This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record.
1. Trial at a Glance
DUAL™ I was a randomized, open-label, parallel-group phase 3 trial evaluating insulin degludec/liraglutide, insulin degludec, and liraglutide in subjects with type 2 diabetes. The registered primary endpoint was mean change from baseline in HbA1c at Week 26.
| Feature | DUAL™ I |
|---|---|
| Trial name | DUAL™ I |
| ClinicalTrials.gov | NCT01336023 |
| Phase | Phase 3 |
| Condition | Diabetes; Diabetes Mellitus, Type 2 |
| Allocation | Randomized |
| Design | Parallel |
| Masking | None |
| Primary purpose | Treatment |
| Enrollment | 1663 |
| Start | May 23, 2011 |
| Primary completion | May 24, 2012 |
| Lead sponsor | Novo Nordisk A/S |
| Sponsor type | Industry |
2. Clinical Question
The primary clinical question was whether the combination of insulin degludec/liraglutide produced a favorable change in HbA1c from baseline to Week 26 compared with each of its individual components.
Population
Subjects with diabetes mellitus, type 2.
Intervention
Insulin degludec/liraglutide.
Comparators
Insulin degludec and liraglutide.
Primary question
What is the treatment difference in mean change from baseline in HbA1c at Week 26, and does it satisfy the prespecified non-inferiority and superiority criteria?
3. Trial Design
Insulin degludec/liraglutide
- Insulin degludec/liraglutide
- Included in both primary treatment contrasts
- Compared with insulin degludec for non-inferiority
- Compared with liraglutide for superiority
Individual components
- Insulin degludec
- Liraglutide
- Each served as a separate comparator for the primary HbA1c analysis
The registry describes the study as randomized, parallel, and unmasked. The primary analysis therefore compares randomized treatment groups at a prespecified Week 26 time point rather than using a time-to-event framework.
4. Endpoints
| Endpoint | Registry definition | Time frame | Statistical analysis posted |
|---|---|---|---|
| Primary endpoint | Mean Change From Baseline in HbA1c (Glycosylated Haemoglobin) at Week 26. Definition: values of mean change in HbA1c. | Week 0, week 26 | Yes |
The registered outcome is expressed as percentage of glycosylated haemoglobin. The registry analysis records the endpoint type as “Binary,” although the endpoint itself is defined as a mean change in HbA1c, a continuous measurement. The posted statistical method is ANCOVA with treatment contrasts.
5. Statistical Methodology
Analysis population
The posted primary analyses used the full analysis set (FAS). The registry states that the FAS included all randomized subjects and that missing data were imputed using last observation carried forward (LOCF). Three subjects did not have their case book signed off because of discontinuation of an investigator's participation in the trial; consequently, one subject from each arm was excluded from the FAS.
| Feature | Posted analysis specification |
|---|---|
| Analysis population | Full analysis set |
| Randomization basis | All randomized subjects, with the stated three-subject exclusion |
| Missing-data method | Last observation carried forward (LOCF) |
| Primary method | ANCOVA |
| Effect measure | Treatment contrast |
| Confidence interval | 95%, two-sided |
| Primary hypotheses | Non-inferiority and superiority |
ANCOVA
ANCOVA, or analysis of covariance, models a continuous outcome while accounting for one or more covariates. In a clinical trial, the model produces an adjusted comparison between treatment groups while using information about baseline or other prespecified covariates when those are included in the model.
For DUAL™ I, the registry identifies ANCOVA as the statistical method for the Week 26 HbA1c treatment contrasts. The treatment contrast is reported as insulin degludec/liraglutide minus the relevant comparator.
A negative treatment contrast indicates a lower mean change in HbA1c for insulin degludec/liraglutide relative to the comparator under the reported analysis convention.
Confidence intervals
Both posted primary analyses report two-sided 95% confidence intervals. The confidence interval provides a range of treatment-difference values compatible with the statistical model and data under the specified confidence procedure. It is more informative about precision than a p-value alone.
Non-inferiority framework
For the comparison with insulin degludec, the registry states that non-inferiority of insulin degludec/liraglutide versus insulin degludec was confirmed when the 95% confidence interval for the treatment difference in change in HbA1c lay entirely below 0.3 percentage points, with the treatment difference defined as insulin degludec/liraglutide minus insulin degludec.
Because the contrast is IDegLira minus IDeg, a sufficiently negative upper confidence limit establishes that the combination remains within the prespecified non-inferiority margin.
Superiority framework
For the comparison with liraglutide, the registry states that superiority of insulin degludec/liraglutide was confirmed when the 95% confidence interval for the treatment difference in change in HbA1c lay entirely below 0%, again with the contrast defined as insulin degludec/liraglutide minus liraglutide.
A confidence interval entirely below zero establishes that the estimated mean change under insulin degludec/liraglutide was lower than that under liraglutide under the reported contrast.
6. Primary Results
The registry contains two formal statistical analyses for the single registered primary endpoint. Both use ANCOVA and report a treatment contrast with a two-sided 95% confidence interval.
Insulin degludec/liraglutide vs insulin degludec
Week 26 HbA1c treatment contrast
95% CI: −0.58% to −0.36% · Non-inferiority
Contrast: IDegLira minus IDeg
The estimated treatment contrast was −0.47%, meaning that the reported mean change in HbA1c was 0.47 percentage points lower with insulin degludec/liraglutide than with insulin degludec under the posted ANCOVA contrast.
The 95% confidence interval was −0.58% to −0.36%. Its entire range is below the prespecified non-inferiority margin of 0.3%, satisfying the registry's stated criterion for non-inferiority.
This does not mean that every individual patient experienced a 0.47-percentage-point difference, nor does the confidence interval describe the range of individual patient responses. It describes uncertainty around the estimated group-level treatment contrast.
The confidence interval is especially important for non-inferiority because the decision depends on whether the interval remains on the acceptable side of the prespecified margin. The estimate alone is not sufficient to establish non-inferiority.
Insulin degludec/liraglutide vs liraglutide
Week 26 HbA1c treatment contrast
95% CI: −0.75% to −0.53% · Superiority
Contrast: IDegLira minus liraglutide
The estimated treatment contrast was −0.64%, meaning that the reported mean change in HbA1c was 0.64 percentage points lower with insulin degludec/liraglutide than with liraglutide under the posted ANCOVA contrast.
The 95% confidence interval was −0.75% to −0.53%. Because the entire interval is below 0%, it satisfies the registry's stated criterion for superiority over liraglutide.
The estimate is a group-level treatment contrast, not an individual treatment effect. It should not be interpreted as saying that each patient experienced exactly a 0.64-percentage-point difference.
The confidence interval also communicates precision: the plausible range of the estimated contrast under the specified statistical framework remains below zero throughout the interval. A confidence interval is not itself a probability statement that a particular value is the true treatment effect.
7. Comparing the Two Primary Hypotheses
| Comparison | Estimate | 95% CI | Hypothesis | Registry criterion |
|---|---|---|---|---|
| IDegLira vs IDeg | −0.47% | −0.58% to −0.36% | Non-inferiority | Entire 95% CI below 0.3% |
| IDegLira vs liraglutide | −0.64% | −0.75% to −0.53% | Superiority | Entire 95% CI below 0% |
The two comparisons answer different statistical questions. The first asks whether insulin degludec/liraglutide remains within a prespecified acceptable difference relative to insulin degludec. The second asks whether the treatment contrast is demonstrably below zero relative to liraglutide.
The numerical estimates should therefore not be compared as though they represented the same hypothesis. A non-inferiority margin and a superiority threshold have different meanings and serve different roles in trial design.
8. Statistical Methods Explained
Why was ANCOVA used?
ANCOVA is appropriate for a continuous endpoint such as change in HbA1c because it estimates a treatment contrast while allowing the analysis model to account for covariates specified for the analysis. The registry identifies ANCOVA as the method used for both primary comparisons.
What does a treatment contrast of −0.47% mean?
The contrast is defined as insulin degludec/liraglutide minus insulin degludec. Therefore, −0.47% represents a lower estimated mean change in HbA1c for insulin degludec/liraglutide by 0.47 percentage points under the posted analysis.
The direction of the contrast matters. If the order of subtraction were reversed, the sign would also reverse even though the underlying treatment comparison would be unchanged.
Why is non-inferiority judged against a margin?
Non-inferiority is not simply a test of whether two treatments differ. The trial specifies a maximum clinically or statistically acceptable disadvantage of the investigational treatment relative to the comparator. Here, the registry identifies a margin of 0.3 percentage points and requires the 95% confidence interval for the treatment difference to lie entirely below that margin.
The observed contrast can therefore be compatible with non-inferiority even though its confidence interval contains values above zero. What matters is its position relative to the prespecified non-inferiority margin.
Why does the superiority analysis use zero instead?
For the IDegLira versus liraglutide comparison, the registry defines superiority by requiring the 95% confidence interval for the treatment difference to lie entirely below 0%. Because the contrast is IDegLira minus liraglutide, values below zero favor the combination on the HbA1c change scale used in the analysis.
What does the 95% confidence interval tell us?
The confidence interval describes statistical uncertainty around the estimated treatment contrast. For IDegLira versus IDeg, the interval from −0.58% to −0.36% remains below the non-inferiority margin. For IDegLira versus liraglutide, the interval from −0.75% to −0.53% remains below zero.
The interval does not describe the distribution of individual patient responses, and it should not be interpreted as saying that there is a 95% probability that the true treatment effect lies inside this particular interval.
What does LOCF contribute to the analysis?
The registry states that missing data in the FAS were imputed using last observation carried forward. LOCF replaces a missing later measurement with the participant's last available observation. This allows an analysis to retain participants with missing Week 26 measurements, but it relies on assumptions about how a participant's last observed value represents the later unobserved value.
LOCF is a missing-data approach; it is not the same as multiple imputation. The broader statistical issue is that the treatment contrast can depend on the assumptions used to handle observations that are not available at the scheduled assessment.
9. Missing Data and the Full Analysis Set
The posted analyses state that the FAS included all randomized subjects and that missing data were handled using LOCF. Three subjects were excluded because their case books were not signed off following discontinuation of an investigator's participation, with one subject from each arm excluded from the FAS.
| Missing-data feature | Registry description |
|---|---|
| Primary analysis population | Full analysis set |
| Starting principle | All randomized subjects |
| Specific exclusions | Three subjects, one from each arm |
| Reason for exclusions | Case book not signed off because of discontinuation of an investigator's participation |
| Missing-data method | LOCF |
10. Safety Results
The registry reports serious adverse events by treatment arm. The affected and at-risk counts are shown below.
| Treatment arm | Serious adverse events | At risk |
|---|---|---|
| Insulin degludec | 22 | 412 |
| Insulin degludec/liraglutide | 38 | 825 |
| Liraglutide | 24 | 412 |
Insulin degludec
22 serious adverse events were reported among 412 subjects at risk.
Insulin degludec/liraglutide
38 serious adverse events were reported among 825 subjects at risk.
Liraglutide
24 serious adverse events were reported among 412 subjects at risk.
Statistical perspective
These are event counts and denominators. They should not be interpreted as a formal between-group safety test because the registry information presented here does not provide a posted statistical comparison for serious adverse events.
11. Why the Analysis Uses Different Hypothesis Frameworks
The DUAL™ I primary analysis is particularly useful for understanding why a single clinical trial can contain both non-inferiority and superiority questions.
| Feature | IDegLira vs IDeg | IDegLira vs liraglutide |
|---|---|---|
| Endpoint | Mean change from baseline in HbA1c at Week 26 | Mean change from baseline in HbA1c at Week 26 |
| Method | ANCOVA | ANCOVA |
| Contrast | IDegLira minus IDeg | IDegLira minus liraglutide |
| Estimate | −0.47% | −0.64% |
| 95% CI | −0.58% to −0.36% | −0.75% to −0.53% |
| Hypothesis | Non-inferiority | Superiority |
| Decision boundary | 0.3% | 0% |
For the non-inferiority comparison, the question is whether the combination's estimated disadvantage, if any, remains smaller than 0.3 percentage points. For the superiority comparison, the question is whether the treatment difference is sufficiently below zero to exclude no difference under the confidence-interval criterion specified by the registry.
12. Interpreting the Primary Estimates Carefully
The reported Week 26 treatment contrast for insulin degludec/liraglutide versus insulin degludec was −0.47%. Because the contrast is defined as combination minus insulin degludec, the negative value indicates a lower estimated mean change in HbA1c for the combination under the ANCOVA analysis.
It does not mean that every individual patient experienced a 0.47-percentage-point difference. It also does not represent an individual-level probability of benefit. The estimate is a group-level treatment contrast generated by the specified statistical model.
The reported Week 26 treatment contrast for insulin degludec/liraglutide versus liraglutide was −0.64%. Under the reported contrast definition, the estimated mean change in HbA1c was 0.64 percentage points lower for the combination.
The posted analyses registry-reported estimates and confidence intervals rather than p-values. In general, a p-value addresses evidence against a null hypothesis under a specified statistical model; it does not quantify the magnitude of a treatment effect. The treatment contrast and its confidence interval are therefore the central quantities for understanding the size and precision of these results.
13. Confidence Intervals and Decision Boundaries
The two primary analyses illustrate two different reference points for interpreting a confidence interval.
| Comparison | 95% CI | Reference point | Interpretation of interval position |
|---|---|---|---|
| IDegLira vs IDeg | −0.58% to −0.36% | 0.3% non-inferiority margin | Entire interval lies below the margin |
| IDegLira vs liraglutide | −0.75% to −0.53% | 0% superiority threshold | Entire interval lies below zero |
This distinction is important. In a superiority analysis, a confidence interval that crosses zero does not exclude no treatment difference. In a non-inferiority analysis, the relevant question is whether the interval crosses the prespecified non-inferiority margin.
14. Limitations
- Open-label design: the registry describes the study as having no masking. Knowledge of treatment assignment can influence behavior, reporting, or other aspects of trial conduct, although the primary HbA1c endpoint is an objective laboratory measurement.
- Missing-data assumptions: the primary analyses used LOCF for missing data. Results can depend on the assumptions underlying that imputation approach.
- Full analysis set exclusions: three randomized subjects were excluded from the FAS, one from each arm, because their case books were not signed off following discontinuation of an investigator's participation.
- Continuous endpoint versus registry classification: the posted analysis metadata classify the primary endpoint type as binary, while the registered endpoint is mean change in HbA1c, a continuous measure.
- Limited posted statistical detail: the registry identifies ANCOVA and the treatment contrasts but does not provide a full model specification in the information summarized here.
- Safety interpretation: serious adverse-event counts and denominators are reported, but the information presented does not include a formal statistical comparison of serious adverse-event rates.
- Multiplicity: the trial contains more than one primary treatment contrast and uses different hypothesis frameworks. Interpretation of the overall confirmatory error rate depends on the prespecified statistical plan.
15. What Non-Inferiority Does and Does Not Establish
Non-inferiority is sometimes incorrectly treated as simply another form of “no difference.” That is not the statistical question.
Here, the registry specifies a non-inferiority margin of 0.3% for the IDegLira minus IDeg treatment difference. The analysis asks whether the uncertainty interval remains entirely below that margin.
The relevant comparison is between the upper confidence limit and the prespecified margin, not merely between the point estimate and zero.
For DUAL™ I, the upper confidence limit was −0.36%, while the margin was 0.3%. The entire interval therefore remains below the specified non-inferiority boundary.
This does not by itself establish that the two treatments have identical effects. Rather, it establishes the statistical criterion specified for acceptable difference under the non-inferiority framework.
16. Why the Trial Matters Statistically
DUAL™ I is a useful teaching example because the primary endpoint is continuous, the treatment comparison uses ANCOVA, missing observations are handled through LOCF, and the two primary contrasts use different hypothesis frameworks.
| Concept | How it appears in DUAL™ I |
|---|---|
| Randomization | Randomized assignment across three parallel treatment arms |
| ANCOVA | Primary method for Week 26 HbA1c treatment contrasts |
| Continuous endpoint | Mean change from baseline in HbA1c |
| Confidence interval | Two-sided 95% intervals reported for both primary contrasts |
| Non-inferiority | IDegLira compared with IDeg using a 0.3% margin |
| Superiority | IDegLira compared with liraglutide against a 0% threshold |
| Missing data | LOCF used in the FAS |
| Safety analysis | Serious adverse-event counts reported by arm |
17. Statistical Methods Explained: A Deeper View
Why is the sign of the treatment contrast important?
The registry defines both primary treatment contrasts as combination minus comparator. Therefore, negative values favor the combination on the reported HbA1c change scale. If the contrast were reported in the opposite order, the numerical sign would change without changing the underlying clinical comparison.
Why is a confidence interval preferable to a point estimate alone?
A point estimate gives one value for the observed treatment contrast. The confidence interval adds information about statistical precision. For DUAL™ I, both intervals are relatively narrow around their respective estimates and remain on the required side of their relevant decision boundaries.
Why does the non-inferiority margin need to be prespecified?
The margin defines what degree of possible disadvantage would still be considered compatible with non-inferiority. Choosing the boundary after seeing the data could make the criterion dependent on the observed result and undermine the intended interpretation of the test.
Why can a non-inferiority result coexist with a negative treatment estimate?
Because non-inferiority does not require the treatment difference to be centered around zero. The treatment can appear numerically better than the comparator while the formal hypothesis asks whether it is sufficiently far from the unacceptable-disadvantage boundary.
Why does LOCF require caution?
LOCF creates an analysis value for a later time point using an earlier observation. That can be useful for retaining subjects in an analysis, but it assumes that the carried-forward observation provides an appropriate representation of the missing measurement. If that assumption is poor, the resulting treatment contrast can be affected.
Why should safety counts not be interpreted as an efficacy-style treatment effect?
The reported serious adverse-event information consists of affected subjects and numbers at risk by arm. Without a posted formal comparison, the counts describe the observed safety experience but do not by themselves establish a statistical difference between treatment groups.
18. Trial Timeline
Trial start
The DUAL™ I phase 3 study began.
Baseline assessment
The registered primary endpoint specifies baseline HbA1c at Week 0 as the reference for change.
Primary endpoint assessment
Mean change from baseline in HbA1c was the registered primary endpoint at Week 26.
Primary completion
The registry records May 24, 2012 as the primary completion date.
19. Primary Results in Context
The two primary results are most clearly understood by keeping the estimate, confidence interval, contrast direction, and hypothesis framework together.
Against insulin degludec
IDegLira minus IDeg was −0.47%, with a 95% CI of −0.58% to −0.36%. The posted hypothesis was non-inferiority, using a 0.3% margin.
Against liraglutide
IDegLira minus liraglutide was −0.64%, with a 95% CI of −0.75% to −0.53%. The posted hypothesis was superiority, using 0% as the reference threshold.
The two confidence intervals are entirely below their respective decision boundaries. That is the central statistical feature of the posted primary analyses.
20. Related Tutorials
Learn more about the methods used in this trial:
21. Related Calculators
22. Sources
- ClinicalTrials.gov: NCT01336023.
- PubMed: PMID 26443290.
- PubMed: PMID 26894800.
- PubMed: PMID 25190523.
- PubMed: PMID 25980900.
- PubMed: PMID 25998481.
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23. Record Summary
DUAL™ I provides a clear example of how a randomized phase 3 trial can use a single continuous primary endpoint to address different statistical questions against different comparators. The Week 26 endpoint was mean change from baseline in HbA1c, analyzed using ANCOVA in the full analysis set with LOCF for missing data. The insulin degludec/liraglutide versus insulin degludec comparison used a non-inferiority framework with a 0.3% margin, while the comparison with liraglutide used a superiority framework with 0% as the reference threshold. The posted confidence intervals were entirely below their respective decision boundaries.
The statistical interpretation is therefore centered on four linked quantities: the treatment contrast, the 95% confidence interval, the prespecified hypothesis framework, and the missing-data assumptions. Safety is a separate component of the evidence, with serious adverse-event counts reported for each treatment arm.