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 Bioavailability of a Fixed Dose Combination Tablet With Empagliflozin (BI 10773) and Metformin Compared With the Monocomponents and Effect of Food on Bioavailability (NCT01211197), a randomized phase 1 study. The primary outcome is Empa: Area Under the Curve 0 to Infinity (AUC0-∞).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01211197 |
| Phase | Phase 1 |
| Condition | Diabetes Mellitus, Type 2 |
| Allocation | Randomized |
| Design model | Crossover |
| Masking | None (open label) |
| Enrollment | 16 |
| Arms in the primary outcome | 3 |
| Lead sponsor | Boehringer Ingelheim |
| Results posted | Yes |
2. Clinical Question
Population
The study enrolled healthy volunteers. The primary pharmacokinetic analysis population included evaluable participants who took at least one dose, had at least one observation for a primary pharmacokinetic endpoint, and had no important protocol violations relevant to pharmacokinetic evaluation. The registry record lists type 2 diabetes mellitus as a condition, but the described study population is healthy volunteers.
Intervention
The intervention of interest was a fixed-dose combination tablet containing BI 10773, also called empagliflozin, and metformin. The official title specifies a 12.5 mg BI 10773 / 1000 mg metformin fixed-dose tablet. The study also examined this tablet administered with food.
Comparator
The principal comparisons were the fixed-dose combination while fasted versus separate BI 10773 and metformin tablets while fasted, and the fixed-dose combination while fasted versus the fixed-dose combination with food. Participants received three treatments in randomized order as part of a crossover study.
Primary question
The primary question concerned relative empagliflozin exposure, measured by the area under the plasma concentration-time curve from zero extrapolated to infinity. The study examined whether the fixed-dose combination’s exposure differed from the separate tablets taken together, and how food related to exposure after the fixed-dose combination. This is a pharmacokinetic question in healthy volunteers, not a test of clinical benefit in people with type 2 diabetes.
3. Trial Design
This was a completed, randomized, open-label, single-dose, three-way crossover Phase I trial in healthy volunteers. The registry lists an enrollment of 16. In a crossover design, participants receive more than one treatment in a planned sequence, so comparisons can be made across treatment periods within the study. The treatment order was randomized. The registry record does not report the sequence details, washout duration, or the timing of each treatment period.
The three treatments were the fixed-dose combination tablet while fasted, separate BI 10773 and metformin tablets while fasted, and the fixed-dose combination tablet with food. The official title identifies the combination as 12.5 mg BI 10773 / 1000 mg metformin. The treatments are described as single-dose administrations. Masking was none, so the study was open-label.
The primary pharmacokinetic endpoint was empagliflozin area under the curve from zero to infinity. The registry describes blood sampling from one hour before administration through 72 hours after administration. The PK analysis population was defined as evaluable subjects who took at least one dose, contributed at least one observation for a primary PK endpoint, and did not have important protocol violations relevant to PK evaluation.
The posted primary endpoint results include 15 for the fasted fixed-dose combination, 16 for the fasted individual tablets, and 14 for the fed fixed-dose combination. These are the reported group counts for that endpoint; the registry record does not explain why they differ. The trial’s own sample-size justification, planned power, randomization sequence details, and protocol-defined analysis plan are not reported in the registry record.
4. Participant Flow and Accounting
The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.
Before assignment: An open label, randomised, three-way crossover study. A washout period of at least 7 days was respected between drug administrations.
Treatment Period 1 (1 Day)
| Stage | FDC Fasted / Individual Tablets Fasted / FDC Fed | FDC Fasted / FDC Fed / Individual Tablets Fasted | Individual Tablets Fasted / FDC Fasted / FDC Fed | Individual Tablets Fasted / FDC Fed / FDC Fasted | FDC Fed / FDC Fasted / Individual Tablets Fasted | FDC Fed / Individual Tablets Fasted / FDC Fasted |
|---|---|---|---|---|---|---|
| STARTED | 3 | 3 | 3 | 3 | 2 | 2 |
| COMPLETED | 3 | 3 | 3 | 3 | 2 | 2 |
| NOT COMPLETED | 0 | 0 | 0 | 0 | 0 | 0 |
Washout Period 1 (7 Days)
| Stage | FDC Fasted / Individual Tablets Fasted / FDC Fed | FDC Fasted / FDC Fed / Individual Tablets Fasted | Individual Tablets Fasted / FDC Fasted / FDC Fed | Individual Tablets Fasted / FDC Fed / FDC Fasted | FDC Fed / FDC Fasted / Individual Tablets Fasted | FDC Fed / Individual Tablets Fasted / FDC Fasted |
|---|---|---|---|---|---|---|
| STARTED | 3 | 3 | 3 | 3 | 2 | 2 |
| COMPLETED | 3 | 3 | 2 | 3 | 2 | 2 |
| NOT COMPLETED | 0 | 0 | 1 | 0 | 0 | 0 |
Reasons for not completing this period:
| Reason | FDC Fasted / Individual Tablets Fasted / FDC Fed | FDC Fasted / FDC Fed / Individual Tablets Fasted | Individual Tablets Fasted / FDC Fasted / FDC Fed | Individual Tablets Fasted / FDC Fed / FDC Fasted | FDC Fed / FDC Fasted / Individual Tablets Fasted | FDC Fed / Individual Tablets Fasted / FDC Fasted |
|---|---|---|---|---|---|---|
| Withdrawal by Subject | 0 | 0 | 1 | 0 | 0 | 0 |
Treatment Period 2 (1 Day)
| Stage | FDC Fasted / Individual Tablets Fasted / FDC Fed | FDC Fasted / FDC Fed / Individual Tablets Fasted | Individual Tablets Fasted / FDC Fasted / FDC Fed | Individual Tablets Fasted / FDC Fed / FDC Fasted | FDC Fed / FDC Fasted / Individual Tablets Fasted | FDC Fed / Individual Tablets Fasted / FDC Fasted |
|---|---|---|---|---|---|---|
| STARTED | 3 | 3 | 2 | 3 | 2 | 2 |
| COMPLETED | 3 | 3 | 2 | 3 | 2 | 2 |
| NOT COMPLETED | 0 | 0 | 0 | 0 | 0 | 0 |
Washout Period 2 (7 Days)
| Stage | FDC Fasted / Individual Tablets Fasted / FDC Fed | FDC Fasted / FDC Fed / Individual Tablets Fasted | Individual Tablets Fasted / FDC Fasted / FDC Fed | Individual Tablets Fasted / FDC Fed / FDC Fasted | FDC Fed / FDC Fasted / Individual Tablets Fasted | FDC Fed / Individual Tablets Fasted / FDC Fasted |
|---|---|---|---|---|---|---|
| STARTED | 3 | 3 | 2 | 3 | 2 | 2 |
| COMPLETED | 2 | 3 | 2 | 3 | 2 | 2 |
| NOT COMPLETED | 1 | 0 | 0 | 0 | 0 | 0 |
Reasons for not completing this period:
| Reason | FDC Fasted / Individual Tablets Fasted / FDC Fed | FDC Fasted / FDC Fed / Individual Tablets Fasted | Individual Tablets Fasted / FDC Fasted / FDC Fed | Individual Tablets Fasted / FDC Fed / FDC Fasted | FDC Fed / FDC Fasted / Individual Tablets Fasted | FDC Fed / Individual Tablets Fasted / FDC Fasted |
|---|---|---|---|---|---|---|
| Adverse Event | 1 | 0 | 0 | 0 | 0 | 0 |
Analysis population for the primary outcome, as defined in the registry: Pharmacokinetic (PK) set included all evaluable subjects who took at least 1 dose of investigational medication, provided at least one observation for at least one primary PK endpoint without important protocol violations relevant to the evaluation of pharmacokinetics.
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.
| Characteristic | Unit | Study Overall |
|---|---|---|
| Participants analysed | 16 | |
| Age, Continuous | years | 35.8 (SD 7.7) |
| Sex: Female, Male: Female | Participants | 9 |
| Sex: Female, Male: Male | Participants | 7 |
6. Primary Endpoint
The registry lists the primary outcome as Empa: Area Under the Curve 0 to Infinity (AUC0-∞), measured over 1 hour (h) before drug administration and 20 minutes (min), 40min, 1 h, 1.5h, 2h, 2.5h, 3h, 4h, 6h, 8h, 10h, 12h, 24h, 34h, 48h, 72h after drug administration.
| Element | Registry entry |
|---|---|
| Result type | Mean |
| Measure of spread | Standard Deviation |
| Unit | nmol*h/L |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is empagliflozin area under the plasma concentration-time curve from zero extrapolated to infinity, abbreviated AUC0-∞. An area-under-the-curve measure represents exposure over time: it incorporates both the concentration of drug in plasma and how long that concentration is observed. Extending the curve to infinity estimates exposure beyond the last measured concentration by extrapolation.
This is a pharmacokinetic endpoint. Comparing it across formulations and food conditions can describe whether measured systemic exposure is similar or differs under the study conditions. It does not directly measure symptom relief, disease control, long-term outcomes, or clinical benefit.
The registry identifies the endpoint as a mean in nmol*h/L and describes concentration sampling from one hour before administration through 72 hours after administration. It labels the dispersion as a standard deviation, but the endpoint description notes that the reported dispersion is actually the coefficient of variation (CV). Those measures are not interchangeable: a standard deviation expresses spread in the outcome’s units, while a CV expresses spread relative to the mean. The posted values should therefore be read with that registry clarification in mind.
The PK analysis set was restricted to evaluable participants meeting the registry’s treatment, observation, and protocol-violation criteria. The registry record does not report further details about how extrapolation was performed or how missing concentration measurements were handled.
7. Results Posted in the Registry
- Individual Tablets Fasted: mean 2,860 versus 2,920 on control; difference -60.00 (95% CI -72.22 to -47.78), standardized effect d = -3.44; z-test p = <0.001.
- FDC Fed: mean 2,710 versus 2,920 on control; difference -210.00 (95% CI -221.36 to -198.64), standardized effect d = -13.43; z-test p = <0.001.
Mean difference: Individual Tablets Fasted
95% CI: -72.22 to -47.78
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 |
|---|---|---|---|---|
| Empa: Area Under the Curve 0 to the Last Quantifiable Data Point (AUC0-tz) | Continuous Endpoint | Mean difference | -60.00 (-72.29 to -47.71) | 2 per arm |
| Metformin: Area Under the Curve 0 to the Last Quantifiable Data Point (AUC0-tz) | Continuous Endpoint | Mean difference | -180.00 (-194.19 to -165.81) | 1 per arm |
Empa: Area Under the Curve 0 to the Last Quantifiable Data Point (AUC0-tz)
- 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 deviations.
- Result:
- Individual Tablets Fasted: mean 2,800 versus 2,860 on control; difference -60.00 (95% CI -72.29 to -47.71), standardized effect d = -3.42; z-test p = <0.001.
- FDC Fed: mean 2,640 versus 2,860 on control; difference -220.00 (95% CI -231.43 to -208.57), standardized effect d = -13.98; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Individual Tablets Fasted 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 FDC Fed than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Metformin: Area Under the Curve 0 to the Last Quantifiable Data Point (AUC0-tz)
- 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 deviations.
- Result:
- Individual Tablets Fasted: mean 9,720 versus 9,900 on control; difference -180.00 (95% CI -194.19 to -165.81), standardized effect d = -8.87; z-test p = <0.001.
- FDC Fed: mean 9,550 versus 9,900 on control; difference -350.00 (95% CI -363.73 to -336.27), standardized effect d = -18.63; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Individual Tablets Fasted 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 FDC Fed than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The available secondary pharmacokinetic results follow a broadly similar pattern to the primary endpoint: the fasted individual tablets and the fasted fixed-dose combination have relatively close reported exposure summaries, while the fed fixed-dose combination has lower posted arithmetic means than the fasted fixed-dose combination. The sponsor’s geometric mean ratio analyses for the reported secondary AUC measures provide another view of these exposure comparisons. They are related pharmacokinetic measures, not separate clinical outcomes.
The secondary endpoints include empagliflozin AUC to the last quantifiable data point and metformin AUC to the last quantifiable data point, as well as listed measures such as time to maximum concentration and terminal elimination parameters. Numerical results are not reported in the registry record for every listed secondary outcome. Where numerical comparisons are available, they should be interpreted alongside the primary result rather than as independent proof of a broader conclusion.
General explanation: secondary outcomes can help characterize different aspects of a treatment’s pharmacokinetic profile, but testing many outcomes creates more opportunities for chance findings. Unless a multiplicity strategy or a prespecified hierarchy is used, unadjusted secondary results carry less confirmatory weight than a clearly specified primary analysis. The registry record does not report a multiplicity adjustment or testing hierarchy. The secondary findings are therefore best treated as supportive and descriptive, with attention to the fact that the sponsor’s model-based results and simple recalculations use different statistical summaries.
The registry lists nine posted secondary measures, while the record does not supply full numerical detail for all listed outcomes. The absence of a numerical result for an outcome means its direction and precision cannot be assessed from the registry record. No conclusion about the unreported secondary measures should be inferred from the available AUC pattern alone.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Empa: Area Under the Curve 0 to the Last Quantifiable Data Point (AUC0-tz)
- Metformin: Area Under the Curve 0 to the Last Quantifiable Data Point (AUC0-tz)
- Time to Maximum Measured Concentration (Tmax)
- Terminal Elimination Rate Constant in Plasma (λz)
- Terminal Half-life in Plasma (T1/2)
- Mean Residence Time in the Body After Oral Administration (MRTpo)
- Apparent Clearance After Extravascular Administration (CL/F)
- Apparent Volume of Distribution During the Terminal Phase (Vz/F)
9. Statistical Interpretation
The primary endpoint’s posted mean was 2920.0 nmol*h/L for the fasted fixed-dose combination, 2860.0 nmol*h/L for the fasted individual tablets, and 2710.0 nmol*h/L for the fed fixed-dose combination. The accompanying dispersion values are identified in the endpoint description as coefficients of variation, not standard deviations. These summaries describe exposure in the analyzed groups; by themselves they do not establish that two formulations are equivalent or that a difference is clinically important.
The sponsor reported an ANOVA-based geometric mean ratio of 100.59 for the fasted fixed-dose combination compared with the fasted individual tablets, with a 90% confidence interval from 95.75 to 105.67. For the fasted fixed-dose combination compared with the fed fixed-dose combination, the reported geometric mean ratio was 94.94, with a 90% confidence interval from 89.85 to 100.33. The registry labels these as non-inferiority or equivalence analyses, but does not report the decision margins in the record. Without the margin and its prespecified interpretation, the ratio and interval alone should not be treated as a complete formal equivalence conclusion.
The simple recalculated comparisons use arithmetic means and unadjusted mean differences. For individual tablets while fasted versus the fasted fixed-dose combination, the recalculated mean difference was -60.0 nmol*h/L, with a 95% confidence interval from -72.22 to -47.78 and p < 0.001. For the fed fixed-dose combination versus the fasted fixed-dose combination, it was -210.0 nmol*h/L, with a 95% confidence interval from -221.4 to -198.6 and p < 0.001. These calculations are not the same estimand or analysis as the sponsor’s geometric mean ratio analysis. They are simple, unadjusted recalculations from posted summary statistics and do not incorporate the trial’s crossover structure.
The calculated confidence intervals are narrow relative to their respective mean differences, and both unadjusted tests produce p < 0.001. These results indicate a clear difference in the posted arithmetic means under those simple comparisons, but statistical separation is not itself evidence of clinical importance. The sponsor’s approach, based on ANOVA and geometric mean ratios, is more directly aligned with its reported relative-bioavailability analysis. The registry does not provide enough detail to reconstruct the full model, its assumptions, or the planned decision rule.
For the fasted formulation comparison, the sponsor’s ratio estimate is near 100, while its interval spans values below and above 100. For the food comparison, the reported ratio is below 100 and the interval also includes 100. A confidence interval describes uncertainty around an estimate under the method used; it does not by itself declare equivalence. The endpoint is pharmacokinetic exposure in healthy volunteers, so these findings should not be extended to clinical outcomes or other populations.
10. Statistical Methods Explained
Statistical interpretation depends on what is being estimated. The sponsor reported geometric mean ratios from ANOVA, while the simple recalculations compare arithmetic means using unadjusted mean differences. A ratio expresses one group’s geometric mean relative to another’s; a mean difference expresses the subtraction of arithmetic means. These are different summaries and answer related, but not identical, statistical questions. The sponsor’s ratio analysis should be read as the registry’s reported analysis, while the recalculations are supplementary descriptive comparisons.
Why use a geometric mean ratio?
General explanation: concentration and exposure measures can be positively skewed, with a relatively small number of high observations creating a long upper tail. For such data, analyses often use logarithms, fit a model on the transformed scale, and then express the contrast after transformation back as a ratio of geometric means. The ratio focuses on proportional differences rather than an absolute change in the original units. The registry reports ANOVA and geometric mean ratios, but the detailed transformation and model specifications are not reported in the registry record.
A ratio of 100.59 is expressed on a scale where 100 represents equal geometric means. Its confidence interval, 95.75 to 105.67, describes a range of values compatible with the reported analysis under its assumptions. Whether that interval meets a formal equivalence or non-inferiority criterion depends on prespecified limits. Those limits are not reported in the registry record, so the interval should not be interpreted as proof of equivalence based only on its proximity to 100.
What does the simple recalculation represent?
General explanation: an unadjusted mean difference is the difference between two group means without adjustment for other variables or a model structure. The recalculated results use the posted group summaries and are labelled recalculated. They are not the sponsor’s ANOVA results. The confidence intervals and p-values attached to these recalculations describe those simple comparisons, not a reproduction of the trial’s crossover analysis.
The study is a three-way crossover, where treatment assignment is made in randomized order and participants receive multiple treatments. In general, crossover analyses can account for within-participant comparisons and may include terms for treatment, period, or sequence, depending on the protocol and model. The posted summary statistics do not contain the participant-level paired observations needed to reconstruct such an analysis. The registry record does not report the full sponsor model or the period and sequence details, so the recalculations should not be read as adjusted crossover estimates.
How should p-values be read?
General explanation: a p-value measures how incompatible the observed data are with a specified statistical null model, assuming that model and its assumptions are correct. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of an effect. The recalculated p-values are unadjusted and apply to the arithmetic mean comparisons. The sponsor analyses do not list p-values for the geometric mean ratio results.
In the setting of multiple outcomes and comparisons, a small unadjusted p-value does not on its own account for the chance of false-positive findings across a family of tests. The registry record does not report a multiplicity adjustment or a hierarchy for interpreting the comparisons. This is especially relevant to secondary endpoints, which are supportive and should not be treated as independent confirmation without a prespecified interpretation plan.
Why can variability matter?
General explanation: variability affects how precisely a mean or ratio is estimated. More variability generally makes estimates less precise when other design features are held fixed. A coefficient of variation describes dispersion relative to the mean and is often useful when outcome scales vary with the level of the measurement. The registry clarifies that the endpoint dispersion is a CV even though the field is described as standard deviation; interpreting it as an SD in nmol*h/L would therefore be incorrect.
All statistical estimates depend on assumptions. For a ratio analysis, assumptions concern the model and transformed outcomes; for a simple mean comparison, assumptions concern the sampling distribution and variability. The registry does not report diagnostics, missing-data procedures, or sensitivity analyses. The posted estimates are informative as summaries, but the record does not allow a full audit of model fit or robustness.
11. Confidence Intervals and Precision
The sponsor’s primary endpoint analysis reports 90% confidence intervals for geometric mean ratios. The interval for the fasted fixed-dose combination compared with the fasted individual tablets is 95.75 to 105.67 around a ratio of 100.59. The interval for the fasted fixed-dose combination compared with the fed fixed-dose combination is 89.85 to 100.33 around a ratio of 94.94. These intervals express uncertainty for the reported model-based ratios.
General explanation: a confidence interval is a range generated by a statistical procedure that, across repeated studies under its assumptions, would contain the underlying parameter at the stated confidence level at the corresponding frequency. It is not a guarantee that the true value lies in this particular interval, and it does not show the range of individual participant responses. The width reflects precision, while the estimate gives the central result.
The simple recalculated mean differences use 95% confidence intervals. For individual tablets versus the fasted fixed-dose combination, the interval is -72.22 to -47.78 nmol*h/L. For the fed combination versus the fasted combination, it is -221.4 to -198.6 nmol*h/L. These intervals concern arithmetic mean differences and must not be substituted for the sponsor’s ratio intervals. Their narrower or wider appearance cannot be compared directly without accounting for the different scales and estimands.
The endpoint groups are small, and the group counts differ by comparison. A confidence interval’s precision is influenced by sample size, variability, and analysis design. In a crossover trial, within-participant covariance can also influence precision, but the summary data do not report it. The registry record does not provide participant-level data or enough model detail to independently evaluate that contribution.
Precision is not the same as relevance. A narrow interval can estimate a difference precisely without establishing whether that difference matters clinically. Here, the endpoint is drug exposure in healthy volunteers, and the registry record does not define a clinically meaningful exposure threshold for interpreting these intervals.
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 | 2 | 2 |
| 75% of the observed effect | 3 | 4 |
| 50% of the observed effect | 6 | 8 |
The sample-size figures are planning illustrations based on observed effects, not the trial’s original design assumptions. The registry’s illustration specifies a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. It considers the full observed effect and fractions of that effect, including 75% and 50%. The displayed counts are participants per arm, not total events.
For each assumed effect, the 80% power column describes the number of participants per arm estimated to give an 80% chance of detecting an effect of that size under the stated planning assumptions, if the effect and model assumptions hold. The 90% power column makes the corresponding estimate for a 90% chance. These are planning targets, not properties measured after the study. This is not observed power.
The illustration shows that planning for a smaller effect generally requires more participants than planning for a larger effect, because a smaller signal is harder to distinguish from variability. Its counts are based on the observed comparisons and should not be treated as a recommendation for a future trial without considering the intended analysis, design, outcome variability, and target effect.
The posted illustration uses equal allocation between two arms, whereas the trial itself was a three-way crossover. The sample-size assumptions for the trial’s original design, including any crossover-specific calculation or allowance for incomplete data, are not reported in the registry record. The planning figures therefore provide context for hypothetical two-arm comparisons, not evidence about the adequacy of the trial’s enrollment.
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 = -60.000; pooled standard deviation σ = 17.428.
- n = 2 × (1.96 + 0.842)2 × 17.4282 / -60.0002 = 1.3, rounded up to 2 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 <- -60 # observed difference in means
sigma <- 17.4275940531893 # 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(1211197)
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 = 2 (80% power), 2 (90% power)
75% of observed effect: n per arm = 3 (80% power), 4 (90% power)
50% of observed effect: n per arm = 6 (80% power), 8 (90% power)
power.t.test: 2.7
Simulated power at n = 2 per arm: 0.463 (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 |
|---|---|---|---|
| ANOVA | Geometric mean ratio 100.59 | 95.75 to 105.67 | not reported |
| ANOVA | Geometric mean ratio 94.94 | 89.85 to 100.33 | not reported |
The registry reports the sponsor’s primary endpoint analysis as an ANOVA of geometric mean ratios. For the fasted fixed-dose combination compared with the fasted individual tablets, the sponsor reports a ratio of 100.59 with a 90% confidence interval from 95.75 to 105.67. For the fasted fixed-dose combination compared with the fed combination, the ratio is 94.94 with a 90% confidence interval from 89.85 to 100.33. The record labels these analyses non-inferiority or equivalence analyses.
The recalculations use arithmetic mean differences and 95% confidence intervals from posted summary statistics. They are unadjusted and do not reproduce the sponsor’s ANOVA or account for the crossover design. As a result, the sponsor estimates and recalculated estimates should be viewed as different analytical summaries rather than competing versions of the same quantity. The registry record indicates no discrepancy between the posted values and the available re-calculations, but the methods and estimands still differ.
The sponsor’s analysis is the relevant source for the registry’s reported relative-bioavailability results. However, the record does not report the equivalence or non-inferiority margins, full ANOVA specification, or other details needed to evaluate the formal decision rule independently. The ratio estimates and intervals can be described, but a formal conclusion under a margin cannot be inferred without that information.
15. Multiplicity, Missing Data and Analysis Populations
The primary endpoint is empagliflozin AUC0-∞, with two reported comparisons: the fasted fixed-dose combination against the fasted individual tablets, and the fasted combination against the fed combination. The registry also lists multiple secondary pharmacokinetic outcomes and reports additional analyses. Considering multiple endpoints and contrasts raises a multiplicity issue: without a prespecified strategy, the chance of at least one false-positive result can increase as more hypotheses are tested.
General explanation: multiplicity can be handled through a hierarchy of hypotheses, adjusted significance thresholds, or other prespecified methods. Such procedures distinguish confirmatory tests from exploratory analyses and help control how results are interpreted across a family of comparisons. The registry record does not report whether an adjustment was planned, which hypotheses were prioritized, or whether the listed comparisons were considered confirmatory or exploratory.
The registry defines the primary PK analysis population using evaluability, dose receipt, availability of at least one primary endpoint observation, and absence of important protocol violations relevant to PK assessment. It reports group counts for the endpoint, but does not report a full participant flow, reasons for exclusions, or the handling of missing observations. Missing-data methods and sensitivity analyses are not reported in the registry record.
For a pharmacokinetic endpoint derived from concentration measurements over time, missing samples can affect the estimated curve and extrapolation. General explanation: an analysis may use explicit rules for handling missing samples, but the effect of missingness depends on when observations are absent and on the analysis method. The record does not state how missing concentration values, incomplete profiles, or values below quantification limits were handled.
The trial’s crossover design also makes the analysis population and treatment-period data important. The registry states that treatment order was randomized and that three treatments were investigated, but period-level completeness, sequence effects, and the model’s handling of within-participant correlation are not reported in the registry record. These omissions limit independent assessment of the sponsor analysis and make the simple recalculations insufficient as a substitute for a full crossover analysis.
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 |
|---|---|---|---|
| FDC Fasted | 0 | 15 | 0.0% |
| Individual Tablets Fasted | 0 | 16 | 0.0% |
| FDC Fed | 0 | 14 | 0.0% |
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 |
|---|---|
| FDC Fasted | 2 of 15 |
| Individual Tablets Fasted | 6 of 16 |
| FDC Fed | 8 of 14 |
Most frequent non-serious adverse event terms
| Event term | Organ system | FDC Fasted | Individual Tablets Fasted | FDC Fed |
|---|---|---|---|---|
| Diarrhoea | Gastrointestinal disorders | 2 of 15 | 3 of 16 | 3 of 14 |
| Headache | Nervous system disorders | 1 of 15 | 1 of 16 | 1 of 14 |
| Dizziness | Nervous system disorders | 0 of 15 | 1 of 16 | 1 of 14 |
| Nasopharyngitis | Infections and infestations | 0 of 15 | 0 of 16 | 1 of 14 |
| Rhinitis | Infections and infestations | 0 of 15 | 0 of 16 | 1 of 14 |
| Urinary tract infection | Infections and infestations | 0 of 15 | 1 of 16 | 0 of 14 |
| Ligament sprain | Injury, poisoning and procedural complications | 0 of 15 | 0 of 16 | 1 of 14 |
| Wound | Injury, poisoning and procedural complications | 0 of 15 | 1 of 16 | 0 of 14 |
| Oropharyngeal pain | Respiratory, thoracic and mediastinal disorders | 0 of 15 | 1 of 16 | 0 of 14 |
| Dermatitis contact | Skin and subcutaneous tissue disorders | 0 of 15 | 0 of 16 | 1 of 14 |
The registry reports no serious adverse events for the fasted fixed-dose combination group, the fasted individual-tablet group, or the fed fixed-dose combination group. The corresponding numbers at risk are 15, 16, and 14. These are the reported serious-event figures for the treatment groups. The record does not list any serious adverse-event terms.
Other, non-serious adverse events are also reported: 2 for the fasted fixed-dose combination, 6 for the fasted individual tablets, and 8 for the fed fixed-dose combination. These event counts are descriptive and should be read with their group-specific numbers at risk. The registry does not provide detailed event terms in the listed summary.
General explanation: absence of a reported serious event in a small study does not establish that a treatment has no serious risks. This trial was a single-dose pharmacokinetic study in healthy volunteers, and its safety summaries are limited to the recorded groups and observation in the registry. Death counts are not reported in the registry record.
17. What the Result Does, and Does Not, Mean
The results describe short-term empagliflozin exposure under three study conditions in healthy volunteers: a fixed-dose combination while fasted, separate BI 10773 and metformin tablets while fasted, and the fixed-dose combination with food. The primary endpoint summarizes exposure over time through an extrapolated AUC. The sponsor’s reported ratios and confidence intervals address relative bioavailability, while the unadjusted recalculations describe arithmetic mean differences.
The pattern of estimates can help characterize formulation and food comparisons within this study. It does not establish how the treatments affect blood glucose, symptoms, complications, quality of life, or other patient outcomes. No clinical outcome endpoint is identified as the primary endpoint. The participants are described as healthy volunteers, so the pharmacokinetic findings should not automatically be generalized to people with type 2 diabetes or to other populations.
The trial’s open-label, randomized, single-dose, three-way crossover design informs how its results should be understood. Random treatment order can reduce systematic order assignment, and a crossover permits repeated treatment conditions within participants. Yet the registry record does not provide all period-level details or enough model information to reconstruct the sponsor’s analysis. The straightforward mean-difference calculations are not a replacement for the sponsor’s model-based comparison.
The reported confidence intervals express statistical precision under their respective analyses. They do not specify whether a difference is clinically important. The registry calls the sponsor analyses non-inferiority or equivalence analyses but does not report the margins that define those conclusions. No formal equivalence claim should be made from the point estimates alone.
In short, the registry supports a description of relative pharmacokinetic exposure in this study. It does not support a treatment recommendation, a conclusion about clinical effectiveness, or a full safety assessment. Further interpretation would require the original analysis plan and model details, the decision margins, and information about how missing or incomplete PK profiles were handled.
18. Why This Trial Matters Statistically
This trial is statistically useful because it separates two related questions: whether a fixed-dose tablet has exposure similar to the separate tablets taken together, and whether food is associated with a change in exposure after the fixed-dose tablet. The three-way crossover design permits those conditions to be examined in randomized treatment order within one study framework. The primary endpoint, empagliflozin AUC0-∞, captures overall plasma exposure rather than a single concentration at one sampling time.
The record also illustrates why the estimand matters. The sponsor reports geometric mean ratios from ANOVA, whereas a simple recalculation from group summaries gives arithmetic mean differences. Both approaches can describe treatment contrasts, but they are not interchangeable. In a crossover trial, analysis of within-participant information may also differ from a comparison of group-level summaries. Reading the reported model and the recalculation as if they were identical would obscure those distinctions.
Another statistical lesson is the role of uncertainty and decision thresholds. A point estimate near 100 on a ratio scale is not, by itself, proof of equivalence. That determination depends on prespecified margins and an analysis plan; the registry record does not report the margins. Confidence intervals communicate precision but do not supply the missing decision rule or determine clinical importance.
Finally, the small Phase I study and its pharmacokinetic focus set clear boundaries on inference. It can describe exposure patterns under the study conditions, but it does not establish clinical outcomes or provide a comprehensive safety assessment. The distinction between pharmacokinetic evidence and clinical effectiveness is central to interpreting the results accurately.
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 population is described as healthy volunteers, limiting direct generalization to people with type 2 diabetes. The study was a single-dose Phase I trial, so its results characterize exposure under the studied administration conditions rather than repeated treatment or long-term outcomes. The registry record does not report demographic details that would allow assessment of how representative participants were.
The study is open-label. For an objective concentration-based pharmacokinetic measure, lack of masking may be less directly influential than for a subjective outcome, but the registry does not report additional safeguards or laboratory procedures. The crossover design depends on treatment-period information and participant-level comparisons; sequence, washout, period, and carryover details are not reported in the registry record.
The sponsor’s ANOVA specification, transformation details, and formal equivalence or non-inferiority margins are also not reported. These omissions prevent an independent check of the decision rule. The simple recalculations are based on posted group summaries and do not account for the paired structure of the crossover design. They should not be used as if they reproduced the sponsor’s primary analysis.
The endpoint description clarifies that the posted dispersion is a coefficient of variation despite being labelled standard deviation. This is important when interpreting variability. Missing concentration data, exclusions, handling of incomplete profiles, and sensitivity analyses are not reported in the registry record. The registry also does not report a multiplicity strategy for the several endpoint measures and comparisons.
Finally, there are no serious adverse events listed in the group summaries, but the study size and single-dose setting limit what can be inferred about uncommon or delayed harms. Death counts are not reported in the registry record. These considerations make the evidence useful for describing relative exposure, but narrow in scope.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Bioavailability of a Fixed Dose Combination Tablet With Empagliflozin (BI 10773) and Metformin Compared With the Monocomponents and Effect of Food on Bioavailability — NCT01211197.
- Registry record last updated 2015-08-21; status last verified 2015-07.
- Results first posted 2015-08-21.
- 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
NCT01211197 is a completed randomized, open-label, single-dose, three-way crossover Phase I study in healthy volunteers. It compared a fixed-dose BI 10773 / metformin tablet while fasted with the individual tablets while fasted, and examined the fixed-dose tablet with and without food. The official title specifies a 12.5 mg / 1000 mg combination.
The primary endpoint was empagliflozin AUC0-∞. The sponsor reported ANOVA geometric mean ratios with 90% confidence intervals. Simple recalculations from posted summaries report unadjusted arithmetic mean differences and 95% confidence intervals; they do not reproduce the crossover analysis. The registry labels the sponsor analyses as non-inferiority or equivalence but does not report decision margins.
The results characterize pharmacokinetic exposure in the study population and do not establish clinical benefit or a complete safety profile. Important details, including the full model, multiplicity plan, missing-data procedures, and original sample-size justification, are not reported in the registry record.