This page provides an independent statistical analysis and educational interpretation of publicly reported results. ClinicalTrials.gov provides the official trial registry record. Numerical trial results on this page are restricted to the results posted in the ClinicalTrials.gov record; calculations added by Clinical Biostats are labelled as such.
1. Trial at a Glance
This page covers the registry results for Linagliptin as Add on to Basal Insulin in the Elderly (NCT02240680), a randomized phase 4 study. The primary outcome is Change From Baseline in Hemoglobin A1c (HbA1c) After 24 Weeks of Treatment..
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02240680 |
| Phase | Phase 4 |
| Condition | Diabetes Mellitus, Type 2 |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 302 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Boehringer Ingelheim |
| Results posted | Yes |
2. Clinical Question
Population
The trial enrolled elderly patients, defined in its summary as 60 years of age and older, with type 2 diabetes and insufficient glycaemic control while receiving stable basal insulin. Stable background therapy with metformin and/or alpha-glucosidase inhibitors was allowed. The registry record reports enrollment of 302 participants, but the primary outcome analysis used a full analysis set of observed cases rather than simply identifying all enrolled participants as analyzed.
Intervention
Participants assigned to the active-treatment arm received linagliptin 5 milligrams orally once daily, added to background basal insulin. The intervention period for the primary outcome was up to 24 weeks. The comparison concerns this add-on regimen in the trial population, not linagliptin used without basal insulin or in other populations.
Comparator
The control arm received a placebo tablet matching linagliptin 5 milligrams, alongside background basal insulin. The trial was randomized, double-blind, and parallel-group. Those design features support a comparison between assigned groups, although the registry record does not report the details of sequence generation, allocation concealment, or how masking was maintained.
Primary question
The primary question was whether the change from baseline in HbA1c after 24 weeks differed between the linagliptin and placebo groups. HbA1c is a measure of glycated hemoglobin used to assess longer-term glycaemic control. The posted group means decreased in both arms, with a larger decrease in the linagliptin arm. The sponsor-reported between-group estimate was a mean difference of -0.63 percentage points, with a 95% confidence interval from -0.81 to -0.46 and p < 0.001. This is a statistical comparison of the posted endpoint, not a complete account of all patient outcomes.
3. Trial Design
NCT02240680 is a completed phase 4 randomized, double-blind, placebo-controlled, parallel-group trial sponsored by Boehringer Ingelheim. The registry record lists enrollment of 302 participants. Its official title describes a 24-week evaluation of once-daily oral linagliptin 5 milligrams as an addition to basal insulin in elderly patients with type 2 diabetes and insufficient glycaemic control. The record also describes stable background therapy with metformin and/or alpha-glucosidase inhibitors as allowed.
Participants were assigned to linagliptin or matching placebo. The posted primary endpoint compares change in HbA1c from baseline to week 24. Baseline is defined in the outcome description as the last observation before administration of any randomized study medication. The arm-level outcome summaries include 149 participants for linagliptin and 147 for placebo; these are the counts attached to the posted primary outcome summaries, not a claim that every enrolled participant contributed an outcome value.
The primary analysis population is described as the full analysis set observed cases. It includes randomized patients in the Treated Set who had a baseline and at least one on-treatment HbA1c value, and uses available data observed while patients were on treatment. The registry description is truncated when it begins to describe values after rescue medication, so the complete handling of those observations is not reported in the registry record.
The registry lists study dates of 2014-09-23 for start and 2017-04-18 for primary completion, and the status is completed. It lists six outcome measures and seven analyses. The endpoint summaries include the primary HbA1c outcome and a fasting plasma glucose outcome, while the other listed secondary outcomes concern hypoglycaemia and HbA1c thresholds or reductions. Detailed methods for randomization, masking, treatment adherence, and the sponsor's original sample-size justification 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: All patients were screened for eligibility to participate in the trial. Subjects attended specialist sites which would then ensure that they (the subject) met all strictly implemented inclusion/exclusion criteria. Subjects were not to be randomised to trial treatment if any one of the specific entry criteria were violated.
Overall Study (Up to 24 Weeks)
| Stage | Placebo (Up to 24 Weeks) | Linagliptin 5 Milligram (Up to 24 Weeks) | Placebo (Up to 52 Weeks) | Linagliptin 5 Milligram (Up to 52 Weeks) |
|---|---|---|---|---|
| STARTED | 151 | 151 | 0 | 0 |
| COMPLETED | 136 | 143 | 0 | 0 |
| NOT COMPLETED | 15 | 8 | 0 | 0 |
Reasons for not completing this period:
| Reason | Placebo (Up to 24 Weeks) | Linagliptin 5 Milligram (Up to 24 Weeks) | Placebo (Up to 52 Weeks) | Linagliptin 5 Milligram (Up to 52 Weeks) |
|---|---|---|---|---|
| Adverse Event | 6 | 6 | 0 | 0 |
| Protocol Violation | 4 | 1 | 0 | 0 |
| Lost to Follow-up | 1 | 0 | 0 | 0 |
| Withdrawal by Subject | 3 | 1 | 0 | 0 |
| Other than specified | 1 | 0 | 0 | 0 |
Japanese Patients (Up to 52 Weeks)
| Stage | Placebo (Up to 24 Weeks) | Linagliptin 5 Milligram (Up to 24 Weeks) | Placebo (Up to 52 Weeks) | Linagliptin 5 Milligram (Up to 52 Weeks) |
|---|---|---|---|---|
| STARTED | 0 | 0 | 50 | 52 |
| COMPLETED | 0 | 0 | 42 | 45 |
| NOT COMPLETED | 0 | 0 | 8 | 7 |
Reasons for not completing this period:
| Reason | Placebo (Up to 24 Weeks) | Linagliptin 5 Milligram (Up to 24 Weeks) | Placebo (Up to 52 Weeks) | Linagliptin 5 Milligram (Up to 52 Weeks) |
|---|---|---|---|---|
| Adverse Event | 0 | 0 | 6 | 7 |
| Protocol Violation | 0 | 0 | 1 | 0 |
| Withdrawal by Subject | 0 | 0 | 1 | 0 |
Analysis population for the primary outcome, as defined in the registry: Full analysis set observed cases (FAS (OC)): Includes all patients randomised in the Treated Set who had a baseline and at least one on-treatment HbA1c value. These analyses used available data as observed while patients were on treatment. All values collected after a patient started rescue medication were excluded from the analysis.
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: Treated set (TS): It includes all patients who were dispensed study medication and were documented to have taken at least one dose of investigational treatment.
| Characteristic | Unit | Placebo (Up to 24 Weeks) | Linagliptin 5 Milligram (Up to 24 Weeks) | Total |
|---|---|---|---|---|
| Participants analysed | 151 | 151 | 302 | |
| Age, Continuous | Years | 72.5 (SD 5.6) | 72.3 (SD 5.1) | 72.4 (SD 5.4) |
| Sex: Female, Male: Female | Participants | 60 | 59 | 119 |
| Sex: Female, Male: Male | Participants | 91 | 92 | 183 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 19 | 15 | 34 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 132 | 136 | 268 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 7 | 4 | 11 |
| Race (NIH/OMB): Asian | Participants | 52 | 52 | 104 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 1 | 1 |
| Race (NIH/OMB): Black or African American | Participants | 10 | 8 | 18 |
| Race (NIH/OMB): White | Participants | 81 | 84 | 165 |
| Race (NIH/OMB): More than one race | Participants | 1 | 2 | 3 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 |
| Hemoglobin A1c (HbA1c) at baseline | Percentage of HbA1c (%) | 8.1 (SD 0.7) | 8.2 (SD 0.8) | 8.2 (SD 0.8) |
6. Primary Endpoint
The registry lists the primary outcome as Change From Baseline in Hemoglobin A1c (HbA1c) After 24 Weeks of Treatment., measured over Baseline and Week 24.
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | Percentage (%) of HbA1c |
| Endpoint classification | Continuous Endpoint |
The primary endpoint measures change from baseline in hemoglobin A1c (HbA1c) after 24 weeks of treatment. HbA1c is glycated hemoglobin: glucose bound to hemoglobin, the blood pigment that carries oxygen. Because it reflects glycaemic exposure over time rather than a single glucose reading, it is used as a measure of chronic glycaemic control. The registry description notes that higher HbA1c indicates poorer control than a value in the normal range.
For this endpoint, baseline means the last observation before any randomized study medication was administered. The outcome is a continuous measure reported in percentage points of HbA1c, and the posted arm summaries are least-squares means with standard errors. The primary analysis population is described as full analysis set observed cases: randomized patients in the Treated Set with a baseline and at least one on-treatment HbA1c value. Available on-treatment observations were used.
Comparing change from baseline between randomized groups focuses on whether the observed average change differed under the two assigned regimens. It is not the same as comparing only final HbA1c values or determining the experience of every participant. The record reports a 24-week endpoint; it does not establish what happened after that period or provide an individual-level account of glycaemic control.
7. Results Posted in the Registry
- Linagliptin 5 Milligram (Up to 24 Weeks): mean -1.01 versus -0.38 on control; difference -0.63 (95% CI -0.81 to -0.45), standardized effect d = -0.80; z-test p = <0.001.
Mean difference: Linagliptin 5 Milligram (Up to 24 Weeks)
95% CI: -0.81 to -0.45
Recalculated from the posted summary statistics
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.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Change From Baseline in Fasting Plasma Glucose (FPG) | Continuous Endpoint | Mean difference | -11.50 (-21.07 to -1.93) | 210 per arm |
Change From Baseline in Fasting Plasma Glucose (FPG)
- Endpoint type: Continuous: a mean value per participant, compared as a difference in means.
- Test: Unadjusted two-sample z-test for the difference in means, using the posted standard errors.
- Result:
- Linagliptin 5 Milligram (Up to 24 Weeks): mean -11.30 versus 0.20 on control; difference -11.50 (95% CI -21.07 to -1.93), standardized effect d = -0.27; z-test p = 0.019.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Linagliptin 5 Milligram (Up to 24 Weeks) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The registry lists secondary outcomes covering hypoglycaemia, HbA1c thresholds or reductions, and fasting plasma glucose. These outcomes broaden the clinical and statistical questions beyond average HbA1c change: they concern glucose-related events, the proportions meeting specified HbA1c criteria, and another continuous measure of glycaemia. The posted results described in the registry record include numerical summaries for fasting plasma glucose, but numerical results for the other listed secondary endpoints are not reported in the registry record.
For fasting plasma glucose, the sponsor-reported analysis gives a mean difference of -11.5 milligram/decilitre, with a 95% confidence interval from -21.0 to -2.0 and p = 0.018. This is directionally consistent with the primary endpoint's larger mean decrease in the linagliptin arm, although the measures and their scales differ. It should be considered additional evidence rather than treated as a substitute for the primary outcome. No numerical result should be inferred for the listed hypoglycaemia or HbA1c-threshold outcomes from the fact that they appear in the registry.
Unadjusted secondary results carry less weight when several outcomes are examined because the chance of at least one apparently notable result can increase as more comparisons are made. General statistical explanation: multiplicity procedures can control this issue by adjusting tests or defining a hierarchy of outcomes in advance. The registry record does not report whether a multiplicity adjustment or hierarchy was used. The secondary findings should therefore be interpreted as supportive or exploratory rather than assumed to have the same confirmatory status as the stated primary endpoint.
The overall posted pattern is compatible with a larger average decrease in both HbA1c and fasting plasma glucose in the linagliptin arm over the reported period. That pattern is not a complete summary of all secondary evidence: several outcomes have no numerical results in the record, and the analysis plan for multiple outcomes is not reported. The missing endpoint results and multiplicity details limit how strongly the secondary outcomes can reinforce the primary comparison.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Percentage of Patients Experiencing at Least One Hypoglycaemia Accompanied by a Prespecified Glucose Value.
- Percentage of Patients With HbA1c<8.0%
- Percentage of Patients With HbA1c on Treatment <7.0%
- Percentage of Patients With HbA1c Lowering by at Least 0.5%.
- Change From Baseline in Fasting Plasma Glucose (FPG)
9. Statistical Interpretation
For the primary endpoint, the placebo arm had a posted mean change of -0.38 percentage points in HbA1c, while the linagliptin arm had a posted mean change of -1.01. The sponsor's mixed models analysis reported a mean difference in final values of -0.63 percentage points for linagliptin relative to placebo, with a 95% confidence interval from -0.81 to -0.46 and p < 0.001. The confidence interval lies below zero, consistent with a larger decrease in the linagliptin arm on the stated scale.
These are group-level results for the observed-case analysis population and the 24-week treatment period. They do not show that every participant experienced a decrease, nor do they describe how individual responses varied. The registry's analysis population requires a baseline and at least one on-treatment HbA1c value; therefore the result should not be treated as a simple summary of every person enrolled. The record's description of rescue-medication handling is incomplete.
A simple unadjusted recalculation from the posted arm summaries gives the same mean difference, -0.63, and an unadjusted p-value of <0.001. That recalculation is not a substitute for the sponsor's mixed models analysis, which is the registry-reported analysis. The sponsor-reported confidence interval and p-value describe that analysis; the recalculated p-value comes from a simpler comparison using the posted summary statistics.
The secondary outcomes offer additional measures of glycaemia and hypoglycaemia, but their evidential strength depends on the analysis methods and the number of outcomes considered. For fasting plasma glucose, the posted mean changes were 0.2 milligram/decilitre in the placebo arm and -11.3 milligram/decilitre in the linagliptin arm. The sponsor-reported mean difference was -11.5, with a 95% confidence interval from -21.0 to -2.0 and p = 0.018. The registry lists other secondary outcomes but does not post numerical results for them in the record.
Statistical evidence for a difference in the primary outcome does not alone characterize clinical importance, durability, safety, or effects outside the studied population and timeframe. Those questions require information beyond the primary mean difference and its confidence interval. The record does not report a threshold for a clinically important HbA1c difference, so the estimate should be read as a measured between-group contrast rather than classified against an unreported threshold.
10. Statistical Methods Explained
The registry reports a mixed models analysis for the primary outcome, expressed as a mean difference in final values. The posted arm summaries, in contrast, present change from baseline as least-squares means with standard errors. The registry identifies the analysis method but does not give the complete model specification, including its covariates, covariance structure, or other implementation details. The statistical interpretation should therefore distinguish the sponsor's reported analysis from a simpler recalculation based on arm summaries.
What does a mean difference describe?
A mean difference compares the average outcome in one group with the average outcome in another group on the same measurement scale. For HbA1c change, the posted linagliptin mean is -1.01 and the placebo mean is -0.38; the reported contrast is -0.63 percentage points. A negative contrast in this presentation indicates a more negative average change in the linagliptin arm. It does not indicate that the same change occurred for every participant, and it does not convey the full distribution of individual outcomes.
The arm values are least-squares means, which are model-based means rather than necessarily raw arithmetic averages. They can account for features included in a fitted model, but which features were included is not reported in the registry record. The sponsor's result is specifically identified as a mixed models analysis. Mixed models can be used to represent outcome data with more than one source of variation or repeated observations, but the exact structure used for this trial is not reported. No assumptions about its specific repeated-measures structure or adjustment variables should be inferred from the method label alone.
What do standard errors and confidence intervals tell us?
A standard error describes the uncertainty in an estimated mean, given the analysis and its assumptions. It is not the spread of individual participant outcomes. The primary arm summaries report standard errors of 0.07 for placebo and 0.06 for linagliptin. A confidence interval for a treatment contrast expresses a range of values compatible with the observed data and the method used to calculate the interval. The sponsor's 95% interval for the primary contrast runs from -0.81 to -0.46. Its position below zero indicates that the reported analysis is inconsistent with a zero difference at the conventional significance level, under that analysis's assumptions.
A confidence interval does not assign a probability to the true effect being inside the particular interval after it has been calculated. Nor does a small p-value measure the size or importance of a difference. The sponsor's primary p-value is reported as < 0.001. It represents the strength of evidence against a no-difference null hypothesis under the analysis, not the probability that the null hypothesis is true.
Why is the recalculation described as approximate?
The simple recalculation uses posted summary statistics rather than participant-level observations or the full sponsor model. For the primary comparison, the recalculated mean difference is -0.63 and the unadjusted p-value is <0.001. The calculation uses standard errors and an approximate pooled standard deviation; the registry-derived recalculation explicitly marks that standard deviation as approximate. Such a calculation does not reproduce the sponsor's mixed models analysis, which may use information or assumptions that cannot be reconstructed from the displayed summaries. The registry record reports no discrepancy between the recalculation and sponsor result. The sponsor's analysis remains the primary reported analysis.
The same distinction applies to the fasting plasma glucose recalculation. The posted arm means and standard errors permit a simple unadjusted comparison, while the sponsor reports a mixed models analysis. The recalculated p-value is 0.019 and the sponsor-reported p-value is 0.018. These values arise from different analysis procedures and should not be treated as interchangeable outputs of one model.
Why can over-dispersion matter?
General statistical explanation: over-dispersion occurs when observed variation is greater than a model assumes. A model that understates variation can produce standard errors that are too small and confidence intervals that are too narrow. For continuous outcomes such as HbA1c, the relevant concern is whether the chosen model adequately represents the observed variability and dependence among measurements. The registry record does not report a specific over-dispersion assessment, and there is no basis to claim that over-dispersion was present or absent in this trial.
What should be inferred from the analysis population?
The primary population is described as full analysis set observed cases. It includes randomized patients in the Treated Set with a baseline and at least one on-treatment HbA1c value, and uses available observations while patients were on treatment. This description matters because observed-case analyses use the measurements that are available rather than automatically filling in missing values. The registry record does not fully report the missing-data strategy, the reasons for missing outcomes, or how observations after rescue medication were handled. Without those details, the possible influence of missingness cannot be assessed from the registry summary alone.
Overall, the reported mixed models estimate and the simple recalculation point to the same direction and reported mean difference for the primary outcome. The model-based sponsor analysis is the relevant posted inferential result; the simpler calculation is a check based on summary statistics, not a replacement or a participant-level reanalysis.
11. Confidence Intervals and Precision
The sponsor-reported primary estimate is a mean difference of -0.63 percentage points in HbA1c, with a 95% confidence interval from -0.81 to -0.46. The interval gives a sense of precision: it describes a range of differences compatible with the data under the sponsor's analysis and its assumptions. Because the interval does not include zero, the reported analysis supports a between-group difference at the conventional 5% significance level. Its width also shows that the estimate is not a single exact value; uncertainty remains about the magnitude.
The interval is expressed on the HbA1c percentage-point scale. It should not be confused with a range containing 95% of participant outcomes, or with an interval describing how much an individual participant's HbA1c might change. It concerns uncertainty in the estimated group contrast. It also does not establish whether every value in the interval would be clinically important: the registry record does not report a threshold for clinical importance.
The recalculated comparison from posted summary statistics has the same reported point estimate, -0.63, and an unadjusted p-value of <0.001. The recalculation is based on an approximate pooled standard deviation rather than the sponsor's complete mixed models analysis. The registry does not flag a discrepancy, but the sponsor's model-based interval and p-value remain the principal inferential results. The reported 95% interval should be interpreted with the stated analysis population and the available-on-treatment data approach in mind.
Precision is specific to the endpoint, population, and period measured. It does not describe uncertainty about the secondary outcomes for which numerical results are not posted, nor does it resolve uncertainty about missing-data handling or longer-term outcomes. A narrow interval can still coexist with limitations in measurement, analysis, or generalizability; confidence intervals quantify sampling uncertainty under a method, not every source of uncertainty in a trial.
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.
| Effect to detect | Participants per arm, 80% power | Participants per arm, 90% power |
|---|---|---|
| 100% of the observed effect | 25 | 34 |
| 75% of the observed effect | 45 | 60 |
| 50% of the observed effect | 100 | 133 |
The planning figures are participants per arm, not total participants and not total events. They are illustrations computed from the observed effect, with the effect to detect set to a stated fraction of that observed effect. The listed assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The trial's own original sample-size justification and design assumptions are not reported in the registry record.
The 80% power column gives the illustrative number of participants per arm for a design with an 80% chance of detecting the specified effect, if the planning assumptions and model are appropriate. The 90% power column gives the corresponding number per arm for a 90% chance. These are prospective planning concepts: power describes a design's operating characteristics under assumed conditions, not the probability that the observed result is correct.
For the primary endpoint, the planning illustration lists 25 participants per arm for 80% power and 34 for 90% power when planning for 100% of the observed effect. At 75% of the observed effect, the listed figures are 45 and 60; at 50%, they are 100 and 133. The table's values are tied to the observed effect in this trial, not to an independently established clinically important difference.
Smaller effects are harder to distinguish from random variation, so the planning figures increase as the assumed effect becomes a smaller fraction of the observed effect. The same principle applies to the fasting plasma glucose illustration, whose listed requirements are larger. These figures do not tell whether the original trial was adequately planned for its intended question and are not observed power. They are illustrations, not a retrospective score of the trial or an estimate of the chance that its result will replicate.
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 z1−α/2 = 1.960) and the desired power (z1−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
- Observed difference Δ = -0.630; pooled standard deviation σ = 0.792.
- n = 2 × (1.96 + 0.842)2 × 0.7922 / -0.6302 = 24.8, rounded up to 25 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 <- -0.63 # observed difference in means
sigma <- 0.792290659919652 # 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(2240680)
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 = 25 (80% power), 34 (90% power)
75% of observed effect: n per arm = 45 (80% power), 60 (90% power)
50% of observed effect: n per arm = 100 (80% power), 133 (90% power)
power.t.test: 25.8
Simulated power at n = 25 per arm: 0.787 (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.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Mixed Models Analysis | Mean Difference (Final Values) -0.63 | -0.81 to -0.46 | < 0.001 |
The sponsor's reported primary analysis is a mixed models analysis of mean difference in final values. It estimates a difference of -0.63, with a 95% confidence interval from -0.81 to -0.46 and p < 0.001. A simple unadjusted recalculation from the posted primary arm summaries also gives a mean difference of -0.63 and p <0.001. The registry flags no discrepancy between the recalculation and sponsor result.
The agreement in the reported point estimate and direction is reassuring as a consistency check, but the procedures are not identical. The recalculation relies on posted summary statistics and an approximate pooled standard deviation; it does not reproduce the sponsor's mixed models analysis or its unavailable model specification. Its p-value should therefore not replace the sponsor-reported p-value. Where the sponsor's own analysis is available, that analysis takes precedence.
A similar distinction applies to fasting plasma glucose. The sponsor reports a mean difference of -11.5, a 95% confidence interval from -21.0 to -2.0, and p = 0.018. The simple recalculation gives an unadjusted p-value of 0.019. These are close but not identical results from different procedures. Neither the similarity nor the difference identifies which model details produced the variation; those details are not reported in the registry record.
15. Multiplicity, Missing Data and Analysis Populations
The registry record lists six outcome measures and seven analyses, including one primary outcome and several secondary outcomes. Examining multiple endpoints can raise the chance of obtaining a small p-value by chance if each is tested separately without accounting for the number or ordering of tests. General statistical explanation: multiplicity can be handled through prespecified procedures such as adjustment of significance levels, a testing hierarchy, or a clearly defined distinction between confirmatory and exploratory outcomes.
Whether any such procedure was planned or used is not reported in the registry record. The record does not specify a multiplicity adjustment for the secondary outcomes or state how the primary and secondary hypotheses were ordered. Accordingly, the primary result should be distinguished from secondary results, and unadjusted secondary p-values should not be interpreted as though they necessarily preserve an overall error rate across all outcomes.
The registry describes the primary analysis population as full analysis set observed cases: randomized patients in the Treated Set with baseline and at least one on-treatment HbA1c value. It states that available data observed while participants were on treatment were used. This clarifies that the primary analysis was not an analysis of every randomized participant regardless of outcome availability. The registry's outcome description is truncated while describing observations after rescue medication; complete details of how those observations were treated are not reported in the registry record.
The record does not report the extent or reasons for missing primary endpoint measurements, a missing-data model, an imputation procedure, or sensitivity analyses testing alternative assumptions about missing data. Those omissions make it difficult to assess whether the observed-case approach could be affected by differences between participants with and without available measurements. The model specification and covariate adjustment are also not reported, limiting independent reconstruction of the sponsor's mixed models analysis.
These gaps do not invalidate the posted estimate, but they constrain what can be independently evaluated. A thorough interpretation would benefit from a complete statistical analysis plan, details of the model and missing-data handling, and results for all prespecified outcomes. The registry summary alone does not establish whether such information exists elsewhere.
16. Safety Results
The registry reports serious adverse events as affected participants divided by participants at risk.
| Arm | Participants with serious adverse events | Participants at risk | Percentage |
|---|---|---|---|
| Placebo (Up to 24 Weeks) | 21 | 151 | 13.9% |
| Linagliptin 5 mg (Up to 24 Weeks) | 19 | 151 | 12.6% |
| Placebo (Up to 52 Weeks) | 7 | 50 | 14.0% |
| Linagliptin 5mg (Up to 52 Weeks) | 13 | 52 | 25.0% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Placebo (Up to 24 Weeks) | 0 of 151 |
| Linagliptin 5 mg (Up to 24 Weeks) | 2 of 151 |
| Placebo (Up to 52 Weeks) | 0 of 50 |
| Linagliptin 5mg (Up to 52 Weeks) | 0 of 52 |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 5% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| Placebo (Up to 24 Weeks) | 58 of 151 |
| Linagliptin 5 mg (Up to 24 Weeks) | 72 of 151 |
| Placebo (Up to 52 Weeks) | 19 of 50 |
| Linagliptin 5mg (Up to 52 Weeks) | 37 of 52 |
Most frequent serious adverse event terms
| Event term | Organ system | Placebo (Up to 24 Weeks) | Linagliptin 5 mg (Up to 24 Weeks) | Placebo (Up to 52 Weeks) | Linagliptin 5mg (Up to 52 Weeks) |
|---|---|---|---|---|---|
| Diabetic retinopathy | Eye disorders | 0 of 151 | 2 of 151 | 0 of 50 | 2 of 52 |
| Osteoarthritis | Musculoskeletal and connective tissue disorders | 1 of 151 | 2 of 151 | 1 of 50 | 0 of 52 |
| Brain stem infarction | Nervous system disorders | 1 of 151 | 1 of 151 | 1 of 50 | 1 of 52 |
| Cardiac failure congestive | Cardiac disorders | 1 of 151 | 2 of 151 | 0 of 50 | 0 of 52 |
| Cataract | Eye disorders | 0 of 151 | 1 of 151 | 0 of 50 | 2 of 52 |
| Hypoglycaemia | Metabolism and nutrition disorders | 0 of 151 | 1 of 151 | 1 of 50 | 1 of 52 |
| Angina pectoris | Cardiac disorders | 0 of 151 | 1 of 151 | 0 of 50 | 1 of 52 |
| Angina unstable | Cardiac disorders | 0 of 151 | 1 of 151 | 0 of 50 | 1 of 52 |
| Cardiac arrest | Cardiac disorders | 0 of 151 | 2 of 151 | 0 of 50 | 0 of 52 |
| Coronary artery disease | Cardiac disorders | 2 of 151 | 0 of 151 | 0 of 50 | 0 of 52 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Placebo (Up to 24 Weeks) | Linagliptin 5 mg (Up to 24 Weeks) | Placebo (Up to 52 Weeks) | Linagliptin 5mg (Up to 52 Weeks) |
|---|---|---|---|---|---|
| Hypoglycaemia | Metabolism and nutrition disorders | 38 of 151 | 51 of 151 | 14 of 50 | 20 of 52 |
| Viral upper respiratory tract infection | Infections and infestations | 8 of 151 | 11 of 151 | 3 of 50 | 11 of 52 |
| Urinary tract infection | Infections and infestations | 9 of 151 | 10 of 151 | 1 of 50 | 1 of 52 |
| Bronchitis | Infections and infestations | 4 of 151 | 7 of 151 | 0 of 50 | 5 of 52 |
| Back pain | Musculoskeletal and connective tissue disorders | 6 of 151 | 5 of 151 | 3 of 50 | 2 of 52 |
| Benign prostatic hyperplasia | Reproductive system and breast disorders | 1 of 151 | 3 of 151 | 0 of 50 | 3 of 52 |
| Constipation | Gastrointestinal disorders | 1 of 151 | 2 of 151 | 0 of 50 | 3 of 52 |
| Large intestine polyp | Gastrointestinal disorders | 0 of 151 | 2 of 151 | 0 of 50 | 3 of 52 |
Serious events with the highest arm-level rate: cataract (3.8%), diabetic retinopathy (3.8%), cholecystitis (2.0%), cholelithiasis (2.0%), pneumonia (2.0%).
The registry reports serious adverse events and other adverse events in groups labelled for up to 24 weeks and up to 52 weeks. For the up-to-24-week groups, serious adverse events were reported for 21 participants in the placebo group, with 151 at risk, and 19 in the linagliptin group, with 151 at risk. Other adverse events were reported for 58 participants in the placebo group and 72 in the linagliptin group. The registry lists 0 deaths in the placebo group and 2 in the linagliptin group for this period.
For the groups labelled up to 52 weeks, the record reports 7 serious adverse events among 50 at risk in the placebo group and 13 among 52 at risk in the linagliptin group. Other adverse events were reported for 19 and 37 participants, respectively; deaths were 0 in both groups. The registry does not explain how the up-to-52-week groups relate to the up-to-24-week groups, so these figures should not be combined or treated as a direct extension without further information.
These are participant counts in registry-defined groups, not a complete safety analysis. They do not convey event timing, severity beyond the serious-event classification, causal attribution, exposure-adjusted rates, or the number of recurrent events. Serious adverse event terms listed include cataract, diabetic retinopathy, cholecystitis, cholelithiasis, pneumonia, and femoral neck fracture. The figures alone do not establish whether an event was caused by treatment or whether group differences are meaningful.
17. What the Result Does, and Does Not, Mean
The primary result describes a difference between randomized groups in average HbA1c change over the 24-week treatment period. The sponsor-reported estimate is -0.63 percentage points, with a 95% confidence interval from -0.81 to -0.46. The interval and p-value indicate statistical evidence of a group difference under the reported mixed models analysis. This is a result about the trial's measured endpoint and analysis population, not a statement about each participant's response.
The result does not establish that every person in the linagliptin arm had a larger decrease, or that no person in the placebo arm did. A group mean can conceal variation in individual changes. The registry record does not provide participant-level distributions, subgroup results, or numerical results for all listed secondary endpoints. It also does not report a threshold for deciding whether the mean difference is clinically important. Statistical evidence and clinical importance are related but distinct questions.
The finding is limited to the population and regimen described: elderly patients with type 2 diabetes and insufficient glycaemic control receiving stable basal insulin, with certain additional background therapies allowed. The treatment comparison is linagliptin 5 milligrams once daily added to basal insulin versus matching placebo added to basal insulin. It does not answer questions about other doses, other treatment combinations, people outside the described population, or outcomes beyond the reported period.
The primary analysis used observed on-treatment HbA1c data in a defined full analysis set. The registry's description of rescue-medication handling is incomplete, and missing-data methods are not reported. These limitations leave uncertainty about how unavailable measurements and post-rescue observations affected the estimated contrast. Safety counts provide additional descriptive information, but do not by themselves establish causal attribution or the overall balance of benefits and harms.
In short, the posted results support a difference in average HbA1c change between the two assigned groups at 24 weeks under the sponsor's analysis. They do not, on their own, establish individual outcomes, longer-term effects, clinical importance, or a complete safety profile.
18. Why This Trial Matters Statistically
This trial is statistically informative because it compares a continuous clinical measure between randomized, blinded, parallel groups and reports both an estimated contrast and its uncertainty. The primary endpoint is change in HbA1c, a measure used to assess chronic glycaemic control. Reporting group means alongside the sponsor's confidence interval makes it possible to distinguish the direction of the result from the precision of its estimated magnitude.
The record also illustrates why an analysis population and method matter. The primary result comes from a full analysis set observed-case population, not necessarily every enrolled participant, and the sponsor used a mixed models analysis. A simple comparison reconstructed from arm summaries agrees on the reported primary mean difference, but it does not reproduce the sponsor's method. This makes clear the value of distinguishing an independent summary-statistic check from the trial's reported analysis.
The secondary outcomes show another important statistical issue: a trial can list several measures, but their interpretation depends on complete reporting and the approach to multiple testing. The registry lists outcomes concerning hypoglycaemia and HbA1c criteria, yet numerical results for those endpoints are not reported in the registry record. Without the full outcome results and multiplicity plan, the secondary evidence cannot be evaluated with the same completeness as the primary comparison.
Finally, the record's sample-size illustrations are tied to fractions of the observed effect and should be understood as planning exercises, not evidence of observed power or of the trial's original design rationale. Together, these features make the trial useful for examining the relationship among a prespecified clinical endpoint, model-based inference, summary-statistic recalculation, uncertainty, and incomplete registry reporting.
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.
Several limitations specific to this trial affect interpretation of the registry summary. The primary analysis population is an observed-case set requiring baseline and at least one on-treatment HbA1c value. The record does not report how many otherwise eligible participants lacked measurements, why data were missing, or whether missingness differed between groups. The outcome description is truncated when it begins to discuss observations after rescue medication, so the complete rescue-medication handling is not reported in the registry record.
The registry identifies a mixed models analysis but does not give its full specification, including covariates, model structure, or assumptions. This limits independent reproduction of the sponsor's confidence interval and p-value. A simple recalculation from posted summaries is necessarily less detailed and uses an approximate pooled standard deviation. Its agreement in point estimate does not establish that all model assumptions or data-handling choices are appropriate.
Numerical results are not reported in the registry record for several listed secondary outcomes, including outcomes related to hypoglycaemia and HbA1c thresholds. The record also does not report a multiplicity procedure, so the confirmatory status of secondary tests is unclear. A full interpretation of the broader set of outcomes would require those results and the analysis plan.
The safety record includes groups labelled up to 24 weeks and up to 52 weeks but does not explain their relationship. The counts do not provide event timing, exposure-adjusted rates, or causal attribution. The registry summary also does not report the trial's original sample-size justification or whether interim analyses were planned or conducted. Generalization is limited to the described elderly population receiving stable basal insulin and the reported treatment period; outcomes beyond that period are not established by these results.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Linagliptin as Add on to Basal Insulin in the Elderly — NCT02240680.
- Registry record last updated 2018-07-03; status last verified 2018-05.
- Results first posted 2018-07-03.
- 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.
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23. Record Summary
NCT02240680 is a completed phase 4 randomized, double-blind, placebo-controlled, parallel-group trial sponsored by Boehringer Ingelheim. It compared once-daily linagliptin 5 milligrams with matching placebo as an addition to stable basal insulin in elderly patients with type 2 diabetes and insufficient glycaemic control. The registry reports enrollment of 302 participants and a 24-week primary endpoint period.
The primary endpoint was change from baseline in HbA1c. In the sponsor-reported mixed models analysis, the mean difference was -0.63 percentage points, with a 95% confidence interval from -0.81 to -0.46 and p < 0.001. The primary analysis used a full analysis set observed-case population. The registry also reports a fasting plasma glucose comparison and safety counts, while numerical results for several listed secondary endpoints are not reported in the registry record.
Interpretation is limited by unreported details of the model, missing-data handling, multiplicity procedures, and the relationship between the safety groups labelled up to 24 weeks and up to 52 weeks.