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 in Patients With Type 2 Diabetes Mellitus (NCT01435616), a randomized phase 3 study. The primary outcome is Change From Baseline to 52 Week Endpoint in Hemoglobin A1c (HbA1c).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01435616 |
| Phase | Phase 3 |
| Condition | Diabetes Mellitus, Type 2 |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | Double |
| Enrollment | 1538 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Eli Lilly and Company |
| Results posted | Yes |
2. Clinical Question
Population
Insulin-naive patients with type 2 diabetes mellitus who were using at least 2 pre-study oral antihyperglycemic medications. The primary analysis population consisted of randomized participants who received at least 1 dose of study medication and had at least 1 post-baseline HbA1c measurement.
Intervention
LY2605541, titrated based on blood glucose readings and administered subcutaneously once daily, in combination with at least 2 pre-study oral antihyperglycemic medications. The arm description gives a treatment duration of 52 or 78 weeks.
Comparator
Insulin glargine, titrated based on blood glucose readings and administered subcutaneously once daily, alongside at least 2 pre-study oral antihyperglycemic medications. The arm description also gives a treatment duration of 52 or 78 weeks.
Primary question
How did HbA1c change from baseline to the 52-week endpoint in the LY2605541 and glargine groups? The study also set out to compare night-time and total hypoglycemia, the proportion reaching specified HbA1c targets without night-time hypoglycemia, and other measures of glycemic control.
The central comparison is between two once-daily basal insulin regimens, not between insulin treatment and no insulin treatment. Both groups continued oral anti-hyperglycemia medications, and both study insulins were titrated using blood glucose readings. The registry describes the study as randomized, double-blind, and parallel-group. It records enrollment of 1538 participants.
The primary outcome was change in HbA1c, a measure used to assess average blood glucose over the preceding 2 to 3 months. The registry identifies the primary endpoint timeframe as baseline to 52 weeks. Although the arm descriptions mention treatment for 52 or 78 weeks, the reason for those two durations is not reported in the registry record. The comparison addressed the measured change at the 52-week endpoint; it does not, by itself, answer every question about longer-term outcomes or all the other planned comparisons.
The registry’s brief description also identifies night-time low blood sugar episodes, total low blood sugar episodes, and reaching blood sugar targets without night-time episodes as study questions. These are distinct outcomes from the primary HbA1c measure. A result on one outcome should not be treated as a substitute for results on the others.
3. Trial Design
The registry describes a phase 3, randomized, double-blind, parallel-group study in patients with type 2 diabetes mellitus. It lists 1538 participants as enrolled and records the study status as completed. The recorded start was 2011-11, and primary completion was 2014-01. Eli Lilly and Company is listed as the sponsor.
Participants were assigned to LY2605541 or insulin glargine. Both were administered subcutaneously once daily, titrated based on blood glucose readings, and used with at least 2 pre-study oral antihyperglycemic medications prescribed by each participant’s personal physician. The arm descriptions state that treatment could continue for 52 or 78 weeks. The primary endpoint, however, is specified at the 52-week endpoint. Further details explaining the treatment-duration options are not reported in the registry record.
Randomization means that assignment to the study groups was by chance, while double masking indicates that the registry classified the study as double-blind. The record does not report the specific people who were masked, the randomization ratio, or the allocation-concealment procedure. It also does not report eligibility criteria beyond the description of insulin-naive patients with type 2 diabetes in the official title and study summary.
The primary analysis population was not simply all enrolled participants: it included randomized participants who had received at least 1 dose of study medication and had at least 1 post-baseline HbA1c measurement. The numbers contributing to the primary arm estimates were 989 for LY2605541 and 523 for glargine. The reason these analysis counts differ from the overall enrollment, and the details of participant flow after randomization, are not reported in the registry record.
The registry gives the primary endpoint model and several stratification factors, but the original sample-size justification and other design assumptions are not reported in the registry record. This distinction matters because a planning illustration based on the observed result is not a description of how the original trial was designed.
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.
Overall Study
| Stage | LY2605541 | Glargine |
|---|---|---|
| STARTED | 1003 | 535 |
| Received at Least 1 Dose of Study Drug | 1003 | 535 |
| COMPLETED | 832 | 455 |
| NOT COMPLETED | 171 | 80 |
Reasons for not completing this period:
| Reason | LY2605541 | Glargine |
|---|---|---|
| Adverse Event | 39 | 21 |
| Death | 7 | 2 |
| Lost to Follow-up | 22 | 13 |
| Protocol Violation | 16 | 13 |
| Withdrawal by Subject | 66 | 24 |
| Physician Decision | 20 | 7 |
| Sponsor Decision | 1 | 0 |
Analysis population for the primary outcome, as defined in the registry: All participants who were randomized, had at least 1 dose of study medication, and at least 1 post-baseline HbA1c measurement.
5. Baseline Characteristics
The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.
Population: All randomized participants.
| Characteristic | Unit | LY2605541 | Glargine | Total |
|---|---|---|---|---|
| Participants analysed | 1003 | 535 | 1538 | |
| Age, Continuous | years | 58.80 (SD 9.85) | 59.35 (SD 9.80) | 58.99 (SD 9.84) |
| Sex: Female, Male: Female | Participants | 453 | 227 | 680 |
| Sex: Female, Male: Male | Participants | 550 | 308 | 858 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 201 | 96 | 297 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 648 | 355 | 1003 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 154 | 84 | 238 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 24 | 15 | 39 |
| Race (NIH/OMB): Asian | Participants | 25 | 12 | 37 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 3 | 2 | 5 |
| Race (NIH/OMB): Black or African American | Participants | 68 | 34 | 102 |
| Race (NIH/OMB): White | Participants | 875 | 469 | 1344 |
| Race (NIH/OMB): More than one race | Participants | 8 | 3 | 11 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 0 | 0 | 0 |
| Region of Enrollment: United States | Participants | 371 | 188 | 559 |
| Region of Enrollment: Slovakia | Participants | 12 | 10 | 22 |
| Region of Enrollment: Greece | Participants | 18 | 12 | 30 |
| Region of Enrollment: Finland | Participants | 6 | 7 | 13 |
| Region of Enrollment: Spain | Participants | 35 | 18 | 53 |
| Region of Enrollment: Turkey | Participants | 7 | 4 | 11 |
| Region of Enrollment: Lithuania | Participants | 8 | 4 | 12 |
| Region of Enrollment: Israel | Participants | 16 | 8 | 24 |
| Region of Enrollment: Russia | Participants | 32 | 18 | 50 |
| Region of Enrollment: Italy | Participants | 24 | 13 | 37 |
6. Primary Endpoint
The registry lists the primary outcome as Change From Baseline to 52 Week Endpoint in Hemoglobin A1c (HbA1c), measured over Baseline, 52 weeks.
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | percentage of HbA1c |
| Endpoint classification | Continuous Endpoint |
The primary endpoint is change from baseline to the 52-week endpoint in hemoglobin A1c, or HbA1c, expressed as a percentage of HbA1c. HbA1c reflects average blood glucose over the preceding 2 to 3 months, so it provides a longer-term measure than an individual blood glucose reading. It is commonly used in trials of diabetes treatments to compare changes in glycemic control over a defined follow-up period.
The registry reports least-squares mean changes rather than raw group averages. These estimates come from a mixed model repeated measures analysis that accounts for baseline HbA1c and includes visit, treatment, visit-by-treatment interaction, and specified stratification factors in the model. The model-based estimates are therefore adjusted for the listed variables. They should not be read as simple arithmetic averages of all measurements collected.
In the primary analysis population, the estimated change was -1.55 percentage points for LY2605541 and -1.25 percentage points for glargine. The reported contrast, expressed as glargine minus LY2605541, was 0.3 percentage points, with a 95% confidence interval from 0.202 to 0.398. A positive contrast in this direction corresponds to a less negative estimated change in the glargine group. The result describes the model-estimated group contrast at the stated endpoint; it does not convey individual responses or establish what happened for every participant.
HbA1c is only one outcome in the study. The registry also describes hypoglycemia, glucose measures, body weight, and other outcomes. A difference in HbA1c should not be taken to imply the same pattern for each of those measures.
7. Results Posted in the Registry
- Glargine: mean -1.25 versus -1.55 on control; difference 0.30 (95% CI 0.20 to 0.40), standardized effect d = 0.32; z-test p = <0.001.
Mean difference: Glargine
95% CI: 0.20 to 0.40
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 |
|---|---|---|---|---|
| Fasting Serum Glucose (By Laboratory Measurement) | Continuous Endpoint | Mean difference | 5.20 (1.08 to 9.32) | 879 per arm |
| Fasting Blood Glucose (By Participant Self-monitored Blood Glucose Readings) | Continuous Endpoint | Mean difference | -0.57 (-3.29 to 2.15) | 32,192 per arm |
| Change From Baseline to 52 Weeks in Body Weight | Continuous Endpoint | Mean difference | 0.51 (0.00 to 1.02) | 1,356 per arm |
Fasting Serum Glucose (By Laboratory Measurement)
- 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:
- Glargine: mean 120.13 versus 114.93 on control; difference 5.20 (95% CI 1.08 to 9.32), standardized effect d = 0.13; z-test p = 0.013.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Glargine than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Fasting Blood Glucose (By Participant Self-monitored Blood Glucose Readings)
- 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:
- Glargine: mean 112.00 versus 112.57 on control; difference -0.57 (95% CI -3.29 to 2.15), standardized effect d = -0.02; z-test p = 0.681.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Glargine and the control. The interval gives the range of effects that remain compatible with the data.
Change From Baseline to 52 Weeks in Body Weight
- 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:
- Glargine: mean 2.57 versus 2.06 on control; difference 0.51 (95% CI 0.00 to 1.02), standardized effect d = 0.11; z-test p = 0.048.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Glargine than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
The secondary outcomes cover several different aspects of treatment: laboratory and self-monitored glucose, HbA1c targets, hypoglycemia, body weight, and insulin dose. These measures are related to the primary HbA1c question but are not interchangeable. Laboratory readings, participant self-monitoring, longer-term glycemic measures, and event counts capture different features of participants’ experience and may show different patterns.
The posted results do not form a uniformly aligned set of contrasts across all these domains. The secondary estimates include differences that are more clearly separated from zero and others with intervals that include zero, while the measures themselves have different units and uncertainty. This variation is a reason to interpret each outcome on its own scale and in light of its confidence interval, rather than treating the secondary results as one combined verdict about the study.
Secondary findings can help describe whether the primary result is accompanied by changes in other measured outcomes, but they generally carry less confirmatory weight when many outcomes are examined and no adjustment for multiple comparisons is reported. A collection of unadjusted tests increases the chance that some results may appear notable through chance variation alone. The registry lists 19 posted secondary outcomes, and the secondary analysis records are not reported. The record does not state whether a hierarchy or other strategy was used to control multiplicity.
The brief study description includes nocturnal and total hypoglycemia and the proportion reaching HbA1c targets without night-time episodes. These questions are clinically distinct from change in HbA1c. The presence of an outcome in the registry’s description does not establish that its analysis was fully reported or that its result supports the same interpretation as the primary endpoint. The secondary evidence is best treated as contextual and exploratory in the absence of a reported multiplicity plan and detailed analysis records.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Rate of Total and Nocturnal Hypoglycemia Events
- Percentage of Participants With Hemoglobin A1c Equal or Less Than 6.5% and Less Than 7.0 %
- Fasting Serum Glucose (By Laboratory Measurement)
- Fasting Blood Glucose (By Participant Self-monitored Blood Glucose Readings)
- 6 Point Self-monitored Blood Glucose (SMBG)
- Change From Baseline to 52 Weeks in Body Weight
- Hemoglobin A1c
- Insulin Dose Per Body Weight
9. Statistical Interpretation
The registry reports estimated HbA1c changes of -1.55 percentage points for LY2605541 and -1.25 percentage points for glargine at the 52-week endpoint. The contrast is 0.3 percentage points for glargine minus LY2605541, with a 95% confidence interval from 0.202 to 0.398. Because the contrast is defined in that direction, positive values indicate a less negative estimated change in the glargine group. The interval does not include zero, and the posted unadjusted p-value is <0.001.
These are least-squares mean estimates from the registry’s mixed model repeated measures analysis, not unadjusted raw averages. The reported model includes baseline HbA1c, country, LDL-C stratum, sulfonylurea/meglitinide use, visit, treatment, and visit-by-treatment interaction. The estimates therefore describe a model-adjusted comparison for the stated analysis population: randomized participants who received at least 1 dose and had at least 1 post-baseline HbA1c measurement.
The point estimate gives the estimated size and direction of the group contrast on the HbA1c scale. The interval gives a range of values compatible with the data and the stated model under the usual confidence-interval interpretation. It is relatively close around the estimate compared with the range of plausible values that could arise in a less precise estimate, but it does not capture every uncertainty in the study. For example, it does not address possible limitations in outcome collection, missing-data assumptions, or unreported features of the protocol.
The posted p-value is unadjusted. It describes how inconsistent the observed contrast is with a null contrast under the statistical model, but it does not quantify the size or clinical importance of the result. The registry does not report a multiplicity adjustment for the range of outcomes, so the p-value should be interpreted with that limitation in mind. The result is a comparison of these study groups at this endpoint, not a statement about every patient or every outcome.
Other posted results give a mixed picture across secondary measures. The registry includes measures based on laboratory glucose testing, participant self-monitoring, and body weight, as well as outcomes related to hypoglycemia and glycemic targets. Their measures differ in meaning and data collection, so they should not be collapsed into a single overall conclusion. Some secondary analyses have estimates that are more precise than others, and all require attention to their confidence intervals and their unadjusted status.
The registry lists 20 outcome measures and 19 posted secondary outcomes, but reports no analysis records for the secondary comparisons. The absence of detailed analysis records limits assessment of the full statistical plan and how outcome-specific models were selected. Results should therefore be read as registry-posted estimates, with particular emphasis on the primary endpoint and appropriate caution about secondary findings.
These results describe group-level estimates and do not establish the response of any individual participant. They also do not provide a complete account of benefits and harms, because the registry record includes only selected outcomes and adverse-event summaries. No medical recommendation follows from the statistical contrast alone.
10. Statistical Methods Explained
The primary endpoint is a continuous outcome: change in HbA1c measured in percentage points. For a continuous outcome, a group estimate describes a location on the measurement scale, and a difference between groups expresses the contrast in those same units. The primary analysis reports least-squares means and standard errors. A least-squares mean is a model-based estimate adjusted for variables included in the model; it need not equal the simple average of the observed values.
What does the primary model do?
The registry identifies a mixed model repeated measures analysis, often abbreviated MMRM. In general, this type of model analyzes repeated measurements from participants over time and accounts for the fact that measurements from the same participant are related. The model can estimate group patterns over the follow-up visits while using the repeated observations included in the analysis. The registry specifies baseline HbA1c, country, LDL-C stratum, sulfonylurea/meglitinide use, visit, treatment, and visit-by-treatment interaction as fixed effects. It does not report additional details about covariance structure, estimation method, or model diagnostics.
The visit-by-treatment interaction allows the modeled treatment contrast to vary by visit rather than requiring a single common contrast across all visits. The stated primary result concerns the 52-week endpoint. Since the record does not provide the full analysis output or protocol, further assumptions about model implementation should not be inferred.
How should the contrast be read?
The contrast is expressed as glargine minus LY2605541. Thus, the reported estimate of 0.3 is a difference in adjusted HbA1c change on that scale. A positive estimate means the glargine change estimate is numerically higher, or less negative, than the LY2605541 estimate. This direction convention is important: reversing the order of subtraction would reverse the sign while leaving the underlying comparison unchanged. The estimate is not a ratio, percentage reduction, or count of participants.
What does a standard error describe?
A standard error describes the estimated sampling variability of an estimate under the fitted model. It is not the same thing as the spread of individual participants’ measurements. Smaller standard errors generally indicate more precise estimates, all else equal, but interpretation depends on the estimator, model, and underlying data. The registry reports standard errors for the arm-level least-squares means, but does not give separate arm-level confidence limits in the primary result.
The confidence interval for the contrast is reported directly. It combines information about the estimate and its uncertainty on the contrast scale. A confidence interval is not a range expected to contain every individual participant’s change, and it is not a guarantee that the true contrast lies in the interval. Rather, under the statistical assumptions and repeated use of the method, intervals constructed this way have a stated coverage interpretation.
Why can over-dispersion matter?
General explanation: over-dispersion occurs when observed variability is greater than a statistical model’s assumed variability. If a model understates the variability, standard errors can be too small and intervals too narrow; if variability is adequately represented, uncertainty estimates are more dependable. Over-dispersion is especially relevant for some count outcomes, where event rates may vary more than a basic count model allows. The primary endpoint is continuous, and the registry does not report an over-dispersion assessment or a count-model analysis for the hypoglycemia outcomes. No conclusion about such a diagnostic can be drawn from the listed results.
How are the secondary estimates different?
The secondary continuous outcomes also use least-squares means and standard errors in the posted results. Their units differ: glucose results are expressed in mg/dL, while body-weight change is in kilograms. A mean difference retains the unit of the outcome, so estimates in those different units cannot be compared by magnitude alone. The registry gives confidence intervals and unadjusted p-values for the listed comparisons. The analysis records for the secondary outcomes are empty, so model specifications beyond the posted summaries are not reported in the registry record.
What do the recalculated planning illustrations represent?
The sample-size illustrations use the observed effect and an approximate pooled standard deviation inferred from the posted summary statistics. Such recalculated values are simple, unadjusted planning calculations, not the trial’s original design calculations. The listed assumptions are a two-sided significance level of 0.05, equal allocation, and a normal approximation. The planning rows scale the effect to detect as a stated fraction of the observed effect. Because the standard deviation is approximate and the calculations do not reproduce the specified MMRM or an outcome-specific design, they should be viewed as rough planning illustrations rather than exact requirements for a future study.
The sponsor’s own analysis is the relevant source for the posted primary estimate; the registry does not flag a discrepancy between its posted summary and the simple recalculation. The planning illustrations do not replace that model-based analysis and do not provide evidence about how the original study’s design was justified.
11. Confidence Intervals and Precision
The primary contrast is 0.3 percentage points for glargine minus LY2605541, with a 95% confidence interval from 0.202 to 0.398. The interval describes uncertainty around the estimated group contrast, not variation among individual participants. Its positive limits indicate that the model-based contrast is above zero throughout the reported interval. The posted p-value, <0.001, is consistent with that interval-based reading under the reported analysis.
Precision is specific to the estimate and analysis. The primary arm estimates use 989 participants for LY2605541 and 523 for glargine in the defined analysis population. The standard errors for the least-squares means are 0.03 and 0.04, respectively. These standard errors describe uncertainty in the arm estimates; they should not be interpreted as standard deviations of participant-level HbA1c changes.
A confidence interval does not address every source of uncertainty. Its conventional interpretation relies on the statistical model and the analysis being appropriate. The registry reports the principal fixed effects but does not report the covariance structure, missing-data assumptions, or model diagnostics. The interval also does not account for uncertainty created by selecting among multiple outcomes unless an appropriate multiplicity procedure is used; such a procedure is not reported in the registry record.
Precision should not be confused with importance. A narrow interval can describe a group contrast precisely without establishing its clinical significance. The registry does not provide a threshold for interpreting the clinical importance of this HbA1c contrast, so that judgment cannot be made from the interval alone.
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 | 153 | 204 |
| 75% of the observed effect | 271 | 362 |
| 50% of the observed effect | 609 | 815 |
The planning figures are participants per arm for the continuous outcomes, not total event counts. The assumptions listed for these illustrations are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set to the stated fraction of the observed effect. The original trial’s sample-size assumptions and justification are not reported in the registry record.
The 80% power column gives the modeled number of participants per arm for an 80% chance of detecting the specified effect under those planning assumptions, if that effect and the calculation assumptions are correct. The 90% power column applies the same idea with a higher target chance of detection. These are prospective planning quantities. They do not describe the probability that this completed trial has found a true effect, and they are not observed power.
Rows for 100% of the observed effect use the observed contrast as the planning target; rows for 75% and 50% use progressively smaller targets. Smaller effects are harder to distinguish from random variation, so they require more participants under the same assumptions. The reported values are per arm, meaning a two-arm plan would allocate that many participants to each group, rather than treating the entry as a combined total.
The illustrations are based on a simple approximation and an estimated pooled standard deviation, not a reproduction of the registry’s repeated-measures primary model. They are useful for understanding how the required scale of a study changes with the target effect and desired power. They should not be mistaken for the enrollment target used in the original study, or for a guarantee that a future study with those numbers would reproduce the posted 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 = 0.300; pooled standard deviation σ = 0.934.
- n = 2 × (1.96 + 0.842)2 × 0.9342 / 0.3002 = 152.0, rounded up to 153 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 <- 0.3 # observed difference in means
sigma <- 0.933635066332715 # 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(1435616)
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 = 153 (80% power), 204 (90% power)
75% of observed effect: n per arm = 271 (80% power), 362 (90% power)
50% of observed effect: n per arm = 609 (80% power), 815 (90% power)
power.t.test: 153
Simulated power at n = 153 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. Multiplicity, Missing Data and Analysis Populations
The registry identifies one primary endpoint and lists numerous secondary outcomes. It reports 20 outcome measures and 19 posted secondary outcomes. When many outcomes are analyzed, the chance of at least one apparently unusual result can rise if each is assessed separately without adjustment. This is the general multiplicity concern: a collection of unadjusted p-values does not have the same interpretation as a single prespecified test.
The registry reports an unadjusted p-value for the primary comparison and unadjusted p-values for the posted secondary comparisons. A multiplicity adjustment, testing hierarchy, or other family-wise error strategy is not reported in the registry record. It is therefore not possible to determine from the record whether the trial protocol used such a procedure, or how the investigators intended to interpret the multiple outcome tests. Secondary p-values should be treated as less definitive than a result supported by a prespecified and reported multiplicity strategy.
The analysis population for the primary endpoint required randomization, at least 1 dose of study medication, and at least 1 post-baseline HbA1c measurement. This is an explicitly defined population, but the registry does not label it as a particular standard analysis set. The number of participants included differs by arm, and endpoint-specific analysis counts also vary. Reasons for missing endpoint measurements or differences in analysis counts are not reported in the registry record.
The primary model is described as MMRM, but the registry does not report its missing-data assumptions, the amount or pattern of missing outcome data, sensitivity analyses, or imputation procedures. General explanation: repeated-measures models can use available measurements without requiring every participant to have a measurement at every visit, but validity depends on assumptions about the missingness process and model specification. The registry description alone does not establish which assumptions were made or whether they were examined.
The original sample-size rationale, interim-analysis plan, and broader statistical analysis plan are not reported in the registry record. These omissions limit independent assessment of prespecification, handling of missing data, and how the analysis addressed the number of outcomes.
15. 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 |
|---|---|---|---|
| LY2605541 | 105 | 1003 | 10.5% |
| Glargine | 73 | 535 | 13.6% |
Other (non-serious) adverse events
Participants with at least one non-serious event at or above the registry's 3% reporting threshold.
| Arm | Participants affected of at risk |
|---|---|
| LY2605541 | 733 of 1003 |
| Glargine | 390 of 535 |
Most frequent serious adverse event terms
| Event term | Organ system | LY2605541 | Glargine |
|---|---|---|---|
| Hypoglycaemia | Metabolism and nutrition disorders | 7 of 1003 | 4 of 535 |
| Coronary artery disease | Cardiac disorders | 3 of 1003 | 5 of 535 |
| Myocardial infarction | Cardiac disorders | 5 of 1003 | 3 of 535 |
| Pneumonia | Infections and infestations | 3 of 1003 | 4 of 535 |
| Atrial fibrillation | Cardiac disorders | 5 of 1003 | 0 of 535 |
| Chest pain | General disorders | 5 of 1003 | 0 of 535 |
| Cellulitis | Infections and infestations | 5 of 1003 | 0 of 535 |
| Transient ischaemic attack | Nervous system disorders | 2 of 1003 | 3 of 535 |
| Acute myocardial infarction | Cardiac disorders | 2 of 1003 | 2 of 535 |
| Angina unstable | Cardiac disorders | 1 of 1003 | 3 of 535 |
Most frequent non-serious adverse event terms
| Event term | Organ system | LY2605541 | Glargine |
|---|---|---|---|
| Nasopharyngitis | Infections and infestations | 141 of 1003 | 82 of 535 |
| Headache | Nervous system disorders | 85 of 1003 | 37 of 535 |
| Upper respiratory tract infection | Infections and infestations | 83 of 1003 | 33 of 535 |
| Back pain | Musculoskeletal and connective tissue disorders | 70 of 1003 | 36 of 535 |
| Diarrhoea | Gastrointestinal disorders | 57 of 1003 | 38 of 535 |
| Influenza | Infections and infestations | 59 of 1003 | 28 of 535 |
| Bronchitis | Infections and infestations | 52 of 1003 | 24 of 535 |
| Arthralgia | Musculoskeletal and connective tissue disorders | 52 of 1003 | 20 of 535 |
| Urinary tract infection | Infections and infestations | 47 of 1003 | 22 of 535 |
| Pain in extremity | Musculoskeletal and connective tissue disorders | 42 of 1003 | 25 of 535 |
Serious events with the highest arm-level rate: coronary artery disease (0.9%), pneumonia (0.7%), hypoglycaemia (0.7%), prostate cancer (0.6%), angina unstable (0.6%).
The registry reports serious adverse events and other adverse events by group, using participants at risk as the denominators. For serious adverse events, 105 of 1003 participants were affected in the LY2605541 group, and 73 of 535 were affected in the glargine group. For other adverse events, the corresponding counts were 733 of 1003 and 390 of 535. These are counts of participants affected, not counts of all event episodes.
The registry lists coronary artery disease at 0.9%, pneumonia at 0.7%, hypoglycaemia at 0.7%, prostate cancer at 0.6%, angina unstable at 0.6%, and myocardial infarction at 0.6% among the top serious adverse-event terms. The record does not provide enough detail in these summaries to assign those listed percentages to a particular treatment group, so they should be read as the reported serious-event terms rather than as a comparative arm-specific list.
Deaths are not reported in the registry record. These summaries do not establish that all adverse events were captured in the same way or provide a complete assessment of event timing, severity, or causality. Counts alone do not show whether an event was caused by treatment, and differences in group size mean that raw counts should not be compared as if the denominators were identical.
16. What the Result Does, and Does Not, Mean
The primary result describes a model-adjusted difference in HbA1c change at 52 weeks among participants meeting the stated primary analysis criteria. It reports group estimates and a confidence interval for their contrast. It does not describe the change for every participant, and it cannot determine how an individual would respond to either regimen.
The endpoint is one measure of glycemic control, and the study also considered other measures. The primary contrast should not be assumed to predict the results for night-time hypoglycemia, total hypoglycemia, body weight, insulin dose, or each glucose measure. Those outcomes address different questions, and the registry’s secondary findings have the additional limitation that no multiplicity plan is reported.
The result also does not establish a clinical importance threshold. The registry gives an estimate and interval but does not report a threshold that would define a meaningful HbA1c difference for this study. Statistical evidence that a contrast is separated from zero is not, on its own, a statement about the size of benefit or harm that matters to patients.
The safety summaries are counts of affected participants and selected event terms. They do not establish causality or provide complete information about the timing and severity of every event. The available summaries therefore cannot stand in for a full assessment of safety outcomes.
Finally, the record describes a particular randomized comparison in insulin-naive patients using at least 2 pre-study oral medications. The findings pertain to the measured study population, regimens, and follow-up described in the record. Further details about eligibility, missing data, longer-term outcomes, and the original statistical plan are not reported. The statistical results alone do not provide medical advice or determine which treatment is appropriate for an individual.
17. Why This Trial Matters Statistically
This trial is statistically informative because it compares two active basal insulin regimens within a randomized, double-blind, parallel-group design and specifies a continuous primary endpoint at a defined follow-up time. Randomization and masking are important design features for limiting some forms of bias, while a prespecified model can clarify what contrast the primary estimate represents. The registry reports the primary model and the variables included in it, allowing readers to distinguish the adjusted endpoint estimate from a simple comparison of raw averages.
The result also illustrates why an estimate should be read together with its uncertainty and analysis definition. The posted contrast is paired with a confidence interval and an unadjusted p-value, and the primary analysis population is described. Those details help interpret the numerical result more responsibly than a p-value alone would.
At the same time, the record shows how much statistical interpretation depends on information beyond the point estimate. Details of multiplicity handling, missing-data assumptions, sample-size justification, and the broader analysis plan are not reported. These gaps matter particularly when a study includes numerous outcomes and only selected analyses are fully described.
The study also demonstrates the distinction between the primary endpoint and a broader set of secondary questions. HbA1c, laboratory glucose, self-monitored glucose, hypoglycemia, and body weight capture different outcomes. Their estimates cannot be compressed into one number without losing the underlying distinctions. The trial is therefore a useful example of reading an adjusted primary comparison alongside less definitive secondary evidence and a limited registry safety summary.
18. 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 does not report the original sample-size calculation or the assumptions used to plan enrollment. The planning illustrations based on the observed effect are not a substitute for that information. They use an approximate standard deviation and simplified assumptions rather than reproducing the primary repeated-measures model.
Several details needed to assess the analysis are absent. The record does not describe the covariance structure for the MMRM, model diagnostics, missing-data assumptions, sensitivity analyses, or the extent and pattern of missing measurements. It defines the primary analysis population but does not explain why participants were excluded from endpoint-specific analyses or why the arm analysis counts differ from overall enrollment.
The registry does not report a multiplicity adjustment or hierarchy for the primary and secondary outcomes. It lists many outcomes, but secondary analysis records are empty. This makes it difficult to establish which secondary analyses were prespecified, how their tests were intended to be interpreted, or whether all planned results are represented in the posted summaries.
The arm descriptions state treatment durations of 52 or 78 weeks, while the primary endpoint is at 52 weeks; the reason for the duration options is not reported. Eligibility details beyond the insulin-naive type 2 diabetes population, randomization ratio, allocation concealment, and masking specifics are also not reported in the registry record. These limits restrict assessment of the study context and of how closely the posted analysis reflects the full protocol.
The adverse-event summary gives counts and selected serious-event terms but does not report deaths, event timing, or enough detail to establish causal relationships. These are limitations of the information in the registry record, not evidence that an unreported event or analysis did or did not occur.
19. Related Tutorials
20. Related Statistical Calculators
21. Sources
- ClinicalTrials.gov: A Study in Patients With Type 2 Diabetes Mellitus — NCT01435616.
- Registry record last updated 2018-04-13; status last verified 2018-03.
- Results first posted 2018-04-13.
- 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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22. Record Summary
NCT01435616 is a completed, randomized, double-blind, phase 3, parallel-group study sponsored by Eli Lilly and Company. It enrolled 1538 insulin-naive patients with type 2 diabetes mellitus and compared once-daily LY2605541 with once-daily insulin glargine, both used alongside at least 2 pre-study oral antihyperglycemic medications.
The primary endpoint was change from baseline to the 52-week endpoint in HbA1c. The registry reports least-squares mean changes of -1.55 for LY2605541 and -1.25 for glargine, with a glargine-minus-LY2605541 contrast of 0.3 and a 95% confidence interval from 0.202 to 0.398. The posted p-value is <0.001.
The record also contains selected secondary results and adverse-event counts. Details of multiplicity handling, missing-data assumptions, and the original sample-size justification are not reported in the registry record.