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 LY2605541 in Participants With Type 2 Diabetes Mellitus (NCT01582451), a randomized phase 3 study. The primary outcome is Change From Baseline to 26-week Endpoint in Hemoglobin A1c (HbA1c).
| Feature | Registry value |
|---|---|
| ClinicalTrials.gov identifier | NCT01582451 |
| Phase | Phase 3 |
| Condition | Diabetes Mellitus, Type 2 |
| Allocation | Randomized |
| Design model | Parallel |
| Masking | None (open label) |
| Enrollment | 466 |
| Arms in the primary outcome | 2 |
| Lead sponsor | Eli Lilly and Company |
| Results posted | Yes |
2. Clinical Question
Population
Participants had type 2 diabetes mellitus and had previously been treated with basal insulin. The primary analysis population comprised participants who were randomized, received at least one dose of study medication, and had evaluable HbA1c data at baseline and after baseline. The registry record lists enrollment of 466.
Intervention
LY2605541 was administered by subcutaneous injection once daily at bedtime. The initial dose was based on the pre-study basal insulin dose and adjusted according to fasting blood glucose. The study compared its use alone or with pre-study oral antihyperglycemic medications with the insulin glargine regimen.
Comparator
Insulin glargine was administered by subcutaneous injection once daily at bedtime. Its initial dose was based on the pre-study basal insulin dose and adjusted according to fasting blood glucose. It was used alone or with pre-study oral antihyperglycemic medications.
Primary question
Among the specified analysis population, how did HbA1c change from baseline to the 26-week endpoint in the LY2605541 and insulin glargine groups? The primary measure is the adjusted mean change in HbA1c, a measure of average blood glucose over time. The registry also describes comparisons involving nighttime and overall hypoglycemia, but the primary endpoint is HbA1c change.
This was an open-label, randomized comparison in participants with type 2 diabetes previously treated with basal insulin. The clinical question is about the difference in average HbA1c change between assigned treatment groups over the stated endpoint period. It does not by itself answer whether either regimen is preferable for an individual, nor does it capture every aspect of blood glucose control, treatment burden, or safety.
The registry describes treatment with either study drug alone or in combination with pre-study oral antihyperglycemic medications. Therefore, the comparison concerns treatment strategies as used in the trial, rather than an isolated comparison of the drugs under all possible background regimens. The record does not report the distribution of background medication use in the primary analysis population.
3. Trial Design
The registry record describes a phase 3, randomized, open-label, parallel-group study of LY2605541 and insulin glargine in participants with type 2 diabetes mellitus previously treated with basal insulin. Enrollment is listed as 466. The study is marked completed. The record lists a start of 2012-05 and primary completion of 2013-05.
Both regimens were given once daily at bedtime by subcutaneous injection. Initial dosing was based on the participant’s pre-study basal insulin dose, with adjustment according to fasting blood glucose. The official title and arm descriptions indicate that treatment could be used alone or alongside pre-study oral antihyperglycemic medications. The insulin glargine description states that up to 3 such medications could be continued when their use was not excluded in combination with insulin. The LY2605541 arm description is incomplete in the registry record, so its specific medication restrictions are not reported in the registry record.
The primary endpoint was change from baseline to the 26-week endpoint in HbA1c. The primary description identifies a mixed model repeated measures analysis, with least-squares means adjusted for stratification factors, visit, treatment, the visit-by-treatment interaction, and baseline HbA1c. The analysis population was restricted to randomized participants who received at least one dose and had evaluable HbA1c data at baseline and after baseline.
Other outcomes listed in the record include HbA1c at 52 weeks, hypoglycemia, fasting glucose measures, insulin dose adjustments, and quality of life. The registry identifies 19 outcome measures and 18 posted secondary outcomes. Details of the original sample-size justification and the trial’s prespecified statistical analysis plan are not reported in the registry record. The masking status is none, so the study was open-label.
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 | Insulin Glargine |
|---|---|---|
| STARTED | 307 | 159 |
| Received at Least 1 Dose of Study Drug | 305 | 159 |
| COMPLETED | 275 | 139 |
| NOT COMPLETED | 32 | 20 |
Reasons for not completing this period:
| Reason | LY2605541 | Insulin Glargine |
|---|---|---|
| Adverse Event | 1 | 3 |
| Death | 3 | 3 |
| Lost to Follow-up | 0 | 2 |
| Protocol Violation | 11 | 3 |
| Withdrawal by Subject | 13 | 9 |
| Physician Decision | 3 | 0 |
| Sponsor Decision | 1 | 0 |
Analysis population for the primary outcome, as defined in the registry: Participants who were randomized, had at least 1 dose of study medication, and had evaluable HbA1c data at both baseline and post-baseline.
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 | Insulin Glargine | Total |
|---|---|---|---|---|
| Participants analysed | 307 | 159 | 466 | |
| Age, Continuous | years | 61.84 (SD 8.52) | 60.38 (SD 10.10) | 61.34 (SD 9.11) |
| Sex: Female, Male: Female | Participants | 132 | 66 | 198 |
| Sex: Female, Male: Male | Participants | 175 | 93 | 268 |
| Ethnicity (NIH/OMB): Hispanic or Latino | Participants | 57 | 25 | 82 |
| Ethnicity (NIH/OMB): Not Hispanic or Latino | Participants | 215 | 115 | 330 |
| Ethnicity (NIH/OMB): Unknown or Not Reported | Participants | 35 | 19 | 54 |
| Race (NIH/OMB): American Indian or Alaska Native | Participants | 2 | 0 | 2 |
| Race (NIH/OMB): Asian | Participants | 4 | 2 | 6 |
| Race (NIH/OMB): Native Hawaiian or Other Pacific Islander | Participants | 1 | 0 | 1 |
| Race (NIH/OMB): Black or African American | Participants | 17 | 9 | 26 |
| Race (NIH/OMB): White | Participants | 280 | 148 | 428 |
| Race (NIH/OMB): More than one race | Participants | 1 | 0 | 1 |
| Race (NIH/OMB): Unknown or Not Reported | Participants | 2 | 0 | 2 |
| Region of Enrollment: United States | Participants | 170 | 85 | 255 |
| Region of Enrollment: Czechia | Participants | 20 | 10 | 30 |
| Region of Enrollment: Greece | Participants | 16 | 5 | 21 |
| Region of Enrollment: Spain | Participants | 27 | 12 | 39 |
| Region of Enrollment: Romania | Participants | 16 | 14 | 30 |
| Region of Enrollment: Israel | Participants | 16 | 8 | 24 |
| Region of Enrollment: Russia | Participants | 17 | 9 | 26 |
| Region of Enrollment: Germany | Participants | 25 | 16 | 41 |
6. Primary Endpoint
The registry lists the primary outcome as Change From Baseline to 26-week Endpoint in Hemoglobin A1c (HbA1c), measured over Baseline, 26 weeks.
| Element | Registry entry |
|---|---|
| Result type | Least Squares Mean |
| Measure of spread | Standard Error |
| Unit | percentage of HbA1c |
| Endpoint classification | Continuous Endpoint |
HbA1c is a laboratory measure used to characterize average blood glucose over a period of time. The registry describes it as reflecting average blood glucose over a 2 to 3 month timeframe. Change from baseline indicates how the measured value shifted during the study, rather than simply describing the endpoint value without reference to the participant’s starting point.
The primary endpoint is the change in HbA1c from baseline to the 26-week endpoint. The registry reports least-squares mean changes, which are model-adjusted estimates rather than simple raw averages. The stated model accounts for baseline HbA1c, visit, treatment, the visit-by-treatment interaction, and stratification factors. This adjustment aims to compare groups while accounting for the variables specified in the model.
HbA1c is useful in a trial because it provides a standardized summary of blood glucose over time and permits comparison of average changes between treatment groups. It does not directly describe day-to-day fluctuations, individual episodes of low blood sugar, or the experience of each participant. Those topics are addressed by other listed outcomes, including hypoglycemia measures and fasting glucose measures. The primary endpoint should therefore be interpreted as one defined measure of glycemic change, not as a complete account of all clinically relevant effects.
The primary analysis population required evaluable HbA1c data at baseline and after baseline, in addition to randomization and at least one dose of study medication. How missing measurements were handled beyond the model description is not reported in the registry record.
7. Results Posted in the Registry
- Insulin Glargine: mean -0.29 versus -0.82 on control; difference 0.53 (95% CI 0.39 to 0.67), standardized effect d = 0.74; z-test p = <0.001.
Mean difference: Insulin Glargine
95% CI: 0.39 to 0.67
Recalculated from the posted summary statistics
8. Secondary Efficacy Endpoints
The registry also posts results for secondary outcomes. For each outcome below, the endpoint type, the test applied to the posted summary statistics, the result and its interpretation are given in turn. Secondary endpoints are usually not adjusted for multiple testing, so they support rather than confirm the primary finding.
| Secondary outcome | Type | Effect measure | Estimate (95% CI) | Planning size, 80% power |
|---|---|---|---|---|
| Change From Baseline to 52 Weeks in HbA1c | Continuous Endpoint | Mean difference | 0.45 (0.30 to 0.60) | 54 per arm |
| Number of Insulin Dose Adjustments to Steady-state | Continuous Endpoint | Mean difference | -1.31 (-1.81 to -0.81) | 67 per arm |
| European Quality of Life - 5 Dimension (EuroQol-5D) Score | Continuous Endpoint | Mean difference | 0.01 (-0.02 to 0.04) | 3,798 per arm |
Change From Baseline to 52 Weeks in HbA1c
- 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:
- Insulin Glargine: mean -0.22 versus -0.67 on control; difference 0.45 (95% CI 0.30 to 0.60), standardized effect d = 0.54; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically higher for Insulin Glargine than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
Number of Insulin Dose Adjustments to Steady-state
- 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:
- Insulin Glargine: mean 2.75 versus 4.06 on control; difference -1.31 (95% CI -1.81 to -0.81), standardized effect d = -0.49; z-test p = <0.001.
- Interpretation:
- The 95% confidence interval excludes no difference, so the mean is statistically lower for Insulin Glargine than for the control. This is an unadjusted, secondary comparison, so it is suggestive rather than confirmatory.
European Quality of Life - 5 Dimension (EuroQol-5D) Score
- 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:
- Insulin Glargine: mean 0.88 versus 0.87 on control; difference 0.01 (95% CI -0.02 to 0.04), standardized effect d = 0.06; z-test p = 0.480.
- Interpretation:
- The 95% confidence interval includes no difference, so these data do not show a statistically significant difference between Insulin Glargine and the control. The interval gives the range of effects that remain compatible with the data.
The secondary outcomes broaden the question beyond the 26-week HbA1c endpoint. They include HbA1c at 52 weeks, hypoglycemia measures, fasting glucose measures, insulin dose adjustments, and quality of life. These outcomes address related but distinct aspects of treatment experience and metabolic control, so they can add context without being interchangeable with the primary endpoint.
Across the secondary outcomes with numerical group summaries and comparisons reported in the registry record, the general pattern is not identical for every measure. The later HbA1c contrast follows the same direction as the primary endpoint, while the dose-adjustment and quality-of-life comparisons convey different kinds of information and different degrees of uncertainty. The endpoint-specific values and their meaning should be assessed individually rather than combined into a single overall treatment claim.
The registry lists other secondary outcomes, including several measures of hypoglycemia, but their numerical results are not reported in the registry record among the results. Without those estimates, it is not possible to infer that the HbA1c pattern was accompanied by a particular pattern of low blood sugar episodes. The study’s stated purpose included those outcomes, making their absence from the reported numerical results an important limit on an overall interpretation.
Secondary findings generally carry less weight when their analysis status, prespecification, and multiplicity handling are unclear. Testing many outcomes increases the chance that at least one result will appear notable by chance, particularly when p-values are unadjusted. The registry record does not report a multiplicity adjustment or a complete set of secondary analysis details. These results are best treated as supportive or exploratory context, rather than as independent confirmation of the primary result.
The secondary outcomes do not replace the primary endpoint. They can help identify whether the observed HbA1c contrast is accompanied by differences in other domains, but each requires its own analysis and uncertainty assessment. A coherent overall assessment would need the full outcome results, the prespecified analysis hierarchy, and the approach to missing data and multiple comparisons, which are not reported in the registry record.
Secondary outcomes registered for this trial, for reference (only those above were recalculated):
- Change From Baseline to 52 Weeks in HbA1c
- Rate of Total and Nocturnal Hypoglycemia Events (Adjusted by 30 Days)
- Percentage of Participants That Have Total and Nocturnal Hypoglycemic Events
- Percentage of Participants With HbA1c Equal to or Less Than (≤) 6.5% and Less Than (<) 7.0%
- Percentage of Participants With HbA1c <7.0% and Without Nocturnal Hypoglycemia
- Fasting Serum Glucose (FSG) (by Laboratory)
- Fasting Blood Glucose (FBG) (by Self Monitoring)
- Intra-participant Variability in Fasting Blood Glucose (FBG)
9. Statistical Interpretation
At the 26-week endpoint, the reported least-squares mean HbA1c change was -0.82 percentage points in the LY2605541 group and -0.29 percentage points in the insulin glargine group. Both reported group estimates are decreases from baseline. The reported mean difference comparing insulin glargine with LY2605541 is 0.53 percentage points, with a recalculated unadjusted confidence interval from 0.389 to 0.671 and an unadjusted p-value of <0.001.
The direction of the contrast follows the reported group means: the decrease in HbA1c was larger in the LY2605541 group. The interval for the recalculated contrast does not include zero, which is consistent with evidence of a difference in these summary data under the unadjusted comparison. This does not establish the size or certainty of an effect in every participant, and it is not a statement that one regimen is medically preferable.
The group means are adjusted least-squares means from the registry-described mixed model repeated measures analysis. The comparison interval and p-value are approximate, unadjusted recalculations from posted summary statistics, not a replacement for the sponsor’s model-based inferential analysis. The registry record does not report a sponsor comparison estimate and confidence interval for the primary treatment contrast in the analyzed results. The recalculated summary should therefore be read as a compact description of the posted group estimates, not as a fully adjusted treatment-effect analysis.
The result concerns the analysis population defined in the endpoint description, rather than every participant included in the enrollment figure. The reported arm counts for the primary endpoint are 302 for LY2605541 and 157 for insulin glargine. These values describe participants contributing to the displayed endpoint results and should not be treated as a count of all randomized participants in either arm.
Statistical significance and clinical importance are distinct questions. A small p-value addresses how compatible the data are with a specified no-difference model under the assumptions of the test; it does not determine whether the observed contrast is important to patients. A threshold for a clinically meaningful HbA1c difference is not reported in the registry record. Interpretation should also take account of the open-label design, the model and population definition, secondary outcomes, missing-data information, and safety reporting.
The study’s stated purpose included nighttime and overall hypoglycemia, but the primary result is HbA1c change. A result on this endpoint cannot by itself establish the pattern of hypoglycemia or settle the balance of benefits and harms across outcomes. Those conclusions require the relevant outcome data and consideration of the trial’s analysis plan, which is not reported in the registry record.
10. Statistical Methods Explained
The primary result is a continuous outcome: HbA1c change is measured on a numeric scale, and the reported group summaries are least-squares means. For a continuous measure, a group mean describes the center of the observed or model-estimated distribution. It does not imply that every participant experienced a change equal to that mean. The standard errors reported alongside the group means describe uncertainty in those estimated means, rather than the spread of individual participant values.
What does the adjusted mean represent?
The registry states that the primary least-squares means were calculated using mixed model repeated measures, abbreviated MMRM in the record. A repeated-measures model is a general approach for analyzing measurements collected at multiple visits. It uses the pattern of available measurements over time and models the relationship among observations from the same participant. The registry description says the model included visit, treatment, visit-by-treatment interaction, baseline HbA1c, and specified stratification factors.
Adjustment means that the reported least-squares means reflect the model’s estimates after accounting for the listed terms. These are not necessarily identical to unadjusted arithmetic averages. The listed stratification factors were country, baseline LDL-C category, and sulfonylurea or meglitinide use. The record does not provide enough detail to reconstruct the full model or determine every implementation choice, such as covariance structure or missing-data assumptions. Those details are not reported in the registry record.
In general, using baseline information in an analysis can improve comparability and precision when that information predicts the outcome. Repeated-measures modeling can use outcome measurements across visits rather than reducing the analysis to a single unadjusted endpoint value. These are general statistical features; the specific conclusions depend on the model’s assumptions and its implementation in this trial.
What does a mean difference describe?
A mean difference expresses the contrast between two group means on the original measurement scale. For the primary result, the reported contrast is 0.53 percentage points for insulin glargine compared with LY2605541. The group estimates are -0.82 and -0.29, respectively. A positive contrast in this stated ordering is consistent with the larger decrease in the LY2605541 group. The treatment contrast is more directly relevant to the randomized comparison than interpreting either group’s change alone, while still depending on the population and analysis used.
The comparison’s confidence interval and p-value in the statistical summary are recalculated, unadjusted estimates from posted summary statistics. They should not be confused with a model-based contrast from the MMRM. An unadjusted comparison does not account for all the terms listed in the primary model description. Since the registry record reports no discrepancy between the available calculations, the posted results remain the basis for interpretation; nevertheless, a sponsor’s own model-based analysis takes precedence over an approximate unadjusted recalculation when both are available.
Why can the standard errors differ from the participant-level spread?
A standard error describes uncertainty in an estimated mean, whereas a standard deviation describes variation among individual observations. The primary outcome reports standard errors for the least-squares means. The comparison summary uses an approximate pooled standard deviation derived from those standard errors and the group counts. That pooled value is an approximation, not a directly reported participant-level standard deviation. It is used for the recalculated standardized effect and planning illustrations, and should not be mistaken for the exact observed spread of HbA1c changes.
General statistical explanation: uncertainty in a mean typically declines as information increases, but its size also depends on the variability in the outcome and the model used. A narrow standard error does not mean participants had nearly identical outcomes. It means the estimated group mean is comparatively precise under the model and data assumptions.
What does the p-value say?
The unadjusted p-value is reported as <0.001. In general, a p-value measures how unusual data at least as discrepant as those observed would be under a specified null hypothesis and test model. It is not the probability that the null hypothesis is true, nor does it quantify the probability that the observed difference is due to chance. It also does not measure clinical importance. Here, the p-value belongs to the recalculated unadjusted comparison, so it should not be presented as the p-value from the registry-described adjusted MMRM unless the record identifies it that way.
Statistical interpretation also depends on how many outcomes and comparisons were examined and whether adjustments were planned. The registry lists many outcomes, but its multiplicity procedure is not reported in the registry record. A small unadjusted p-value for the primary endpoint is relevant evidence for that contrast, but it does not answer questions about the family of tests or the credibility of unadjusted secondary findings.
Why does over-dispersion matter?
General explanation: over-dispersion occurs when observed variation is greater than a statistical model expects. It is especially relevant for count outcomes, such as event rates, because a model that assumes too little variation can make standard errors too small and confidence intervals too narrow. The primary HbA1c endpoint is continuous, not an event count. Hypoglycemia rate outcomes could raise different modeling questions, but the registry information does not specify the detailed analysis model for those outcomes. Whether over-dispersion was assessed or addressed is not reported in the registry record.
Finally, all model-based interpretations are conditional on the analysis population, measurements, and assumptions. The primary population required evaluable measurements at baseline and after baseline. The record does not report a full missing-data sensitivity analysis, the handling of protocol deviations, or the original prespecified analysis plan. Those omissions limit independent assessment of the analysis choices, even though the main model and several adjustment terms are described.
11. Confidence Intervals and Precision
The recalculated unadjusted confidence interval for the primary mean difference extends from 0.389 to 0.671 percentage points, with the contrast defined as insulin glargine compared with LY2605541. A confidence interval is a range of values compatible with the data and the statistical procedure under its assumptions. In repeated use, intervals constructed by the same method would cover the true parameter at the stated confidence level at the corresponding long-run rate; the confidence level is not specified for this recalculated interval in the registry record.
The interval lies on the positive side of zero, consistent with a larger decrease in the LY2605541 group than in the insulin glargine group, given the reported ordering of the contrast. The interval also conveys uncertainty about the magnitude: it is not a claim that the true contrast is exactly the reported point estimate. The estimated means themselves have standard errors of 0.04 for LY2605541 and 0.06 for insulin glargine.
These precision statements need an important qualification. The confidence interval and p-value are unadjusted recalculations from posted summary statistics, and the pooled standard deviation used in related calculations is approximate. They are not the confidence interval and test from the registry-described MMRM treatment contrast. The MMRM includes baseline HbA1c and other specified factors, while the recalculation does not reproduce that adjustment. The registry record does not report the sponsor’s own confidence interval for the primary contrast.
Precision is not the same as clinical relevance. A confidence interval can describe statistical uncertainty without establishing whether values across its range would matter to patients. A clinically important threshold is not reported in the registry record. Nor does a confidence interval describe the spread of individual responses; participant outcomes may vary more widely than uncertainty in a group mean suggests.
The interval also applies to the defined endpoint and analysis population. It does not resolve uncertainty about unmeasured outcomes, missing data, or the generalizability of the result beyond the enrolled population. The open-label design and the absence of reported multiplicity details are additional context when assessing the strength of the overall evidence.
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 | 29 | 39 |
| 75% of the observed effect | 51 | 68 |
| 50% of the observed effect | 115 | 153 |
The planning figures are illustrations based on the observed effect, not the trial’s original design calculations. The registry record’s planning assumptions are a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. The effect to detect is set as the stated fraction of the observed effect. For these continuous outcomes, the figures are participants per arm; the note about total events applies to time-to-event outcomes, not these mean comparisons.
The 80% power column means the illustrated number of participants per arm that would give an 80% chance of detecting the specified effect under the planning assumptions, if that effect and those assumptions were correct. The 90% power column represents a higher target chance of detecting that effect. These values are planning quantities, not outcomes observed in this trial.
Each planning row considers a different assumed effect size: 100%, 75%, or 50% of the observed effect. A smaller effect is harder to distinguish from random variation, so the illustration requires more participants per arm as the assumed effect becomes smaller. The displayed figures are particularly dependent on the observed effect and approximate variability used in the calculation; they should not be treated as a guarantee that a future study will achieve its target power.
This is not observed power. Observed power is not a useful substitute for the effect estimate and its uncertainty after a study has been completed. These illustrations instead show how design requirements can change when the target effect or desired power changes. The trial’s own original sample-size assumptions, including its prespecified effect target and power calculation, are not reported in the registry record.
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 = 0.530; pooled standard deviation σ = 0.715.
- n = 2 × (1.96 + 0.842)2 × 0.7152 / 0.5302 = 28.6, rounded up to 29 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 <- 0.53 # observed difference in means
sigma <- 0.714976396299046 # 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(1582451)
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 = 29 (80% power), 39 (90% power)
75% of observed effect: n per arm = 51 (80% power), 68 (90% power)
50% of observed effect: n per arm = 115 (80% power), 153 (90% power)
power.t.test: 29.6
Simulated power at n = 29 per arm: 0.791 (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 lists a primary HbA1c endpoint and numerous secondary outcomes, including measures of HbA1c, hypoglycemia, fasting glucose, dose adjustment, and quality of life. When several outcomes or comparisons are tested, the chance of at least one apparently notable result can increase. Statistical methods can address this issue through a prespecified testing hierarchy or other multiplicity adjustment. The use of such a procedure is not reported in the registry record.
The unadjusted p-values attached to recalculated comparisons should therefore be interpreted as tests of individual contrasts, not as evidence that the full family of outcomes has been controlled for multiple testing. The record does not state which secondary endpoints were confirmatory, whether any were exploratory, or how interpretation was planned across endpoints. The original statistical analysis plan and interim analysis information are not reported in the registry record.
For the primary endpoint, the defined analysis population included randomized participants who received at least one dose and had evaluable HbA1c at baseline and after baseline. This clarifies which participants contributed to that endpoint analysis, but it does not describe all randomized participants’ outcomes or explain why data might not have been evaluable. The registry describes an MMRM analysis but does not report the full missing-data assumptions, imputation methods, sensitivity analyses, or the handling of participants who discontinued treatment.
In general, repeated-measures models can use available outcome measurements under assumptions about the relationship between missingness and observed data. If those assumptions are not appropriate, estimates may be sensitive to missingness. This is a general statistical concern; the registry record does not provide enough detail to determine whether the assumptions were assessed or how robust the primary result was to alternative missing-data approaches.
The record also does not report a complete analysis population definition for every secondary endpoint, the treatment of protocol deviations, or all analysis-specific participant counts. These omissions restrict independent evaluation of how closely each analysis followed the randomized comparison. They do not negate the reported endpoint estimates, but they limit assessment of multiplicity, missing data, and the full range of analyses.
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 | 36 | 305 | 11.8% |
| Insulin Glargine | 22 | 159 | 13.8% |
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 | 223 of 305 |
| Insulin Glargine | 104 of 159 |
Most frequent serious adverse event terms
| Event term | Organ system | LY2605541 | Insulin Glargine |
|---|---|---|---|
| Acute myocardial infarction | Cardiac disorders | 2 of 305 | 2 of 159 |
| Coronary artery disease | Cardiac disorders | 1 of 305 | 2 of 159 |
| Asthma | Respiratory, thoracic and mediastinal disorders | 2 of 305 | 1 of 159 |
| Acute coronary syndrome | Cardiac disorders | 0 of 305 | 2 of 159 |
| Atrial fibrillation | Cardiac disorders | 0 of 305 | 2 of 159 |
| Cardiac failure congestive | Cardiac disorders | 0 of 305 | 2 of 159 |
| Myocardial infarction | Cardiac disorders | 0 of 305 | 2 of 159 |
| Chest pain | General disorders | 2 of 305 | 0 of 159 |
| Fall | Injury, poisoning and procedural complications | 2 of 305 | 0 of 159 |
| Hepatic enzyme increased | Investigations | 2 of 305 | 0 of 159 |
Most frequent non-serious adverse event terms
| Event term | Organ system | LY2605541 | Insulin Glargine |
|---|---|---|---|
| Nasopharyngitis | Infections and infestations | 50 of 305 | 27 of 159 |
| Back pain | Musculoskeletal and connective tissue disorders | 21 of 305 | 9 of 159 |
| Sinusitis | Infections and infestations | 18 of 305 | 9 of 159 |
| Headache | Nervous system disorders | 15 of 305 | 12 of 159 |
| Diarrhoea | Gastrointestinal disorders | 19 of 305 | 6 of 159 |
| Cough | Respiratory, thoracic and mediastinal disorders | 16 of 305 | 9 of 159 |
| Influenza | Infections and infestations | 13 of 305 | 11 of 159 |
| Upper respiratory tract infection | Infections and infestations | 16 of 305 | 8 of 159 |
| Arthralgia | Musculoskeletal and connective tissue disorders | 15 of 305 | 7 of 159 |
| Bronchitis | Infections and infestations | 14 of 305 | 5 of 159 |
Serious events with the highest arm-level rate: ovarian cyst (1.5%), acute coronary syndrome (1.3%), acute myocardial infarction (1.3%), atrial fibrillation (1.3%), cardiac failure congestive (1.3%).
The registry reports serious adverse events for each treatment group using a number at risk and a number affected. For LY2605541, 36 of 305 participants at risk were reported as affected by a serious adverse event. For insulin glargine, the corresponding figures were 22 of 159. These are counts of participants affected as reported in the registry; they are not event rates adjusted for time at risk, and the record does not describe a comparative statistical analysis for these figures.
The most frequently listed serious adverse event terms include ovarian cyst at 1.5%, and acute coronary syndrome, acute myocardial infarction, atrial fibrillation, cardiac failure congestive, and coronary artery disease, each at 1.3%. These terms and percentages should be read as registry listings, not as proof that a treatment caused an event. The registry record does not provide enough context in these figures to establish causality or compare risks formally.
Other adverse events were reported in 223 of 305 participants at risk in the LY2605541 group and 104 of 159 in the insulin glargine group. The record does not provide a statistical comparison of these counts in the information. Death counts are not reported in the registry record. Adverse-event counts are not a substitute for the primary efficacy endpoint, and they should be interpreted alongside the study design and the completeness of safety follow-up.
16. What the Result Does, and Does Not, Mean
The primary result describes an average change in HbA1c among participants meeting the endpoint analysis criteria. The reported least-squares mean change was -0.82 in the LY2605541 group and -0.29 in the insulin glargine group at the 26-week endpoint. The recalculated unadjusted mean difference was 0.53 percentage points, with an interval from 0.389 to 0.671. In this comparison, the estimated decrease was larger in the LY2605541 group.
This finding does not mean that every participant experienced a decrease of the same size, or that an individual participant’s response can be predicted from the group mean. It also does not establish whether the estimated difference is clinically important, because a threshold for clinical importance is not reported in the registry record. Statistical evidence about an average contrast and a judgment about its clinical meaning are separate.
The result does not establish a complete benefit-harm comparison. The study purpose included nighttime and overall hypoglycemia, but the relevant numerical secondary results are not reported in the registry record among the results. Safety counts are reported, but the registry summary does not give a formal comparative analysis of those counts. Therefore, the HbA1c result alone cannot characterize all dimensions of treatment outcome.
The comparison was open-label, and the treatment strategies could include pre-study oral antihyperglycemic medications. The result therefore applies to the trial’s treatment context and analysis population, not necessarily to every clinical setting or regimen. The primary analysis used a model adjusted for specified factors, while the confidence interval and p-value discussed in the recalculated comparison are unadjusted approximations. The sponsor’s own model-based analysis takes precedence if available.
The finding should be considered together with the trial’s design, endpoint definition, precision, missing-data limitations, multiplicity information, and safety reporting. It is evidence about the posted summary results for a particular endpoint, not medical advice and not a universal claim about treatment effects.
17. Why This Trial Matters Statistically
This trial illustrates why a treatment comparison should be interpreted through its endpoint and analysis population, rather than by looking only at the direction of two group means. The primary outcome is a change from baseline in HbA1c, and the registry identifies a model-adjusted analysis that accounts for baseline HbA1c and other specified factors. That model description matters because adjusted estimates and unadjusted summaries answer related but not identical statistical questions.
It also shows the distinction between reported model results and recalculated comparisons. The group estimates are least-squares means from the described repeated-measures model, whereas the contrast interval and p-value are approximate, unadjusted recalculations from summary statistics. Both can help describe the evidence, but they should not be treated as interchangeable. A recalculation is not a substitute for the sponsor’s own model-based analysis.
The registry outcome list also illustrates that a primary endpoint is only one component of a clinical trial. HbA1c, hypoglycemia, fasting glucose, dose adjustments, and quality of life address different questions. Without complete numerical results and multiplicity information, a reader cannot infer that a primary endpoint pattern holds across all other outcomes.
Finally, the planning illustrations demonstrate how sample-size requirements depend on the effect size selected and the desired power. They are not evidence about the power the completed trial actually achieved, nor are they the trial’s original design assumptions. Keeping design illustrations separate from observed results helps avoid treating a post-study calculation as a prospective justification.
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 provides a useful description of the primary endpoint and its adjustment model, but it does not report the full statistical analysis plan. Details such as the model’s covariance structure, the handling of missing measurements, and sensitivity analyses are not reported in the registry record. The stated analysis population also requires evaluable baseline and post-baseline HbA1c data, so the primary result does not describe all enrolled participants.
The treatment comparison was open-label. The registry does not describe blinding of outcome assessment, and the record states that masking was none. HbA1c is a laboratory measure, but open-label treatment can still be relevant to treatment behavior, co-interventions, and outcomes that involve reporting or clinical decisions. The degree to which this affected any particular result is not reported in the registry record.
The primary comparison’s confidence interval and p-value are unadjusted recalculations based on posted summary statistics, with an approximate pooled standard deviation. They do not reproduce the registry-described MMRM contrast. Consequently, they should not be interpreted as if they were the sponsor’s adjusted treatment comparison. A sponsor-reported primary contrast with its own interval is not reported in the registry record.
Many secondary outcomes are listed, but the registry does not report numerical results for all of them in the results. Multiplicity handling is also not reported. This limits conclusions about outcomes beyond the primary endpoint and makes unadjusted secondary findings less definitive. Safety figures are counts of affected participants, without a reported formal comparison in this summary; death counts are not reported in the registry record.
The primary endpoint is a group-average measure over a defined period. It does not capture all individual response patterns, daily glucose variability, or the complete balance of benefits and harms. The original sample-size justification and the trial’s detailed analysis plan are not reported in the registry record, which further limits assessment of how the final analyses compare with the original design intentions.
19. Related Tutorials
20. Related Statistical Calculators
21. Sources
- ClinicalTrials.gov: A Study of LY2605541 in Participants With Type 2 Diabetes Mellitus — NCT01582451.
- Registry record last updated 2018-04-20; status last verified 2018-03.
- Results first posted 2018-04-20.
- 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
The registry record describes a completed, phase 3, randomized, open-label, parallel-group comparison of LY2605541 and insulin glargine in participants with type 2 diabetes previously treated with basal insulin. Enrollment is listed as 466. Both regimens were administered once daily at bedtime by subcutaneous injection, with dose adjustment based on fasting blood glucose.
The primary endpoint was change from baseline to the 26-week endpoint in HbA1c. The reported least-squares mean changes were -0.82 for LY2605541 and -0.29 for insulin glargine. The recalculated unadjusted mean difference was 0.53, with a confidence interval from 0.389 to 0.671 and an unadjusted p-value of <0.001. These recalculations do not replace the model-based analysis described in the registry.
The registry also lists secondary outcomes and serious adverse event counts. Full multiplicity procedures, missing-data sensitivity analyses, original sample-size assumptions, and numerical results for all listed outcomes are not reported in the registry record.