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 Comparison of the Safety and Efficacy of HOE901-U300 With Lantus in Older Patients With Type2 Diabetes Insufficiently Controlled on Their Current Antidiabetic Medications (NCT02320721), a randomized phase 3 study. The primary outcome is Change in HbA1c From Baseline to Week 26.
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT02320721 |
| Phase | Phase 3 |
| Condition | Type 2 Diabetes Mellitus |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 1014 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Sanofi |
| Results posted | Yes |
2. Clinical Question
Population
Older patients with type 2 diabetes whose condition was inadequately controlled on their current antidiabetic regimens. The registry record describes regimens either without insulin or using basal insulin as the only insulin. It does not report an age threshold or additional eligibility details in the information.
Intervention
Insulin glargine HOE901-U300, given once daily up to Week 26 alongside stable non-insulin antihyperglycemic therapy.
Comparator
Lantus, insulin glargine at 100 U/mL, given once daily up to Week 26 alongside stable non-insulin antihyperglycemic therapy.
Primary question
How did HbA1c change from baseline to Week 26 in the two randomized groups, and did the sponsor’s analysis support its stated non-inferiority objective? HbA1c is a measure of glycated hemoglobin. The primary endpoint compares adjusted mean change, not the proportion of participants who reached a particular HbA1c target.
The study also set out to compare several hypoglycemia outcomes, including events during nighttime periods and events at any time of day. The registry describes those secondary objectives as superiority questions, but the posted estimates alone do not establish that one treatment was superior. Their interpretation depends on the estimates, uncertainty, analysis approach, and how multiple comparisons were handled. The registry record does not report the non-inferiority margin or a complete account of the study’s decision rules, so the primary objective cannot be judged from the point estimates alone.
3. Trial Design
This was a Phase 3, randomized, open-label, two-arm, parallel-group, multicenter study. The registry lists an enrollment of 1014 and records the study as completed. The planned treatment period was 26 weeks. Participants were assigned to HOE901-U300 or Lantus, with each given once daily alongside stable non-insulin antihyperglycemic therapy.
Because the study was open-label, participants and study personnel were not masked to treatment assignment. Randomization helps balance measured and unmeasured characteristics between groups on average, while lack of masking can affect care, reporting, or outcome assessment in ways that depend on the outcome. HbA1c is a laboratory measure, but the registry record does not describe additional safeguards or assessment procedures. The details of randomization procedures, allocation concealment, and site-level implementation are not reported in the registry record.
The primary outcome was change in HbA1c from baseline to Week 26. Its reported analysis used adjusted least-squares means from an analysis of covariance after multiple imputation of missing data, with post-baseline HbA1c data during the randomized period included. The primary analysis population was the intent-to-treat population: randomized participants were analyzed according to their assigned group, whether or not they used the treatment kit. The arm-level endpoint summaries include 508 participants in the HOE901-U300 group and 506 in the Lantus group.
The registry also lists hypoglycemia outcomes, HbA1c target attainment, fasting plasma glucose, well-being, and rescue therapy among secondary outcomes. The record does not provide enough information to reconstruct all eligibility criteria, treatment adjustments, visit schedules, or analysis details. Original sample-size assumptions and the full statistical 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: A total of 1014 participants were randomized in 1:1 ratio to either HOE901-U300 or Lantus, stratified by screening hemoglobin A1c (HbA1c) values (\<8% or ≥8%); previous use of insulin (insulin-naïve versus pre-treated); and use of sulfonylurea or meglitinides at screening ('yes' versus 'no').
Overall Study
| Stage | HOE901-U300 | Lantus |
|---|---|---|
| STARTED | 508 | 506 |
| Treated (Safety Population) | 508 | 505 |
| COMPLETED | 481 | 472 |
| NOT COMPLETED | 27 | 34 |
Reasons for not completing this period:
| Reason | HOE901-U300 | Lantus |
|---|---|---|
| Adverse Event | 6 | 6 |
| Lack of Efficacy | 2 | 0 |
| Poor compliance to protocol | 3 | 7 |
| Randomized but not treated | 0 | 1 |
| Hypoglycemia | 1 | 0 |
| Other than specified above | 15 | 20 |
Analysis population for the primary outcome, as defined in the registry: Intent-to-treat (ITT) population included all randomized participants regardless of whether the treatment kit was used, and analyzed according to the treatment group allocated by randomization.
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: Baseline population included all randomized participants.
| Characteristic | Unit | HOE901-U300 | Lantus | Total |
|---|---|---|---|---|
| Participants analysed | 508 | 506 | 1014 | |
| Age, Continuous | years | 71.1 (SD 4.9) | 70.8 (SD 4.8) | 71.0 (SD 4.9) |
| Sex: Female, Male: Female | Participants | 258 | 229 | 487 |
| Sex: Female, Male: Male | Participants | 250 | 277 | 527 |
| Body Mass Index (BMI) | kg/m^2 | 30.9 (SD 5.5) | 31.2 (SD 5.7) | 31.1 (SD 5.6) |
| Duration of Type 2 Diabetes | years | 15.29 (SD 8.17) | 15.35 (SD 7.70) | 15.32 (SD 7.93) |
| Baseline Glycated Hemoglobin A1c (HbA1c) | percentage of HbA1c | 8.20 (SD 0.91) | 8.22 (SD 0.92) | 8.21 (SD 0.91) |
| Randomization strata of insulin: Insulin-naive | Participants | 166 | 165 | 331 |
| Randomization strata of insulin: Insulin pre-treated | Participants | 342 | 341 | 683 |
| Age Group: <75 years of age | Participants | 373 | 400 | 773 |
| Age Group: ≥75 years of age | Participants | 135 | 106 | 241 |
6. Primary Endpoint
The registry lists the primary outcome as Change in HbA1c From Baseline to Week 26, measured over Baseline, Week 26.
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | percentage of hemoglobin |
| Endpoint classification | Continuous Endpoint |
The primary endpoint measures the change in glycated hemoglobin A1c from baseline to Week 26. HbA1c reflects glycation of hemoglobin and is used in diabetes studies as a measure of longer-term glycemic status. An endpoint based on change allows the analysis to compare how the measured level shifted during the study, rather than comparing only a single final measurement.
The registry reports adjusted least-squares mean changes: -0.89 percentage points of hemoglobin for HOE901-U300 and -0.91 for Lantus. These are model-adjusted means, not raw averages. The stated analysis used analysis of covariance and multiple imputation for missing data. Adjusted estimates can account for factors included in the model, but the registry record does not report every model specification needed to reproduce them.
The study’s primary objective was non-inferiority. That is a framework for asking whether the treatment under evaluation is not unacceptably worse than the comparator according to a prespecified margin. A small difference between estimated mean changes does not by itself establish non-inferiority: interpretation also requires the margin and the planned decision rule. The margin is not reported in the registry record. HbA1c change is also distinct from the secondary outcomes that count participants with hypoglycemia or meeting HbA1c thresholds; those address different aspects of the observed data.
7. Results Posted in the Registry
- Lantus: mean -0.91 versus -0.89 on control; difference -0.02 (95% CI -0.13 to 0.09), standardized effect d = -0.02; z-test p = 0.724.
Mean difference: Lantus
95% CI: -0.13 to 0.09
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 |
|---|---|---|---|---|
| Percentage of Participants With At Least One Severe and/ or Confirmed (≤3.9 mmol/L [70 mg/dL]) Nocturnal Hypoglycemia (22:00 to 08:59 Hours Next Morning) During 26-Week Randomized Period | Binary Endpoint | Risk difference | -0.6 pts (-6.7 to 5.5) | 108,865 per arm |
| Percentage of Participants With At Least One Severe and/ or Confirmed (≤3.9 mmol/L [70 mg/dL]) Nocturnal Hypoglycemia (00:00 to 05:59 Hours) During 26-Week Randomized Period | Binary Endpoint | Risk difference | +2.3 pts (-2.8 to 7.3) | 5,197 per arm |
| Percentage of Participants With At Least One Severe and/ or Confirmed (≤3.9 mmol/L [70 mg/dL]) Hypoglycemia Occurring at Any Time of the Day During 26-Week Randomized Period | Binary Endpoint | Risk difference | +3.2 pts (-2.8 to 9.2) | 3,646 per arm |
Percentage of Participants With At Least One Severe and/ or Confirmed (≤3.9 mmol/L [70 mg/dL]) Nocturnal Hypoglycemia (22:00 to 08:59 Hours Next Morning) During 26-Week Randomized Period
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Lantus: 47.6% (241/506) versus 48.2% (245/508) on control; risk difference -0.6 percentage points (95% CI -6.7 to 5.5), risk ratio 0.99 (0.87–1.12); unadjusted two-proportion z-test p = 0.848.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Lantus and the control. The interval gives the range of effects that remain compatible with the data.
Percentage of Participants With At Least One Severe and/ or Confirmed (≤3.9 mmol/L [70 mg/dL]) Nocturnal Hypoglycemia (00:00 to 05:59 Hours) During 26-Week Randomized Period
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Lantus: 22.5% (114/506) versus 20.3% (103/508) on control; risk difference 2.3 percentage points (95% CI -2.8 to 7.3), risk ratio 1.11 (0.88–1.41); unadjusted two-proportion z-test p = 0.382.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Lantus and the control. The interval gives the range of effects that remain compatible with the data.
Percentage of Participants With At Least One Severe and/ or Confirmed (≤3.9 mmol/L [70 mg/dL]) Hypoglycemia Occurring at Any Time of the Day During 26-Week Randomized Period
- Endpoint type: Binary: the percentage of participants with the event (counts rebuilt from the posted percentages and group sizes).
- Test: Unadjusted two-proportion z-test, with a Wald 95% confidence interval for the risk difference.
- Result:
- Lantus: 62.6% (317/506) versus 59.4% (302/508) on control; risk difference 3.2 percentage points (95% CI -2.8 to 9.2), risk ratio 1.05 (0.96–1.16); unadjusted two-proportion z-test p = 0.296.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Lantus and the control. The interval gives the range of effects that remain compatible with the data.
Across the three posted hypoglycemia comparisons, the group percentages are close in the broad sense that none of the re-calculated risk-difference confidence intervals excludes zero. The sponsor-reported relative-risk analysis for the 22:00 to 08:59 outcome also has an interval that includes 1, and its p-value is 0.842. These summaries do not provide clear evidence of a between-group difference in those outcomes, but absence of clear evidence is not proof that the groups are equivalent.
The secondary findings address event occurrence over specified time windows, whereas the primary endpoint addresses adjusted mean change in HbA1c. They therefore complement rather than duplicate the primary result. Similar-looking estimates across these different measures do not establish a single overall treatment effect, and the secondary outcomes do not resolve the non-inferiority question for HbA1c.
Unadjusted secondary comparisons carry less weight for confirmatory interpretation for two reasons. First, the registry does not provide sponsor analyses for two of the three posted hypoglycemia comparisons, so the simple re-calculations may not match the planned analysis. Second, many secondary outcomes and comparisons create a multiplicity concern: when many hypotheses are examined, the chance of finding an apparently notable result by chance can increase. The registry record does not report whether or how multiplicity was controlled. The secondary results should therefore be treated as supportive or descriptive rather than as independent confirmation of the primary objective.
Other listed secondary outcomes include HbA1c target attainment, fasting plasma glucose, well-being, and rescue therapy. Numerical results for those outcomes are not included in the record details summarized in this analysis; their results are not reported in the registry record.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Percentage of Participants With At Least One Severe and/ or Confirmed (≤3.9 mmol/L [70 mg/dL]) Nocturnal Hypoglycemia (22:00 to 08:59 Hours Next Morning) During 26-Week Randomized Period
- Percentage of Participants With At Least One Severe and/ or Confirmed (≤3.9 mmol/L [70 mg/dL]) Nocturnal Hypoglycemia (00:00 to 05:59 Hours) During 26-Week Randomized Period
- Percentage of Participants With At Least One Severe and/ or Confirmed (≤3.9 mmol/L [70 mg/dL]) Hypoglycemia Occurring at Any Time of the Day During 26-Week Randomized Period
- Percentage of Participants With HbA1c <7.5% or HbA1c <7% During 26-Week Randomized Period
- Percentage of Participants With HbA1c <7.5% or <7.0% at Week 26 and No Severe and/or Confirmed (≤3.9 mmol/L [70 mg/dL]) Hypoglycemia During 26-Week Randomized Period
- Change in Fasting Plasma Glucose (FPG) From Baseline to Week 26
- Change in World Health Organization-5 (WHO-5) Well-Being Questionnaire Percentage Score From Baseline to Week 26
- Percentage of Participants Requiring Rescue Therapy Over the 26 Weeks of Treatment
9. Statistical Interpretation
The adjusted mean change in HbA1c was -0.89 percentage points of hemoglobin with HOE901-U300 and -0.91 with Lantus. Both estimates represent decreases from baseline. The registry’s reported between-group least-squares mean difference was 0.02, with a 95% confidence interval from -0.092 to 0.129. The registry identifies the analysis as non-inferiority, but does not report a p-value for it in the posted results.
The reported confidence interval is compatible with a range of underlying differences, including values on either side of no difference. Whether that interval satisfies a non-inferiority criterion depends on the prespecified margin and the direction used for the contrast. The margin is not reported in the registry record, so the numerical estimate and interval cannot independently confirm the study’s non-inferiority conclusion. The registry record’s stated objective should not be confused with a conclusion that can be verified from the posted estimate alone.
A separate unadjusted re-calculation from the posted group summaries gives a mean difference of -0.02, with a 95% confidence interval from -0.131 to 0.091 and an unadjusted p-value of 0.724. This re-calculation expresses the contrast in the opposite direction from the sponsor’s reported 0.02 estimate: the sponsor’s contrast is consistent with HOE901-U300 minus Lantus, while the re-calculation is Lantus minus HOE901-U300. The re-calculation is not a substitute for the adjusted analysis. The two estimates also come from different analytical approaches, and the sponsor’s own analysis is the relevant analysis for the trial’s stated primary objective.
The posted summaries do not show a large separation between the adjusted group means, but a small point estimate is not proof of equivalence. A non-significant test of difference would not establish that two treatments are equivalent or that either is non-inferior; those claims require a suitable prespecified framework. The registry record does not report the non-inferiority margin or enough protocol detail to assess that framework fully.
The secondary hypoglycemia outcomes also have uncertainty, and their unadjusted comparisons should be interpreted cautiously. They do not alter what the primary endpoint measures. Taken together, the posted results describe group estimates over the 26-week randomized period; they do not establish what would happen beyond that period or in people outside the trial population.
10. Statistical Methods Explained
The primary endpoint is continuous: each participant’s HbA1c change is measured on a scale, and the analysis estimates group means and a contrast between them. The registry reports least-squares means, which are model-based adjusted means. Unlike a simple arithmetic average, a least-squares mean reflects the fitted analysis model and its included terms. The registry describes an analysis of covariance (ANCOVA), but the full model specification is not reported in the registry record.
What does adjustment do?
In general, ANCOVA estimates a treatment contrast while accounting for covariates included in the model. Adjustment can improve precision or address baseline differences represented by those covariates. It does not guarantee that every source of bias is removed, and it cannot compensate for important variables that were not measured or not included. The posted description does not identify all covariates or provide enough detail to reproduce the model.
Why use multiple imputation?
Some participants may not have an observed HbA1c measurement at every planned time. Multiple imputation is a general approach that creates several plausible completed datasets, analyzes each, and combines the results to reflect uncertainty from missing values under the imputation assumptions. The registry says that multiple imputation was used and that post-baseline HbA1c data during the randomized period were included. It does not report the imputation model, the assumptions about why data were missing, or sensitivity analyses for departures from those assumptions. Consequently, the effect of missing-data assumptions cannot be evaluated from the posted description alone.
What is a confidence interval?
In general, a confidence interval describes the range of estimates reasonably compatible with the data and the analysis assumptions at its stated confidence level. It is not a range containing a known proportion of individual participant outcomes, and it does not give the probability that the true effect lies within that particular interval. A wider interval reflects less precision than a narrower interval on the same scale. For the primary endpoint, the sponsor reports a 95% confidence interval for the adjusted mean difference.
How does non-inferiority differ from testing for a difference?
In general, a non-inferiority analysis asks whether the result rules out an unacceptable loss relative to a comparator, using a margin set before the results are known. The direction of the contrast and the margin determine which boundary must be excluded. A confidence interval that includes zero may still meet a non-inferiority criterion if the relevant boundary is elsewhere; conversely, a small estimated difference alone does not establish non-inferiority. The registry does not report the margin, so the criterion cannot be checked from the posted results. The sponsor’s reported analysis is identified as non-inferiority, but its method and p-value are not listed.
What does the re-calculation represent?
The re-calculated primary contrast uses posted summary statistics and is explicitly unadjusted. It is not the same as the sponsor’s adjusted ANCOVA estimate with multiple imputation. The unadjusted p-value tests a difference under the re-calculation’s assumptions; it does not test the sponsor’s non-inferiority hypothesis. A p-value is a measure of how incompatible the observed data are with a specified null hypothesis under the model, not the probability that the null hypothesis is true or that a treatment has no effect.
For binary secondary outcomes, the posted group percentages describe the proportion with at least one event during the specified period. In general, a risk difference expresses the difference between group proportions, while a relative risk compares them as a ratio. These measures answer related but distinct questions. The registry reports a Cochran-Mantel-Haenszel relative risk analysis for the nocturnal outcome from 22:00 to 08:59, with a 95% confidence interval and p-value. The other two posted binary comparisons do not include sponsor-reported analyses. The simple re-calculations are not substitutes for analyses that may account for stratification, covariates, or other features of the trial.
Over-dispersion is a general concern when count or binary data vary more than a model assumes; ignoring it can make uncertainty estimates too narrow. The primary outcome is continuous and reported as adjusted means with standard errors, while the secondary outcomes are binary proportions. The registry record does not state that an over-dispersion adjustment was used or needed for these outcomes, so no claim about such an adjustment can be made.
11. Confidence Intervals and Precision
The primary sponsor-reported estimate is a least-squares mean difference of 0.02, with a 95% confidence interval from -0.092 to 0.129. Because the interval spans zero, the posted estimate is compatible with differences in either direction under the reported contrast. The interval conveys uncertainty around the group comparison; it does not show the range of individual HbA1c changes.
The unadjusted re-calculation gives -0.02, with a 95% confidence interval from -0.131 to 0.091. Its contrast runs in the reverse direction from the sponsor-reported estimate, and it is based on posted summary statistics rather than the sponsor’s adjusted model. The confidence intervals are not interchangeable, since the analyses differ. The registry record lists no p-value for the sponsor’s primary non-inferiority analysis.
For the reported relative risk analysis of hypoglycemia from 22:00 to 08:59, the estimate is 1.01, with a 95% confidence interval from 0.890 to 1.153. The interval includes 1, the value corresponding to equal relative risk. For the other posted secondary comparisons, the re-calculated risk-difference intervals are -0.068 to 0.056 for the 22:00 to 08:59 outcome, -0.028 to 0.073 for the 00:00 to 05:59 outcome, and -0.028 to 0.092 for hypoglycemia at any time of day. Each interval includes zero, indicating that the posted summaries do not precisely distinguish a difference from no difference on the risk-difference scale.
These intervals do not establish equivalence. Precision should be judged in relation to a clinically and statistically meaningful threshold, and the non-inferiority margin is not reported in the registry record. The interval widths also do not account for uncertainty from unreported design details or analysis choices.
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 | 31,903 | 42,708 |
| 75% of the observed effect | 56,716 | 75,926 |
| 50% of the observed effect | 127,609 | 170,832 |
The planning illustrations give participants per arm for the continuous primary endpoint and the binary secondary outcomes. They are not totals across both arms. No time-to-event sample-size illustration is posted, so the rule for reporting total events does not apply to the listed planning figures. For the primary endpoint, the illustration gives 31,903 participants per arm for 80% power and 42,708 participants per arm for 90% power when planning for 100% of the observed effect. The corresponding figures are larger when planning for 75% or 50% of that effect.
In general, 80% power means that a study designed under the stated assumptions would have an 80% chance of detecting the specified effect using the stated test, if that effect were the true one. The 90% power column describes the analogous planning target at a higher chance of detection. These are design calculations, not guarantees about a particular future study. Smaller effects are harder to distinguish from random variation and therefore require more participants under otherwise unchanged assumptions.
The registry’s planning illustration uses a two-sided significance level of 0.05, equal allocation between arms, a normal approximation, and an effect set to the stated fraction of the observed effect. The figures are based on the observed effect rather than the trial’s original design assumptions; those original assumptions are not reported in the registry record. This is not observed power. It should not be read as a retrospective measure of how likely the completed trial was to detect its result.
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 = -0.020; pooled standard deviation σ = 0.902.
- n = 2 × (1.96 + 0.842)2 × 0.9022 / -0.0202 = 31,902.2, rounded up to 31,903 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 <- -0.02 # observed difference in means
sigma <- 0.901615690721352 # 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(2320721)
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 = 31,903 (80% power), 42,708 (90% power)
75% of observed effect: n per arm = 56,716 (80% power), 75,926 (90% power)
50% of observed effect: n per arm = 127,609 (80% power), 170,832 (90% power)
power.t.test: 31903.2
Simulated power at n = 31,903 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 |
|---|---|---|---|
| not stated | LS Mean Difference 0.02 | -0.092 to 0.129 | not reported |
The sponsor-reported primary analysis is the analysis identified in the registry as the non-inferiority analysis. It reports a least-squares mean difference of 0.02 and a 95% confidence interval from -0.092 to 0.129. The registry does not list a p-value or the non-inferiority margin, so the stated decision criterion cannot be independently checked from the posted record.
The unadjusted re-calculation gives a mean difference of -0.02 with a 95% confidence interval from -0.131 to 0.091 and p = 0.724. The signs differ because the contrast is expressed in the opposite direction: the sponsor’s estimate corresponds to HOE901-U300 relative to Lantus, while the re-calculation expresses Lantus relative to HOE901-U300. The re-calculation also does not use the sponsor’s adjusted ANCOVA with multiple imputation. It therefore provides a descriptive check on the posted summaries, not a replacement test of the trial’s non-inferiority objective.
The registry record does not flag a discrepancy between the posted sponsor analysis and the re-calculation. Nonetheless, the sponsor’s own adjusted analysis takes precedence for interpreting the trial’s stated primary question. Its interval should be considered alongside the missing non-inferiority margin and the limitations of the available analysis description.
15. Multiplicity, Missing Data and Analysis Populations
The primary analysis used the intent-to-treat population, defined in the registry as all randomized participants analyzed according to assigned treatment, regardless of whether the treatment kit was used. This preserves the randomized comparison and avoids excluding participants solely because they did not use the kit. The registry does not describe other analysis populations for the primary endpoint, such as a per-protocol population, so their role in the non-inferiority assessment is not reported in the registry record.
Missing HbA1c data were addressed using multiple imputation, with post-baseline HbA1c data during the 26-week randomized period included. Multiple imputation relies on assumptions about the relationship between observed and missing data. The imputation model, reasons for missingness, number of imputations, and sensitivity analyses are not reported in the registry record. Without those details, the robustness of the primary estimate to alternative missing-data assumptions cannot be evaluated.
The trial lists multiple secondary outcomes, including several hypoglycemia definitions and other clinical measures. Testing many outcomes can increase the chance of a nominally unusual result even when there is no true effect. General approaches to address this include prespecifying a testing sequence, adjusting significance thresholds, or clearly treating secondary results as exploratory. The registry record does not report a multiplicity strategy or whether the secondary tests were intended to support formal claims. Thus, individual unadjusted secondary p-values should not be interpreted as if they were the sole planned test.
The primary endpoint is identified as a non-inferiority objective, but the margin and detailed decision procedure are not reported in the registry record. The record also does not report interim analyses, a sample-size justification, or the original design assumptions. Those omissions limit assessment of the planned operating characteristics and of how the final analysis relates to the original protocol.
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 |
|---|---|---|---|
| HOE901-U300 | 41 | 508 | 8.1% |
| Lantus | 34 | 505 | 6.7% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| HOE901-U300 | 1 of 508 |
| Lantus | 0 of 505 |
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 |
|---|---|
| HOE901-U300 | 62 of 508 |
| Lantus | 64 of 505 |
Most frequent serious adverse event terms
| Event term | Organ system | HOE901-U300 | Lantus |
|---|---|---|---|
| Coronary artery disease | Cardiac disorders | 2 of 508 | 2 of 505 |
| Pneumonia | Infections and infestations | 1 of 508 | 3 of 505 |
| Prostate cancer | Neoplasms benign, malignant and unspecified (incl cysts and polyps) | 3 of 508 | 1 of 505 |
| Acute myocardial infarction | Cardiac disorders | 2 of 508 | 1 of 505 |
| Hypertensive crisis | Vascular disorders | 1 of 508 | 2 of 505 |
| Angina unstable | Cardiac disorders | 2 of 508 | 0 of 505 |
| Atrial fibrillation | Cardiac disorders | 0 of 508 | 2 of 505 |
| Pyelonephritis | Infections and infestations | 0 of 508 | 2 of 505 |
| Hypoglycaemia | Metabolism and nutrition disorders | 1 of 508 | 1 of 505 |
| Basal cell carcinoma | Neoplasms benign, malignant and unspecified (incl cysts and polyps) | 1 of 508 | 1 of 505 |
Most frequent non-serious adverse event terms
| Event term | Organ system | HOE901-U300 | Lantus |
|---|---|---|---|
| Nasopharyngitis | Infections and infestations | 37 of 508 | 38 of 505 |
| Upper respiratory tract infection | Infections and infestations | 27 of 508 | 28 of 505 |
Serious events with the highest arm-level rate: pneumonia (0.6%), prostate cancer (0.6%), atrial fibrillation (0.4%), coronary artery disease (0.4%), pyelonephritis (0.4%).
The registry reports serious adverse events in 41 participants at risk in the HOE901-U300 group and 34 at risk in the Lantus group. Other adverse events are reported for 62 of 508 in the HOE901-U300 group and 64 of 505 in the Lantus group. The registry reports 1 death in the HOE901-U300 group and 0 in the Lantus group. These are posted counts, not adjusted comparisons of risk.
The serious-event terms listed most often include pneumonia and prostate cancer, each reported as 0.6%, and atrial fibrillation, coronary artery disease, pyelonephritis, and hypertensive crisis, each reported as 0.4%. These percentages are registry-reported values. The record does not provide enough detail in this summary to determine whether participants could contribute more than one event or how event terms were grouped across participants.
Safety counts are descriptive and should not be interpreted as proving a difference or absence of a difference between groups. The registry record does not provide comparative confidence intervals or a detailed safety analysis plan in the information. The counts also do not establish causation for any event.
17. What the Result Does, and Does Not, Mean
The posted primary estimates show decreases in adjusted mean HbA1c from baseline in both groups over the 26-week randomized period: -0.89 percentage points of hemoglobin for HOE901-U300 and -0.91 for Lantus. The sponsor-reported contrast is 0.02, with a 95% confidence interval from -0.092 to 0.129. Those numbers describe the observed trial analysis; they are not a guarantee of the same result in other settings or over longer follow-up.
The study’s objective was non-inferiority, but the margin needed to assess that claim is not reported in the registry record. Accordingly, the estimates alone do not establish non-inferiority, equivalence, or superiority. The unadjusted re-calculation is a different analysis and does not replace the sponsor’s adjusted result. Secondary hypoglycemia estimates are also imprecise and should be interpreted in light of their analysis details and the unreported multiplicity approach.
The findings apply to the randomized study population and treatment conditions described in the record: older people with type 2 diabetes on the specified background regimens, assigned to once-daily insulin glargine formulations with stable non-insulin therapy. The exact age eligibility threshold and further population characteristics are not reported in the registry record. The record does not establish how the results generalize to people with different clinical characteristics, treatment regimens, or follow-up durations.
Statistical interpretation is not a treatment recommendation. Decisions about care require clinical context and evidence beyond a single registry record. The data can support an assessment of the reported estimates and their precision, while leaving important questions about the protocol, non-inferiority margin, missing-data assumptions, and multiplicity unresolved.
18. Why This Trial Matters Statistically
This trial illustrates why a small difference between group means is not enough to establish non-inferiority. The registry reports similar adjusted HbA1c changes, but a non-inferiority conclusion depends on a prespecified margin and a confidence interval assessed against that margin. Without the margin, readers cannot determine whether the interval meets the study’s intended criterion, even though the analysis is labeled non-inferiority.
It also demonstrates the distinction between a sponsor’s adjusted analysis and a simple re-calculation from summary statistics. The sponsor’s method uses ANCOVA and multiple imputation, while the re-calculation is unadjusted. Their estimates are expressed in opposite contrast directions, and their intervals are not identical. Understanding those differences helps prevent an unadjusted p-value from being mistaken for the formal primary test.
The secondary outcomes show why statistical uncertainty and multiplicity matter. Several event definitions are examined, and the record does not describe a correction or testing hierarchy. A result from one secondary comparison should not be isolated from the broader set of questions or treated as decisive evidence.
Finally, the planning illustrations are not evidence about the completed trial’s power. They use observed effects and stated illustrative assumptions, whereas the original design assumptions are not reported. Separating post hoc planning illustrations from the original design prevents readers from confusing an estimate of future sample needs with observed trial performance.
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 registry record leaves important design and analysis details unavailable. It does not report the non-inferiority margin, the original sample-size justification, or the original design assumptions. Those details are central to assessing whether the primary objective was met and how the trial was planned. The reported primary analysis is identified as non-inferiority, but its method and p-value are not listed.
The primary model description is incomplete for independent reproduction. ANCOVA and multiple imputation are named, but the full covariate set, imputation model, missing-data assumptions, and sensitivity analyses are not reported in the registry record. The effect of alternative assumptions about missing data therefore cannot be assessed.
The study was open-label, and the record does not describe allocation concealment or safeguards against effects of treatment knowledge on care and reporting. Randomization supports a group comparison, but open-label conduct remains relevant when considering outcomes that may depend on participant reporting or clinical decisions. The registry does not report an age threshold or enough population detail to assess the representativeness of the enrolled group.
For secondary outcomes, sponsor-reported analyses are available for only one of the three posted hypoglycemia comparisons. The registry does not report the multiplicity strategy, and other listed secondary outcomes do not have numerical results in the record details. Safety findings are reported as counts without comparative uncertainty estimates in this summary. The 26-week treatment period also limits conclusions about longer-term outcomes.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: Comparison of the Safety and Efficacy of HOE901-U300 With Lantus in Older Patients With Type2 Diabetes Insufficiently Controlled on Their Current Antidiabetic Medications — NCT02320721.
- Registry record last updated 2020-04-21; status last verified 2020-04.
- Results first posted 2017-07-11.
- 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
NCT02320721 is a completed, randomized, open-label, Phase 3, two-arm, parallel-group, multicenter study comparing once-daily HOE901-U300 with Lantus in older patients with type 2 diabetes. Both treatments were used alongside stable non-insulin antihyperglycemic therapy, with a 26-week randomized period.
The primary endpoint was change in HbA1c from baseline to Week 26. The sponsor reported adjusted least-squares mean changes of -0.89 and -0.91, with a mean difference of 0.02 and a 95% confidence interval from -0.092 to 0.129. The study’s non-inferiority margin is not reported in the registry record, limiting independent assessment of that objective. The record also lists hypoglycemia outcomes and other secondary measures, alongside descriptive adverse-event counts.