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 A Study of LY900014 Compared to Insulin Lispro (Humalog) in Adults With Type 2 Diabetes (NCT03952143), a randomized phase 3 study. The primary outcome is Change From Baseline in Hemoglobin A1c (HbA1c).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT03952143 |
| Phase | Phase 3 |
| Condition | Type 2 Diabetes Mellitus |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 628 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Eli Lilly and Company |
| Results posted | Yes |
2. Clinical Question
Population
Adults with type 2 diabetes mellitus. The primary analysis population comprised randomized participants with baseline and at least one post-baseline HbA1c measurement.
Intervention
LY900014, given subcutaneously 0–2 minutes before each meal, together with once-daily basal insulin glargine or insulin degludec.
Comparator
Insulin lispro (Humalog), given subcutaneously 0–2 minutes before each meal, with the same options for once-daily basal insulin.
Primary question
How did HbA1c change from baseline to Week 26 in the two treatment groups, and what does the adjusted between-group comparison indicate about the difference?
The registry describes a prospective, randomized, double-blind comparison. Both groups used mealtime insulin alongside basal insulin; the contrast concerns LY900014 versus insulin lispro, not the use of mealtime insulin versus no mealtime insulin. The primary endpoint was change in HbA1c, a measure used to reflect average plasma glucose over a prolonged period.
The registry also lists postmeal glucose excursions during a mixed-meal tolerance test and several other secondary outcomes, including hypoglycemia, insulin dose, and glucose-related measures. These outcomes provide additional dimensions of comparison, but they do not replace the primary endpoint. The posted results need to be interpreted as comparisons within this trial and its stated analysis population, rather than as evidence about every person with type 2 diabetes or every possible insulin regimen.
3. Trial Design
This was a phase 3, randomized, double-blind, parallel-group trial sponsored by Eli Lilly and Company. The registry reports enrollment of 628 and a completed study. The recorded study start was 2019-05-27, and primary completion was 2021-01-20. These registry entries describe the trial’s recorded conduct; the original design rationale and sample-size justification are not reported in the registry record.
The comparison assigned participants to LY900014 or insulin lispro (Humalog). Both were administered subcutaneously shortly before meals, with either insulin glargine or insulin degludec as once-daily basal insulin. The registry describes the two mealtime regimens with the same timing and basal-insulin options, which focuses the comparison on the mealtime insulin under those treatment conditions.
Randomization is intended to make treatment groups comparable on average, while double masking is intended to reduce the influence of treatment knowledge on participants’ experiences and assessments. These are general design principles; the registry record does not report additional details about how randomization was generated, how masking was maintained, or who was masked. The allocation ratio and any stratification procedures beyond those described in the primary model are not reported in the registry record.
The primary endpoint was assessed at baseline and Week 26. Its analysis used a mixed model repeated measures approach and included baseline HbA1c, pooled country, specified treatment-entry strata, treatment, time, and treatment-by-time terms. The registry identifies the primary analysis population as randomized participants with baseline and at least one post-baseline HbA1c value. The record does not report the trial’s planned handling of every type of missing observation, the original sample-size assumptions, or details of interim analyses.
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: The purpose of the lead-in period (prior to randomization) was to titrate basal insulin, obtain preliminary diagnostic laboratory tests, and determine baseline hypoglycemia rates. Participants were then randomized into the treatment groups in a 2:1 ratio (LY900014:insulin lispro).
Lead-In Period
| Stage | Insulin Lispro (Humalog) Lead-in | Insulin Lispro (Humalog) | LY900014 |
|---|---|---|---|
| STARTED | 628 | 0 | 0 |
| Participants Who Received at Least One Dose | 628 | 0 | 0 |
| COMPLETED | 595 | 0 | 0 |
| NOT COMPLETED | 33 | 0 | 0 |
Reasons for not completing this period:
| Reason | Insulin Lispro (Humalog) Lead-in | Insulin Lispro (Humalog) | LY900014 |
|---|---|---|---|
| Adverse Event | 2 | 0 | 0 |
| Lack of Efficacy | 2 | 0 | 0 |
| Physician Decision | 5 | 0 | 0 |
| Protocol Violation | 5 | 0 | 0 |
| Withdrawal by Subject | 19 | 0 | 0 |
Treatment Period
| Stage | Insulin Lispro (Humalog) Lead-in | Insulin Lispro (Humalog) | LY900014 |
|---|---|---|---|
| STARTED | 0 | 200 | 395 |
| Participants Who Received at Least One Dose | 0 | 200 | 395 |
| COMPLETED | 0 | 191 | 359 |
| NOT COMPLETED | 0 | 9 | 36 |
Reasons for not completing this period:
| Reason | Insulin Lispro (Humalog) Lead-in | Insulin Lispro (Humalog) | LY900014 |
|---|---|---|---|
| Adverse Event | 0 | 0 | 1 |
| Lost to Follow-up | 0 | 2 | 0 |
| Physician Decision | 0 | 0 | 2 |
| Protocol Violation | 0 | 0 | 1 |
| Withdrawal by Subject | 0 | 5 | 26 |
| Due to COVID 19 restrictions | 0 | 2 | 5 |
| Participant had taken prohibited concomitant medication | 0 | 0 | 1 |
Analysis population for the primary outcome, as defined in the registry: All randomized Participants with baseline and at least one post-baseline HbA1c data.
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: All randomized participants.
| Characteristic | Unit | Insulin Lispro (Humalog) | LY900014 | Total |
|---|---|---|---|---|
| Participants analysed | 200 | 395 | 595 | |
| Age, Continuous | years | 58.70 (SD 9.48) | 58.30 (SD 9.26) | 58.50 (SD 9.33) |
| Sex: Female, Male: Female | Participants | 93 | 182 | 275 |
| Sex: Female, Male: Male | Participants | 107 | 213 | 320 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 5 | 11 | 16 |
| Race (NIH/OMB): Asian | Participants | 162 | 319 | 481 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): Black or African American | Participants | 0 | 0 | 0 |
| Race (NIH/OMB): White | Participants | 29 | 53 | 82 |
| Race (NIH/OMB): More than one race | Participants | 4 | 12 | 16 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 |
| Region of Enrollment: Argentina | Participants | 18 | 32 | 50 |
| Region of Enrollment: China | Participants | 162 | 319 | 481 |
| Region of Enrollment: Mexico | Participants | 20 | 44 | 64 |
| Hemoglobin A1c (HbA1c) | Percentage of HbA1c | 7.78 (SD 0.88) | 7.73 (SD 0.87) | 7.74 (SD 0.88) |
6. Primary Endpoint
The registry lists the primary outcome as Change From Baseline in Hemoglobin A1c (HbA1c), measured over Baseline, Week 26.
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | Percentage of HbA1c |
| Endpoint classification | Continuous Endpoint |
The primary endpoint was change from baseline in hemoglobin A1c (HbA1c), measured as a percentage of HbA1c, at baseline and Week 26. HbA1c is the glycosylated fraction of hemoglobin A. Because it reflects average plasma glucose over a prolonged period, it captures a different time scale from an individual glucose measurement or a meal-related excursion.
Change from baseline expresses the observed endpoint in relation to each participant’s starting measurement. Comparing changes between randomized groups can therefore address whether the groups’ average HbA1c trajectories differed over the study period. The reported group summaries are least-squares means, which are model-based estimates rather than simple arithmetic averages. The sponsor’s analysis estimated an adjusted difference between those means using a repeated-measures model.
HbA1c is used in this trial as a glycemic outcome, but its statistical role should be kept distinct from the trial’s other endpoints. Postmeal glucose excursions describe response around a meal test, while hypoglycemia outcomes describe events. A result on one measure does not by itself determine the results on the others. The registry record does not state a clinical threshold for interpreting the size of an HbA1c difference, and a numerical difference alone does not establish its clinical importance.
7. Results Posted in the Registry
- LY900014: mean -0.56 versus -0.63 on control; difference 0.07 (95% CI -0.08 to 0.22), standardized effect d = 0.08; z-test p = 0.360.
Mean difference: LY900014
95% CI: -0.08 to 0.22
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 |
|---|---|---|---|---|
| 1-hour Postprandial Glucose (PPG) Excursion During Mixed-Meal Tolerance Test (MMTT) | Continuous Endpoint | Mean difference | -14.60 (-25.03 to -4.17) | 266 per arm |
| 2-hour PPG Excursion During MMTT | Continuous Endpoint | Mean difference | -21.80 (-35.14 to -8.46) | 195 per arm |
| Rate of Severe Hypoglycemia | Event-Rate Endpoint | Rate ratio | 0.26 (0.02 to 2.82) | 2,104 per arm |
1-hour Postprandial Glucose (PPG) Excursion During Mixed-Meal Tolerance Test (MMTT)
- 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:
- LY900014: mean 86.20 versus 100.80 on control; difference -14.60 (95% CI -25.03 to -4.17), standardized effect d = -0.24; z-test p = 0.006.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for LY900014 than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
2-hour PPG Excursion During MMTT
- 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:
- LY900014: mean 111.40 versus 133.20 on control; difference -21.80 (95% CI -35.14 to -8.46), standardized effect d = -0.28; z-test p = 0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for LY900014 than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Rate of Severe Hypoglycemia
- Endpoint type: Event rate: events per unit of follow-up, compared as a rate ratio.
- Test: Poisson rate ratio, based on the estimated number of events and follow-up time.
- Result:
- LY900014: 0.52 versus 2.00 (Events per 100 participant years) on control; rate ratio 0.26 (95% CI 0.02–2.82, approximate, Poisson model); p ≈ 0.268.
- Interpretation:
- The 95% confidence interval includes no difference (a ratio of 1), so these data do not show a statistically significant difference between LY900014 and the control. The interval gives the range of effects that remain compatible with the data.
The secondary outcomes cover several aspects of glycemic response and safety rather than a single common measure. Among the posted numerical comparisons, the postmeal glucose excursion estimates were lower for LY900014 than for insulin lispro, and the sponsor’s corresponding analyses were labeled superiority. The severe-hypoglycemia rate estimate was also lower for LY900014, but its interval was broad and included the no-difference value. This combination illustrates why a point estimate’s direction should be considered alongside its uncertainty.
The primary endpoint concerns change in HbA1c over the study period, whereas postmeal excursions focus on response during a mixed-meal tolerance test. These measures address related but distinct questions. The secondary pattern therefore adds context but does not replace or determine the primary endpoint result. Nor does a directionally favorable result on one secondary measure establish a general conclusion across all outcomes.
The registry lists other secondary outcome domains, including symptomatic postmeal hypoglycemia, 1,5-AG, self-monitoring blood glucose, insulin dose, and HbA1c thresholds. Results for an outcome not described in the posted numerical comparisons are not reported in the registry record. The record lists 26 analyses, and a multiplicity adjustment strategy is not reported. When many outcomes or comparisons are examined, some apparently unusual results may arise by chance even if no underlying difference exists. Unadjusted secondary p-values consequently carry less weight than a clearly prespecified primary analysis and should be interpreted as exploratory unless the analysis plan establishes otherwise.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- 1-hour Postprandial Glucose (PPG) Excursion During Mixed-Meal Tolerance Test (MMTT)
- 2-hour PPG Excursion During MMTT
- Rate of Severe Hypoglycemia
- Rate of Documented Symptomatic Postmeal Hypoglycemia
- Change From Baseline in 1,5-Anhydroglucitol (1,5-AG)
- Change From Baseline in 10-Point Self-Monitoring Blood Glucose (SMBG) Values
- Change From Baseline in Insulin Dose
- Percentage of Participants With HbA1c <7% and ≤6.5%
9. Statistical Interpretation
At Week 26, the posted least-squares mean change in HbA1c was -0.63 for insulin lispro and -0.56 for LY900014. The sponsor’s adjusted mixed-model analysis reported an LS mean difference of 0.07, with a 95% confidence interval from -0.07 to 0.21 and p = 0.321. The interval includes zero, so the reported estimate is compatible with no between-group difference as well as with differences in either direction within the interval.
The sponsor labels this analysis as a non-inferiority analysis. That label describes the analysis objective, but the non-inferiority margin and the decision rule are not reported in the registry record. Without the margin, the reported estimate and confidence interval cannot by themselves establish whether the prespecified non-inferiority criterion was met. The record’s p-value should not be interpreted as a direct probability that the treatments are equivalent.
A simple unadjusted recalculation from the posted summary statistics gives a mean difference of 0.07 and an unadjusted p-value of 0.36. Its interval also spans zero. This recalculation is not the trial’s fitted model: the sponsor’s analysis accounts for baseline and other model terms, while the recalculation uses the posted group summaries. The recalculation is therefore a check on the summary data, not a substitute for the sponsor’s prespecified analysis. The record does not flag a discrepancy between these results.
The secondary results offer additional context. The two postmeal glucose excursion outcomes had lower posted least-squares means for LY900014 than for insulin lispro, and the sponsor’s reported analyses for those outcomes were labeled superiority. The severe-hypoglycemia rate estimate was also lower for LY900014, but its confidence interval was wide and included values on both sides of no rate difference. Those secondary comparisons should not be treated as interchangeable with the primary HbA1c analysis.
Statistical interpretation also depends on the number of outcomes and analyses considered, the analysis populations, and the extent of missing data. The registry lists multiple secondary outcomes and 26 analyses. A multiplicity adjustment strategy is not reported in the registry record, so unadjusted secondary p-values warrant caution. The registry also does not provide enough detail to assess all missing-data assumptions or every analysis decision. Overall, the posted statistics describe estimates and their uncertainty for this trial; they do not, on their own, settle questions about clinical importance or generalizability.
10. Statistical Methods Explained
The primary endpoint is continuous: it records a measured value on a scale where differences in the measurement can be represented numerically. The registry reports least-squares means and standard errors for the treatment groups. A least-squares mean is a model-based group estimate adjusted for the terms included in the model; it is not necessarily the same as the raw average of all observed values. A standard error describes the estimated uncertainty in a mean estimate, rather than the spread of individual participant measurements.
What does the repeated-measures model do?
The sponsor used a mixed model repeated measures (MMRM) analysis for HbA1c. In general, repeated-measures models analyze measurements collected over time while accounting for the fact that observations from the same participant are related. The reported model included baseline, pooled country, number of bolus at study entry stratum, type of basal at lead-in stratum, treatment, time, and treatment-by-time. The treatment-by-time term allows the modeled difference between treatment groups to vary over time. The registry identifies Type III sums of squares for the model.
The registry’s description is not a complete statistical analysis plan. Details such as the covariance structure, degrees-of-freedom method, and the model’s exact missing-data assumptions are not reported in the registry record. General statistical interpretation of MMRM estimates depends on the model being suitable for the measurements and on its assumptions. The model’s inclusion in a registry description does not establish that every assumption holds.
How should the between-group estimate be read?
The sponsor reported an LS mean difference of 0.07 for LY900014 relative to insulin lispro. The estimate is expressed in the HbA1c measurement scale. A positive estimate means the fitted change for LY900014 was higher than the fitted change for insulin lispro under the stated comparison direction. The confidence interval gives a range of values compatible with the data and the analysis, subject to the model’s assumptions. Because that interval spans zero, the data do not pinpoint a direction of difference with high precision.
The recalculation uses the reported group means and standard errors to form an unadjusted comparison. It is useful as a transparent summary-statistic check, but it does not recreate the sponsor’s MMRM. Adjusted and unadjusted analyses can differ because they use different information and modeling assumptions. The sponsor’s analysis is the trial’s reported analysis; the recalculation is supplementary and should not be treated as a replacement.
Why are the secondary analyses different?
The postmeal glucose outcomes were analyzed with ANCOVA, according to the registry. ANCOVA is a general approach for comparing group outcomes while adjusting for one or more covariates. The sponsor reported LS mean differences, confidence intervals, and p-values for these outcomes. The exact covariates in those ANCOVA models are not reported in the registry record. Their estimates therefore need to be interpreted as the sponsor reported them, without assuming unlisted adjustment terms.
The severe-hypoglycemia outcome is a rate, not a continuous mean. Its unit is events per 100 participant years, and its comparison is a rate ratio. A rate accounts for time under observation, rather than treating each participant as having the same observation duration. General rate comparisons are sensitive to the number of events and the amount of follow-up. The record describes a Poisson-based recalculation; that calculation is distinct from a fitted analysis whose full details are not reported. The reported rate-ratio confidence interval is broad, so the estimate is imprecise.
What do p-values and confidence intervals contribute?
A p-value measures how unusual the data, or more extreme data, would be under a specified null model and its assumptions. It is not the probability that the null hypothesis is true, and it does not measure the size or importance of an effect. A confidence interval conveys both a range of estimates compatible with the analysis and the degree of precision. Neither statistic removes the need to consider the study design, model, multiplicity, and outcome relevance.
The sponsor’s primary p-value is part of a non-inferiority analysis, but the margin required to interpret that analysis is not reported in the registry record. In general, a non-inferiority conclusion depends on comparing the confidence interval with a prespecified margin. A p-value alone cannot supply that missing criterion. The secondary p-values are also not reported with a multiplicity strategy, so they should be viewed as outcome-specific evidence rather than as a guaranteed family-wise conclusion.
Why does over-dispersion matter for event counts?
As a general statistical point, a simple Poisson model assumes that event-count variation is linked to the event rate in a particular way. If observed variation exceeds that assumption, over-dispersion can make standard errors too small and intervals too narrow unless the analysis accounts for it. The registry does not report an assessment of over-dispersion or a fuller model specification for the serious hypoglycemia rate. This limits what can be inferred about the precision of an independent rate-based recalculation.
11. Confidence Intervals and Precision
A confidence interval describes statistical uncertainty around an estimate under the analysis assumptions. A narrower interval indicates greater precision, while a wider interval leaves more possible values compatible with the data. It is not a range containing a known fixed proportion of individual participant outcomes, nor does it express the probability that the treatment difference lies inside the particular interval.
For the primary endpoint, the sponsor’s adjusted estimate was 0.07, with a 95% confidence interval from -0.07 to 0.21. The interval crosses zero, so it includes no difference as well as positive and negative differences. Its endpoints also show that the data do not identify a single precise value for the between-group difference. Whether the interval meets a non-inferiority criterion cannot be determined from the registry record because the margin is not reported.
The recalculated primary interval also spans zero. It is based on summary statistics and is not the same interval as the sponsor’s model-based interval. The sponsor’s reported interval is the appropriate one to cite for the sponsor’s adjusted analysis; the recalculated interval is supplementary.
The two sponsor-reported postmeal glucose intervals lie below zero, while the severe-hypoglycemia rate-ratio interval is wide and includes the value representing no rate difference. These intervals describe different scales and different endpoints, so their widths should not be compared as if they measured the same quantity. For the rate outcome, limited event information can contribute to uncertainty; the registry does not provide a fuller explanation of its interval construction. Precision is only one part of interpretation: statistical uncertainty does not resolve clinical importance, bias, or whether an endpoint captures a patient-relevant effect.
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 | 2,540 | 3,400 |
| 75% of the observed effect | 4,515 | 6,044 |
| 50% of the observed effect | 10,157 | 13,597 |
The planning values are illustrations based on the observed effects, not the trial’s original design calculation. For the continuous outcomes and the severe-hypoglycemia rate illustration, the displayed figures are participants per arm. The general planning assumptions are a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. Each scenario targets the stated fraction of the observed effect. A separate time-to-event planning display would express its requirement as total events, but the listed planning figures are per arm.
Read each planning scenario as a conditional question: if a future study aimed to detect the stated fraction of the observed effect under those assumptions, how many participants per arm would be required? The 80% power column represents a design with an 80% chance of detecting an effect of that specified size when the assumed effect and model conditions hold. The 90% power column represents a higher target chance, and therefore generally requires more participants for the same target effect. These are design probabilities under assumptions, not probabilities that a result is true.
For each endpoint, the rows consider 100%, 75%, and 50% of the observed effect. The smaller target effects require more participants because they are harder to distinguish from random variation. This is not observed power: it is a planning illustration, and the values do not establish the power of the completed trial.
The original trial’s own sample-size assumptions and justification are not reported in the registry record. The planning values should therefore not be read as evidence about the sponsor’s original design decisions. They also assume the stated approximation and allocation; other design features, missing outcomes, or analysis methods could affect requirements in a real study. A planning curve communicates the same general relationship between target effect size and required enrollment: smaller effects call for larger study sizes under otherwise fixed 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 = 0.070; pooled standard deviation σ = 0.890.
- n = 2 × (1.96 + 0.842)2 × 0.8902 / 0.0702 = 2,539.2, rounded up to 2,540 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 <- 0.07 # observed difference in means
sigma <- 0.89027414394099 # 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(3952143)
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 = 2,540 (80% power), 3,400 (90% power)
75% of observed effect: n per arm = 4,515 (80% power), 6,044 (90% power)
50% of observed effect: n per arm = 10,157 (80% power), 13,597 (90% power)
power.t.test: 2540.1
Simulated power at n = 2,540 per arm: 0.799 (20000 replicates)
The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.
14. Analyses Reported by the Sponsor
| Method | Estimate | 95% CI | P-value |
|---|---|---|---|
| Mixed Models Analysis | LS Mean Difference 0.07 | -0.07 to 0.21 | 0.321 |
The sponsor’s primary result comes from the reported mixed-model analysis, which adjusted for the terms listed in the registry. It estimated an LS mean difference of 0.07, with a 95% confidence interval from -0.07 to 0.21 and p = 0.321. The analysis is labeled non-inferiority in the registry. The non-inferiority margin and decision rule are not reported in the registry record, so the numerical result cannot be independently evaluated against that criterion from the registry entries alone.
The recalculation uses the posted means and standard errors to make a simple unadjusted comparison. It gives a mean difference of 0.07 and p = 0.36, with an interval spanning zero. It does not reproduce the sponsor’s adjusted model or its analysis population and assumptions. The registry does not flag a discrepancy between the results. The sponsor’s analysis should be read as the reported trial analysis, while the recalculation is a supplementary check based on summary statistics.
Differences between adjusted and unadjusted results can arise from model terms, data handling, and analysis specifications. The registry does not provide enough detail to attribute any difference to a particular factor. Neither the p-value nor the confidence interval alone establishes equivalence; interpretation of the stated non-inferiority objective requires the missing margin and its prespecified rule.
15. Multiplicity, Missing Data and Analysis Populations
The registry lists a primary endpoint, multiple secondary outcomes, and 26 analyses. Testing multiple hypotheses raises a multiplicity issue: as the number of statistical comparisons increases, the chance of at least one small p-value under null conditions can increase. Statistical methods can address this through prespecified procedures, but a multiplicity adjustment strategy is not reported in the registry record. It is therefore not possible to determine from the registry whether secondary p-values were adjusted, how any testing hierarchy was defined, or which outcomes were intended to support confirmatory claims.
The primary analysis population is specified as all randomized participants with baseline and at least one post-baseline HbA1c measurement. This definition makes the availability of follow-up data relevant to inclusion in the primary analysis. The record does not report the number of participants excluded from that analysis for missing measurements, the reasons for missingness, or a detailed comparison of missingness between groups. It also does not report a sensitivity analysis for departures from the assumptions used by the repeated-measures model.
In general, MMRM can use available repeated measurements without requiring every participant to have a complete set of observations. The validity of its estimates still depends on model assumptions about the data and missingness. This general property does not establish which missing-data mechanism applied in this trial. Specific imputation procedures, if any, and further missing-data sensitivity analyses are not reported in the registry record.
The registry reports the model terms for the primary endpoint but not a full statistical analysis plan. The non-inferiority margin is also not reported, limiting assessment of the primary objective. Details of the randomization procedure, planned interim analyses, and additional model specifications are not reported in the registry record. These omissions do not show that a procedure was absent; they mean the registry record does not provide the information needed to evaluate it.
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 |
|---|---|---|---|
| Insulin Lispro (Humalog) Lead-in | 17 | 628 | 2.7% |
| Insulin Lispro (Humalog) | 15 | 200 | 7.5% |
| LY900014 | 33 | 395 | 8.4% |
Deaths
| Arm | Deaths (participants affected of at risk) |
|---|---|
| Insulin Lispro (Humalog) Lead-in | 0 of 628 |
| Insulin Lispro (Humalog) | 1 of 200 |
| LY900014 | 0 of 395 |
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 |
|---|---|
| Insulin Lispro (Humalog) Lead-in | 29 of 628 |
| Insulin Lispro (Humalog) | 14 of 200 |
| LY900014 | 21 of 395 |
Most frequent serious adverse event terms
| Event term | Organ system | Insulin Lispro (Humalog) Lead-in | Insulin Lispro (Humalog) | LY900014 |
|---|---|---|---|---|
| Cerebral infarction | Nervous system disorders | 2 of 628 | 0 of 200 | 4 of 395 |
| Angina unstable | Cardiac disorders | 3 of 628 | 0 of 200 | 2 of 395 |
| Acute myocardial infarction | Cardiac disorders | 1 of 628 | 1 of 200 | 1 of 395 |
| Arteriosclerosis coronary artery | Cardiac disorders | 0 of 628 | 0 of 200 | 3 of 395 |
| Pneumonia | Infections and infestations | 2 of 628 | 0 of 200 | 1 of 395 |
| Cerebral ischaemia | Nervous system disorders | 1 of 628 | 0 of 200 | 2 of 395 |
| Lacunar infarction | Nervous system disorders | 2 of 628 | 0 of 200 | 1 of 395 |
| Coronary artery disease | Cardiac disorders | 0 of 628 | 1 of 200 | 1 of 395 |
| Diabetic retinopathy | Eye disorders | 1 of 628 | 1 of 200 | 0 of 395 |
| Vitreous haemorrhage | Eye disorders | 1 of 628 | 0 of 200 | 1 of 395 |
Most frequent non-serious adverse event terms
| Event term | Organ system | Insulin Lispro (Humalog) Lead-in | Insulin Lispro (Humalog) | LY900014 |
|---|---|---|---|---|
| Upper respiratory tract infection | Infections and infestations | 29 of 628 | 14 of 200 | 21 of 395 |
Serious events with the highest arm-level rate: cerebral infarction (1.0%), arteriosclerosis coronary artery (0.8%), angina unstable (0.5%), intervertebral disc protrusion (0.5%), cerebral ischaemia (0.5%).
The safety record reports serious adverse events and other adverse events by listed group, with the number at risk and the number affected. In the insulin lispro lead-in group, 17 participants had a serious adverse event and 29 had another adverse event, with 628 at risk. In the insulin lispro group, the corresponding counts were 15 and 14, with 200 at risk. In the LY900014 group, the counts were 33 and 21, with 395 at risk. These are registry counts; they are not adjusted comparisons and should not be converted into comparative conclusions without an appropriate analysis.
The lead-in group is listed separately from the treatment groups, so its figures should not be treated as a direct randomized comparison with either treatment group. The registry reports one death in the insulin lispro group and none in the other listed groups. It also lists serious-event terms and percentages, including cerebral infarction at 1.0% and coronary artery arteriosclerosis at 0.8%. The registry does not provide enough detail in these summary figures to infer causation or comparative risk.
Adverse-event counts alone do not establish that an event was caused by a treatment. Interpretation also depends on exposure duration, event definitions, ascertainment, and the relevant analysis. The record’s serious adverse event summaries should therefore be read as descriptive safety information, not as proof of a treatment effect or absence of harm.
17. What the Result Does, and Does Not, Mean
The results describe a randomized comparison of two mealtime insulin regimens, each used with basal insulin, in adults with type 2 diabetes. The primary model estimated a between-group HbA1c change difference of 0.07, and its 95% confidence interval included zero. This is a statement about the estimate and its uncertainty under the reported analysis, not a conclusion that the regimens are identical.
The non-inferiority label indicates the type of primary analysis reported, but interpretation of a non-inferiority objective requires the margin and decision rule. Those details are not reported in the registry record. The result therefore cannot be independently assessed against the planned non-inferiority threshold using the registry information alone. Similarly, an unadjusted p-value does not quantify clinical importance or the probability that one treatment is preferable.
The secondary results suggest that some measured postmeal glucose outcomes differed between groups in the reported analyses. They concern different endpoints from HbA1c and are subject to the uncertainty and multiplicity limitations. The severe-hypoglycemia rate estimate is particularly imprecise, as indicated by its wide interval. These findings do not establish a broad safety or effectiveness conclusion.
The findings apply most directly to the trial population, treatment schedules, follow-up period, and analysis definitions recorded in the registry. They do not automatically extend to other populations, doses, treatment combinations, or longer periods. The trial’s reported completion status and enrollment do not resolve uncertainties about missing outcomes, unreported analysis details, or the clinical meaning of a numerical difference. Statistical evidence should be read as one component of a broader assessment, not as individual medical advice.
18. Why This Trial Matters Statistically
This trial illustrates why a treatment comparison is not adequately described by a single point estimate. The primary result includes an adjusted estimate, a confidence interval, and a p-value, each answering a different statistical question. The confidence interval conveys uncertainty around the difference, while the p-value evaluates the result under a particular null model. Neither replaces information about the non-inferiority margin, which is not reported in the registry record.
It also demonstrates the distinction between the sponsor’s model-based analysis and an unadjusted recalculation from group summaries. The recalculation can serve as a transparent check, but it cannot reproduce the full repeated-measures model. Keeping these analyses distinct helps prevent a convenient summary calculation from being mistaken for the trial’s reported inference.
The range of secondary endpoints makes multiplicity important. Postmeal glucose, longer-term HbA1c change, hypoglycemia, and other measures are related but not interchangeable. A pattern across outcomes can add context, yet unadjusted comparisons require restraint when many analyses are listed. The severe-event rate further shows why effect estimates must be read with their intervals, especially when event information is limited.
Finally, registry transparency affects interpretability. The record provides the primary model terms and identifies the analysis population, but does not report the non-inferiority margin, a multiplicity strategy, or a detailed missing-data plan. Recognizing what is documented and what remains unreported is part of sound statistical reading. This does not invalidate the posted results; it defines the limits of what can be concluded from the record.
19. Limitations
- The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
- Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.
Several trial-specific details needed for a fuller assessment are not reported in the registry record. These include the original sample-size justification, the non-inferiority margin, the allocation ratio, the randomization-generation procedure, and details of how masking was maintained. The absence of these details from the registry record does not establish that they were not specified elsewhere; it limits independent assessment from this record.
The primary model description lists its covariates and terms but does not report its covariance structure, degrees-of-freedom approach, or detailed missing-data assumptions. The primary analysis population requires baseline and post-baseline HbA1c data, but counts and reasons for missing measurements are not reported. Sensitivity analyses addressing missingness are also not reported in the registry record.
The registry does not report a multiplicity adjustment strategy for the multiple secondary outcomes and analyses. The detailed covariates for the ANCOVA comparisons are not reported, and the fuller analysis method for the serious-hypoglycemia rate is not described. The rate estimate has a broad confidence interval, which limits precision. Secondary p-values should consequently be interpreted cautiously.
Safety summaries are descriptive counts by group and do not by themselves establish causation or comparative risk. The lead-in group is separately reported, and these counts should not be conflated with the randomized treatment comparison. Finally, the posted results concern the recorded population, regimens, and follow-up; broader generalizability and clinical importance cannot be established from these statistics alone.
20. Related Tutorials
21. Related Statistical Calculators
22. Sources
- ClinicalTrials.gov: A Study of LY900014 Compared to Insulin Lispro (Humalog) in Adults With Type 2 Diabetes — NCT03952143.
- Registry record last updated 2022-02-08; status last verified 2022-01.
- Results first posted 2022-02-08.
- 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 describes a completed phase 3, randomized, double-blind, parallel comparison of LY900014 and insulin lispro (Humalog) in adults with type 2 diabetes. Both mealtime insulins were used with once-daily insulin glargine or insulin degludec. Enrollment was 628.
The primary endpoint was change in HbA1c from baseline to Week 26. The sponsor reported an adjusted LS mean difference of 0.07, with a 95% confidence interval from -0.07 to 0.21 and p = 0.321, in an analysis labeled non-inferiority. The non-inferiority margin is not reported in the registry record. The unadjusted recalculation is supplementary and also has an interval spanning zero.
Secondary results include postmeal glucose and severe-hypoglycemia comparisons. Their interpretation is limited by uncertainty and the unreported multiplicity strategy. Missing-data details and several analysis specifications are also not reported in the registry record. The statistics describe the posted trial results but do not alone establish clinical importance or a general conclusion beyond the studied setting.