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 Empagliflozin as Adjunctive to Insulin Therapy Over 26 Weeks in Patients With T1DM (EASE-3) (NCT02580591), a randomized phase 3 study. The primary outcome is Change From Baseline in Glycated Hemoglobin (HbA1c) at Week 26 for Full Analysis Set (FAS) (Observed Cases [OC]).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02580591 |
| Phase | Phase 3 |
| Condition | Diabetes Mellitus, Type 1 |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 977 |
| Arms in the primary outcome | 4 |
| Lead sponsor | Boehringer Ingelheim |
| Results posted | Yes |
2. Clinical Question
Population
People with type 1 diabetes mellitus who participated in the trial. The primary endpoint analysis used the full analysis set of treated participants with a baseline HbA1c measurement and at least one on-treatment HbA1c measurement. The primary analysis is described as using observed cases.
Intervention
Once-daily oral empagliflozin at 2.5 mg, 10 mg or 25 mg, given as adjunctive therapy to insulin. The registry describes the study as examining efficacy, safety, tolerability and pharmacokinetics over 26 weeks.
Comparator
Matching placebo alongside insulin. The trial was randomized, double blind and parallel group. Further details of the allocation process are not reported in the registry record.
Primary question
How did HbA1c change from baseline to week 26 in each empagliflozin dose group compared with placebo? The primary outcome was the adjusted mean change in HbA1c, measured as a percentage. The registry also lists outcomes involving symptomatic hypoglycemic adverse events, body weight, total daily insulin dose, and systolic and diastolic blood pressure.
The central statistical comparison is between each dose group and placebo, rather than a direct comparison among the three doses. The posted results describe estimated changes within arms and sponsor-reported contrasts against placebo. Those comparisons address the measured endpoint over the stated follow-up; they do not, on their own, establish how findings would generalize beyond the analyzed participants or the registry’s outcome definitions. The registry record does not report a separate primary comparison among dose groups.
3. Trial Design
This was a Phase III, randomized, double-blind, placebo-controlled, parallel-group trial in people with type 1 diabetes mellitus. Empagliflozin was studied as adjunctive therapy to insulin over 26 weeks. The arms were placebo matching empagliflozin and empagliflozin at 2.5 mg, 10 mg or 25 mg. The registry lists total enrollment as 977. Its brief summary describes an intended study of 960 patients; the registry record does not explain the difference between that description and the enrollment entry.
The trial status is completed. The registry lists the start date as 2015-12-22 and primary completion as 2017-09-12. The sponsor was Boehringer Ingelheim. Randomization and double masking can reduce some forms of allocation and assessment bias, but those design labels alone do not describe how the sequence was generated, how concealment was maintained, or how masking was implemented. Those operational details are not reported in the registry record.
The primary endpoint was change from baseline in HbA1c at week 26. Its analysis population was the full analysis set, defined for this endpoint as treated participants with a baseline and at least one on-treatment HbA1c measurement; the outcome is further identified as observed cases. The posted arm counts for this endpoint range from 237 to 244, while the analysis population counts differ from the enrollment total. Reasons for those differences and details of participant flow are not reported in the registry record.
The registry lists six outcome measures and 24 analyses. It names secondary outcomes concerning confirmed-glucose symptomatic hypoglycemic adverse events, body weight, total daily insulin dose, and blood pressure. The registry record does not report the trial’s original sample-size justification, its allocation ratio, or a complete analysis plan. The available result therefore describes the recorded trial design and posted outcomes, not unreported design decisions.
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: 6-Week T1DM therapy (insulin) optimisation period followed by a 2-Week placebo run-in period before randomization. Patients who successfully completed both of the periods were randomized into the 26-Week double-blind treatment period. All treatments were administered in addition to optimized insulin therapy.
Overall Study
| Stage | Placebo Matching Empagliflozin | Empagliflozin 2.5 Milligram (mg) | Empagliflozin 10 mg | Empagliflozin 25 mg |
|---|---|---|---|---|
| STARTED | 242 | 242 | 248 | 245 |
| Treated | 241 | 241 | 248 | 245 |
| COMPLETED | 224 | 232 | 235 | 233 |
| NOT COMPLETED | 18 | 10 | 13 | 12 |
Reasons for not completing this period:
| Reason | Placebo Matching Empagliflozin | Empagliflozin 2.5 Milligram (mg) | Empagliflozin 10 mg | Empagliflozin 25 mg |
|---|---|---|---|---|
| Adverse Event | 0 | 1 | 2 | 5 |
| Protocol Violation | 3 | 2 | 1 | 1 |
| Lost to Follow-up | 5 | 3 | 3 | 1 |
| Withdrawal by Subject | 6 | 1 | 2 | 3 |
| Not treated | 1 | 1 | 0 | 0 |
| Other than specified | 3 | 2 | 5 | 2 |
Analysis population for the primary outcome, as defined in the registry: Full analysis set (FAS) (observed cases \[OC\]): Patients in the Treated Set (TS) who had a baseline and at least 1 on-treatment HbA1c measurement.
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: Randomised set (RS): All patients from the Screened set (SCR) who were randomised to trial medication, regardless of whether any trial medication was taken.
| Characteristic | Unit | Placebo Matching Empagliflozin | Empagliflozin 2.5 Milligram (mg) | Empagliflozin 10 mg | Empagliflozin 25 mg | Total |
|---|---|---|---|---|---|---|
| Participants analysed | 242 | 242 | 248 | 245 | 977 | |
| Age, Continuous | Years | 42.3 (SD 13.2) | 43.4 (SD 14.3) | 42.3 (SD 13.2) | 44.4 (SD 13.6) | 43.1 (SD 13.6) |
| Sex: Female, Male: Female | Participants | 126 | 120 | 132 | 121 | 499 |
| Sex: Female, Male: Male | Participants | 116 | 122 | 116 | 124 | 478 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 215 | 220 | 233 | 224 | 892 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 27 | 22 | 15 | 21 | 85 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 | 0 | 0 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 7 | 0 | 1 | 5 | 13 |
| Race (NIH/OMB): Asian | Participants | 2 | 2 | 2 | 5 | 11 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 1 | 0 | 0 | 0 | 1 |
| Race (NIH/OMB): Black or African American | Participants | 5 | 3 | 10 | 4 | 22 |
| Race (NIH/OMB): White | Participants | 227 | 234 | 234 | 231 | 926 |
| Race (NIH/OMB): More than one race | Participants | 0 | 3 | 1 | 0 | 4 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 | 0 | 0 |
6. Primary Endpoint
The registry lists the primary outcome as Change From Baseline in Glycated Hemoglobin (HbA1c) at Week 26 for Full Analysis Set (FAS) (Observed Cases [OC]), measured over Baseline to week 26.
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | Percentage (%) |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is change from baseline in glycated hemoglobin, or HbA1c, at week 26, measured in percentage units. HbA1c is a continuous measure, and the registry describes the reported arm results as least-squares mean changes. It defines baseline as the last observed measurement before administration of randomized trial medication. The least-squares mean is described as an adjusted mean change from baseline.
HbA1c is used as a trial outcome because it provides a quantitative measure of glycemia over time and can be compared across randomized groups. In general, analyzing change from baseline can account for the starting measurement when assessing how an outcome shifts during follow-up. The endpoint’s continuous scale also allows the estimated average change and uncertainty around comparisons to be described directly.
The registry specifies the full analysis set for this outcome as participants in the treated set who had both a baseline value and at least one on-treatment HbA1c measurement. It further labels the analysis as observed cases. Thus the posted endpoint is not described as an analysis of every enrolled participant regardless of measurement availability. The registry record does not report additional details about missing-outcome handling or the assumptions used for observations that were not available.
The endpoint is a group-level summary. It does not show the spread of individual participant responses in full, nor does a group mean describe every participant’s experience. Interpretation should therefore consider the estimated contrast, its interval of uncertainty, the analysis population, and the sponsor’s specified model, rather than treating the average change as a prediction for an individual.
7. Results Posted in the Registry
- Empagliflozin 2.5 Milligram (mg): mean -0.09 versus 0.20 on control; difference -0.29 (95% CI -0.43 to -0.15), standardized effect d = -0.38; z-test p = <0.001.
- Empagliflozin 10 mg: mean -0.25 versus 0.20 on control; difference -0.45 (95% CI -0.59 to -0.31), standardized effect d = -0.58; z-test p = <0.001.
- Empagliflozin 25 mg: mean -0.33 versus 0.20 on control; difference -0.53 (95% CI -0.67 to -0.39), standardized effect d = -0.68; z-test p = <0.001.
Mean difference: Empagliflozin 2.5 Milligram (mg)
95% CI: -0.43 to -0.15
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 Body Weight at Week 26 | Continuous Endpoint | Mean difference | -1.76 (-2.31 to -1.21) | 49 per arm |
| Change From Baseline in Total Daily Insulin Dose (TDID) at Week 26 | Continuous Endpoint | Mean difference | -0.05 (-0.07 to -0.03) | 71 per arm |
Change From Baseline in Body Weight at Week 26
- 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:
- Empagliflozin 2.5 Milligram (mg): mean -1.55 versus 0.21 on control; difference -1.76 (95% CI -2.31 to -1.21), standardized effect d = -0.57; z-test p = <0.001.
- Empagliflozin 10 mg: mean -2.83 versus 0.21 on control; difference -3.04 (95% CI -3.59 to -2.49), standardized effect d = -0.98; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Empagliflozin 2.5 Milligram (mg) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Empagliflozin 10 mg than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Change From Baseline in Total Daily Insulin Dose (TDID) at Week 26
- 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:
- Empagliflozin 2.5 Milligram (mg): mean -0.06 versus -0.01 on control; difference -0.05 (95% CI -0.07 to -0.03), standardized effect d = -0.47; z-test p = <0.001.
- Empagliflozin 10 mg: mean -0.08 versus -0.01 on control; difference -0.07 (95% CI -0.09 to -0.05), standardized effect d = -0.67; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Empagliflozin 2.5 Milligram (mg) than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Empagliflozin 10 mg than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The secondary outcomes broaden the measured picture beyond HbA1c, including body weight, total daily insulin dose, blood pressure, and symptomatic hypoglycemic adverse events with confirmed plasma glucose. The posted continuous summaries include changes in body weight and insulin dose across the randomized groups. These outcomes are related to the same treatment period but measure different aspects of participants’ experience and should be interpreted as distinct endpoints rather than as extensions of the HbA1c measure.
Overall, the posted secondary continuous results show a pattern of between-group differences for body weight and insulin dose, alongside the primary HbA1c comparisons. They can add context to the primary findings, but they do not independently establish the primary result or demonstrate that one outcome caused a change in another. The registry record does not provide a complete account of the secondary outcome analysis plan, including whether each listed outcome was confirmatory or exploratory.
Unadjusted secondary comparisons carry less inferential weight when many outcomes and contrasts are examined. General explanation: conducting multiple tests without an adjustment or an explicitly hierarchical strategy increases the chance of at least one apparently strong result arising by chance. The registry lists six outcome measures and 24 analyses, but whether multiplicity was controlled, and how, is not reported in the registry record. Secondary results are therefore best read as supportive or descriptive unless the analysis plan establishes a confirmatory role.
Not all named outcomes have complete numerical summaries in the record described by the posted results. The registry record does not report enough information to interpret every named secondary measure or to establish a comprehensive profile across all of them. The available findings should be understood within the set of outcomes and analyses that are actually posted, rather than generalized to unreported endpoints.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Rate Per Patient-year of Investigator-reported Symptomatic Hypoglycemic Adverse Events (AEs) With Confirmed Plasma Glucose (PG)
- Change From Baseline in Body Weight at Week 26
- Change From Baseline in Total Daily Insulin Dose (TDID) at Week 26
- Change From Baseline in Systolic Blood Pressure (SBP) and Diastolic Blood Pressure (DBP) at Week 26
9. Statistical Interpretation
In the primary endpoint results, mean HbA1c change was 0.2 in the placebo group, compared with -0.09 for empagliflozin 2.5 mg, -0.25 for 10 mg and -0.33 for 25 mg. The posted values are least-squares mean changes from baseline to week 26, with standard errors of 0.05 in each arm. These within-arm values describe average changes; the comparison with placebo is the more direct summary of the randomized treatment contrast.
The sponsor’s repeated-measures analyses reported mean differences of -0.28 for 2.5 mg, -0.45 for 10 mg and -0.52 for 25 mg, each compared with placebo. The corresponding reported confidence intervals were -0.46 to -0.11 at 99% for 2.5 mg, -0.60 to -0.30 at 97.5% for 10 mg, and -0.68 to -0.37 at 97.5% for 25 mg. Each sponsor-reported p-value was < 0.001. The signs indicate that the estimated change in each empagliflozin group was lower than the estimated change in the placebo group under the sponsor’s comparison.
Simple unadjusted recalculations from the posted arm summaries gave mean differences of -0.29, -0.45 and -0.53 for the 2.5 mg, 10 mg and 25 mg comparisons, respectively. Their unadjusted p-values were each <0.001. These calculations use the posted arm summaries and are not a substitute for the sponsor’s repeated-measures model. The estimates are close in magnitude to the sponsor’s reported contrasts, but the methods and interval levels are not identical.
Across the three dose comparisons, the posted point estimates become more negative as dose increases. That pattern is descriptive; it should not be treated as a formally tested dose-response relationship, since a dose-trend analysis is not reported in the registry record. Nor do the comparisons establish that the dose groups differ from one another. The endpoint findings are averages over the analyzed participants and the specified follow-up, not evidence about outcomes outside that setting.
The registry also posts secondary outcome results for body weight and total daily insulin dose. Those outcomes generally have changes in different directions across the empagliflozin arms than the placebo arm, but their interpretation depends on their own analysis populations, model details and multiplicity context. They provide additional measured outcomes, not independent confirmation of the primary endpoint. Safety counts likewise describe reported events and should not be interpreted as a complete account of every possible harm or as a comparison adjusted for uncertainty.
10. Statistical Methods Explained
The primary result is a comparison of a continuous outcome: change in HbA1c from baseline to week 26. The registry reports least-squares mean changes with standard errors within each arm. A least-squares mean is a model-based adjusted mean, rather than simply an unadjusted arithmetic average. The registry describes it as an adjusted mean change from baseline, but does not report all covariates or other details needed to reproduce that adjustment.
What does the repeated-measures model contribute?
The sponsor’s reported comparisons use a mixed effect model repeat measurement. In general, a repeated-measures model can use measurements collected at multiple time points and represent their correlation within a participant. A mixed model can also account for specified fixed and random effects. The exact model terms, covariance structure, estimation choices and missing-data assumptions are not reported in the registry record, so those details should not be inferred from the method label alone.
The sponsor reports mean differences between each empagliflozin group and placebo, along with confidence intervals and p-values. These are the analyses to use when describing the sponsor’s own statistical conclusions. They are not numerically identical to the simple recalculations because the sponsor’s model and the recalculations do not use the same analysis procedure. The registry record does not indicate that the posted result summaries are a complete model specification.
What is an unadjusted recalculation?
General explanation: an unadjusted recalculation based on arm-level means estimates a contrast by comparing the two posted means directly. It does not recreate a repeated-measures model or adjust for other variables. Its standard error and confidence interval are calculated from summary information rather than individual participant records. In this analysis, the arm standard errors are used to obtain approximate variability for the recalculation. Such estimates are useful as a transparent check on the scale and direction of the reported contrast, but they should not replace the sponsor’s analysis.
The recalculated primary contrasts are -0.29 for 2.5 mg, -0.45 for 10 mg and -0.53 for 25 mg, each relative to placebo. The recalculated p-values are each <0.001. These are unadjusted comparisons. The registry record does not report a multiplicity adjustment for these recalculations; they should not be interpreted as multiplicity-controlled tests.
How should p-values be read?
General explanation: a p-value describes how compatible data are with a specified null hypothesis under the assumptions of the analysis. It is not the probability that the null hypothesis is true, and it does not measure the size or practical importance of an effect. A small p-value does not by itself establish that the model assumptions are appropriate, that all relevant outcomes were measured, or that the result will generalize. The reported p-values should be read alongside the contrast estimates and their confidence intervals.
The sponsor’s p-values are all reported as < 0.001 for the primary comparisons. The recalculated p-values are reported as <0.001. The difference in displayed thresholds does not mean the analyses are interchangeable: the sponsor uses a repeated-measures model, while the recalculation is a simple unadjusted comparison of posted summaries. The registry record does not provide enough detail to assess all inferential choices behind the sponsor’s analysis.
Why can dispersion and approximation matter?
General explanation: a standard error describes uncertainty in an estimated mean, whereas a standard deviation describes variability among individual observations. They answer different questions. A standard error is affected by both the data’s variability and the number of observations. Where only standard errors and sample sizes are posted, reconstructing a standard deviation requires assumptions; the recalculated pooled standard deviations and standardized effects are therefore marked as approximate in the underlying statistical work. They are not direct participant-level estimates.
General explanation: over-dispersion occurs when observed variability is greater than assumed by a statistical model. If a model understates variability, uncertainty intervals can be too narrow and tests can appear more decisive than warranted. The registry record does not report whether over-dispersion was assessed or whether any correction was used. This is a general modeling consideration, not a claim that over-dispersion occurred in this trial.
The registry identifies the primary analysis population as the full analysis set of treated participants with a baseline and at least one on-treatment HbA1c result, using observed cases. This definition indicates that outcome availability is relevant to inclusion in the endpoint analysis. General explanation: estimates can be affected if the availability of measurements is related to outcome values or treatment experience. The registry record does not report the extent or reasons for missing HbA1c measurements, nor does it describe sensitivity analyses for missing data.
Finally, the registry lists multiple outcomes and analyses. When many comparisons are made, the chance of at least one apparently notable result can increase if each is judged without accounting for the others. Whether and how multiplicity was handled for the primary and secondary analyses is not reported in the registry record. Statistical significance should therefore be considered with the prespecified analysis plan and the broader set of analyses in mind; the record does not provide that complete context.
11. Confidence Intervals and Precision
Confidence intervals describe uncertainty around an estimated contrast under the model and assumptions used to calculate them. General explanation: an interval is not a guarantee that the true effect lies within its endpoints, and its confidence level is a repeated-sampling property of the method. A narrower interval indicates greater precision for that estimate under those assumptions; a wider interval indicates greater uncertainty. The interval should be considered together with the estimate, analysis method and endpoint definition.
For HbA1c, the sponsor reported a 99% interval of -0.46 to -0.11 for the 2.5 mg comparison, and 97.5% intervals of -0.60 to -0.30 for 10 mg and -0.68 to -0.37 for 25 mg. Each interval lies below zero. The corresponding sponsor-reported p-values were < 0.001. These intervals quantify uncertainty for the reported mean differences under the sponsor’s repeated-measures analyses; they do not convey the range of individual participant responses.
The sponsor’s intervals use different confidence levels across comparisons. That matters when comparing interval widths: width depends on both uncertainty and the confidence level, so widths at different levels are not directly equivalent measures of precision. The registry record does not explain the reason for the different interval levels or report the multiplicity procedure that may relate to them.
The simple unadjusted recalculations also have uncertainty intervals, but they arise from approximate variability reconstructed from the posted summaries and are not the sponsor’s model-based intervals. The recalculated point estimates are similar in magnitude to the sponsor’s reported contrasts, but that similarity does not make the methods interchangeable. The sponsor’s model-based result takes precedence when describing the sponsor’s analysis; the recalculations are supplementary statistical checks.
Precision also depends on the analysis population and available measurements. The primary result is based on observed cases meeting the stated full analysis set definition, not necessarily every enrolled participant. The registry record does not report enough information about missing outcome data to determine how that affects precision or whether missingness could influence the estimate.
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 | 111 | 149 |
| 75% of the observed effect | 198 | 264 |
| 50% of the observed effect | 444 | 594 |
The planning figures are participants per arm for comparisons between two groups, not total events. They are planning illustrations based on the observed effect, rather than the trial’s original design calculations. The listed assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation; the effect to detect is the stated fraction of the observed effect. The trial’s own original sample-size assumptions and justification 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 assumed effect under those planning assumptions, if the assumptions hold. The 90% power column gives the corresponding per-arm planning count for a 90% chance. These are theoretical design calculations, not probabilities that the completed trial found a true effect. This is not observed power.
The rows that plan for 100%, 75% or 50% of the observed effect illustrate how the assumed effect size changes the required sample. A smaller target effect requires more participants per arm to achieve the same planned power, all else held constant. The figures are specific to each comparison and outcome’s observed estimate and variability; they should not be treated as a general sample-size recommendation or as evidence that the trial was designed using these exact assumptions.
The original enrollment was 977, and the primary endpoint analysis counts ranged from 237 to 244 per arm. Those observed analysis counts and the illustrative planning counts serve different purposes: one describes participants in the posted analysis, and the other describes hypothetical planning under stated assumptions.
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 = -0.290; pooled standard deviation σ = 0.771.
- n = 2 × (1.96 + 0.842)2 × 0.7712 / -0.2902 = 110.8, rounded up to 111 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 <- -0.29 # observed difference in means
sigma <- 0.770553465183391 # 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(2580591)
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 = 111 (80% power), 149 (90% power)
75% of observed effect: n per arm = 198 (80% power), 264 (90% power)
50% of observed effect: n per arm = 444 (80% power), 594 (90% power)
power.t.test: 111.8
Simulated power at n = 111 per arm: 0.798 (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 effect Model Repeat Measurement | Mean Difference (Final Values) -0.28 | -0.46 to -0.11 | < 0.001 |
| Mixed effect Model Repeat Measurement | Mean Difference (Final Values) -0.45 | -0.60 to -0.30 | < 0.001 |
| Mixed effect Model Repeat Measurement | Mean Difference (Final Values) -0.52 | -0.68 to -0.37 | < 0.001 |
The sponsor’s primary analyses use a mixed effect model repeat measurement and report mean differences against placebo. Those reported estimates are -0.28 for 2.5 mg, -0.45 for 10 mg and -0.52 for 25 mg. The registry reports confidence intervals and p-values for each sponsor comparison. These are the appropriate results to cite when describing the sponsor’s own analysis.
Simple unadjusted recalculations from the posted arm-level summaries give corresponding mean differences of -0.29, -0.45 and -0.53. The recalculated p-values are each <0.001. The estimates are close to the sponsor’s estimates in magnitude, but the recalculations use a different approach and do not reproduce the sponsor’s repeated-measures model. Their intervals and p-values are therefore supplementary rather than replacements for the sponsor’s model-based results.
The registry identifies no discrepancy flag for these results. The record does not report enough model detail to independently reproduce the sponsor’s analyses from participant-level data. As a result, numerical agreement between a summary-based recalculation and the sponsor estimate is a consistency check, not a full validation of the model or its assumptions.
15. Multiplicity, Missing Data and Analysis Populations
Multiplicity arises when several hypotheses or outcomes are assessed. Even if each individual test uses a conventional threshold, the overall chance of at least one false-positive finding can rise as the number of tests increases. General explanation: strategies for addressing this include prespecifying a hierarchy of endpoints, adjusting significance thresholds, or clearly distinguishing confirmatory from exploratory analyses. The appropriate approach depends on the trial’s objectives and analysis plan.
The registry lists six outcome measures and 24 analyses. It reports sponsor p-values for the primary comparisons and some secondary comparisons, but the registry record does not report whether multiplicity was adjusted, which comparisons were included in any adjustment, or how the different confidence levels for primary comparisons were selected. Consequently, the p-values should be interpreted as reported for their respective analyses, not assumed to control the overall error rate across all outcomes and comparisons.
The record does not report whether interim analyses were planned or conducted, nor does it provide a full statistical analysis plan. It also does not report the trial’s original sample-size justification, so the relationship between the planned enrollment and any target power cannot be assessed from this record.
For the primary endpoint, the population is the full analysis set of treated participants with a baseline and at least one on-treatment HbA1c measurement, and the results are labeled observed cases. The registry record does not report the number or reasons for missing endpoint measurements, the handling of missing data within the repeated-measures analysis, or sensitivity analyses under alternative missing-data assumptions. Those omissions limit assessment of how robust the estimates are to incomplete follow-up.
These gaps do not negate the reported estimates, but they constrain the strength of conclusions about confirmatory evidence and robustness. The posted statistical results can be described as reported, while the unreported multiplicity, interim, and missing-data procedures remain unknown.
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 Matching Empagliflozin | 16 | 241 | 6.6% |
| Empagliflozin 2.5 Milligram (mg) | 13 | 241 | 5.4% |
| Empagliflozin 10 mg | 21 | 248 | 8.5% |
| Empagliflozin 25 mg | 16 | 245 | 6.5% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Placebo Matching Empagliflozin | 0 of 241 |
| Empagliflozin 2.5 Milligram (mg) | 0 of 241 |
| Empagliflozin 10 mg | 0 of 248 |
| Empagliflozin 25 mg | 1 of 245 |
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 Matching Empagliflozin | 153 of 241 |
| Empagliflozin 2.5 Milligram (mg) | 146 of 241 |
| Empagliflozin 10 mg | 172 of 248 |
| Empagliflozin 25 mg | 162 of 245 |
Most frequent serious adverse event terms
| Event term | Organ system | Placebo Matching Empagliflozin | Empagliflozin 2.5 Milligram (mg) | Empagliflozin 10 mg | Empagliflozin 25 mg |
|---|---|---|---|---|---|
| Diabetic ketoacidosis | Metabolism and nutrition disorders | 2 of 241 | 2 of 241 | 6 of 248 | 5 of 245 |
| Hypoglycaemia | Metabolism and nutrition disorders | 4 of 241 | 3 of 241 | 3 of 248 | 0 of 245 |
| Ketoacidosis | Metabolism and nutrition disorders | 1 of 241 | 1 of 241 | 3 of 248 | 2 of 245 |
| Ketosis | Metabolism and nutrition disorders | 0 of 241 | 1 of 241 | 0 of 248 | 3 of 245 |
| Vomiting | Gastrointestinal disorders | 0 of 241 | 0 of 241 | 2 of 248 | 1 of 245 |
| Basal cell carcinoma | Neoplasms benign, malignant and unspecified (incl cysts and polyps) | 2 of 241 | 1 of 241 | 0 of 248 | 0 of 245 |
| Angina unstable | Cardiac disorders | 0 of 241 | 2 of 241 | 0 of 248 | 0 of 245 |
| Abdominal pain | Gastrointestinal disorders | 0 of 241 | 0 of 241 | 2 of 248 | 0 of 245 |
| Chest pain | General disorders | 1 of 241 | 0 of 241 | 1 of 248 | 0 of 245 |
| Acetonaemia | Metabolism and nutrition disorders | 0 of 241 | 1 of 241 | 1 of 248 | 0 of 245 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Placebo Matching Empagliflozin | Empagliflozin 2.5 Milligram (mg) | Empagliflozin 10 mg | Empagliflozin 25 mg |
|---|---|---|---|---|---|
| Hypoglycaemia | Metabolism and nutrition disorders | 144 of 241 | 137 of 241 | 162 of 248 | 151 of 245 |
| Nasopharyngitis | Infections and infestations | 24 of 241 | 23 of 241 | 22 of 248 | 26 of 245 |
| Urinary tract infection | Infections and infestations | 12 of 241 | 12 of 241 | 9 of 248 | 16 of 245 |
| Blood ketone body increased | Investigations | 3 of 241 | 4 of 241 | 15 of 248 | 10 of 245 |
Serious events with the highest arm-level rate: diabetic ketoacidosis (2.4%), hypoglycaemia (1.7%), ketosis (1.2%), ketoacidosis (1.2%), angina unstable (0.8%).
Safety counts should be read as counts of participants affected in each group, with the corresponding number at risk stated in the registry. Serious adverse events were reported for 16 of 241 participants in the placebo group, 13 of 241 in the 2.5 mg group, 21 of 248 in the 10 mg group, and 16 of 245 in the 25 mg group. These are descriptive counts; they do not by themselves establish whether groups differ statistically or account for uncertainty in the comparisons.
Other adverse events were reported for 153 of 241 participants receiving placebo, 146 of 241 receiving 2.5 mg, 172 of 248 receiving 10 mg, and 162 of 245 receiving 25 mg. The registry reports zero deaths in the placebo, 2.5 mg and 10 mg groups, and one death in the 25 mg group. The record does not provide causal attribution for these figures in the registry record described.
The most frequent listed serious adverse event terms include diabetic ketoacidosis at 2.4%, hypoglycaemia at 1.7%, ketosis at 1.2%, ketoacidosis at 1.2%, unstable angina at 0.8%, and basal cell carcinoma at 0.8%. Event terms may describe specific reported categories; the registry record does not explain whether related terms overlap. Counts and listed terms are not a complete characterization of safety, and should be interpreted alongside the trial’s follow-up and event definitions.
17. What the Result Does, and Does Not, Mean
The posted primary results describe lower mean HbA1c change estimates in each empagliflozin group than in the placebo group over the 26-week study period. The sponsor’s repeated-measures analyses report mean differences of -0.28, -0.45 and -0.52 for the 2.5 mg, 10 mg and 25 mg comparisons, with confidence intervals below zero and p-values of < 0.001. These findings summarize the specified endpoint and analysis population in this trial.
They do not establish how an individual participant’s HbA1c would change, whether the observed differences are important for every clinical context, or whether the estimates apply to people not represented in the analyzed groups. A mean difference is a group-level estimate, and its confidence interval expresses statistical uncertainty under the analysis method rather than variation in individual responses.
The results also do not establish a formally tested dose-response relation. Although the posted estimates are more negative across the increasing dose groups, the registry record does not report a dose-trend test or a direct statistical comparison among dose groups. The comparisons provided are each against placebo.
The secondary and safety findings add measured context but do not resolve the limitations of the primary analysis. Their interpretation is affected by multiple outcomes, analysis populations, and missing details about multiplicity and missing data. The serious adverse event counts are descriptive and are not, by themselves, proof of equivalence or difference between groups.
In general, a trial result is one part of a broader evidence base. The registry record does not report enough information about the full analysis plan, missingness, or all outcomes to support conclusions beyond what the posted measures and comparisons directly address. These statistical findings are not individual medical guidance and do not determine treatment choices.
18. Why This Trial Matters Statistically
This trial is statistically informative because it compares three doses with placebo within a randomized, double-blind, parallel-group design and reports a continuous primary endpoint at a specified follow-up. The primary summaries include both arm-level adjusted changes and sponsor-reported contrasts, allowing readers to distinguish within-group changes from the randomized comparisons that address the central trial question.
The sponsor’s repeated-measures estimates and the simple recalculations are close in magnitude. That offers a useful check that the contrast scale is understandable from the posted summaries, while also illustrating why methods matter: the model-based analysis uses a different approach from the summary-based recalculation. The two sets of results should not be treated as identical analyses.
The record also makes clear that statistical interpretation is not limited to whether a p-value crosses a threshold. The magnitude and precision of the contrasts, the analysis population, the confidence levels, and the breadth of secondary analyses all affect how much can be concluded. Missing details about multiplicity, missing data and the original design assumptions limit assessment of the full inferential framework.
Finally, the posted secondary measures and serious adverse event counts illustrate that trials assess more than one dimension of outcomes. Their presence broadens context, but multiple analyses require careful interpretation and do not automatically provide independent confirmation. The main statistical lesson is to read the estimate, uncertainty, design and analysis population together, and to distinguish reported sponsor results from transparent but simpler recalculations.
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.
The primary analysis is defined as observed cases within the full analysis set: treated participants with a baseline and at least one on-treatment HbA1c result. The registry record does not report the amount or reasons for missing HbA1c data, the detailed missing-data assumptions of the repeated-measures model, or sensitivity analyses. The impact of incomplete outcome data therefore cannot be fully assessed from the registry results.
The registry does not report the full model specification, including all adjustment terms and covariance assumptions. The sponsor’s estimates can be reported as its own repeated-measures analyses, but their complete independent reproduction is not possible from the arm summaries alone. The recalculations use approximate variability derived from posted summary statistics and are unadjusted; they are not substitutes for participant-level analyses.
Multiplicity handling is also not reported. The record lists multiple outcome measures and analyses, but does not state whether a hierarchy or correction was used, or which results were intended to be confirmatory. The varying confidence levels for sponsor-reported primary comparisons are present in the results, but the reason for those levels is not reported.
The registry record does not report the original sample-size justification, interim analysis procedures, or a complete statistical plan. It also does not explain the difference between the brief summary’s 960 patients and the enrollment entry of 977. Further, the primary endpoint counts differ by arm from the enrollment total, and reasons for those analysis counts are not stated.
Safety results are aggregate counts and listed event terms. The record does not provide enough information to assess every event’s timing, attribution, severity distribution, or possible overlap among event categories. These limitations call for a bounded interpretation of the posted results rather than assumptions about unreported procedures or outcomes.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Empagliflozin as Adjunctive to Insulin Therapy Over 26 Weeks in Patients With T1DM (EASE-3) — NCT02580591.
- Registry record last updated 2018-11-02; status last verified 2018-10.
- Results first posted 2018-11-02.
- 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
The registry record describes a completed Phase III randomized, double-blind, parallel-group trial of empagliflozin as adjunctive therapy to insulin in type 1 diabetes mellitus. It compares placebo with empagliflozin at 2.5 mg, 10 mg and 25 mg over 26 weeks, with total enrollment listed as 977.
The primary endpoint is change from baseline in HbA1c at week 26 for the full analysis set of treated participants with baseline and at least one on-treatment measurement, using observed cases. The sponsor reports repeated-measures comparisons against placebo; simple unadjusted recalculations from arm summaries are similar in magnitude but use a different method.
Secondary outcome summaries include body weight and total daily insulin dose, while the registry also names hypoglycemic adverse events and blood pressure outcomes. Serious adverse event counts and deaths are reported by group. The registry record does not report the complete statistical plan, original sample-size justification, multiplicity procedures, or detailed missing-data handling, limiting assessment of those aspects.