Effect of Liraglutide for Weight Management in Pubertal Adolescent Subjects With Obesity: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Effect of Liraglutide for Weight Management in Pubertal Adolescent Subjects With Obesity (NCT02918279), a randomized phase 3 study. The primary outcome is Change in BMI SDS (Week 0, Week 56).

2. Clinical Question

3. Trial Design

The registry identifies this as a phase 3, randomized, double-blind, parallel-group, placebo-controlled trial. It was conducted globally, according to the brief summary. Random allocation assigned participants to liraglutide or placebo; the record does not describe the allocation procedure in further detail. Double masking means the record characterizes the trial as blinded, but which specific people were masked is not reported in the registry record.

The official title describes a 56-week trial followed by a 26-week period off study drug. The primary endpoint was assessed at week 56, comparing change from the week 0 baseline. The record also lists secondary outcomes involving BMI, body weight, waist circumference, BMI SDS at additional time points, and the proportions meeting specified BMI reduction thresholds. The numerical results for those other outcomes are not reported in the registry record details used for this account.

The trial is marked completed. Its enrollment is listed as 251, while the primary endpoint arm summaries report 113 participants in the liraglutide group and 105 in the placebo group. Those endpoint analysis counts differ from the enrollment figure because they refer to a specified analysis and outcome, not simply to enrollment. The registry record does not explain every reason for the difference between those counts.

The primary outcome description identifies a full analysis set based on randomization, receipt of at least one dose, and availability of post-randomization data. It also states that available data after treatment discontinuation were used, and that the week 56 results included participants who discontinued trial product but attended follow-up. Details of the original trial's sample-size justification, planned interim analyses, and full 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.

Before assignment: This trial consisted of a 12-week run-in period, during which participants received counselling on healthy nutrition and physical activity. Completed numbers include participants who completed the trial without prematurely discontinuing the trial product and participants who discontinued the trial product but came for the week 82 follow-up visit.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Results are based on the full analysis set (FAS) which included all randomised participants who had received at least one dose of trial product and had any post-randomisation data (according to the intention-to-treat \[ITT\] principle). "Overall Number of Participants Analyzed" = number of participants with available data.

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: Results are based on the full analysis set (FAS) which included all randomised participants who had received at least one dose of trial product and had any post-randomisation data (according to the intention-to-treat \[ITT\] principle).

6. Primary Endpoint

The registry lists the primary outcome as Change in BMI SDS (Week 0, Week 56), measured over Week 0, week 56.

The primary endpoint was change in BMI SDS from week 0 to week 56, measured in SDS score units. BMI SDS is a standardized measure that places a participant's BMI in relation to reference values that vary by age and sex. The registry describes calculation using reference parameters for the median, skewness, and variation coefficient, and says the method follows the WHO Multicentre Growth Reference. Scores below -3 and above 3 were adjusted as described in the WHO instruction.

Using a standardized score rather than raw BMI is intended to make BMI interpretable against age- and sex-specific growth references in children and adolescents. In general, standardization can help describe where a measurement lies relative to a reference distribution, while the change in that score describes movement on that standardized scale over time. It is not the same quantity as change in body weight or change in BMI itself; those are listed separately among the secondary outcomes.

The endpoint is a mean of a continuous measure. The posted arm summaries give the average change and standard deviation in each arm. A negative change represents a lower BMI SDS at the endpoint than at baseline. The result is a group-level summary, not a description of every participant's individual change. The primary outcome description says all available data were used, including data collected after trial product discontinuation, and includes week 56 follow-up for participants who discontinued study product early.

7. Results Posted in the Registry

• Liraglutide 3.0 mg: mean -0.25 versus -0.02 on control; difference -0.23 (95% CI -0.37 to -0.09), standardized effect d = -0.44; z-test p = 0.001.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary endpoint is continuous: each participant has a BMI SDS change, and the arm summaries describe the mean and standard deviation of those changes. A mean summarizes the central tendency of the observations. A standard deviation describes how spread out individual values are around the mean; it is not the uncertainty interval for the estimated mean or treatment difference.

What does the randomized comparison estimate?

In general, randomization aims to make the assigned groups comparable, on average, with respect to factors that could affect the outcome. The treatment difference compares outcomes between the randomized groups. For the posted primary analysis, the sponsor reports an ANCOVA treatment difference of -0.22. ANCOVA is a regression-based method that can compare groups while accounting for specified covariates. The registry record does not identify the covariates used in this analysis, so the exact adjustment cannot be described from the record.

The recalculated comparison is unadjusted and uses the posted arm means and standard deviations. An unadjusted comparison does not apply ANCOVA covariate adjustment. It is useful as a check on the scale and direction of the arm-level result, but it does not replace the trial's own analysis. The recalculated estimate is -0.23, with a confidence interval from -0.370 to -0.090 and p = 0.001. The sponsor's reported ANCOVA estimate is -0.22, with a 95% confidence interval from -0.37 to -0.08 and p = 0.002.

What does the confidence interval express?

In general, a confidence interval describes the uncertainty around an estimated quantity under a statistical procedure and its assumptions. It gives a range of values reasonably compatible with the observed data and model at the stated confidence level. It is not a range containing a specified proportion of individual participant outcomes, and it does not mean that the true value has a particular probability of lying in the realized interval. The sponsor's interval is labeled 95% in the registry record.

The interval's position relative to zero is relevant when the quantity is a between-group difference. Zero would correspond to no difference on the measurement scale under the comparison. The sponsor interval runs from -0.37 to -0.08, while the recalculated interval runs from -0.370 to -0.090. Both are on the negative side of zero. That interpretation concerns statistical compatibility under the relevant method; it does not settle clinical importance or individual response.

Why distinguish ANCOVA from a simple recalculation?

General statistical explanation: regression adjustment can change an estimate and its standard error because it uses information from the covariates in the model. The effect depends on the adjustment variables and their relationship to the outcome. A simple reanalysis based only on posted summary statistics cannot recreate an individual-level ANCOVA model. The registry does not report the covariate details or participant-level data needed to do so. Therefore the sponsor's analysis remains the primary result for interpreting the trial, while the unadjusted calculation is an approximate descriptive comparison.

How should variation be understood?

The arm standard deviations are 0.51 for liraglutide 3.0 mg and 0.54 for placebo. In general, variation among participants means that a group average does not capture each person's result. A standard deviation helps describe that spread, but it does not show the shape of the outcome distribution or identify outliers. The registry describes the endpoint as a mean of a continuous measure and reports standard deviations; further distributional diagnostics are not reported in the registry record.

General statistical explanation: if an outcome distribution is strongly skewed or contains unusual values, the mean and standard deviation may not fully characterize it. The record does not report a distributional assessment for this endpoint, so no claim about normality or skewness is warranted. The BMI SDS calculation itself includes a specified adjustment for scores outside the reference bounds described in the registry outcome definition; that is part of the endpoint construction, not evidence about the observed distribution.

What is the analysis population?

The primary outcome description says the full analysis set included randomized participants who received at least one dose and had any post-randomization data, following the intention-to-treat principle as stated in the record. The wording indicates that randomized assignment was the basis of the analysis population, with additional receipt-of-dose and post-randomization-data conditions. It is therefore important not to interpret the endpoint counts as the original enrollment count. The record also says available data after treatment discontinuation were included and describes week 56 results for participants who stopped trial product early but attended follow-up.

General statistical explanation: missing observations can affect an estimate if the chance of having an observed outcome is related to the outcome itself or to treatment assignment. Using available measurements after treatment discontinuation helps retain those observations, but it does not by itself specify how other missing week 56 values were handled. The imputation approach, assumptions about missingness, and sensitivity analyses are not reported in the registry record. Those omissions limit independent assessment of robustness.

What do p-values add?

In general, a p-value measures how surprising data at least as incompatible with a specified null model would be, assuming that model and the analysis assumptions hold. It is not the probability that the null hypothesis is true, nor a measure of the size or importance of a difference. The sponsor reports p = 0.002 for the primary ANCOVA comparison, and the unadjusted recalculation reports p = 0.001. The p-values belong to different analyses and should not be treated as interchangeable.

The registry identifies one reported analysis for the posted primary comparison and lists numerous outcome measures, including secondary outcomes. Whether and how the broader testing burden was handled is not reported in the registry record. Without that information, the nominal primary p-value should be understood as the result for the stated endpoint and analysis, not as a complete account of multiplicity across every measured outcome.

10. Confidence Intervals and Precision

The sponsor-reported treatment difference for change in BMI SDS is -0.22. Its 95% confidence interval extends from -0.37 to -0.08. This interval communicates uncertainty around the estimated group difference under the sponsor's ANCOVA analysis. The entire interval is below zero, so the values compatible with that interval are on the negative side of the no-difference point for this contrast. The interval does not describe the range of changes among individual participants.

The recalculated unadjusted estimate is -0.23, with a confidence interval from -0.370 to -0.090. That interval is based on the posted summary statistics and differs slightly from the sponsor's model-based interval. The recalculated interval has more digits because those are the reported rounded values for that calculation; they should not be mistaken for greater certainty than the sponsor result. The recalculation is not a substitute for the trial's own adjusted analysis.

In general, a narrower confidence interval indicates greater precision for an estimate under a given method, while a wider interval indicates more uncertainty. Precision is not the same as clinical importance. The confidence interval also does not account for every possible source of uncertainty, such as unreported analytic choices or potential bias from missing outcomes. The registry does not report enough detail to evaluate all such sources.

The posted arm standard deviations, 0.51 and 0.54, describe participant-level spread rather than precision of the treatment difference. The standard errors reported for the recalculation are 0.048 for liraglutide and 0.053 for placebo. These quantities are related to uncertainty in the estimated arm means, but should not be confused with the standard deviations or the sponsor's confidence interval.

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 expressed as participants per arm, not as a combined total or as total events. They are planning illustrations based on the observed effect, not the original trial's design justification. The registry record does not report the original sample-size assumptions.

The listed assumptions for these illustrations are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. Each planning scenario uses a stated fraction of the observed effect as the effect to detect. The rows describe planning for 100%, 75%, or 50% of the observed effect. For example, planning for 75% of the observed effect gives 146 participants per arm for 80% power and 195 participants per arm for 90% power.

The 80% power column means the illustrative number of participants per arm under which the specified design would have an 80% chance of detecting the chosen effect at the stated significance level, if the assumptions hold. The 90% column gives the corresponding planning number for a higher chance of detection under those same assumptions. These are design calculations, not guarantees about what a future study will observe. The entries for 100% of the observed effect are 82 participants per arm for 80% power and 110 participants per arm for 90% power. For 50% of the observed effect, the corresponding figures are 327 and 438 participants per arm.

Smaller effects require more participants to detect under the same general planning assumptions. This is not observed power: it does not describe the probability that the completed trial detected its result, and it cannot establish whether the study was adequately designed. The original trial's design assumptions are not reported in the registry record.

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 = -0.230; pooled standard deviation σ = 0.525.
2. n = 2 × (1.96 + 0.842)² × 0.525² / -0.230² = 81.7, rounded up to 82 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 <- -0.23                      # observed difference in means
sigma <- 0.524658619167423                     # 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(2918279)
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 = 82 (80% power), 110 (90% power)
 75% of observed effect: n per arm = 146 (80% power), 195 (90% power)
 50% of observed effect: n per arm = 327 (80% power), 438 (90% power)
power.t.test: 82.7 
Simulated power at n = 82 per arm: 0.793 (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. Analyses Reported by the Sponsor

The registry reports the sponsor's primary comparison as an ANCOVA treatment difference of -0.22, with a 95% confidence interval from -0.37 to -0.08 and p = 0.002. The separate recalculation uses the posted arm means and standard deviations to produce an unadjusted mean difference of -0.23, with a confidence interval from -0.370 to -0.090 and p = 0.001.

The two estimates are close in direction and magnitude, but they come from different methods. ANCOVA is the reported trial analysis; the recalculation does not reproduce its covariate adjustment because the necessary model details and participant-level data are not reported in the registry record. The recalculation is best read as an unadjusted check using summary statistics, not as a replacement for the sponsor's analysis.

The registry discrepancy indicator is false. Under the stated interpretation rule, there is no flagged discrepancy requiring a change in precedence. The sponsor's own analysis remains the primary result because it is the trial's reported analysis, while the recalculated result offers a transparent comparison based on the posted summaries.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists 61 outcome measures and 60 secondary outcomes posted. The primary endpoint is change in BMI SDS from week 0 to week 56. The listed secondary outcomes include BMI SDS at additional time points, BMI, body weight in several units, waist circumference, and proportions reaching specified BMI reduction thresholds. The numerical results for these secondary outcomes are not reported in the registry record details used.

When a study tests multiple outcomes or multiple time points, the chance of obtaining at least one small p-value by chance can increase. General statistical explanation: multiplicity procedures can control or otherwise address that issue, depending on the research questions and analysis plan. The registry record does not report whether a multiplicity adjustment was planned, which outcomes were included in any testing hierarchy, or how the primary endpoint was treated relative to secondary outcomes. Thus, the reported primary p-value should be interpreted as attached to its stated analysis; the wider multiplicity strategy is not reported in the registry record.

The primary outcome definition states that the full analysis set included randomized participants who had received at least one dose and had post-randomization data, in keeping with the intention-to-treat principle as described in the record. It also says all available data were used, including data collected after treatment discontinuation. Participants who prematurely discontinued trial product but attended the week 56 follow-up visit were included in the described results.

These statements clarify which observed data could contribute, but they do not fully describe how missing endpoint values were treated. The imputation method, assumptions about missingness, and sensitivity analyses are not reported in the registry record. It is also not reported whether additional analyses using different analysis populations were performed. Those details matter because conclusions can depend on how incomplete follow-up is handled, particularly if missingness differs by arm or is associated with outcome values.

15. Safety Results

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

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: completed suicide (0.8%), myositis (0.8%), post procedural haemorrhage (0.8%), appendicitis (0.8%), cholecystitis acute (0.8%).

The registry reports serious adverse events for 125 participants at risk in the liraglutide 3.0 mg group, with 3 affected, and for 126 participants at risk in the placebo group, with 5 affected. It reports other adverse events for 125 at risk in the liraglutide group, with 100 affected, and 126 at risk in the placebo group, with 84 affected. The registry also lists 1 death in the liraglutide group and 0 in the placebo group.

These are descriptive counts from the registry record. They do not, on their own, establish that an event was caused by the assigned study product, and the record details do not provide event timing or participant-level context. The serious-event terms listed include completed suicide, myositis, post procedural haemorrhage, appendicitis, cholecystitis acute, and cholelithiasis; each is listed as 0.8%. The record does not provide enough detail to infer the relationship of each listed event to treatment.

Serious adverse events and other adverse events are different reporting categories, and the counts should not be combined. These figures are not a substitute for a detailed safety analysis, which would require information such as event definitions, timing, severity, exposure, and attribution. The registry figures describe what was reported, not a causal comparison.

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

The primary result describes a difference between the randomized groups in mean change in BMI SDS at week 56. The sponsor's ANCOVA estimate is -0.22, with a 95% confidence interval from -0.37 to -0.08 and p = 0.002. The arm-level mean changes were -0.25 for liraglutide 3.0 mg and -0.02 for placebo. Together, these values indicate that the observed average change was more negative in the liraglutide arm on this standardized BMI measure.

This finding is specific to BMI SDS, a score referenced to age- and sex-specific growth values. It is not a result in kilograms, pounds, raw BMI units, or percentage change. The registry lists those measures separately among secondary outcomes, but their numerical findings are not reported in the registry record details used. Nor does an average group difference imply that every participant changed by the same amount or in the same direction.

The confidence interval gives a range of uncertainty for the estimated treatment difference under the sponsor's analysis. It does not resolve uncertainty about unreported analytic choices, missing-data assumptions, or the broader set of outcomes examined. The registry does not report the multiplicity strategy or a full account of missing-data methods. These limits affect how broadly the result can be interpreted.

The primary assessment was at week 56. The official title describes a later 26-week period off study drug, but the primary result does not answer whether the endpoint difference persisted during that period. The registry lists secondary BMI SDS assessments at later time points, but numerical results for them are not reported in the registry record details used.

Accordingly, the posted result supports a statistical comparison of the defined groups on the stated endpoint and time point. It does not establish a universal effect, predict an individual participant's outcome, or provide a complete account of long-term outcomes or safety. No medical advice or treatment recommendation follows from these statistics alone.

17. Why This Trial Matters Statistically

This trial illustrates why an endpoint's measurement scale matters. BMI SDS expresses BMI relative to age- and sex-specific reference values, whereas raw BMI and body weight answer different measurement questions. The primary result is therefore interpretable as a change on a standardized growth-reference scale, not as a direct amount of weight change. The registry's method description also specifies how the score was calculated and how extreme scores were adjusted.

It also shows the importance of distinguishing the reported model-based analysis from a summary-statistic recalculation. The sponsor reports an ANCOVA estimate; a simple unadjusted comparison from arm means and standard deviations produces a nearby but not identical estimate. Reporting both can help readers understand the scale and direction of the result, while preserving the sponsor's analysis as the principal trial result.

The distinction between enrollment and endpoint analysis counts is another useful statistical point. The registry lists enrollment as 251, while the primary outcome arm summaries contain 113 and 105 participants. These refer to different stages or definitions and should not be casually treated as interchangeable. The analysis population and treatment of data after discontinuation are also central to interpreting who contributed information to the endpoint.

Finally, precision, multiplicity, missing outcomes, and the planned design are separate questions. A confidence interval describes uncertainty under the fitted analysis; it does not answer whether multiple outcomes were adjusted for or whether missing-data assumptions were robust. The planning illustrations are not the trial's original justification and are not observed power. Keeping these concepts distinct prevents a single p-value or sample-size figure from being asked to answer more than it can.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The registry record does not provide the covariates used in the sponsor's ANCOVA, so the adjusted result cannot be independently reconstructed from the information. It also does not report the full statistical analysis plan, original sample-size justification, or any interim-analysis plan. The planning illustrations based on the observed effect should not be mistaken for the trial's prespecified design.

The endpoint analysis population was defined as randomized participants who received at least one dose and had post-randomization data. The outcome description says available data after treatment discontinuation were used and includes participants who discontinued trial product but attended week 56 follow-up. However, imputation procedures, assumptions about missing outcomes, and sensitivity analyses are not reported in the registry record. The difference between enrollment and analyzed arm counts is not fully explained in the record details.

The registry lists many outcome measures, but the numeric results cover the primary endpoint. Numerical findings for secondary endpoints, including later BMI SDS assessments and body-weight measures, are not reported in the registry record details used. The approach to multiplicity across the outcome set is also not reported.

The primary result concerns week 56, even though the official title describes a later off-study-drug period. The numerical information does not establish what happened at the later follow-up. Finally, the posted serious adverse-event counts and terms lack detail on timing, individual circumstances, and attribution, limiting interpretation of safety patterns.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Effect of Liraglutide for Weight Management in Pubertal Adolescent Subjects With Obesity — NCT02918279.
• Registry record last updated 2020-04-27; status last verified 2020-04.
• Results first posted 2020-04-27.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

The registry record describes a completed, phase 3, randomized, double-blind, parallel-group, placebo-controlled trial of liraglutide for weight management in pubertal adolescents with obesity. The official title describes a 56-week treatment period followed by a 26-week period off study drug.

The primary endpoint was change in BMI SDS from week 0 to week 56. The sponsor-reported ANCOVA treatment difference was -0.22, with a 95% confidence interval from -0.37 to -0.08 and p = 0.002. The registry also reports arm means of -0.25 for liraglutide 3.0 mg and -0.02 for placebo.

The primary outcome description identifies a full analysis set and states that available data after treatment discontinuation were used. Details of multiplicity, missing-data methods, the original sample-size assumptions, and some model specifications are not reported in the registry record. The listed planning figures are illustrations based on the observed effect, not the original design rationale or observed power.