the planning figures rise as the fraction of the observed effect becomes smaller.

These figures are not observed power. They are not evidence that the completed study had a particular probability of detecting an effect, and they do not establish that the observed effect will recur. Because the illustration is anchored to the observed effect, it is sensitive to the uncertainty and possible exaggeration of an effect estimated in a small study. It should be read as a conditional planning calculation, not as a recommendation or a substitute for an original design rationale.

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 = -0.593; pooled standard deviation σ = 0.240.
2. n = 2 × (1.96 + 0.842)² × 0.240² / -0.593² = 2.6, rounded up to 3 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 <- -0.593                      # observed difference in means
sigma <- 0.240416305603426                     # 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(1483651)
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 = 3 (80% power), 4 (90% power)
 75% of observed effect: n per arm = 5 (80% power), 7 (90% power)
 50% of observed effect: n per arm = 11 (80% power), 14 (90% power)
power.t.test: 3.8 
Simulated power at n = 3 per arm: 0.619 (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 lists one primary outcome measure and no posted secondary outcome results. It posts one inferential comparison, high versus low insulin infusion, with an unadjusted p-value. It does not report a statistical comparison involving the medium insulin condition or an overall test across all three conditions.

Multiplicity arises when several hypotheses or outcomes are tested: the chance of at least one small p-value can increase as the number of tests grows. In general, a prespecified testing strategy or an adjustment can address this issue. The registry does not report whether additional comparisons were planned, whether any multiplicity procedure was used, or whether the posted comparison was the only planned test. The label “unadjusted” should not be taken to establish the complete testing history.

The record does not report how missing observations were handled, why outcome denominators differ by condition, or the analysis populations used. It also does not identify whether all randomized participants contributed to each posted summary. These details are particularly relevant to a crossover design, where participation in multiple conditions and the availability of measurements at each condition affect the analysis.

The registry does not post an analysis model or explain how it accounted for repeated measurements within participants, treatment sequence, or period. It does not report an intention-to-treat or per-protocol analysis population. These omissions prevent a full assessment of the relationship between the randomized design and the posted estimate. They are not evidence that a particular method was or was not used outside the registry record.

14. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

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 serious adverse event figures report zero affected participants in the low insulin infusion group, zero in the medium insulin infusion group, and zero in the high insulin infusion group. The corresponding numbers at risk are 10, 9, and 10. These are the registry’s group-level entries; they do not establish that no other type of safety event occurred.

The record lists other adverse events affecting 7 participants in the low insulin group, 8 in the medium insulin group, and 5 in the high insulin group, with the same group-specific numbers at risk as those reported for the serious-event summaries. The registry does not provide event terms or severity breakdowns for these other events in the posted safety information. Death counts are not reported in the registry record.

These counts are descriptive. The registry does not post a statistical comparison of adverse events across insulin conditions, and the crossover design means the groups should not automatically be read as independent parallel groups. The record does not clarify whether the same person could contribute to more than one condition’s safety figures or how events were assigned. The counts therefore do not establish comparative safety or support conclusions beyond the entries recorded for these conditions.

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

The posted results describe a lower mean glucose area under the curve in the high insulin infusion condition than in the low condition, with a reported mean difference of -0.593 and an unadjusted p-value of <0.001. The interval for that comparison excludes zero. These findings concern the measured glucose response over 60 minutes after glucagon administration, normalized per microgram of glucagon, under the study conditions.

The results do not show that glucagon does or does not work in general, and they do not establish a clinical benefit or harm. The endpoint is a measured glucose-production response, not a reported patient-centered outcome. The record does not report outcomes such as longer-term glucose control or clinical events. The observed condition summaries also do not establish a tested trend across low, medium, and high insulin, because inferential comparisons involving the medium condition are not posted.

The study enrolled 11, and the posted outcome summaries have condition-specific denominators of 10, 9, and 10. The registry does not explain these differences or detail the analysis model. That limits how completely the precision and potential sources of bias can be assessed, especially given the crossover design.

The finding is therefore best read narrowly: in this registry’s reported comparison, the mean primary endpoint was lower for high than for low insulin infusion. It does not establish the size or direction of responses for every individual, demonstrate what would happen in other populations or dosing conditions, or answer broader questions about closed-loop glycemic control. Those questions are not resolved by the posted primary endpoint result.

16. Why This Trial Matters Statistically

This trial addresses a statistical question in which the same people may contribute measurements under several conditions. That crossover structure creates a useful opportunity to compare responses while reducing the influence of stable differences between participants. It also makes the analysis method important: uncertainty estimates should reflect the relationship among repeated measurements, and potentially the order and timing of conditions.

The registry identifies randomized condition sequences and reports a continuous endpoint with means and standard deviations. It also posts a high-versus-low mean difference and confidence interval. Together, these elements show why a point estimate, its uncertainty, and the design must be considered together. A small p-value alone does not describe the magnitude, variability, or generalizability of the measured response.

The condition summaries include a medium insulin group, but the registry posts no inferential comparison involving that condition. This illustrates the distinction between descriptive summaries and tested contrasts: means can describe a pattern, while a statistical claim about differences requires a specified comparison and analysis. The registry does not report whether an overall trend was tested.

The record also demonstrates the limits of registry-level reporting. Enrollment and outcome denominators are not the same information, and the record does not explain their relationship. Without the analysis population, handling of missing measurements, or model details, readers cannot fully assess how the posted estimate reflects the randomized crossover design. Clear reporting of those choices is central to evaluating precision and reproducibility.

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 study’s enrollment is listed as 11, while outcome summaries are based on 10 observations for low insulin, 9 for medium insulin, and 10 for high insulin. The registry does not explain the differences, so the participant flow and reasons for unavailable measurements cannot be determined from the record. The original sample-size justification is also not reported.

Although the design is described as randomized, single-masked, and crossover, the registry does not describe who was masked, how randomization was generated or implemented, or how the analysis accounted for within-participant measurements. It does not report sequence or period effects, washout procedures, the precise infusion rates, or the glucagon dose. These omissions make it difficult to assess the full design and its possible sources of bias.

The primary endpoint is a laboratory-based glucose response measured during the 60 minutes after glucagon administration. The record does not report other clinical outcomes or secondary outcome results. Its findings therefore apply to this endpoint and study setting; broader effects are not established by the posted outcome.

The registry posts one comparison and no analysis records. The test or model, missing-data approach, analysis population, and any adjustment for multiple comparisons are not reported. The safety record gives group counts but does not report event terms for other adverse events or a statistical comparison. These limitations reflect what the registry record documents; they should not be taken as proof that unreported procedures were absent from the study.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Physiologic Response to Glucagon at Varying Insulin Levels — NCT01483651.
• Registry record last updated 2016-03-29; status last verified 2016-03.
• Results first posted 2014-09-22.
• 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

The registry describes a completed randomized, single-masked crossover study of glucagon response during low, medium, and high insulin infusion in people with type 1 diabetes mellitus. Enrollment is listed as 11. The primary endpoint is area under the curve for glucose above baseline, measured for 60 minutes after each glucagon administration and expressed per microgram of glucagon delivered.

Posted mean endpoint values are 0.623 for low insulin, 0.59 for medium insulin, and 0.03 for high insulin. The posted high-versus-low comparison reports a mean difference of -0.593, a confidence interval excluding zero, and an unadjusted p-value of <0.001. No secondary outcome results or additional analysis records are posted.

Serious adverse event counts are zero in each condition; other adverse events are also recorded. The registry does not report the detailed analysis plan, reasons for differing outcome denominators, or several design and safety details. The posted results should be interpreted as a narrow comparison of the primary measured response under the stated study conditions.