Liraglutide Effect and Action in Diabetes: Evaluation of Cardiovascular Outcome Results: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Liraglutide Effect and Action in Diabetes: Evaluation of Cardiovascular Outcome Results (NCT01179048), a randomized phase 3 study. The primary outcome is Time From Randomisation to First Occurrence of Cardiovascular Death, Non-fatal Myocardial Infarction, or Non-fatal Stroke (a Composite Cardiovascular Outcome).

2. Clinical Question

The registry describes a randomized, double-blind, placebo-controlled trial of liraglutide in subjects with type 2 diabetes. Its stated aim was to determine the long-term effect of liraglutide on cardiovascular events. The primary question was whether the time from randomisation to a first occurrence of cardiovascular death, non-fatal myocardial infarction, or non-fatal stroke differed between the liraglutide and placebo groups.

The primary endpoint is a composite: it counts the first occurrence of any one of its listed cardiovascular events, rather than requiring that a participant experience every component. The registry also lists an expanded cardiovascular composite and other secondary outcomes, but these do not replace the prespecified primary question. The posted group percentages describe the proportion experiencing a first primary event over the stated follow-up period. They are useful for understanding the observed event burden, while the registry-reported Cox analysis addresses the timing of events.

3. Trial Design

This was a phase 3, randomized, double-blind, parallel-group, placebo-controlled trial. The registry records an enrollment of 9341 and identifies Novo Nordisk A/S as the sponsor. The trial is marked completed. Its recorded start date is 2010-08-31, and its primary completion date is 2015-12-17.

The registry says the trial was conducted in Africa, Asia, Europe, and North and South America. It lists liraglutide and placebo as the interventions and identifies the primary analysis population as all randomised subjects. The arm descriptions contain no additional detail. Dosing, treatment duration, adherence procedures, and rules for changing or stopping treatment are not reported in the registry record.

Random allocation is intended, in general, to make the groups comparable at the outset with respect to both measured and unmeasured factors. Double masking is intended, in general, to reduce the influence of knowledge of treatment assignment on participants’ experiences and on outcome assessment. These design features support a comparative interpretation, but they do not by themselves establish how missing observations, treatment changes, or particular analytic decisions were handled.

The primary timeframe runs from randomisation (visit 3; month 0) to last contact (visit 16; up to month 60+30 days). The same timeframe is listed for the secondary outcomes described in the registry. Details of the visit schedule beyond those labels, the duration of exposure for individual participants, and the handling of censoring are not reported in the registry record. The registry’s total enrollment is a study-level figure; group-specific denominators for the primary endpoint are reported separately.

The original sample-size justification and design assumptions are not reported in the registry record. The planning illustrations associated with the posted results use stated assumptions and the observed effect; they should not be mistaken for the trial’s original design calculation.

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: All subjects received placebo (0.6 mg/day) during the open labeled run-in period of 2-3 weeks and were instructed on how to administer the trial product. During this period the subjects demonstrated that they could adhere to the injection regimen in the trial.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: All randomised subjects.

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: All the randomised subjects.

6. Primary Endpoint

The registry lists the primary outcome as Time From Randomisation to First Occurrence of Cardiovascular Death, Non-fatal Myocardial Infarction, or Non-fatal Stroke (a Composite Cardiovascular Outcome), measured over from randomisation (visit 3; month 0) to last contact (visit 16; up to month 60+30 days).

The primary endpoint is the time from randomisation to the first occurrence of cardiovascular death, non-fatal myocardial infarction, or non-fatal stroke. It is a composite cardiovascular outcome: any one of the listed events can qualify as the first event. The registry also reports the percentage of subjects experiencing such a first event during follow-up.

In general, a composite endpoint can capture several clinically important event types in one outcome and can provide more events for analysis than any single component might provide. Its interpretation depends on which components are included and whether the components differ in frequency or importance. A composite result does not establish that each component has the same pattern or magnitude of association. The registry lists analyses of individual components among the secondary outcomes, but the primary composite remains the principal question described by the record.

The endpoint is expressed both as a time-to-event question and as an event percentage. These summaries answer related but distinct questions. The percentage describes how many subjects in each group experienced an event over the stated follow-up; a Cox hazard ratio compares event rates over time under the model. The registry does not report the detailed rules used to define qualifying events, adjudicate them, or handle participants without an observed event in the analysis.

7. Results Posted in the Registry

• Liraglutide: 13.0% (607/4668) versus 14.9% (696/4672) on control; risk difference -1.9 percentage points (95% CI -3.3 to -0.5), risk ratio 0.87 (0.79–0.97); unadjusted two-proportion z-test p = 0.008.

8. Secondary Efficacy Endpoints

The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.

Time From Rand. to First Occurrence of an Expanded Composite Cardiovascular Outcome Defined as Either Cardiovascular Death, Non-fatal Myocardial Infarction, Non-fatal Stroke, Revascularisation, Hospitalisation for Unstable Angina or for Heart Failure.

• Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Liraglutide: 20.3% (948/4668) versus 22.7% (1061/4672) on control; risk difference -2.4 percentage points (95% CI -4.1 to -0.7), risk ratio 0.89 (0.83–0.97); unadjusted two-proportion z-test p = 0.005.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the proportion with the event is statistically lower for Liraglutide than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

Time From Randomisation to All Cause Death

• Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Liraglutide: 8.2% (383/4668) versus 9.6% (449/4672) on control; risk difference -1.4 percentage points (95% CI -2.6 to -0.3), risk ratio 0.85 (0.75–0.97); unadjusted two-proportion z-test p = 0.017.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the proportion with the event is statistically lower for Liraglutide than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

Time From Randomisation to First Occurrence of a Composite Microvascular Outcome

• Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
• Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
• Result:
  • Liraglutide: 7.6% (355/4668) versus 8.9% (416/4672) on control; risk difference -1.3 percentage points (95% CI -2.4 to -0.2), risk ratio 0.85 (0.75–0.98); unadjusted two-proportion z-test p = 0.023.
• Interpretation:
  • The 95% confidence interval excludes no difference, so the proportion with the event is statistically lower for Liraglutide than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.

The posted secondary results cover an expanded cardiovascular composite, all-cause death, and a composite microvascular outcome, among other secondary outcomes listed in the registry. For the secondary comparisons with reported group estimates, the event percentages are lower in the liraglutide group than in the placebo group. The reported Cox analyses also have a direction consistent with lower event occurrence in the liraglutide group. This broad directional pattern is aligned with the primary comparison, but it does not make the secondary outcomes equivalent to the primary endpoint.

Secondary endpoints differ in clinical content and event frequency, and each addresses a separate question. An expanded cardiovascular composite includes additional event types beyond the primary composite. All-cause death and the composite microvascular outcome represent different outcome domains. A pattern across these measures can provide context, but it cannot establish that every component or outcome has the same effect. The registry names additional secondary component outcomes, and the complete set of reported results is not fully represented in the available summary.

Secondary results generally carry less confirmatory weight when multiple outcomes are examined and no multiplicity strategy is reported. In general, testing many outcomes increases the opportunity for at least one apparently strong result to arise by chance under null hypotheses. A prespecified hierarchy or adjustment can address this issue, but the registry’s multiplicity plan is not reported in the registry record. Therefore, the secondary findings are best treated as supportive or exploratory context, not as independent confirmation of the primary comparison.

The posted secondary comparisons also use time-to-event analyses for which the registry gives Cox hazard ratios. Their interpretation depends on the same broad model considerations as the primary Cox result, while each outcome has its own event definition and frequency. The registry record does not report detailed model specifications or outcome adjudication procedures for these comparisons.

Secondary outcomes registered for this trial, for reference (only those above were recalculated):

• Time From Rand. to First Occurrence of an Expanded Composite Cardiovascular Outcome Defined as Either Cardiovascular Death, Non-fatal Myocardial Infarction, Non-fatal Stroke, Revascularisation, Hospitalisation for Unstable Angina or for Heart Failure.
• Time From Randomisation to All Cause Death
• Time From Randomisation to Each Individual Component of the Expanded Composite Cardiovascular Outcome
• Time From Randomisation to First Occurrence of a Composite Microvascular Outcome
• Time From Randomisation to Each Individual Component of the Composite Microvascular Outcome and to the Retinopathy and Nephropathy Composite Outcomes Separately.

9. Statistical Interpretation

10. Statistical Methods Explained

The posted results combine a direct comparison of event percentages with a registry-reported time-to-event analysis. Each approach summarizes a different aspect of the outcome. The event percentages show the proportion of subjects with a first event during the recorded follow-up. The Cox analysis uses event timing and is reported as a hazard ratio.

What does a risk difference describe?

In general, a risk difference is the event proportion in one group minus the event proportion in the comparison group. A value below zero means the event proportion is lower in the first group under that subtraction order; a value above zero means it is higher. The recalculated primary risk difference is -0.019, with a 95% confidence interval from -0.033 to -0.005. This is an unadjusted recalculation from the posted group summaries, not the Cox model result.

The risk difference is an absolute comparison of event proportions. It does not account for when events occurred within follow-up. It is also sensitive to the length and completeness of follow-up represented by the percentages. The registry gives a common timeframe label, but detailed follow-up and censoring information is not reported in the registry record. The risk difference should therefore be read as the simple summary it is, rather than as a replacement for a time-to-event analysis.

What does a Cox hazard ratio describe?

In general, a Cox model compares the hazard of an event over time between groups. A hazard is the event rate at a given time among people who have not yet experienced the event, under the model’s setup. A hazard ratio is a relative summary of those hazards, not a ratio of the total event percentages and not a statement about the event timing of any particular participant. The registry reports a primary hazard ratio of 0.868 and a 95% confidence interval from 0.778 to 0.968.

The Cox method uses time-to-event information and can account for differing observed follow-up through its treatment of event and censoring times. That general explanation does not establish which censoring rules, covariates, or model checks were used in this trial. Those details are not reported in the registry record. A hazard ratio also commonly relies on a proportional-hazards assumption; whether that assumption was assessed or how it was handled is not reported in the registry record.

Why are the two estimates not identical in meaning?

The risk difference and hazard ratio have different scales and use different aspects of the outcome data. The first contrasts event proportions; the second is a model-based comparison over time. General statistical interpretation therefore treats them as complementary rather than interchangeable. A confidence interval for one measure cannot be transferred to the other. In this trial, the sponsor-reported Cox analysis is the time-to-event result, while the recalculated risk difference is an unadjusted summary from the posted proportions.

The registry lists both non-inferiority or equivalence and superiority or other analysis categories for the primary Cox result. In general, a non-inferiority analysis asks whether data rule out an unacceptable loss according to a prespecified margin, while a superiority analysis asks whether evidence supports a difference in a specified direction. The margin, detailed hypotheses, and testing sequence are not reported in the registry record. The labels and p-values should be described as recorded; they do not reveal the full protocol or statistical plan.

How should p-values be read?

In general, a p-value describes how unusual data at least as incompatible with a specified null hypothesis would be if that null model and its assumptions were true. It is not the probability that the null hypothesis is true, the probability that the finding is due to chance, or a measure of clinical importance. The registry reports p = 0.008 for the unadjusted risk-difference recalculation, p < 0.001 for the non-inferiority or equivalence Cox analysis, and p = 0.005 for the superiority or other Cox analysis. These p-values correspond to different analyses and should not be treated as a single test.

The registry’s own statistical plan, including any covariate adjustment, handling of repeated or related outcomes, and formal multiplicity procedure, is not reported in the registry record. Without those details, the p-values alone cannot establish which comparisons were designated confirmatory or how the overall chance of a false-positive conclusion was controlled.

11. Confidence Intervals and Precision

The primary recalculated risk difference is -0.019, with a 95% confidence interval from -0.033 to -0.005. The interval conveys uncertainty around the unadjusted difference in event proportions. In general, a confidence interval is a range produced by a method designed to cover the underlying parameter at its stated confidence level over repeated applications of that method, assuming the method’s conditions hold. It is not a range containing a known proportion of individual outcomes.

The primary registry-reported Cox hazard ratio is 0.868, with a 95% confidence interval from 0.778 to 0.968. This interval describes precision on the hazard-ratio scale, not the scale of the risk difference. The two intervals cannot be compared as though they measured the same quantity. The reported limits are fairly close to the corresponding estimates, but how much precision is adequate depends on the question and the range of effects that would matter; that judgment is not specified by the registry.

For both measures, an interval’s width reflects sampling uncertainty under the analysis used, but not every source of uncertainty. It does not account for possible bias from missing outcomes, outcome classification, model misspecification, or selective reporting. The registry record does not report details sufficient to evaluate all of those issues. Confidence intervals also do not indicate the probability that the estimate is exactly correct.

The registry reports estimates and intervals for the primary analysis and several secondary analyses. Secondary comparisons raise additional uncertainty when multiple outcomes are examined, particularly when no adjustment strategy is reported. The intervals should be considered alongside the outcome’s status, analysis method, and multiplicity context rather than interpreted as stand-alone proof.

12. 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 illustrate how sample-size requirements change when the effect targeted for detection is set to a stated fraction of the observed effect. They are planning illustrations, not a reconstruction of the trial’s original design calculation. The original sample-size justification and design assumptions are not reported in the registry record.

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. For binary outcomes, the figures are participants per arm. For time-to-event outcomes, the figures are total events, using the Schoenfeld method. The primary endpoint is reported as a percentage of subjects with an event, so its planning figures are participants per arm.

The 80% power column means the number of participants per arm, or total events for a time-to-event calculation, estimated to give an 80% chance of detecting the specified effect under the stated assumptions if that effect is real. The 90% power column uses the same idea with a higher target chance of detection. These are planning probabilities conditional on the assumed effect and statistical model; they do not tell whether the completed trial had a particular probability of success.

Planning for a smaller effect requires more information, and therefore more participants or events, than planning for a larger effect under otherwise similar assumptions. The figures are not observed power. Their purpose is to show the scale of a future study under the stated assumptions, not to explain the design choices made for this completed trial.

13. 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, p₀ and p₁ are the control and treatment proportions, and p̄ is their average.

Worked calculation for this trial

1. Control proportion p₀ = 0.149; treatment proportion p₁ = 0.130; average p̄ = 0.140.
2. First term: z_1−α/2 × √[2p̄(1−p̄)] = 1.96 × 0.4900 = 0.9604.
3. Second term: z_1−β × √[p₀(1−p₀) + p₁(1−p₁)] = 0.842 × 0.4898 = 0.4122.
4. n = (0.9604 + 0.4122)² / (-0.0189)² = 5,252.8, rounded up to 5,253 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
p0 <- 0.148972602739726                          # control proportion
p1 <- 0.130034275921165                          # treatment proportion
n_per_arm <- function(power, frac = 1) {
  q1 <- p0 + (p1 - p0) * frac               # smaller effect = fraction of the observed difference
  pbar <- (p0 + q1) / 2
  z_b <- qnorm(power)
  ceiling(round((z_a * sqrt(2 * pbar * (1 - pbar)) + z_b * sqrt(p0 * (1 - p0) + q1 * (1 - q1)))^2 / (q1 - p0)^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 (unrounded n per arm)
cat("power.prop.test:", round(power.prop.test(p1 = p0, p2 = p1, power = 0.80)$n, 1), "\n")

# Simulation: how often does the z-test reject at the 80%-power sample size?
set.seed(1179048)
n    <- n_per_arm(0.80)
reps <- 20000
x0 <- rbinom(reps, n, p0); x1 <- rbinom(reps, n, p1)
ph <- (x0 + x1) / (2 * n)
z  <- ((x1 - x0) / n) / sqrt(ph * (1 - ph) * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(z) > z_a, na.rm = TRUE), reps))

Output from running the code

100% of observed effect: n per arm = 5,253 (80% power), 7,032 (90% power)
 75% of observed effect: n per arm = 9,472 (80% power), 12,680 (90% power)
 50% of observed effect: n per arm = 21,609 (80% power), 28,928 (90% power)
power.prop.test: 5252.8 
Simulated power at n = 5,253 per arm: 0.806 (20000 replicates)

The simulation draws many pairs of event counts at the planned sample size and counts how often the two-proportion z-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.

14. Analyses Reported by the Sponsor

The registry-reported Cox analysis is the trial’s time-to-event comparison: the primary hazard ratio is 0.868, with a 95% confidence interval from 0.778 to 0.968. The record lists p < 0.001 for the non-inferiority or equivalence analysis and p = 0.005 for the superiority or other analysis. It gives the analysis method as regression, Cox.

The recalculated risk difference is a separate, simple unadjusted comparison of the posted event proportions. It is -0.019, with a 95% confidence interval from -0.033 to -0.005 and p = 0.008. Because it summarizes proportions rather than event timing, it should not be read as a substitute for the Cox result. Differences in estimand and method mean the numerical estimates and p-values need not match.

The registry does not report the full Cox model specification, covariates, analysis population beyond the primary population description, or the complete testing procedure. The recalculation cannot recover those details. The registry record does not flag a discrepancy between the recalculation and the reported analysis; the two summaries should be understood according to the different methods they represent.

15. Multiplicity, Missing Data and Analysis Populations

The registry lists a primary cardiovascular composite and multiple secondary outcomes, including expanded cardiovascular, mortality, and microvascular outcomes. It also lists individual components of some composites. When several outcomes are tested, the chance of at least one misleadingly strong result can increase. In general, multiplicity procedures—such as a prespecified testing sequence or statistical adjustment—are used to manage that issue.

A multiplicity adjustment, testing hierarchy, allocation of the overall error rate, or distinction between confirmatory and exploratory secondary analyses is not reported in the registry record. The existence of reported p-values should not be taken to mean that a particular correction was used. Without a documented strategy, secondary p-values should be interpreted cautiously and in the context of the primary result.

The primary population is described as all randomised subjects. The specific analysis population used for each reported model, including whether every randomised subject was included in each analysis, is not reported in the registry record. The registry does not describe the handling of missing endpoint data, participants lost to follow-up, censoring rules, or sensitivity analyses for missing data. These details matter because time-to-event estimates depend on the event and follow-up information available for analysis.

The registry also does not report imputation procedures, assumptions about missingness, or how treatment discontinuation and treatment changes were handled. Those omissions do not establish that the trial failed to address these issues; they mean that the registry record alone does not specify the approach. The original statistical analysis plan and sample-size justification are not reported in the registry record. As a result, the full relationship between the posted analyses and the planned confirmatory strategy cannot be assessed from the registry entry alone.

16. 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 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: acute myocardial infarction (4.0%), angina unstable (3.2%), pneumonia (3.0%), cardiac failure (2.9%), coronary revascularisation (2.8%).

The registry lists serious adverse-event figures for both treatment groups. In the liraglutide group, 2320 participants are listed as affected among 4668 at risk; in the placebo group, 2354 are listed as affected among 4672 at risk. The registry also lists other adverse events: 684 affected among 4668 at risk in the liraglutide group, and 210 among 4672 at risk in the placebo group. The record does not provide a definition of the “other” category in the summary.

The most frequently listed serious-event terms include acute myocardial infarction at 4.0%, unstable angina at 3.2%, pneumonia at 3.0%, cardiac failure at 2.9%, coronary revascularisation at 2.8%, and congestive cardiac failure at 2.8%. These terms are presented as registry safety listings; the record does not provide enough detail to infer causality, severity within each term, or whether events were related to treatment.

Safety counts should be read with their stated denominators and category definitions. Death counts in the adverse-event summary are not reported in the registry record. The serious-event figures are not a substitute for the primary efficacy analysis, and this summary alone does not establish a complete comparative safety profile.

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

The posted primary results show a lower event percentage for the liraglutide group than for the placebo group over the registry’s stated follow-up period. The unadjusted risk-difference interval is on the negative side of zero, and the registry-reported Cox estimate has a 95% confidence interval from 0.778 to 0.968. Together, these statistics describe the direction and precision of the recorded primary comparison under the reported summaries and model.

They do not establish that each component of the composite changed in the same way. The primary endpoint combines cardiovascular death, non-fatal myocardial infarction, and non-fatal stroke. A composite estimate cannot reveal which component contributed most to the observed result, and separate component results require their own interpretation. The registry lists component outcomes among secondary outcomes, but those analyses have the limitations of secondary comparisons.

The results also do not by themselves explain the biological or clinical importance of the observed difference, the balance of benefits and harms for an individual, or how the findings apply to people outside the study population. Participant characteristics and many details of conduct and analysis are not reported in the registry record. Statistical estimates describe group-level comparisons and do not predict an individual participant’s outcome.

The registry’s endpoint percentages and Cox hazard ratio are different summaries. The percentages describe the share of subjects with a recorded event; the Cox result compares hazards over time under a statistical model. Neither is a complete description of all possible outcomes or uncertainty. The record does not report all methods needed to independently evaluate the model assumptions, missing data, and multiplicity handling.

Accordingly, the result is best understood as a randomized comparison with a lower observed primary event percentage in the liraglutide group and a Cox estimate in the same direction. It is not a universal claim about treatment, every cardiovascular component, or outcomes beyond those measured and reported.

18. Why This Trial Matters Statistically

This trial is statistically notable because its primary question combines a clinically defined composite with a time-to-event analysis. The event percentages offer an intuitive group-level summary, while the Cox hazard ratio incorporates the timing of events. Reading both helps distinguish absolute differences in observed proportions from relative comparisons of event rates over time.

The trial is recorded as randomized, double-blind, parallel-group, and placebo-controlled. In general, these design features are intended to support a fair comparison and reduce some sources of bias. The primary population is identified as all randomised subjects, which gives readers a clear population label for the endpoint. The registry also reports both a trial-level enrollment and arm-specific denominators for the primary outcome.

The distinction between the primary endpoint and secondary outcomes matters. A composite can provide a single main outcome, but interpretation still depends on its component events. Secondary outcomes add breadth, yet multiple comparisons require attention to prespecification and multiplicity. Because the registry does not report the multiplicity plan, the secondary results should not be treated as independent confirmation at the same level as the primary analysis.

The posted confidence intervals make precision part of the interpretation rather than leaving the reader with a point estimate alone. The contrast between the unadjusted recalculation and the registry-reported Cox result also illustrates why methods and estimands must be stated plainly. Neither summary is a complete substitute for the other, and the registry’s incomplete details on model specification and missing-data handling leave some methodological questions unresolved.

Finally, the planning illustrations demonstrate how assumptions about target effect and power affect required information. They are distinct from the completed trial’s original design rationale, which is not reported in the registry record. Keeping observed results, model-based inference, and future-study planning separate is essential to sound interpretation.

19. 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.
• Participant counts were reconstructed from posted percentages and arm sizes, so small rounding differences are possible.

Several trial-specific details that would help assess the results are not reported in the registry record. These include participant characteristics, event-definition and adjudication procedures, treatment dosing and adherence, and the detailed conduct of follow-up. The registry identifies broad geographic regions but does not give site-level or population-composition information in the record.

The primary outcome is a composite, so the overall comparison may conceal differences among cardiovascular death, non-fatal myocardial infarction, and non-fatal stroke. The registry lists component outcomes as secondary, but the available secondary summary does not provide a full account of every component result. The expanded cardiovascular composite also includes additional event types, which makes it a distinct endpoint rather than a direct duplicate of the primary outcome.

The Cox model is identified, but its specification, covariate adjustment, proportional-hazards assessment, and censoring rules are not reported in the registry record. Missing-data procedures and sensitivity analyses are likewise not reported. The multiplicity plan and the original sample-size justification are not reported, limiting assessment of the prespecified inferential framework.

The safety summary lists affected counts and several serious-event terms, but it does not provide detailed causal attribution or a complete event narrative. Death counts in the adverse-event summary are not reported in the registry record. These limitations mean that the registry supports a description of the posted comparisons, but not a full reconstruction of trial conduct or every component of the analysis.

20. Related Tutorials

21. Related Statistical Calculators

22. Sources

• ClinicalTrials.gov: Liraglutide Effect and Action in Diabetes: Evaluation of Cardiovascular Outcome Results — NCT01179048.
• Registry record last updated 2019-07-17; status last verified 2019-07.
• Results first posted 2017-03-01.
• 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.

23. Record Summary

The registry identifies NCT01179048 as a completed phase 3, randomized, double-blind, parallel-group, placebo-controlled trial of liraglutide versus placebo in type 2 diabetes. Enrollment is recorded as 9341, and the primary analysis population is described as all randomised subjects. The primary endpoint is time to first cardiovascular death, non-fatal myocardial infarction, or non-fatal stroke.

The posted primary event percentages are 13.0% for liraglutide and 14.9% for placebo. The registry-reported Cox hazard ratio is 0.868, with a 95% confidence interval from 0.778 to 0.968. The simple unadjusted risk-difference recalculation is -0.019, with a 95% confidence interval from -0.033 to -0.005.

The registry also lists secondary cardiovascular, mortality, and microvascular outcomes, plus serious adverse-event summaries. Details of multiplicity, missing-data handling, the full Cox model, and the original sample-size justification are not reported in the registry record.