Liraglutide Versus Insulin Mono-therapy in the Closed Loop Setting: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Liraglutide Versus Insulin Mono-therapy in the Closed Loop Setting (NCT01755416), a randomized phase 2 study. The primary outcome is Blood Glucose Measures in Subjects on Closed Loop With Insulin and Liraglutide, Compared to the Closed Loop With Insulin Alone.

2. Clinical Question

3. Trial Design

The registry record describes a phase 2, randomized, open-label crossover trial. The study compared closed-loop insulin with closed-loop insulin plus liraglutide, using an ePID algorithm and Enlite sensors. In a crossover design, participants receive more than one treatment condition, so comparisons can be made within the same participant. The registry record does not report the order of treatment conditions, whether a washout period was used, or how period and sequence effects were handled.

The intervention descriptions specify about 27 hours of device use in each arm. For the liraglutide condition, the description specifies a single 1.2 mg injection before dinner on Day 1. In the insulin-alone condition, participants were not on study medication. The record lists enrollment of 18; the primary outcome results report 15 participants in each arm. How the outcome population relates to the enrollment figure is not reported in the registry record.

The study status is completed. The recorded study start is 2013-01, and the primary completion is 2015-01. The registry record does not describe the protocol's original sample-size justification, the planned statistical model, or any interim analyses. It also does not report details about allocation concealment or blinding beyond identifying the trial as randomized and open label.

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.

First Intervention ( Upto 2 Days)

Reasons for not completing this period:

Second Intervention (Upto 2 Days)

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 Blood Glucose Measures in Subjects on Closed Loop With Insulin and Liraglutide, Compared to the Closed Loop With Insulin Alone, measured over 0-1500 min.

The primary endpoint is described as a measure of targeted blood glucose levels in the closed-loop setting, comparing insulin plus liraglutide with insulin monotherapy. It is a continuous measure reported as a mean in mg/dl, with standard deviations for each arm. The outcome timeframe is 0-1500 min.

Blood glucose is relevant to the stated study question because the trial aimed to assess post-prandial glycemic excursions under closed-loop glucose control. A mean summarizes the average glucose level across the measured timeframe. It is useful for comparing overall levels, but it does not by itself describe the timing, size, or frequency of peaks after meals. The posted primary endpoint is not separately identified as a post-prandial-only measurement, and the registry record does not report a distinct excursion metric.

Standard deviation describes the spread of individual measurements around an arm's mean. It is not the same as the uncertainty in the estimated difference between arms. The comparison's confidence interval addresses that uncertainty. Neither the mean nor its spread alone establishes whether the observed difference is statistically persuasive or clinically important; interpretation also depends on the comparison estimate, its precision, and the endpoint's clinical context, which is not reported in the registry record.

7. Results Posted in the Registry

• Closed Loop/Insulin/Liraglutide: mean 144.60 versus 159.70 on control; difference -15.10 (95% CI -46.74 to 16.54), standardized effect d = -0.34; z-test p = 0.350.

8. Statistical Interpretation

9. Statistical Methods Explained

The endpoint is continuous, so it is summarized with a mean and standard deviation in each treatment condition. A mean provides a central summary of the measured glucose values. A standard deviation describes their dispersion around that mean. Larger dispersion means measurements are more spread out, while smaller dispersion means they are more clustered. Dispersion is not the same as uncertainty in the treatment comparison: the latter depends on the amount of information and on the analysis used.

What does the mean difference describe?

The reported mean difference is -15.1 mg/dl for insulin plus liraglutide compared with insulin alone. A difference compares the two condition means on the scale of the outcome, so it retains the original unit, mg/dl. The sign depends on the direction of the comparison: a negative value means the mean for the liraglutide condition was lower than the mean for the insulin-alone condition in the posted comparison. It does not describe every participant's response, and it does not indicate how the difference varied over time.

What does the confidence interval add?

A confidence interval describes uncertainty around an estimate under the method's assumptions. The posted interval is -46.74 to 16.54 mg/dl. Its inclusion of zero means that the range includes no mean difference, as well as values on either side. The interval should be considered alongside the point estimate: relying on the estimate alone would conceal how uncertain the comparison is. A confidence interval is not a range containing a known proportion of individual participant outcomes, and it is not a probability statement about the true effect after the data have been observed.

How should the p-value be read?

The unadjusted p-value is 0.35. In general, a p-value describes how unusual data at least as incompatible with a specified null model would be if that model and the analysis assumptions held. It does not give the probability that the null hypothesis is true. It also does not measure clinical importance. The registry record does not report an adjusted p-value or a multiplicity procedure, so the posted p-value should be read as unadjusted.

Why does the crossover structure matter?

A crossover study exposes participants to multiple treatment conditions. When properly analyzed, within-participant comparisons can account for stable differences between participants and may be more informative than treating each condition as an unrelated group. However, observations from the same participant are correlated. The analysis needs to reflect that dependence and may also need to address treatment order, period effects, or carryover. The registry record does not report the statistical model or how these features were handled. The posted arm summaries do not show the paired participant-level changes, so they do not independently establish whether the comparison used the crossover structure.

General statistical context: if variation is greater than a model assumes, uncertainty estimates and tests can be misleading. Methods that account for over-dispersion or other departures from model assumptions can improve calibration when such departures are present. The registry record does not report an over-dispersion assessment or a model that can be evaluated for this outcome. No specific claim about over-dispersion can therefore be made from the posted summaries.

The comparison also depends on the definition and measurement of the endpoint. The registered measure is mean blood glucose over 0-1500 min, while the stated objective concerns post-prandial excursions. A time-averaged mean can summarize overall glucose levels without showing meal-specific peaks or the pattern of change. The registry record does not report a distinct post-prandial endpoint alongside the posted mean.

Finally, statistical evidence and clinical importance are separate considerations. The estimated difference and its interval describe the observed scale and precision; the registry record does not state a threshold for a clinically important change. The posted results therefore support interpretation of the numerical comparison but do not, on their own, establish a clinical conclusion.

10. Confidence Intervals and Precision

The estimated mean difference is -15.1 mg/dl, with a reported confidence interval from -46.74 to 16.54 mg/dl. This interval is broad enough to include zero and estimates in both directions. It therefore does not isolate a single direction of difference with high precision. The point estimate alone suggests a lower mean in the liraglutide condition, but the interval indicates substantial uncertainty around that estimate.

Confidence intervals express uncertainty in an estimated quantity under the assumptions of the statistical method. They do not describe the range of glucose values for individual participants. The arm-level standard deviations, 50.9 mg/dl and 36.3 mg/dl, describe variability in the outcome values, rather than uncertainty in the treatment difference. These two forms of variation answer different questions.

The registry record identifies a crossover design, but does not report the analysis method or the within-participant covariance used in the comparison. In crossover data, the precision of a treatment contrast can depend on how outcomes within the same participant are related. Without that analysis detail or participant-level paired results, the confidence interval cannot be independently assessed for its treatment of the design. The record also does not report a clinically important difference threshold, so the interval cannot be classified against such a threshold.

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 events. The displayed planning values use the observed effect as a reference and consider planning for 100% of that effect, 75% of the observed effect, and 50% of the observed effect. For each assumed effect, the figures give the participants per arm for 80% power and the participants per arm for 90% power.

The stated planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is the stated fraction of the observed effect. The registry record does not report the original trial's sample-size justification or its original planning assumptions, so these figures are planning illustrations rather than a reconstruction of the trial design.

In general, power is the chance that a specified analysis will detect an effect of the size assumed when that effect is present, subject to the planning assumptions. The 80% power column gives the estimated participants per arm for a design with 80% power under those assumptions; the 90% column does the same for 90% power. Greater power generally requires more information. Smaller effects are harder to distinguish from background variation and therefore require more participants. The figures are not observed power: they are forward-looking planning illustrations based on the observed effect, not a measure of the probability that the completed trial's result is correct.

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 = -15.100; pooled standard deviation σ = 44.207.
2. n = 2 × (1.96 + 0.842)² × 44.207² / -15.100² = 134.5, rounded up to 135 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 <- -15.1                      # observed difference in means
sigma <- 44.2068999139275                     # 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(1755416)
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 = 135 (80% power), 181 (90% power)
 75% of observed effect: n per arm = 240 (80% power), 321 (90% power)
 50% of observed effect: n per arm = 539 (80% power), 721 (90% power)
power.t.test: 135.5 
Simulated power at n = 135 per arm: 0.797 (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 measure and no posted secondary outcomes. It does not report a multiplicity adjustment, a hierarchy of tests, or a prespecified strategy for controlling false-positive findings across multiple comparisons. The unadjusted p-value is 0.35. Because no multiplicity plan is reported, it is not possible to determine whether any adjustment was planned or applied outside the posted result.

The registry record also lists no posted analyses. It does not describe the statistical model, the handling of missing observations, or whether all randomized participants were included in the primary analysis. The population field for the primary outcome is blank, and the registry record does not define an intention-to-treat, per-protocol, or other analysis population. These items are important for understanding which observations contributed to the estimate and how incomplete measurements were treated.

The crossover design raises additional analysis questions. The registry record does not state how treatment sequence, period effects, carryover, or within-participant correlation were addressed. It also does not report the treatment order or washout arrangements. These details matter because the same participant contributes to more than one treatment condition, and the comparison should reflect the dependence between those observations.

The registry record lists enrollment of 18, while each arm's posted primary outcome summary reports 15 participants. It does not explain the relationship between these figures or give reasons for any difference. No conclusion about exclusions, withdrawal, or missing data can be drawn from the counts alone.

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 5% reporting threshold.

The serious adverse event figures report zero serious adverse events affecting participants at risk in the Closed Loop/Insulin group and zero in the Closed Loop/Insulin/Liraglutide group. The record also reports zero other adverse events affecting participants at risk in each group, and zero deaths in each group. The serious adverse event terms list is empty.

These figures describe events recorded in the registry for the reported groups. They do not show that no adverse events of any kind occurred outside the event categories reported, and they do not establish equivalent safety between the conditions. The registry record does not provide further detail about event definitions, ascertainment procedures, duration of safety follow-up, or the severity of other events beyond the reported counts. The outcomes were collected in a short device-use setting described as about 27 hours, so the posted counts should be understood within that study context.

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

The posted results show a lower mean blood glucose value in the insulin-plus-liraglutide condition than in the insulin-alone condition. The reported mean difference is -15.1 mg/dl. The confidence interval, -46.74 to 16.54 mg/dl, includes zero and spans values in both directions, while the unadjusted p-value is 0.35. Together, these statistics indicate that the comparison is imprecise and does not provide strong statistical evidence of a difference under the assumptions of the reported calculation.

This is not evidence that the conditions are identical. A confidence interval that includes zero can still be compatible with nonzero differences; the interval gives a range of estimates consistent with the data and method. Nor does the point estimate establish a clinically meaningful effect. The registry record does not report a threshold for clinical importance, and it does not report a separate post-prandial excursion result despite describing that as the study's aim.

The trial's crossover design could make within-participant information relevant to the treatment comparison, but the statistical method and paired results are not reported in the registry record. The arm summaries alone do not show the participant-level pattern or explain how the crossover structure contributed to the estimate. The short device-use setting and the outcome timeframe also limit the result to the registered conditions and measurement period.

The findings therefore describe the posted glucose summaries and their uncertainty. They do not establish that liraglutide improves or worsens glucose outcomes, that the treatments are equivalent, or that the results apply beyond the studied setting. The safety counts similarly describe the events recorded for these groups and do not establish comparative safety.

16. Why This Trial Matters Statistically

This trial is statistically informative as an example of a continuous endpoint studied in a randomized crossover design. The outcome is summarized with arm means and standard deviations, and the treatment contrast is reported with a confidence interval and an unadjusted p-value. Those summaries illustrate why an effect estimate should be interpreted together with its uncertainty rather than as a standalone result.

The crossover design is central to understanding the analysis. Because participants receive multiple conditions, within-participant comparisons may be useful, but the statistical approach must account for correlation between measurements and potentially for period or sequence effects. The registry record identifies the design but does not report how the analysis handled these features. That distinction matters: arm-level summaries do not reveal the paired variation that can influence precision.

The endpoint also highlights the importance of matching the scientific question to the measurement. The stated aim concerns post-prandial excursions, while the posted primary outcome is mean blood glucose over 0-1500 min. A mean can be useful for overall level, but does not provide a meal-specific pattern by itself. Readers should distinguish the registered objective from the actual reported measure.

Finally, the estimate is not precise enough to settle the direction of the difference. Its confidence interval includes zero, and the registry record does not report a clinical importance threshold. The trial therefore demonstrates how design, endpoint definition, analysis transparency, and precision all shape interpretation—not just the sign of a point estimate.

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 outcome summary reports 15 participants in each arm, while the registry record lists enrollment of 18. The record does not explain the relationship between these figures, identify the analysis population, or report how missing observations were handled. This prevents a clear accounting of who contributed to the primary result.

The trial is described as a crossover, but the registry record does not report treatment sequence, washout arrangements, or the statistical method used to account for within-participant dependence. It is therefore not possible to assess from the registry record whether period, sequence, or carryover effects were addressed. The arm-level means and standard deviations do not provide the paired changes needed to inspect those features.

The primary endpoint is mean blood glucose over 0-1500 min, while the stated aim concerns post-prandial excursions. The registry record does not report a separate meal-related excursion result. It also does not report the original sample-size justification, clinical importance threshold, multiplicity plan, or interim analysis approach. No secondary outcomes are posted, and no analyses are listed.

The intervention descriptions specify about 27 hours of closed-loop device use, including a single 1.2 mg liraglutide injection before dinner on Day 1 in the combination condition. The findings therefore concern the conditions and timeframe described in this record; broader or longer-term outcomes are not reported. These limitations constrain interpretation of both the estimated difference and the safety counts.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Liraglutide Versus Insulin Mono-therapy in the Closed Loop Setting — NCT01755416.
• Registry record last updated 2018-08-21; status last verified 2018-08.
• Results first posted 2018-08-21.
• 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 record describes a completed phase 2 randomized, open-label crossover study in type 1 diabetes. It compared closed-loop insulin alone with closed-loop insulin plus liraglutide using an ePID algorithm and Enlite sensors. The recorded study start is 2013-01, and primary completion is 2015-01.

The primary outcome is mean blood glucose in mg/dl over 0-1500 min. The posted mean difference for insulin plus liraglutide compared with insulin alone is -15.1 mg/dl, with a confidence interval from -46.74 to 16.54 mg/dl and an unadjusted p-value of 0.35. The interval includes zero, and the registry record does not report a separate post-prandial excursion result or the crossover analysis method.

The registry record reports zero serious adverse events, zero other adverse events, and zero deaths in each group. It does not report the original sample-size justification, analysis population, missing-data handling, or multiplicity plan.