A Study for Patients With Diabetes Mellitus (IOPA): Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for A Study for Patients With Diabetes Mellitus (IOPA) (NCT00420095), a randomized phase 4 study. The primary outcome is Glycosylated Hemoglobin (HbA1c) Value at 12 Week Endpoint.

2. Clinical Question

The clinical question concerns a continuous laboratory measure rather than a count of clinical events. Because the study used a crossover design, participants received both treatments and could serve as their own control for between-treatment comparisons. The comparison therefore focuses on HbA1c under each treatment within the study population, with the registry’s reported analysis using a mixed model.

The registry lists changes in HbA1c, fasting blood glucose, and total daily insulin dose among the secondary outcomes, as well as target HbA1c attainment, laboratory parameters, and hypoglycemia rate. The posted primary result is a mean HbA1c value at the 12-week endpoint. It should be read as an estimate for the defined analysis population and trial conditions, not as a result for every person with diabetes or every insulin regimen.

3. Trial Design

This was a phase 4 randomized crossover study of human insulin mix 30/70 and insulin lispro low mix. The registry lists the study as completed, with enrollment of 117. The start is recorded as 2007-01 and primary completion as 2008-01. Eli Lilly and Company is listed as the sponsor.

The official study title describes patients with type 1 or type 2 diabetes using insulin treated twice daily. The brief summary identifies the population as Chinese patients with type 1 or type 2 diabetes. The registry describes the treatment comparison as one of glycemic control measured by HbA1c. Masking is listed as none, so the study was open-label according to the registry classification.

In a crossover study, participants receive each treatment in different periods, allowing within-participant comparisons. The primary outcome description says that each patient served as their own control for between-treatment comparisons. This design can account for stable differences between participants, but interpretation depends on the period structure and how period-related effects are handled. The registry record does not report treatment sequence details, washout arrangements, or other implementation details.

The primary endpoint population is described as randomized patients who completed the study with no major protocol violations. The outcome description says that data from two periods were combined, but the registry record does not report further details about that process in the available description. The posted arm summaries each include 113 participants. Those arm summaries do not, by themselves, explain how participants contributed across periods or why the primary endpoint population differed from the enrollment figure.

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

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: Includes all randomized patients who completed the study with no major protocol violations. Crossover study design allows for the comparison of the effect of two treatments on the same patients, each patient served as own control for between-treatment comparisons. The data from two periods were combined and analyzed.

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.

6. Primary Endpoint

The registry lists the primary outcome as Glycosylated Hemoglobin (HbA1c) Value at 12 Week Endpoint, measured over Baseline and 12 weeks of each treatment.

The primary endpoint is the HbA1c value at the 12-week endpoint of each treatment period, reported as a mean and expressed as percent of glycosylated hemoglobin. HbA1c reflects average blood glucose over the previous 12 weeks of treatment, according to the endpoint description. It is used as a continuous measure of glycemic control: the analysis compares average values rather than classifying each participant only as above or below a target.

A mean provides a concise description of the center of the observed measurements, while the accompanying confidence interval describes uncertainty around that estimate. The registry gives baseline and 12 weeks of each treatment as the timeframe. The primary outcome title emphasizes the endpoint value, while the secondary outcomes separately list changes from baseline to 12 weeks for HbA1c and other measures.

The endpoint is clinically relevant to the stated study purpose, but a measured HbA1c difference is not itself a complete account of treatment experience or safety. Other listed outcomes include fasting blood glucose, insulin dose, target HbA1c attainment, laboratory parameters, and hypoglycemia rate. The registry record does not report a clinically important difference threshold for the primary endpoint.

7. Results Posted in the Registry

• Insulin Lispro Low Mix: mean 7.96 versus 7.91 on control; difference 0.05 (95% CI -0.29 to 0.39), standardized effect d = 0.04; z-test p = 0.773.

8. Statistical Interpretation

9. Statistical Methods Explained

The primary outcome is continuous: HbA1c is recorded as a numerical percentage and summarized with a mean. A mean difference expresses the contrast between average values on the measurement scale. In this crossover study, however, participants received both treatments, so the comparison is not simply a comparison between two unrelated sets of people. The registry identifies a mixed-model analysis for the sponsor’s primary comparison, which is suited to representing structured data such as repeated observations within participants.

What does a mixed model do?

In general, a mixed model can represent both treatment effects and the correlation among repeated measurements from the same participant. This matters because measurements from one person are usually more alike than measurements from different people. Treating repeated observations as independent can misstate uncertainty. The registry names a mixed-model analysis and describes the crossover structure, but does not report the model formula, covariance structure, included terms, or estimation details. Those details are not reported in the registry record.

The primary analysis population is described as randomized participants who completed the study with no major protocol violations. This is a restricted description, not necessarily the same as an analysis of every randomized participant regardless of completion or protocol deviations. The registry record does not report a full participant flow or explain how missing endpoint measurements were handled. Without that information, it is not possible to assess whether the model used all available observations or how exclusions affected the result.

How should the recalculation be read?

The unadjusted recalculation uses the posted arm-level summary statistics to estimate a simple difference between means. It reports an estimate of 0.05, a 95% confidence interval from -0.289 to 0.389, and an unadjusted p-value of 0.773. This is a descriptive cross-check, not a reconstruction of the sponsor’s mixed model. In particular, the summary statistics do not provide the within-participant covariance needed to reproduce a paired crossover analysis. The recalculated interval and p-value should therefore not be treated as the trial’s primary inferential result.

The sponsor’s mixed-model estimate is -0.05, with a 95% confidence interval from -0.20 to 0.10 and p = 0.497. The two estimates use opposite contrast directions, as indicated by the posted arm means and the reported net difference. Their differing intervals and p-values reflect distinct analyses, not a contradiction that can be resolved from the marginal arm summaries alone. The registry does not flag a discrepancy between the sponsor result and the posted summary statistics.

What does a p-value tell the reader?

In general, a p-value measures how incompatible the observed data are with a specified null model, under the assumptions of the analysis. It is not the probability that the null hypothesis is true, and it does not measure the size or clinical importance of an effect. A p-value also does not establish equivalence. For a non-inferiority or equivalence conclusion, interpretation depends on the prespecified margin and decision procedure. Although the registry classifies the reported analysis as non-inferiority or equivalence, the margin and decision rule are not reported in the registry record.

The registry lists seven outcome measures and seven analyses, including the primary measure and secondary outcomes. It does not report whether or how multiplicity was addressed. When many outcomes or comparisons are considered, the chance of a nominally notable result can increase; general methods include prespecifying a primary outcome and adjusting or otherwise controlling interpretation across multiple tests. Without a reported plan, the secondary results should be treated as exploratory rather than assumed to have confirmatory error control.

Dispersion and uncertainty are different ideas. The reported spread values for the treatment groups are 1.158 and 1.373, while the arm-level mean confidence intervals describe uncertainty in the estimated means. In general, variability among participant measurements is not the same as uncertainty in the mean. For repeated crossover observations, the correlation between periods also affects uncertainty in the treatment contrast. The registry record does not provide the participant-level data or covariance information needed to independently reconstruct that uncertainty.

In general, over-dispersion means that observed variability is greater than a model assumes. If present, standard errors based on an overly restrictive variance assumption can be too small, making confidence intervals too narrow and tests too optimistic. The primary HbA1c outcome is continuous, and no over-dispersion assessment is reported in the registry record. This concept is more directly relevant to outcomes such as event counts or rates, including the listed hypoglycemia rate, where extra variation beyond a simple count model can matter.

The registry identifies the endpoint timeframe as baseline and 12 weeks of each treatment. It also lists changes from baseline as secondary outcomes. The distinction matters: an endpoint comparison and a change-from-baseline comparison answer related but not identical questions. The record does not report enough detail to infer which adjustment, if any, was used for baseline values in the sponsor’s primary model.

10. Confidence Intervals and Precision

Confidence intervals describe a range of values reasonably compatible with the data and the assumptions of the analysis. They communicate precision more directly than a p-value alone: a narrow interval indicates a more precise estimate, while a wide interval leaves greater uncertainty about the size and direction of the contrast. They are not guarantees that the true value lies inside the interval, nor do they assign probabilities to individual values without additional assumptions.

For the sponsor’s mixed-model comparison, the reported net mean difference is -0.05, with a 95% confidence interval from -0.20 to 0.10. The interval includes zero and extends to values in either direction. The result therefore does not pin down the treatment contrast to a single value, even though the point estimate is close to zero. The meaning of the interval for a non-inferiority or equivalence claim depends on the prespecified margin, which is not reported in the registry record.

The unadjusted recalculation has a wider 95% confidence interval, from -0.289 to 0.389, around its mean difference estimate of 0.05. It is based on posted summary statistics rather than the mixed model’s crossover structure. Its width should not be taken as a definitive assessment of the primary analysis’s precision. The arm-specific mean intervals are 7.67 to 8.15 for human insulin mix 30/70 and 7.72 to 8.2 for insulin lispro low mix; those intervals describe each mean, not the within-participant difference.

More precision would require more information about the paired observations and analysis details, not simply a comparison of the arm intervals. The registry record does not report the covariance between treatment periods or the prespecified precision target. Thus, the posted estimates support a cautious reading: the average contrast is small in the analyses reported, but its exact size remains uncertain.

11. 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.

The planning figures are illustrations based on the observed effect, not the trial’s original design assumptions. The registry record does not report the original sample-size justification. The 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 to the stated fraction of the observed effect. These are participants-per-arm figures, not total event counts; the time-to-event convention of total events does not apply to this continuous endpoint.

The 80% power column gives the planned participants per arm for a design with an 80% chance of detecting the specified effect under the planning assumptions, if that effect is real and the assumptions hold. The 90% power column gives the corresponding planning number for a 90% chance. Neither column is the number enrolled in this trial or a claim about the trial’s achieved ability to detect an effect. This is not observed power.

The rows consider planning for 100%, 75%, and 50% of the observed effect. As the effect assumed for planning becomes smaller, more participants are needed to distinguish it from random variation with the stated power. The figures are especially sensitive to the observed effect used as their starting point: a small observed difference can produce very large planning requirements when a fraction of it is the target. These values are illustrative rather than a recommendation for a future study. A design decision would also require a clinically justified effect target, an appropriate model for the crossover structure, and design assumptions not reported in the registry record.

12. 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 z_1−α/2 = 1.960) and the desired power (z_1−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

1. Observed difference Δ = 0.050; pooled standard deviation σ = 1.302.
2. n = 2 × (1.96 + 0.842)² × 1.302² / 0.050² = 10,639.0, rounded up to 10,640 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 <- 0.0499999999999998                      # observed difference in means
sigma <- 1.30167442625484                     # 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(420095)
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 = 10,640 (80% power), 14,243 (90% power)
 75% of observed effect: n per arm = 18,914 (80% power), 25,321 (90% power)
 50% of observed effect: n per arm = 42,557 (80% power), 56,971 (90% power)
power.t.test: 10640 
Simulated power at n = 10,640 per arm: 0.803 (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.

13. Analyses Reported by the Sponsor

The registry reports the sponsor’s primary comparison as a mixed-model analysis, with a net mean difference of -0.05, a 95% confidence interval from -0.20 to 0.10, and p = 0.497. It classifies this analysis as non-inferiority or equivalence. The registry does not report the margin, model specification, or detailed decision rule, so the classification alone is not enough to evaluate the strength of a non-inferiority or equivalence conclusion.

The separate recalculation is a simple unadjusted contrast from the posted arm summaries. It estimates a mean difference of 0.05, with a 95% confidence interval from -0.289 to 0.389 and p = 0.773. It does not incorporate the participant-level pairing or the mixed-model structure described for the crossover trial. The contrast directions differ, and the recalculation is not intended to reproduce the sponsor analysis.

The registry does not flag a discrepancy between the analyses. The sponsor’s mixed-model result is the more relevant reported analysis for the stated crossover comparison; the recalculation is a limited reference based on marginal summaries. The two should not be combined or treated as interchangeable estimates.

14. Multiplicity, Missing Data and Analysis Populations

The registry lists seven outcome measures and seven analyses. The primary outcome is HbA1c at the 12-week endpoint. Six secondary outcomes are listed: change in HbA1c, change in fasting blood glucose, change in total daily insulin dose, achievement of HbA1c targets of <=7% and <=6.5%, laboratory parameters differing from baseline, and hypoglycemia rate per participant per 30 days.

The registry record does not report whether multiplicity was addressed, whether outcomes were prioritized beyond the designated primary endpoint, or whether a sequential testing strategy was used. When multiple outcomes are tested, isolated findings can arise by chance more often than with a single prespecified test. This general concern does not mean that a reported result is invalid; it means that interpretation depends on the analysis plan and how the family of comparisons was handled. The secondary outcomes should not be assumed to have adjusted p-values or confirmatory status.

The primary population is described as randomized patients who completed the study with no major protocol violations. The record does not report whether an intention-to-treat population, a per-protocol population, or other analysis populations were separately defined or analyzed. The stated population resembles a completer population with a protocol-violation restriction, but the registry’s wording does not establish a fuller classification beyond that description.

Missing-data handling is not reported in the registry record. It is therefore unclear how incomplete treatment periods, missing endpoint values, or withdrawals were handled in the model. The registry reports enrollment of 117 and arm summaries of 113 participants for each treatment, but does not provide a flow accounting or explain the relationship between those counts and the primary analysis population. No assumptions about the causes or consequences of missingness can be established from these figures alone.

The record also does not report interim analyses, a detailed statistical analysis plan, or sensitivity analyses for missing data. Those omissions limit assessment of whether the results depend on particular population definitions or modeling choices.

15. What the Result Does, and Does Not, Mean

The posted results show similar average HbA1c values during the two treatment periods in the analyzed population: 7.91 for human insulin mix 30/70 and 7.96 for insulin lispro low mix. The sponsor’s mixed-model estimate of the net mean difference is -0.05, with a 95% confidence interval from -0.20 to 0.10. The unadjusted recalculation is also close to zero, although it uses a different method and has a wider interval.

A small point estimate does not demonstrate that the treatments are identical. The confidence interval represents uncertainty about the contrast, and the registry does not report the clinically acceptable margin required to interpret a non-inferiority or equivalence analysis. The reported p-value is not a measure of the probability that the treatments are equivalent and cannot by itself establish that conclusion.

The results apply to the study’s endpoint population and its treatment periods. The record describes Chinese patients with type 1 or type 2 diabetes, and the primary population as randomized participants who completed the study with no major protocol violations. The results do not automatically generalize to other populations, treatment schedules, or clinical settings.

The primary endpoint captures HbA1c, not every dimension of glycemic control, treatment burden, or safety. The registry lists additional outcomes, but their results are not included in the registry record for this analysis. The adverse-event information includes counts of affected participants but lacks the at-risk denominators needed to interpret rates. No medical conclusion about an individual treatment choice follows from the primary endpoint alone.

In short, the reported estimates are centered near no average difference, but their precision, analysis population, and incomplete reporting limit the conclusions that can be drawn. The registry’s non-inferiority or equivalence classification should be read together with the missing margin and analysis details, rather than as proof of equivalence.

16. Why This Trial Matters Statistically

This trial is statistically instructive because it uses a crossover design for a continuous outcome. In this design, each participant can contribute observations under both treatments, so the treatment contrast depends on within-participant information. A mixed model can account for this structure, while a simple comparison of arm summaries cannot fully recover it. The difference between the sponsor’s analysis and the unadjusted recalculation illustrates why analysis design matters as much as the reported means.

The reported treatment means are close, and the sponsor’s model-based interval is comparatively centered near zero. Yet a near-zero estimate is not the same as a demonstrated equivalence result. Equivalence and non-inferiority require a prespecified margin and an analysis that evaluates the estimate against that margin. The registry classifies the analysis accordingly, but does not provide the margin or decision rule. This highlights why conclusions must be judged using both the numerical result and the design information that gives it meaning.

The example also shows the distinction between statistical significance and precision. The reported p-values do not establish the size or clinical importance of a difference. Confidence intervals convey a range of plausible contrasts, while the crossover structure and analysis population affect how those intervals should be interpreted.

Finally, planning numbers derived from an observed effect can be dramatic when that effect is small, but they are illustrations rather than the original trial rationale or an assessment of achieved power. Readers should separate those planning calculations from the study’s enrollment and from the primary inference. That distinction is important whenever observed estimates are reused to sketch future sample sizes.

17. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The registry record leaves important design and analysis details unspecified. Although the study is identified as randomized and crossover, treatment sequence, period structure, washout arrangements, and possible handling of period effects are not reported in the available description. These details matter when interpreting repeated treatment periods.

The sponsor’s result is labeled a non-inferiority or equivalence analysis, but the registry record does not report the margin or the prespecified decision rule. The mixed-model specification and the analysis plan are also not reported. This prevents a full assessment of whether the model and conclusion align with the intended hypothesis.

The primary population excludes participants who did not complete the study or had major protocol violations, according to the outcome description. The registry record does not provide a participant flow, a detailed account of exclusions, or missing-data methods. It also does not explain the relation between enrollment of 117 and the posted summaries of 113 participants for each treatment.

The listed adverse-event counts have no reported at-risk denominators. The serious-event entries include 2 affected participants for human insulin mix 30/70 and 1 for insulin lispro low mix; other affected-event counts are 19 and 23, respectively. The registry does not report death counts in these results. Three serious-event terms are each listed at 0.9%, but the record does not provide enough context to assess event rates across treatment exposure.

Finally, the available results include six secondary outcomes by name but not their numerical findings. Multiplicity handling, interim analyses, and the original sample-size justification are not reported in the registry record. These limits constrain conclusions about secondary outcomes, safety, missingness, and the basis for the study’s design.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: A Study for Patients With Diabetes Mellitus (IOPA) — NCT00420095.
• Registry record last updated 2009-06-17; status last verified 2009-06.
• Results first posted 2009-06-05.
• 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.

21. Record Summary

NCT00420095 is a completed phase 4 randomized, open-label crossover study sponsored by Eli Lilly and Company. It enrolled 117 Chinese patients with type 1 or type 2 diabetes and compared human insulin mix 30/70 with insulin lispro low mix. The primary outcome was mean HbA1c at the 12-week endpoint of each treatment.

The sponsor-reported mixed-model analysis gives a net mean difference of -0.05, with a 95% confidence interval from -0.20 to 0.10 and p = 0.497. The registry classifies the analysis as non-inferiority or equivalence, but the margin and decision rule are not reported. A simple unadjusted recalculation gives a mean difference of 0.05, with a 95% confidence interval from -0.289 to 0.389 and p = 0.773; it does not reproduce the crossover model.

The registry lists six secondary outcomes. Details about multiplicity, missing-data handling, treatment sequence, and the original sample-size rationale are not reported in the registry record.