Racial Differences in Vagal Control of Glucose Homeostasis: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Racial Differences in Vagal Control of Glucose Homeostasis (NCT02365285), a randomized phase 1, phase 2 study. The primary outcome is Change in Oxidative Stress: Baseline to 2 Hours.

2. Clinical Question

The clinical question is therefore narrower than the full hypothesis: how did the reported oxidation marker change during galantamine and placebo treatment, and what does the recorded contrast indicate about the change among African-American participants? The outcome is presented as a continuous measure in pg /ml, summarized by means and standard deviations. The registry’s posted summaries are descriptive, while the listed galantamine-versus-placebo contrast gives an unadjusted comparison based on those summaries.

The study’s crossover format means participants were assigned to treatment sequences rather than to a single treatment throughout. That format can support comparisons within the same person, but the registry record does not describe a crossover-specific analysis of the primary outcome. It also does not report a direct test of whether treatment effects differed between African-American and White participants. Accordingly, the reported contrast should not be read as an estimate of a racial difference in response.

3. Trial Design

This was a randomized, double-masked crossover trial listed as phase 1 and phase 2. The registry reports enrollment of 23 participants and a completed status. The recorded start was 2015-03, and primary completion was 2017-10-05. Obesity is the listed condition. Vanderbilt University Medical Center is the sponsor.

The two described sequences were galantamine 16 mg by mouth as a one-time dose followed by placebo at the second visit, and placebo capsule by mouth as a one-time dose followed by galantamine 16 mg at the second visit. Thus the intended design exposed participants to both galantamine and placebo in an order assigned at random. The record does not report the interval between visits, the details of sequence allocation, or how masking was maintained. It also does not explain how the listed Intralipid and heparin interventions relate to the primary outcome or to the sequence descriptions.

The primary outcome is titled change in oxidative stress from baseline to 2 hours. It is defined as measurement of F-2 isoprostanes as a marker of oxidation. The registry reports four descriptive group summaries: galantamine and placebo for African-American participants, and galantamine and placebo for White participants. The reported outcome sample sizes are 13 for each African-American treatment summary and 7 for each White treatment summary. These are outcome-summary counts, not a full account of the sequence allocation or participant flow.

The registry notes that 2 white participants dropped out due to nausea and 1 African-American participant was withdrawn by physician decision. It does not report whether these participants contributed any outcome data, the timing of their withdrawal, or the rules used to include observations in the summaries. The original sample-size justification and the trial’s own statistical analysis plan are not reported in the registry record. Although the record lists two outcome measures, it does not list posted inferential analyses.

In a crossover study, treatment sequence, period, and possible carryover can matter when estimating a treatment contrast. The registry does not report whether these design features were modeled or tested. The available contrast should therefore be interpreted as an unadjusted comparison of the posted summary statistics rather than as a documented analysis accounting for all features of the crossover design.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Before assignment: 52 participants were screen failures and did not receive an intervention.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: 2 white participants dropped out due to nausea. 1 African-American was withdrawn, MD decision.

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 Change in Oxidative Stress: Baseline to 2 Hours, measured over Baseline to 2 hours.

The primary endpoint is change in F-2 isoprostanes from baseline to 2 hours, reported in pg /ml. F-2 isoprostanes are identified in the registry as a marker of oxidation, so the endpoint is intended to quantify change in an oxidative-stress marker over the stated period. The outcome is continuous and is summarized using a mean and standard deviation.

A biomarker gives a measurable biological outcome that can be compared across treatment conditions. In general, measuring change from baseline can describe how a participant’s marker level differs over the specified follow-up period, rather than describing only the level at one time. The registry’s wording names the interval as baseline to 2 hours, but it does not provide further detail on the measurement procedure, laboratory methods, or how multiple measurements were combined into the reported change.

The endpoint is a marker, not a direct measure of every part of the investigators’ stated hypothesis. The brief summary also refers to parasympathetic nervous system activity, but no result for that outcome is included in the posted primary summaries. The record does not report a validated threshold for a meaningful change in F-2 isoprostanes, nor does it explain how changes in the marker relate to longer-term clinical outcomes. Therefore, the endpoint supports interpretation of the reported biomarker values only; it does not by itself establish broader physiological or clinical effects.

The reported means are −0.003 for galantamine and 0.01 for placebo among African-American participants. Among White participants, the reported mean is −0.006 under both galantamine and placebo. These are group summaries of change. The precision and analysis limitations matter when interpreting the differences between them.

7. Results Posted in the Registry

• Galantamine 16 mg (African-American): mean -0.00 versus 0.01 on control; difference -0.01 (95% CI -0.02 to -0.00), standardized effect d = -0.85; z-test p = 0.030.

8. Statistical Interpretation

9. Statistical Methods Explained

Continuous outcomes are often summarized by a mean and a standard deviation. The mean describes the average reported change, while the standard deviation describes how spread out the individual observations are around that average. A mean is not a description of every participant’s result: participants can have changes above or below it. The reported standard deviations help convey that variability, but they do not show the full distribution or whether the data contain unusual observations.

What does the mean difference represent?

The listed contrast is a mean difference for African-American participants. It compares the placebo mean of 0.01 with the galantamine mean of −0.003 and reports galantamine minus placebo as −0.013. A negative difference means that the galantamine group summary is lower than the placebo summary under this subtraction order. The contrast is based on the reported means, not on a separately posted participant-level model. The registry does not report an adjusted estimate.

In general, a mean difference is expressed in the same units as the outcome. Its interpretation depends on the outcome definition, the order of subtraction, and the study design. Here the endpoint is change in F-2 isoprostanes from baseline to 2 hours, in pg /ml. Because the trial is crossover, an analysis may need to account for repeated measurements from the same participants, treatment sequence, and period. The record does not report whether these features were included in the listed comparison.

Why does the crossover design matter?

In a crossover design, the same participant receives more than one treatment in different periods. A within-participant analysis can use the fact that each person serves as their own comparison, which may account for stable differences between participants. That analysis also depends on assumptions about the periods and whether an earlier treatment has an effect that carries into a later period. General statistical practice is to describe how sequence and period are handled and whether carryover is considered. Those details are not reported in the registry record.

The posted summaries give a sample size and a mean for each treatment within each racial group, but do not state whether those are paired observations or how they were analyzed. The listed contrast is an unadjusted summary-statistic recalculation. It should not be mistaken for a documented crossover model. In particular, the registry does not provide a standard error based on within-person differences or an analysis that explicitly models treatment, period, sequence, and participant.

What does a confidence interval convey?

In general, a confidence interval describes the uncertainty around an estimate under the assumptions of the method used to calculate it. Wider intervals indicate less precision; narrower intervals indicate more precision, conditional on the model and data. The listed interval for the African-American contrast is wholly negative and excludes zero. That indicates the unadjusted calculation is compatible with a negative contrast rather than a contrast of zero, under its assumptions. It does not guarantee that the true effect lies in the interval, nor does it account for analysis choices that are not reported.

Intervals are most informative when the estimate, analysis population, model, and interval procedure are all clear. Here the bounds are listed, but the registry does not state a crossover-specific method or a multiplicity adjustment. No confidence intervals are reported for the White group summaries. The precision of the African-American contrast therefore should not be generalized to the racial comparison or to other outcomes.

How should the p-value be understood?

In general, a p-value measures how unusual the observed data, or data more extreme, would be under a specified null hypothesis and model. It is not the probability that the null hypothesis is true. The reported unadjusted p-value is 0.03. Its interpretation depends on the analysis assumptions, including whether the method appropriately handles the crossover observations and whether other outcomes or comparisons were considered.

The registry lists 0 posted analyses, although it gives descriptive outcome results and a contrast. The precise sponsor analysis, any planned hypothesis tests, and any adjustment for multiple comparisons are not reported. The unadjusted p-value should therefore be treated as a calculation attached to the listed summary-statistic contrast, not as a complete account of the trial’s planned inferential analysis.

Why can variability and sample size affect precision?

In general, more variability makes an average contrast harder to estimate precisely when sample size is held constant. More observations can improve precision, but the amount of improvement depends on the design and analysis. The reported standard deviations indicate variation in the measured changes. The outcome summaries include 13 participants per treatment summary in the African-American group and 7 per treatment summary in the White group. These counts do not establish how many complete paired observations were available or how missing measurements were handled.

The sample-size illustrations use the observed contrast as a planning reference and then consider fractions of that effect. They are not the trial’s original design justification. The trial’s own sample-size assumptions, including its planned target effect and analysis method, are not reported in the registry record. The illustrations cannot establish what power the completed trial had.

Finally, all of these methods describe statistical summaries, not clinical importance. The registry does not state a clinically meaningful threshold for F-2 isoprostanes or connect this short-term change to a patient-centered outcome. Statistical evidence, precision, study design, and relevance to a broader hypothesis are distinct considerations.

10. Confidence Intervals and Precision

The listed African-American mean difference is −0.013, with a confidence interval entirely below zero. The interval excludes zero under the unadjusted calculation, which indicates that this calculation does not include no difference as a compatible value at its stated confidence level. The registry does not identify a crossover-specific interval method, so the interval should be interpreted as conditional on the simple summary-statistic approach behind the contrast.

A confidence interval communicates uncertainty around an estimate, not the probability that a particular effect is true. In general, a wider interval reflects less precision and a narrower interval reflects greater precision, given the method and data. The interval’s position and width should be considered together: a point estimate alone can appear more definite than the available data warrant. The outcome summaries are based on 13 participants per treatment summary among African-American participants and 7 per treatment summary among White participants.

Precision is not the same as clinical importance. The record does not report a threshold for a meaningful change in F-2 isoprostanes. It also does not report confidence intervals for the White treatment summaries, a direct comparison between racial groups, or an interval for a treatment-by-race contrast. Therefore, the precision of the listed African-American comparison cannot answer whether responses differ across racial groups.

The interval does not account for uncertainties that are not represented in the calculation, such as the choice of a crossover analysis, handling of incomplete observations, or multiplicity. These analysis details are not reported in the registry record. The confidence interval is useful for describing the uncertainty of the listed unadjusted contrast, but it cannot compensate for missing information about the planned model and analysis population.

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 participants per arm, not total events. They illustrate how many participants per arm would be needed under stated assumptions for a two-sided significance level of 0.05, equal allocation between two arms, and a normal approximation. The effect used for planning is a stated fraction of the observed effect. The displayed scenarios consider planning for 100%, 75%, and 50% of the observed effect.

The 80% power column gives the number of participants per arm that the planning calculation associates with an 80% chance of detecting the selected effect under those assumptions, if that effect were the true effect and the assumptions held. The 90% power column gives the corresponding number per arm for a 90% chance. Power is a property of a planned design under specified assumptions; it is not a probability that a particular result is correct.

The calculation uses the observed contrast as a reference rather than the trial’s original design target. Smaller effects are harder to detect and therefore require more participants under the same assumptions. This is a planning illustration, not observed power. The trial’s original sample-size justification, target effect, and design assumptions are not reported in the registry record.

Because the trial is described as crossover, the equal-allocation, two-arm normal-approximation illustration should not be taken as a reconstruction of the trial’s own design calculations. The registry does not report a sample-size method based on paired outcomes or the within-participant variability. The figures are useful for illustrating how assumed effect size and desired power affect planning, but not for determining whether the completed study was adequately powered.

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 = -0.013; pooled standard deviation σ = 0.015.
2. n = 2 × (1.96 + 0.842)² × 0.015² / -0.013² = 21.7, rounded up to 22 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 <- -0.013                      # observed difference in means
sigma <- 0.0152970585407784                     # 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(2365285)
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 = 22 (80% power), 30 (90% power)
 75% of observed effect: n per arm = 39 (80% power), 52 (90% power)
 50% of observed effect: n per arm = 87 (80% power), 117 (90% power)
power.t.test: 22.7 
Simulated power at n = 22 per arm: 0.783 (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. Multiplicity, Missing Data and Analysis Populations

The registry record lists two outcome measures and 0 posted analyses. It does not report which outcomes were designated primary in the original analysis plan beyond the listed primary outcome, whether additional comparisons were planned, or whether multiplicity was considered. When several outcomes or contrasts are tested, the chance of at least one apparently unusual result can increase. General statistical approaches may adjust inference for multiple testing or distinguish confirmatory from exploratory analyses, but no such approach is reported.

The listed p-value and confidence interval are unadjusted. Their interpretation is therefore limited to the single summary-statistic contrast as calculated. The record does not report an adjustment for the other outcome measure, comparisons across racial groups, or any additional analyses. It also does not report whether the contrast was specified before results were examined.

Missing-data handling is not described. The registry notes that 2 white participants dropped out due to nausea and 1 African-American participant was withdrawn by physician decision. It does not say whether these participants had baseline or follow-up measurements, whether their data were included in any summaries, or how incomplete crossover periods were handled. The reasons for the withdrawals are recorded, but their statistical treatment is not.

Analysis populations are not defined. The record does not state whether the reported summaries use all randomized participants, participants with complete outcome data, or another set. It also does not report an intention-to-treat analysis, a per-protocol analysis, or rules for handling protocol deviations. In a crossover trial, incomplete data from one period may affect which within-person treatment comparisons are available, but the handling of such cases is not reported.

These omissions limit how fully the posted estimate can be interpreted. The registry record does not report a statistical analysis plan, missing-data method, multiplicity strategy, or analysis-population definition. They should not be inferred from the descriptive summaries or from the trial’s randomized, double-masked crossover designation.

14. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 0% reporting threshold.

Most frequent non-serious adverse event terms

The serious adverse event summaries report zero affected participants in every listed group. The numbers at risk are 14 for galantamine among African-American participants, 9 for galantamine among White participants, 14 for placebo among African-American participants, and 9 for placebo among White participants. The registry also reports zero deaths in each group. These are counts as recorded, not estimates of comparative risk.

For other adverse events, the recorded affected counts are 4 with galantamine among African-American participants, 6 with galantamine among White participants, 2 with placebo among African-American participants, and 2 with placebo among White participants. The record does not provide event descriptions in the listed summary, event severity beyond the serious-versus-other grouping, timing, or an analysis comparing groups. The counts alone do not establish whether an event was caused by treatment.

The safety denominators differ from the outcome-summary counts: the safety groups list 14 and 9 at risk, while the outcome summaries list 13 and 7 per treatment. The record does not explain this difference. It notes withdrawals due to nausea and physician decision, but does not state how those withdrawals relate to each safety denominator. Safety counts should therefore be read with their own listed at-risk numbers, not assumed to match the outcome-analysis populations.

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

The posted results describe short-term changes in F-2 isoprostanes, a marker of oxidation, under galantamine and placebo among African-American and White participants. The African-American summaries show a mean of −0.003 with galantamine and 0.01 with placebo, with a listed unadjusted mean difference of −0.013. The associated confidence interval is entirely negative, and the unadjusted p-value is 0.03. These values describe the registry’s summary-statistic contrast.

The results do not establish that galantamine restores parasympathetic nervous system activity. Although restoration of that activity appears in the stated hypothesis, the posted primary outcome summaries concern F-2 isoprostanes, and a result for parasympathetic activity is not reported in the registry record. The results also do not establish a difference in treatment response between African-American and White participants. A direct comparison of treatment effects across those groups is not reported.

The result does not establish a sustained change or a change in a clinical outcome. The endpoint is measured from baseline to 2 hours, and the registry does not report longer-term follow-up results or a threshold for a clinically meaningful change. Statistical evidence for a contrast on a biomarker is not equivalent to evidence of a broader clinical benefit.

Interpretation is also constrained by the limited outcome samples, the crossover design, and missing details about the analysis. The registry does not report whether the contrast accounts for repeated observations, treatment period, sequence, or incomplete data. It does not identify the analysis population or describe multiplicity handling. These limits do not erase the posted numbers, but they constrain the conclusions that can be drawn from them.

The appropriate reading is therefore specific: the registry reports a negative unadjusted galantamine-minus-placebo contrast in the African-American outcome summaries. The precision and meaning of that contrast depend on assumptions and design features that are not fully documented. It should not be generalized to unreported outcomes, racial comparisons, or effects beyond the stated measurement period.

16. Why This Trial Matters Statistically

This trial raises statistical issues that are common in small randomized crossover studies. Because each participant is intended to receive both treatments, the analysis can depend on within-person comparisons rather than on treating each treatment summary as independent. That distinction affects the estimated uncertainty. The registry gives treatment-specific means, standard deviations, sample sizes, and an unadjusted contrast, but does not report a crossover-specific model or the paired variability needed to evaluate such a model.

The trial also places a biological hypothesis about racial differences alongside treatment comparisons within racial groups. Those are different statistical questions. A treatment contrast in one group does not establish that the contrast differs in another group. To address that claim, an analysis would need to estimate and test the difference between treatment effects across groups. Such a result is not reported in the registry record.

Small outcome samples make clear reporting of uncertainty and analysis choices especially important. The African-American summaries contain 13 participants per treatment, and the White summaries contain 7 per treatment. The listed contrast has a confidence interval, but the registry does not describe how the crossover structure, withdrawals, or multiple outcomes were addressed. The effect estimate should be read alongside those gaps rather than in isolation.

The record is also a useful example of distinguishing a planning illustration from the original trial design. The posted sample-size figures are based on the observed effect under stated assumptions; the original sample-size justification is not reported. Such illustrations can help show how planning responds to effect size and desired power, but they cannot reconstruct the design rationale or establish the completed study’s power.

Clear reporting of analysis populations, missing-data rules, period and sequence handling, and the treatment-by-group question would make the statistical evidence easier to assess. These matters are important because the biological interpretation depends not only on the direction of a mean but also on what was estimated and how uncertainty was calculated.

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 outcome summaries include relatively small groups, with 13 participants in each African-American treatment summary and 7 in each White treatment summary. The registry records withdrawals of 2 white participants due to nausea and 1 African-American participant by physician decision, but does not describe their outcome-data availability or inclusion in the analysis. The relationship between those withdrawals and the reported outcome and safety sample sizes is not reported.

The study is described as randomized, double-masked, and crossover, yet the registry does not explain the interval between treatment visits, the handling of treatment sequence or period, or whether carryover was considered. The reported contrast is an unadjusted recalculation from summary statistics, rather than a documented crossover-specific analysis. The analysis population and missing-data procedures are not reported.

The endpoint is a short-term biomarker change from baseline to 2 hours. The registry does not report measurement procedures or a threshold for a meaningful change, nor does it provide a result for parasympathetic activity despite that outcome’s place in the stated hypothesis. It also does not report a direct comparison of treatment effects between African-American and White participants.

Only a limited description of interventions is available. Galantamine and placebo sequence descriptions are given, while the role of Intralipid and heparin in the primary outcome is not reported in the registry record. The original statistical plan, sample-size justification, and multiplicity approach are also not reported. These gaps limit interpretation of the reported contrast and prevent a complete assessment of how the trial’s intended analyses relate to its posted summaries.

18. Related Tutorials

19. Related Statistical Calculators

20. Sources

• ClinicalTrials.gov: Racial Differences in Vagal Control of Glucose Homeostasis — NCT02365285.
• Registry record last updated 2019-03-19; status last verified 2019-02.
• Results first posted 2019-03-19.
• 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

The registry describes a completed randomized, double-masked, phase 1 and phase 2 crossover study sponsored by Vanderbilt University Medical Center. It lists 23 participants, obesity as the condition, and galantamine 16 mg and placebo treatment sequences. The primary outcome is change in F-2 isoprostanes from baseline to 2 hours, reported as a marker of oxidation.

Among African-American participants, the registry reports mean changes of −0.003 with galantamine and 0.01 with placebo. The listed unadjusted mean difference is −0.013, with an unadjusted p-value of 0.03. White-participant means are −0.006 under both treatments. A direct comparison of treatment effects between racial groups is not reported.

The record does not report a crossover-specific analysis, analysis-population definition, missing-data method, multiplicity strategy, or the trial’s original sample-size justification. Those details are important context for interpreting the reported summary-statistic contrast.